{
  "recorded_at": "2026-10-02T16:44:40.288463+00:00",
  "benchmark_source_sha256": "1f567742f6b2b71e94b90bcdf9c10e70c58952d53a061c3a8a110d5541fe2344",
  "metric": "warmed per-dispatch Metal GPU timestamps and synchronized wall latency; compilation and allocation excluded",
  "pair_order": [
    "baseline",
    "current",
    "current",
    "baseline"
  ],
  "precision_comparison": {
    "class": "same_storage_precision",
    "same_weight_representation": true,
    "storage": "identical FP16 or FP32 inputs and outputs per case",
    "arithmetic": "SIMD-group FP32 accumulation; RELAXED_PRECISION=False for both variants",
    "reference": "seeded NumPy FP32 matmul checked before timing every case",
    "bitwise_exact": false
  },
  "configuration": {
    "warmup_ms": 200.0,
    "rep_ms": 500.0,
    "seed": 431,
    "cooldown_seconds": 2.0
  },
  "samples": {
    "baseline": [
      {
        "root": "/private/tmp/metile-layout-baseline.Jdz5Ug",
        "compiler_implementation_sha256": "a052f8823627e3c7880bb620fe2574677ec08383e7cbd3e1c766ec2eb8d13c38",
        "device": "Apple M5",
        "metal_compiler": "Apple metal version 32023.864 (metalfe-32023.864)\nTarget: air64-apple-darwin25.2.0\nThread model: posix\nInstalledDir: /private/var/run/com.apple.security.cryptexd/mnt/com.apple.MobileAsset.MetalToolchain-v17.3.7003.10.GzPOjD/Metal.xctoolchain/usr/metal/current/bin",
        "platform": "macOS-26.2-arm64-arm-64bit",
        "cases": [
          {
            "name": "float16_64x64x64",
            "dtype": "float16",
            "shape": [
              64,
              64,
              64
            ],
            "seed": 431,
            "schedule": {
              "backend": "simdgroup",
              "double_buffer": true,
              "BLOCK_M": 64,
              "BLOCK_N": 64,
              "BLOCK_K": 16,
              "RELAXED_PRECISION": false
            },
            "input_sha256": "f7743c34dfc78564a28e726c1924c410fbdb76f4158beba809e487c7fdc4d8b3",
            "correctness": {
              "reference": "NumPy FP32 matmul rounded to the output storage dtype",
              "max_absolute_error": 0.0,
              "rtol": 0.002,
              "atol": 0.002
            },
            "source_sha256": "925bd354b757114e81e8fe33b26e1821d01d90e9e0e26ac3dc4207f5dfc30f3b",
            "execution_report": {
              "plan": {
                "backend": "simdgroup",
                "threadgroup_size": [
                  128,
                  1,
                  1
                ],
                "simdgroup_grid": [
                  2,
                  2
                ],
                "tile_shape": [
                  64,
                  64,
                  16
                ],
                "staging": "threadgroup",
                "vector_width": null,
                "double_buffer": true,
                "reasons": [
                  "The selected SIMDgroup grid partitions 8x8 accumulator fragments without overlap.",
                  "Cooperative loads stage operand tiles in threadgroup memory."
                ],
                "cooperative_layout": "8x8 simdgroup_matrix fragments",
                "outer_bounds_proven": true
              },
              "passes": [
                "pad_shared_memory",
                "double_buffer_k_loop",
                "vectorize_loads",
                "serpentine_mma",
                "preload_mma_tiles",
                "block_swizzle",
                "fold_constants"
              ],
              "loops": [
                {
                  "induction_variable": "kb",
                  "kind": "loop",
                  "lanes": 128,
                  "elements_per_lane": 1,
                  "iteration_step": 16
                },
                {
                  "induction_variable": "kk",
                  "kind": "loop",
                  "lanes": 128,
                  "elements_per_lane": 1,
                  "iteration_step": 8
                }
              ],
              "allocations": [
                {
                  "name": "shared_a_0",
                  "address_space": "threadgroup",
                  "element_type": "half",
                  "elements": 1088,
                  "bytes": 2176
                },
                {
                  "name": "shared_a_1",
                  "address_space": "threadgroup",
                  "element_type": "half",
                  "elements": 1088,
                  "bytes": 2176
                },
                {
                  "name": "shared_b_0",
                  "address_space": "threadgroup",
                  "element_type": "half",
                  "elements": 1040,
                  "bytes": 2080
                },
                {
                  "name": "shared_b_1",
                  "address_space": "threadgroup",
                  "element_type": "half",
                  "elements": 1040,
                  "bytes": 2080
                }
              ],
              "double_buffered": true,
              "vectorized_loads": 0,
              "epilogue_regions": 0,
              "notes": [
                "Layout widths describe emitted Metal operations, not final machine instructions.",
                "Masked tails may use scalar accesses even when aligned interiors are vectorized."
              ]
            },
            "timing": {
              "samples": 1383,
              "gpu_us": 64.29170025512576,
              "wall_us": 365.084,
              "gpu_min_max_us": [
                64.1250517219305,
                77.75000995025039
              ],
              "wall_min_max_us": [
                141.791,
                463.209
              ]
            },
            "status": "ok"
          },
          {
            "name": "float16_256x256x256",
            "dtype": "float16",
            "shape": [
              256,
              256,
              256
            ],
            "seed": 432,
            "schedule": {
              "backend": "simdgroup",
              "double_buffer": true,
              "BLOCK_M": 64,
              "BLOCK_N": 64,
              "BLOCK_K": 16,
              "RELAXED_PRECISION": false
            },
            "input_sha256": "93ab6d6120e1756849446ff813e60fbd0616fa9eec32fbbd8c515ecaa3488b3d",
            "correctness": {
              "reference": "NumPy FP32 matmul rounded to the output storage dtype",
              "max_absolute_error": 0.0,
              "rtol": 0.002,
              "atol": 0.002
            },
            "source_sha256": "925bd354b757114e81e8fe33b26e1821d01d90e9e0e26ac3dc4207f5dfc30f3b",
            "execution_report": {
              "plan": {
                "backend": "simdgroup",
                "threadgroup_size": [
                  128,
                  1,
                  1
                ],
                "simdgroup_grid": [
                  2,
                  2
                ],
                "tile_shape": [
                  64,
                  64,
                  16
                ],
                "staging": "threadgroup",
                "vector_width": null,
                "double_buffer": true,
                "reasons": [
                  "The selected SIMDgroup grid partitions 8x8 accumulator fragments without overlap.",
                  "Cooperative loads stage operand tiles in threadgroup memory."
                ],
                "cooperative_layout": "8x8 simdgroup_matrix fragments",
                "outer_bounds_proven": true
              },
              "passes": [
                "pad_shared_memory",
                "double_buffer_k_loop",
                "vectorize_loads",
                "serpentine_mma",
                "preload_mma_tiles",
                "block_swizzle",
                "fold_constants"
              ],
              "loops": [
                {
                  "induction_variable": "kb",
                  "kind": "loop",
                  "lanes": 128,
                  "elements_per_lane": 1,
                  "iteration_step": 16
                },
                {
                  "induction_variable": "kk",
                  "kind": "loop",
                  "lanes": 128,
                  "elements_per_lane": 1,
                  "iteration_step": 8
                }
              ],
              "allocations": [
                {
                  "name": "shared_a_0",
                  "address_space": "threadgroup",
                  "element_type": "half",
                  "elements": 1088,
                  "bytes": 2176
                },
                {
                  "name": "shared_a_1",
                  "address_space": "threadgroup",
                  "element_type": "half",
                  "elements": 1088,
                  "bytes": 2176
                },
                {
                  "name": "shared_b_0",
                  "address_space": "threadgroup",
                  "element_type": "half",
                  "elements": 1040,
                  "bytes": 2080
                },
                {
                  "name": "shared_b_1",
                  "address_space": "threadgroup",
                  "element_type": "half",
                  "elements": 1040,
                  "bytes": 2080
                }
              ],
              "double_buffered": true,
              "vectorized_loads": 0,
              "epilogue_regions": 0,
              "notes": [
                "Layout widths describe emitted Metal operations, not final machine instructions.",
                "Masked tails may use scalar accesses even when aligned interiors are vectorized."
              ]
            },
            "timing": {
              "samples": 1005,
              "gpu_us": 191.8749767355621,
              "wall_us": 500.875,
              "gpu_min_max_us": [
                188.74998204410076,
                271.9166805036366
              ],
              "wall_min_max_us": [
                283.625,
                587.792
              ]
            },
            "status": "ok"
          },
          {
            "name": "float16_1024x1024x1024",
            "dtype": "float16",
            "shape": [
              1024,
              1024,
              1024
            ],
            "seed": 433,
            "schedule": {
              "backend": "simdgroup",
              "double_buffer": true,
              "BLOCK_M": 64,
              "BLOCK_N": 64,
              "BLOCK_K": 16,
              "RELAXED_PRECISION": false
            },
            "input_sha256": "a3cdef8bbc69c848e84c524701f359db6268c696607cea04283a35e3be9e32c1",
            "correctness": {
              "reference": "NumPy FP32 matmul rounded to the output storage dtype",
              "max_absolute_error": 0.0,
              "rtol": 0.002,
              "atol": 0.002
            },
            "source_sha256": "925bd354b757114e81e8fe33b26e1821d01d90e9e0e26ac3dc4207f5dfc30f3b",
            "execution_report": {
              "plan": {
                "backend": "simdgroup",
                "threadgroup_size": [
                  128,
                  1,
                  1
                ],
                "simdgroup_grid": [
                  2,
                  2
                ],
                "tile_shape": [
                  64,
                  64,
                  16
                ],
                "staging": "threadgroup",
                "vector_width": null,
                "double_buffer": true,
                "reasons": [
                  "The selected SIMDgroup grid partitions 8x8 accumulator fragments without overlap.",
                  "Cooperative loads stage operand tiles in threadgroup memory."
                ],
                "cooperative_layout": "8x8 simdgroup_matrix fragments",
                "outer_bounds_proven": true
              },
              "passes": [
                "pad_shared_memory",
                "double_buffer_k_loop",
                "vectorize_loads",
                "serpentine_mma",
                "preload_mma_tiles",
                "block_swizzle",
                "fold_constants"
              ],
              "loops": [
                {
                  "induction_variable": "kb",
                  "kind": "loop",
                  "lanes": 128,
                  "elements_per_lane": 1,
                  "iteration_step": 16
                },
                {
                  "induction_variable": "kk",
                  "kind": "loop",
                  "lanes": 128,
                  "elements_per_lane": 1,
                  "iteration_step": 8
                }
              ],
              "allocations": [
                {
                  "name": "shared_a_0",
                  "address_space": "threadgroup",
                  "element_type": "half",
                  "elements": 1088,
                  "bytes": 2176
                },
                {
                  "name": "shared_a_1",
                  "address_space": "threadgroup",
                  "element_type": "half",
                  "elements": 1088,
                  "bytes": 2176
                },
                {
                  "name": "shared_b_0",
                  "address_space": "threadgroup",
                  "element_type": "half",
                  "elements": 1040,
                  "bytes": 2080
                },
                {
                  "name": "shared_b_1",
                  "address_space": "threadgroup",
                  "element_type": "half",
                  "elements": 1040,
                  "bytes": 2080
                }
              ],
              "double_buffered": true,
              "vectorized_loads": 0,
              "epilogue_regions": 0,
              "notes": [
                "Layout widths describe emitted Metal operations, not final machine instructions.",
                "Masked tails may use scalar accesses even when aligned interiors are vectorized."
              ]
            },
            "timing": {
              "samples": 483,
              "gpu_us": 817.4583199433982,
              "wall_us": 1031.667,
              "gpu_min_max_us": [
                801.7499931156635,
                1262.7500109374523
              ],
              "wall_min_max_us": [
                896.2090000000001,
                1476.625
              ]
            },
            "status": "ok"
          },
          {
            "name": "float16_257x255x259",
            "dtype": "float16",
            "shape": [
              257,
              255,
              259
            ],
            "seed": 434,
            "schedule": {
              "backend": "simdgroup",
              "double_buffer": true,
              "BLOCK_M": 64,
              "BLOCK_N": 64,
              "BLOCK_K": 16,
              "RELAXED_PRECISION": false
            },
            "input_sha256": "9b256a8e5e5aa03086c616dbb685bfb3b2a3838b8a2de16524f12307645110ef",
            "correctness": {
              "reference": "NumPy FP32 matmul rounded to the output storage dtype",
              "max_absolute_error": 0.0,
              "rtol": 0.002,
              "atol": 0.002
            },
            "source_sha256": "925bd354b757114e81e8fe33b26e1821d01d90e9e0e26ac3dc4207f5dfc30f3b",
            "execution_report": {
              "plan": {
                "backend": "simdgroup",
                "threadgroup_size": [
                  128,
                  1,
                  1
                ],
                "simdgroup_grid": [
                  2,
                  2
                ],
                "tile_shape": [
                  64,
                  64,
                  16
                ],
                "staging": "threadgroup",
                "vector_width": null,
                "double_buffer": true,
                "reasons": [
                  "The selected SIMDgroup grid partitions 8x8 accumulator fragments without overlap.",
                  "Cooperative loads stage operand tiles in threadgroup memory."
                ],
                "cooperative_layout": "8x8 simdgroup_matrix fragments",
                "outer_bounds_proven": false
              },
              "passes": [
                "pad_shared_memory",
                "double_buffer_k_loop",
                "vectorize_loads",
                "serpentine_mma",
                "preload_mma_tiles",
                "block_swizzle",
                "fold_constants"
              ],
              "loops": [
                {
                  "induction_variable": "kb",
                  "kind": "loop",
                  "lanes": 128,
                  "elements_per_lane": 1,
                  "iteration_step": 16
                },
                {
                  "induction_variable": "kk",
                  "kind": "loop",
                  "lanes": 128,
                  "elements_per_lane": 1,
                  "iteration_step": 8
                }
              ],
              "allocations": [
                {
                  "name": "shared_a_0",
                  "address_space": "threadgroup",
                  "element_type": "half",
                  "elements": 1088,
                  "bytes": 2176
                },
                {
                  "name": "shared_a_1",
                  "address_space": "threadgroup",
                  "element_type": "half",
                  "elements": 1088,
                  "bytes": 2176
                },
                {
                  "name": "shared_b_0",
                  "address_space": "threadgroup",
                  "element_type": "half",
                  "elements": 1040,
                  "bytes": 2080
                },
                {
                  "name": "shared_b_1",
                  "address_space": "threadgroup",
                  "element_type": "half",
                  "elements": 1040,
                  "bytes": 2080
                }
              ],
              "double_buffered": true,
              "vectorized_loads": 0,
              "epilogue_regions": 0,
              "notes": [
                "Layout widths describe emitted Metal operations, not final machine instructions.",
                "Masked tails may use scalar accesses even when aligned interiors are vectorized."
              ]
            },
            "timing": {
              "samples": 1494,
              "gpu_us": 57.95829929411411,
              "wall_us": 281.021,
              "gpu_min_max_us": [
                41.99997056275606,
                222.5416828878224
              ],
              "wall_min_max_us": [
                121.583,
                571.208
              ]
            },
            "status": "ok"
          },
          {
            "name": "float32_64x64x64",
            "dtype": "float32",
            "shape": [
              64,
              64,
              64
            ],
            "seed": 435,
            "schedule": {
              "backend": "simdgroup",
              "double_buffer": true,
              "BLOCK_M": 64,
              "BLOCK_N": 64,
              "BLOCK_K": 16,
              "RELAXED_PRECISION": false
            },
            "input_sha256": "5daffc014e3bf6c7425a716bc5a36f0a9f5ac3d06a994a5e9e8084b7cfb9cd1b",
            "correctness": {
              "reference": "NumPy FP32 matmul rounded to the output storage dtype",
              "max_absolute_error": 0.0,
              "rtol": 0.0003,
              "atol": 3e-05
            },
            "source_sha256": "f3f104bd99ff3f71a2487b1d00cfd450cf4ed9085888a27b979798e443a98808",
            "execution_report": {
              "plan": {
                "backend": "simdgroup",
                "threadgroup_size": [
                  128,
                  1,
                  1
                ],
                "simdgroup_grid": [
                  2,
                  2
                ],
                "tile_shape": [
                  64,
                  64,
                  16
                ],
                "staging": "threadgroup",
                "vector_width": null,
                "double_buffer": true,
                "reasons": [
                  "The selected SIMDgroup grid partitions 8x8 accumulator fragments without overlap.",
                  "Cooperative loads stage operand tiles in threadgroup memory."
                ],
                "cooperative_layout": "8x8 simdgroup_matrix fragments",
                "outer_bounds_proven": true
              },
              "passes": [
                "pad_shared_memory",
                "double_buffer_k_loop",
                "vectorize_loads",
                "serpentine_mma",
                "preload_mma_tiles",
                "block_swizzle",
                "fold_constants"
              ],
              "loops": [
                {
                  "induction_variable": "kb",
                  "kind": "loop",
                  "lanes": 128,
                  "elements_per_lane": 1,
                  "iteration_step": 16
                },
                {
                  "induction_variable": "kk",
                  "kind": "loop",
                  "lanes": 128,
                  "elements_per_lane": 1,
                  "iteration_step": 8
                }
              ],
              "allocations": [
                {
                  "name": "shared_a_0",
                  "address_space": "threadgroup",
                  "element_type": "float",
                  "elements": 1088,
                  "bytes": 4352
                },
                {
                  "name": "shared_a_1",
                  "address_space": "threadgroup",
                  "element_type": "float",
                  "elements": 1088,
                  "bytes": 4352
                },
                {
                  "name": "shared_b_0",
                  "address_space": "threadgroup",
                  "element_type": "float",
                  "elements": 1040,
                  "bytes": 4160
                },
                {
                  "name": "shared_b_1",
                  "address_space": "threadgroup",
                  "element_type": "float",
                  "elements": 1040,
                  "bytes": 4160
                }
              ],
              "double_buffered": true,
              "vectorized_loads": 0,
              "epilogue_regions": 0,
              "notes": [
                "Layout widths describe emitted Metal operations, not final machine instructions.",
                "Masked tails may use scalar accesses even when aligned interiors are vectorized."
              ]
            },
            "timing": {
              "samples": 1361,
              "gpu_us": 68.49999772384763,
              "wall_us": 371.375,
              "gpu_min_max_us": [
                68.29167250543833,
                189.74998965859413
              ],
              "wall_min_max_us": [
                150.708,
                458.875
              ]
            },
            "status": "ok"
          },
          {
            "name": "float32_256x256x256",
            "dtype": "float32",
            "shape": [
              256,
              256,
              256
            ],
            "seed": 436,
            "schedule": {
              "backend": "simdgroup",
              "double_buffer": true,
              "BLOCK_M": 64,
              "BLOCK_N": 64,
              "BLOCK_K": 16,
              "RELAXED_PRECISION": false
            },
            "input_sha256": "ceba1209c2607c35efa378403bf1bd3a583a3330944ee09239152ee064143b95",
            "correctness": {
              "reference": "NumPy FP32 matmul rounded to the output storage dtype",
              "max_absolute_error": 0.0,
              "rtol": 0.0003,
              "atol": 3e-05
            },
            "source_sha256": "f3f104bd99ff3f71a2487b1d00cfd450cf4ed9085888a27b979798e443a98808",
            "execution_report": {
              "plan": {
                "backend": "simdgroup",
                "threadgroup_size": [
                  128,
                  1,
                  1
                ],
                "simdgroup_grid": [
                  2,
                  2
                ],
                "tile_shape": [
                  64,
                  64,
                  16
                ],
                "staging": "threadgroup",
                "vector_width": null,
                "double_buffer": true,
                "reasons": [
                  "The selected SIMDgroup grid partitions 8x8 accumulator fragments without overlap.",
                  "Cooperative loads stage operand tiles in threadgroup memory."
                ],
                "cooperative_layout": "8x8 simdgroup_matrix fragments",
                "outer_bounds_proven": true
              },
              "passes": [
                "pad_shared_memory",
                "double_buffer_k_loop",
                "vectorize_loads",
                "serpentine_mma",
                "preload_mma_tiles",
                "block_swizzle",
                "fold_constants"
              ],
              "loops": [
                {
                  "induction_variable": "kb",
                  "kind": "loop",
                  "lanes": 128,
                  "elements_per_lane": 1,
                  "iteration_step": 16
                },
                {
                  "induction_variable": "kk",
                  "kind": "loop",
                  "lanes": 128,
                  "elements_per_lane": 1,
                  "iteration_step": 8
                }
              ],
              "allocations": [
                {
                  "name": "shared_a_0",
                  "address_space": "threadgroup",
                  "element_type": "float",
                  "elements": 1088,
                  "bytes": 4352
                },
                {
                  "name": "shared_a_1",
                  "address_space": "threadgroup",
                  "element_type": "float",
                  "elements": 1088,
                  "bytes": 4352
                },
                {
                  "name": "shared_b_0",
                  "address_space": "threadgroup",
                  "element_type": "float",
                  "elements": 1040,
                  "bytes": 4160
                },
                {
                  "name": "shared_b_1",
                  "address_space": "threadgroup",
                  "element_type": "float",
                  "elements": 1040,
                  "bytes": 4160
                }
              ],
              "double_buffered": true,
              "vectorized_loads": 0,
              "epilogue_regions": 0,
              "notes": [
                "Layout widths describe emitted Metal operations, not final machine instructions.",
                "Masked tails may use scalar accesses even when aligned interiors are vectorized."
              ]
            },
            "timing": {
              "samples": 967,
              "gpu_us": 212.7499901689589,
              "wall_us": 520.25,
              "gpu_min_max_us": [
                210.3750011883676,
                240.24996673688293
              ],
              "wall_min_max_us": [
                303.666,
                603.917
              ]
            },
            "status": "ok"
          },
          {
            "name": "float32_1024x1024x1024",
            "dtype": "float32",
            "shape": [
              1024,
              1024,
              1024
            ],
            "seed": 437,
            "schedule": {
              "backend": "simdgroup",
              "double_buffer": true,
              "BLOCK_M": 64,
              "BLOCK_N": 64,
              "BLOCK_K": 16,
              "RELAXED_PRECISION": false
            },
            "input_sha256": "16ed3544359adfe6ed4ecc94e89ed08c70fd5aeef3243f80b2009c2096d05f8c",
            "correctness": {
              "reference": "NumPy FP32 matmul rounded to the output storage dtype",
              "max_absolute_error": 0.0,
              "rtol": 0.0003,
              "atol": 3e-05
            },
            "source_sha256": "f3f104bd99ff3f71a2487b1d00cfd450cf4ed9085888a27b979798e443a98808",
            "execution_report": {
              "plan": {
                "backend": "simdgroup",
                "threadgroup_size": [
                  128,
                  1,
                  1
                ],
                "simdgroup_grid": [
                  2,
                  2
                ],
                "tile_shape": [
                  64,
                  64,
                  16
                ],
                "staging": "threadgroup",
                "vector_width": null,
                "double_buffer": true,
                "reasons": [
                  "The selected SIMDgroup grid partitions 8x8 accumulator fragments without overlap.",
                  "Cooperative loads stage operand tiles in threadgroup memory."
                ],
                "cooperative_layout": "8x8 simdgroup_matrix fragments",
                "outer_bounds_proven": true
              },
              "passes": [
                "pad_shared_memory",
                "double_buffer_k_loop",
                "vectorize_loads",
                "serpentine_mma",
                "preload_mma_tiles",
                "block_swizzle",
                "fold_constants"
              ],
              "loops": [
                {
                  "induction_variable": "kb",
                  "kind": "loop",
                  "lanes": 128,
                  "elements_per_lane": 1,
                  "iteration_step": 16
                },
                {
                  "induction_variable": "kk",
                  "kind": "loop",
                  "lanes": 128,
                  "elements_per_lane": 1,
                  "iteration_step": 8
                }
              ],
              "allocations": [
                {
                  "name": "shared_a_0",
                  "address_space": "threadgroup",
                  "element_type": "float",
                  "elements": 1088,
                  "bytes": 4352
                },
                {
                  "name": "shared_a_1",
                  "address_space": "threadgroup",
                  "element_type": "float",
                  "elements": 1088,
                  "bytes": 4352
                },
                {
                  "name": "shared_b_0",
                  "address_space": "threadgroup",
                  "element_type": "float",
                  "elements": 1040,
                  "bytes": 4160
                },
                {
                  "name": "shared_b_1",
                  "address_space": "threadgroup",
                  "element_type": "float",
                  "elements": 1040,
                  "bytes": 4160
                }
              ],
              "double_buffered": true,
              "vectorized_loads": 0,
              "epilogue_regions": 0,
              "notes": [
                "Layout widths describe emitted Metal operations, not final machine instructions.",
                "Masked tails may use scalar accesses even when aligned interiors are vectorized."
              ]
            },
            "timing": {
              "samples": 405,
              "gpu_us": 981.2916978262365,
              "wall_us": 1199.167,
              "gpu_min_max_us": [
                970.3333489596844,
                1196.2083517573774
              ],
              "wall_min_max_us": [
                1105.042,
                7811.625
              ]
            },
            "status": "ok"
          },
          {
            "name": "float32_257x255x259",
            "dtype": "float32",
            "shape": [
              257,
              255,
              259
            ],
            "seed": 438,
            "schedule": {
              "backend": "simdgroup",
              "double_buffer": true,
              "BLOCK_M": 64,
              "BLOCK_N": 64,
              "BLOCK_K": 16,
              "RELAXED_PRECISION": false
            },
            "input_sha256": "acff8f3e2b353c103ecee705731d3d2c8c26b98f0a80634d1fd4a06c38113a26",
            "correctness": {
              "reference": "NumPy FP32 matmul rounded to the output storage dtype",
              "max_absolute_error": 0.0,
              "rtol": 0.0003,
              "atol": 3e-05
            },
            "source_sha256": "f3f104bd99ff3f71a2487b1d00cfd450cf4ed9085888a27b979798e443a98808",
            "execution_report": {
              "plan": {
                "backend": "simdgroup",
                "threadgroup_size": [
                  128,
                  1,
                  1
                ],
                "simdgroup_grid": [
                  2,
                  2
                ],
                "tile_shape": [
                  64,
                  64,
                  16
                ],
                "staging": "threadgroup",
                "vector_width": null,
                "double_buffer": true,
                "reasons": [
                  "The selected SIMDgroup grid partitions 8x8 accumulator fragments without overlap.",
                  "Cooperative loads stage operand tiles in threadgroup memory."
                ],
                "cooperative_layout": "8x8 simdgroup_matrix fragments",
                "outer_bounds_proven": false
              },
              "passes": [
                "pad_shared_memory",
                "double_buffer_k_loop",
                "vectorize_loads",
                "serpentine_mma",
                "preload_mma_tiles",
                "block_swizzle",
                "fold_constants"
              ],
              "loops": [
                {
                  "induction_variable": "kb",
                  "kind": "loop",
                  "lanes": 128,
                  "elements_per_lane": 1,
                  "iteration_step": 16
                },
                {
                  "induction_variable": "kk",
                  "kind": "loop",
                  "lanes": 128,
                  "elements_per_lane": 1,
                  "iteration_step": 8
                }
              ],
              "allocations": [
                {
                  "name": "shared_a_0",
                  "address_space": "threadgroup",
                  "element_type": "float",
                  "elements": 1088,
                  "bytes": 4352
                },
                {
                  "name": "shared_a_1",
                  "address_space": "threadgroup",
                  "element_type": "float",
                  "elements": 1088,
                  "bytes": 4352
                },
                {
                  "name": "shared_b_0",
                  "address_space": "threadgroup",
                  "element_type": "float",
                  "elements": 1040,
                  "bytes": 4160
                },
                {
                  "name": "shared_b_1",
                  "address_space": "threadgroup",
                  "element_type": "float",
                  "elements": 1040,
                  "bytes": 4160
                }
              ],
              "double_buffered": true,
              "vectorized_loads": 0,
              "epilogue_regions": 0,
              "notes": [
                "Layout widths describe emitted Metal operations, not final machine instructions.",
                "Masked tails may use scalar accesses even when aligned interiors are vectorized."
              ]
            },
            "timing": {
              "samples": 1520,
              "gpu_us": 58.2499778829515,
              "wall_us": 280.29150000000004,
              "gpu_min_max_us": [
                45.41664384305477,
                244.666647631675
              ],
              "wall_min_max_us": [
                133.791,
                588.417
              ]
            },
            "status": "ok"
          }
        ]
      },
      {
        "root": "/private/tmp/metile-layout-baseline.Jdz5Ug",
        "compiler_implementation_sha256": "a052f8823627e3c7880bb620fe2574677ec08383e7cbd3e1c766ec2eb8d13c38",
        "device": "Apple M5",
        "metal_compiler": "Apple metal version 32023.864 (metalfe-32023.864)\nTarget: air64-apple-darwin25.2.0\nThread model: posix\nInstalledDir: /private/var/run/com.apple.security.cryptexd/mnt/com.apple.MobileAsset.MetalToolchain-v17.3.7003.10.GzPOjD/Metal.xctoolchain/usr/metal/current/bin",
        "platform": "macOS-26.2-arm64-arm-64bit",
        "cases": [
          {
            "name": "float16_64x64x64",
            "dtype": "float16",
            "shape": [
              64,
              64,
              64
            ],
            "seed": 431,
            "schedule": {
              "backend": "simdgroup",
              "double_buffer": true,
              "BLOCK_M": 64,
              "BLOCK_N": 64,
              "BLOCK_K": 16,
              "RELAXED_PRECISION": false
            },
            "input_sha256": "f7743c34dfc78564a28e726c1924c410fbdb76f4158beba809e487c7fdc4d8b3",
            "correctness": {
              "reference": "NumPy FP32 matmul rounded to the output storage dtype",
              "max_absolute_error": 0.0,
              "rtol": 0.002,
              "atol": 0.002
            },
            "source_sha256": "925bd354b757114e81e8fe33b26e1821d01d90e9e0e26ac3dc4207f5dfc30f3b",
            "execution_report": {
              "plan": {
                "backend": "simdgroup",
                "threadgroup_size": [
                  128,
                  1,
                  1
                ],
                "simdgroup_grid": [
                  2,
                  2
                ],
                "tile_shape": [
                  64,
                  64,
                  16
                ],
                "staging": "threadgroup",
                "vector_width": null,
                "double_buffer": true,
                "reasons": [
                  "The selected SIMDgroup grid partitions 8x8 accumulator fragments without overlap.",
                  "Cooperative loads stage operand tiles in threadgroup memory."
                ],
                "cooperative_layout": "8x8 simdgroup_matrix fragments",
                "outer_bounds_proven": true
              },
              "passes": [
                "pad_shared_memory",
                "double_buffer_k_loop",
                "vectorize_loads",
                "serpentine_mma",
                "preload_mma_tiles",
                "block_swizzle",
                "fold_constants"
              ],
              "loops": [
                {
                  "induction_variable": "kb",
                  "kind": "loop",
                  "lanes": 128,
                  "elements_per_lane": 1,
                  "iteration_step": 16
                },
                {
                  "induction_variable": "kk",
                  "kind": "loop",
                  "lanes": 128,
                  "elements_per_lane": 1,
                  "iteration_step": 8
                }
              ],
              "allocations": [
                {
                  "name": "shared_a_0",
                  "address_space": "threadgroup",
                  "element_type": "half",
                  "elements": 1088,
                  "bytes": 2176
                },
                {
                  "name": "shared_a_1",
                  "address_space": "threadgroup",
                  "element_type": "half",
                  "elements": 1088,
                  "bytes": 2176
                },
                {
                  "name": "shared_b_0",
                  "address_space": "threadgroup",
                  "element_type": "half",
                  "elements": 1040,
                  "bytes": 2080
                },
                {
                  "name": "shared_b_1",
                  "address_space": "threadgroup",
                  "element_type": "half",
                  "elements": 1040,
                  "bytes": 2080
                }
              ],
              "double_buffered": true,
              "vectorized_loads": 0,
              "epilogue_regions": 0,
              "notes": [
                "Layout widths describe emitted Metal operations, not final machine instructions.",
                "Masked tails may use scalar accesses even when aligned interiors are vectorized."
              ]
            },
            "timing": {
              "samples": 1371,
              "gpu_us": 64.87499922513962,
              "wall_us": 368.958,
              "gpu_min_max_us": [
                64.62499732151628,
                78.62498750910163
              ],
              "wall_min_max_us": [
                142.459,
                449.208
              ]
            },
            "status": "ok"
          },
          {
            "name": "float16_256x256x256",
            "dtype": "float16",
            "shape": [
              256,
              256,
              256
            ],
            "seed": 432,
            "schedule": {
              "backend": "simdgroup",
              "double_buffer": true,
              "BLOCK_M": 64,
              "BLOCK_N": 64,
              "BLOCK_K": 16,
              "RELAXED_PRECISION": false
            },
            "input_sha256": "93ab6d6120e1756849446ff813e60fbd0616fa9eec32fbbd8c515ecaa3488b3d",
            "correctness": {
              "reference": "NumPy FP32 matmul rounded to the output storage dtype",
              "max_absolute_error": 0.0,
              "rtol": 0.002,
              "atol": 0.002
            },
            "source_sha256": "925bd354b757114e81e8fe33b26e1821d01d90e9e0e26ac3dc4207f5dfc30f3b",
            "execution_report": {
              "plan": {
                "backend": "simdgroup",
                "threadgroup_size": [
                  128,
                  1,
                  1
                ],
                "simdgroup_grid": [
                  2,
                  2
                ],
                "tile_shape": [
                  64,
                  64,
                  16
                ],
                "staging": "threadgroup",
                "vector_width": null,
                "double_buffer": true,
                "reasons": [
                  "The selected SIMDgroup grid partitions 8x8 accumulator fragments without overlap.",
                  "Cooperative loads stage operand tiles in threadgroup memory."
                ],
                "cooperative_layout": "8x8 simdgroup_matrix fragments",
                "outer_bounds_proven": true
              },
              "passes": [
                "pad_shared_memory",
                "double_buffer_k_loop",
                "vectorize_loads",
                "serpentine_mma",
                "preload_mma_tiles",
                "block_swizzle",
                "fold_constants"
              ],
              "loops": [
                {
                  "induction_variable": "kb",
                  "kind": "loop",
                  "lanes": 128,
                  "elements_per_lane": 1,
                  "iteration_step": 16
                },
                {
                  "induction_variable": "kk",
                  "kind": "loop",
                  "lanes": 128,
                  "elements_per_lane": 1,
                  "iteration_step": 8
                }
              ],
              "allocations": [
                {
                  "name": "shared_a_0",
                  "address_space": "threadgroup",
                  "element_type": "half",
                  "elements": 1088,
                  "bytes": 2176
                },
                {
                  "name": "shared_a_1",
                  "address_space": "threadgroup",
                  "element_type": "half",
                  "elements": 1088,
                  "bytes": 2176
                },
                {
                  "name": "shared_b_0",
                  "address_space": "threadgroup",
                  "element_type": "half",
                  "elements": 1040,
                  "bytes": 2080
                },
                {
                  "name": "shared_b_1",
                  "address_space": "threadgroup",
                  "element_type": "half",
                  "elements": 1040,
                  "bytes": 2080
                }
              ],
              "double_buffered": true,
              "vectorized_loads": 0,
              "epilogue_regions": 0,
              "notes": [
                "Layout widths describe emitted Metal operations, not final machine instructions.",
                "Masked tails may use scalar accesses even when aligned interiors are vectorized."
              ]
            },
            "timing": {
              "samples": 999,
              "gpu_us": 192.0000067912042,
              "wall_us": 504.166,
              "gpu_min_max_us": [
                188.9999839477241,
                219.62495520710945
              ],
              "wall_min_max_us": [
                273.333,
                625.333
              ]
            },
            "status": "ok"
          },
          {
            "name": "float16_1024x1024x1024",
            "dtype": "float16",
            "shape": [
              1024,
              1024,
              1024
            ],
            "seed": 433,
            "schedule": {
              "backend": "simdgroup",
              "double_buffer": true,
              "BLOCK_M": 64,
              "BLOCK_N": 64,
              "BLOCK_K": 16,
              "RELAXED_PRECISION": false
            },
            "input_sha256": "a3cdef8bbc69c848e84c524701f359db6268c696607cea04283a35e3be9e32c1",
            "correctness": {
              "reference": "NumPy FP32 matmul rounded to the output storage dtype",
              "max_absolute_error": 0.0,
              "rtol": 0.002,
              "atol": 0.002
            },
            "source_sha256": "925bd354b757114e81e8fe33b26e1821d01d90e9e0e26ac3dc4207f5dfc30f3b",
            "execution_report": {
              "plan": {
                "backend": "simdgroup",
                "threadgroup_size": [
                  128,
                  1,
                  1
                ],
                "simdgroup_grid": [
                  2,
                  2
                ],
                "tile_shape": [
                  64,
                  64,
                  16
                ],
                "staging": "threadgroup",
                "vector_width": null,
                "double_buffer": true,
                "reasons": [
                  "The selected SIMDgroup grid partitions 8x8 accumulator fragments without overlap.",
                  "Cooperative loads stage operand tiles in threadgroup memory."
                ],
                "cooperative_layout": "8x8 simdgroup_matrix fragments",
                "outer_bounds_proven": true
              },
              "passes": [
                "pad_shared_memory",
                "double_buffer_k_loop",
                "vectorize_loads",
                "serpentine_mma",
                "preload_mma_tiles",
                "block_swizzle",
                "fold_constants"
              ],
              "loops": [
                {
                  "induction_variable": "kb",
                  "kind": "loop",
                  "lanes": 128,
                  "elements_per_lane": 1,
                  "iteration_step": 16
                },
                {
                  "induction_variable": "kk",
                  "kind": "loop",
                  "lanes": 128,
                  "elements_per_lane": 1,
                  "iteration_step": 8
                }
              ],
              "allocations": [
                {
                  "name": "shared_a_0",
                  "address_space": "threadgroup",
                  "element_type": "half",
                  "elements": 1088,
                  "bytes": 2176
                },
                {
                  "name": "shared_a_1",
                  "address_space": "threadgroup",
                  "element_type": "half",
                  "elements": 1088,
                  "bytes": 2176
                },
                {
                  "name": "shared_b_0",
                  "address_space": "threadgroup",
                  "element_type": "half",
                  "elements": 1040,
                  "bytes": 2080
                },
                {
                  "name": "shared_b_1",
                  "address_space": "threadgroup",
                  "element_type": "half",
                  "elements": 1040,
                  "bytes": 2080
                }
              ],
              "double_buffered": true,
              "vectorized_loads": 0,
              "epilogue_regions": 0,
              "notes": [
                "Layout widths describe emitted Metal operations, not final machine instructions.",
                "Masked tails may use scalar accesses even when aligned interiors are vectorized."
              ]
            },
            "timing": {
              "samples": 485,
              "gpu_us": 817.3332898877561,
              "wall_us": 1030.5,
              "gpu_min_max_us": [
                799.2916507646441,
                889.7499646991491
              ],
              "wall_min_max_us": [
                916.583,
                1142.375
              ]
            },
            "status": "ok"
          },
          {
            "name": "float16_257x255x259",
            "dtype": "float16",
            "shape": [
              257,
              255,
              259
            ],
            "seed": 434,
            "schedule": {
              "backend": "simdgroup",
              "double_buffer": true,
              "BLOCK_M": 64,
              "BLOCK_N": 64,
              "BLOCK_K": 16,
              "RELAXED_PRECISION": false
            },
            "input_sha256": "9b256a8e5e5aa03086c616dbb685bfb3b2a3838b8a2de16524f12307645110ef",
            "correctness": {
              "reference": "NumPy FP32 matmul rounded to the output storage dtype",
              "max_absolute_error": 0.0,
              "rtol": 0.002,
              "atol": 0.002
            },
            "source_sha256": "925bd354b757114e81e8fe33b26e1821d01d90e9e0e26ac3dc4207f5dfc30f3b",
            "execution_report": {
              "plan": {
                "backend": "simdgroup",
                "threadgroup_size": [
                  128,
                  1,
                  1
                ],
                "simdgroup_grid": [
                  2,
                  2
                ],
                "tile_shape": [
                  64,
                  64,
                  16
                ],
                "staging": "threadgroup",
                "vector_width": null,
                "double_buffer": true,
                "reasons": [
                  "The selected SIMDgroup grid partitions 8x8 accumulator fragments without overlap.",
                  "Cooperative loads stage operand tiles in threadgroup memory."
                ],
                "cooperative_layout": "8x8 simdgroup_matrix fragments",
                "outer_bounds_proven": false
              },
              "passes": [
                "pad_shared_memory",
                "double_buffer_k_loop",
                "vectorize_loads",
                "serpentine_mma",
                "preload_mma_tiles",
                "block_swizzle",
                "fold_constants"
              ],
              "loops": [
                {
                  "induction_variable": "kb",
                  "kind": "loop",
                  "lanes": 128,
                  "elements_per_lane": 1,
                  "iteration_step": 16
                },
                {
                  "induction_variable": "kk",
                  "kind": "loop",
                  "lanes": 128,
                  "elements_per_lane": 1,
                  "iteration_step": 8
                }
              ],
              "allocations": [
                {
                  "name": "shared_a_0",
                  "address_space": "threadgroup",
                  "element_type": "half",
                  "elements": 1088,
                  "bytes": 2176
                },
                {
                  "name": "shared_a_1",
                  "address_space": "threadgroup",
                  "element_type": "half",
                  "elements": 1088,
                  "bytes": 2176
                },
                {
                  "name": "shared_b_0",
                  "address_space": "threadgroup",
                  "element_type": "half",
                  "elements": 1040,
                  "bytes": 2080
                },
                {
                  "name": "shared_b_1",
                  "address_space": "threadgroup",
                  "element_type": "half",
                  "elements": 1040,
                  "bytes": 2080
                }
              ],
              "double_buffered": true,
              "vectorized_loads": 0,
              "epilogue_regions": 0,
              "notes": [
                "Layout widths describe emitted Metal operations, not final machine instructions.",
                "Masked tails may use scalar accesses even when aligned interiors are vectorized."
              ]
            },
            "timing": {
              "samples": 1495,
              "gpu_us": 57.75003228336573,
              "wall_us": 279.208,
              "gpu_min_max_us": [
                41.91667539998889,
                224.87499518319964
              ],
              "wall_min_max_us": [
                124.917,
                574.125
              ]
            },
            "status": "ok"
          },
          {
            "name": "float32_64x64x64",
            "dtype": "float32",
            "shape": [
              64,
              64,
              64
            ],
            "seed": 435,
            "schedule": {
              "backend": "simdgroup",
              "double_buffer": true,
              "BLOCK_M": 64,
              "BLOCK_N": 64,
              "BLOCK_K": 16,
              "RELAXED_PRECISION": false
            },
            "input_sha256": "5daffc014e3bf6c7425a716bc5a36f0a9f5ac3d06a994a5e9e8084b7cfb9cd1b",
            "correctness": {
              "reference": "NumPy FP32 matmul rounded to the output storage dtype",
              "max_absolute_error": 0.0,
              "rtol": 0.0003,
              "atol": 3e-05
            },
            "source_sha256": "f3f104bd99ff3f71a2487b1d00cfd450cf4ed9085888a27b979798e443a98808",
            "execution_report": {
              "plan": {
                "backend": "simdgroup",
                "threadgroup_size": [
                  128,
                  1,
                  1
                ],
                "simdgroup_grid": [
                  2,
                  2
                ],
                "tile_shape": [
                  64,
                  64,
                  16
                ],
                "staging": "threadgroup",
                "vector_width": null,
                "double_buffer": true,
                "reasons": [
                  "The selected SIMDgroup grid partitions 8x8 accumulator fragments without overlap.",
                  "Cooperative loads stage operand tiles in threadgroup memory."
                ],
                "cooperative_layout": "8x8 simdgroup_matrix fragments",
                "outer_bounds_proven": true
              },
              "passes": [
                "pad_shared_memory",
                "double_buffer_k_loop",
                "vectorize_loads",
                "serpentine_mma",
                "preload_mma_tiles",
                "block_swizzle",
                "fold_constants"
              ],
              "loops": [
                {
                  "induction_variable": "kb",
                  "kind": "loop",
                  "lanes": 128,
                  "elements_per_lane": 1,
                  "iteration_step": 16
                },
                {
                  "induction_variable": "kk",
                  "kind": "loop",
                  "lanes": 128,
                  "elements_per_lane": 1,
                  "iteration_step": 8
                }
              ],
              "allocations": [
                {
                  "name": "shared_a_0",
                  "address_space": "threadgroup",
                  "element_type": "float",
                  "elements": 1088,
                  "bytes": 4352
                },
                {
                  "name": "shared_a_1",
                  "address_space": "threadgroup",
                  "element_type": "float",
                  "elements": 1088,
                  "bytes": 4352
                },
                {
                  "name": "shared_b_0",
                  "address_space": "threadgroup",
                  "element_type": "float",
                  "elements": 1040,
                  "bytes": 4160
                },
                {
                  "name": "shared_b_1",
                  "address_space": "threadgroup",
                  "element_type": "float",
                  "elements": 1040,
                  "bytes": 4160
                }
              ],
              "double_buffered": true,
              "vectorized_loads": 0,
              "epilogue_regions": 0,
              "notes": [
                "Layout widths describe emitted Metal operations, not final machine instructions.",
                "Masked tails may use scalar accesses even when aligned interiors are vectorized."
              ]
            },
            "timing": {
              "samples": 1357,
              "gpu_us": 68.29161429777741,
              "wall_us": 374.25,
              "gpu_min_max_us": [
                68.12496576458216,
                86.74996206536889
              ],
              "wall_min_max_us": [
                156.75,
                469.834
              ]
            },
            "status": "ok"
          },
          {
            "name": "float32_256x256x256",
            "dtype": "float32",
            "shape": [
              256,
              256,
              256
            ],
            "seed": 436,
            "schedule": {
              "backend": "simdgroup",
              "double_buffer": true,
              "BLOCK_M": 64,
              "BLOCK_N": 64,
              "BLOCK_K": 16,
              "RELAXED_PRECISION": false
            },
            "input_sha256": "ceba1209c2607c35efa378403bf1bd3a583a3330944ee09239152ee064143b95",
            "correctness": {
              "reference": "NumPy FP32 matmul rounded to the output storage dtype",
              "max_absolute_error": 0.0,
              "rtol": 0.0003,
              "atol": 3e-05
            },
            "source_sha256": "f3f104bd99ff3f71a2487b1d00cfd450cf4ed9085888a27b979798e443a98808",
            "execution_report": {
              "plan": {
                "backend": "simdgroup",
                "threadgroup_size": [
                  128,
                  1,
                  1
                ],
                "simdgroup_grid": [
                  2,
                  2
                ],
                "tile_shape": [
                  64,
                  64,
                  16
                ],
                "staging": "threadgroup",
                "vector_width": null,
                "double_buffer": true,
                "reasons": [
                  "The selected SIMDgroup grid partitions 8x8 accumulator fragments without overlap.",
                  "Cooperative loads stage operand tiles in threadgroup memory."
                ],
                "cooperative_layout": "8x8 simdgroup_matrix fragments",
                "outer_bounds_proven": true
              },
              "passes": [
                "pad_shared_memory",
                "double_buffer_k_loop",
                "vectorize_loads",
                "serpentine_mma",
                "preload_mma_tiles",
                "block_swizzle",
                "fold_constants"
              ],
              "loops": [
                {
                  "induction_variable": "kb",
                  "kind": "loop",
                  "lanes": 128,
                  "elements_per_lane": 1,
                  "iteration_step": 16
                },
                {
                  "induction_variable": "kk",
                  "kind": "loop",
                  "lanes": 128,
                  "elements_per_lane": 1,
                  "iteration_step": 8
                }
              ],
              "allocations": [
                {
                  "name": "shared_a_0",
                  "address_space": "threadgroup",
                  "element_type": "float",
                  "elements": 1088,
                  "bytes": 4352
                },
                {
                  "name": "shared_a_1",
                  "address_space": "threadgroup",
                  "element_type": "float",
                  "elements": 1088,
                  "bytes": 4352
                },
                {
                  "name": "shared_b_0",
                  "address_space": "threadgroup",
                  "element_type": "float",
                  "elements": 1040,
                  "bytes": 4160
                },
                {
                  "name": "shared_b_1",
                  "address_space": "threadgroup",
                  "element_type": "float",
                  "elements": 1040,
                  "bytes": 4160
                }
              ],
              "double_buffered": true,
              "vectorized_loads": 0,
              "epilogue_regions": 0,
              "notes": [
                "Layout widths describe emitted Metal operations, not final machine instructions.",
                "Masked tails may use scalar accesses even when aligned interiors are vectorized."
              ]
            },
            "timing": {
              "samples": 964,
              "gpu_us": 212.99999207258224,
              "wall_us": 521.625,
              "gpu_min_max_us": [
                208.37498595938087,
                239.66666776686907
              ],
              "wall_min_max_us": [
                302.708,
                609.75
              ]
            },
            "status": "ok"
          },
          {
            "name": "float32_1024x1024x1024",
            "dtype": "float32",
            "shape": [
              1024,
              1024,
              1024
            ],
            "seed": 437,
            "schedule": {
              "backend": "simdgroup",
              "double_buffer": true,
              "BLOCK_M": 64,
              "BLOCK_N": 64,
              "BLOCK_K": 16,
              "RELAXED_PRECISION": false
            },
            "input_sha256": "16ed3544359adfe6ed4ecc94e89ed08c70fd5aeef3243f80b2009c2096d05f8c",
            "correctness": {
              "reference": "NumPy FP32 matmul rounded to the output storage dtype",
              "max_absolute_error": 0.0,
              "rtol": 0.0003,
              "atol": 3e-05
            },
            "source_sha256": "f3f104bd99ff3f71a2487b1d00cfd450cf4ed9085888a27b979798e443a98808",
            "execution_report": {
              "plan": {
                "backend": "simdgroup",
                "threadgroup_size": [
                  128,
                  1,
                  1
                ],
                "simdgroup_grid": [
                  2,
                  2
                ],
                "tile_shape": [
                  64,
                  64,
                  16
                ],
                "staging": "threadgroup",
                "vector_width": null,
                "double_buffer": true,
                "reasons": [
                  "The selected SIMDgroup grid partitions 8x8 accumulator fragments without overlap.",
                  "Cooperative loads stage operand tiles in threadgroup memory."
                ],
                "cooperative_layout": "8x8 simdgroup_matrix fragments",
                "outer_bounds_proven": true
              },
              "passes": [
                "pad_shared_memory",
                "double_buffer_k_loop",
                "vectorize_loads",
                "serpentine_mma",
                "preload_mma_tiles",
                "block_swizzle",
                "fold_constants"
              ],
              "loops": [
                {
                  "induction_variable": "kb",
                  "kind": "loop",
                  "lanes": 128,
                  "elements_per_lane": 1,
                  "iteration_step": 16
                },
                {
                  "induction_variable": "kk",
                  "kind": "loop",
                  "lanes": 128,
                  "elements_per_lane": 1,
                  "iteration_step": 8
                }
              ],
              "allocations": [
                {
                  "name": "shared_a_0",
                  "address_space": "threadgroup",
                  "element_type": "float",
                  "elements": 1088,
                  "bytes": 4352
                },
                {
                  "name": "shared_a_1",
                  "address_space": "threadgroup",
                  "element_type": "float",
                  "elements": 1088,
                  "bytes": 4352
                },
                {
                  "name": "shared_b_0",
                  "address_space": "threadgroup",
                  "element_type": "float",
                  "elements": 1040,
                  "bytes": 4160
                },
                {
                  "name": "shared_b_1",
                  "address_space": "threadgroup",
                  "element_type": "float",
                  "elements": 1040,
                  "bytes": 4160
                }
              ],
              "double_buffered": true,
              "vectorized_loads": 0,
              "epilogue_regions": 0,
              "notes": [
                "Layout widths describe emitted Metal operations, not final machine instructions.",
                "Masked tails may use scalar accesses even when aligned interiors are vectorized."
              ]
            },
            "timing": {
              "samples": 413,
              "gpu_us": 984.8750196397305,
              "wall_us": 1202.541,
              "gpu_min_max_us": [
                972.0000089146197,
                1111.0000195913017
              ],
              "wall_min_max_us": [
                1117.833,
                1374.375
              ]
            },
            "status": "ok"
          },
          {
            "name": "float32_257x255x259",
            "dtype": "float32",
            "shape": [
              257,
              255,
              259
            ],
            "seed": 438,
            "schedule": {
              "backend": "simdgroup",
              "double_buffer": true,
              "BLOCK_M": 64,
              "BLOCK_N": 64,
              "BLOCK_K": 16,
              "RELAXED_PRECISION": false
            },
            "input_sha256": "acff8f3e2b353c103ecee705731d3d2c8c26b98f0a80634d1fd4a06c38113a26",
            "correctness": {
              "reference": "NumPy FP32 matmul rounded to the output storage dtype",
              "max_absolute_error": 0.0,
              "rtol": 0.0003,
              "atol": 3e-05
            },
            "source_sha256": "f3f104bd99ff3f71a2487b1d00cfd450cf4ed9085888a27b979798e443a98808",
            "execution_report": {
              "plan": {
                "backend": "simdgroup",
                "threadgroup_size": [
                  128,
                  1,
                  1
                ],
                "simdgroup_grid": [
                  2,
                  2
                ],
                "tile_shape": [
                  64,
                  64,
                  16
                ],
                "staging": "threadgroup",
                "vector_width": null,
                "double_buffer": true,
                "reasons": [
                  "The selected SIMDgroup grid partitions 8x8 accumulator fragments without overlap.",
                  "Cooperative loads stage operand tiles in threadgroup memory."
                ],
                "cooperative_layout": "8x8 simdgroup_matrix fragments",
                "outer_bounds_proven": false
              },
              "passes": [
                "pad_shared_memory",
                "double_buffer_k_loop",
                "vectorize_loads",
                "serpentine_mma",
                "preload_mma_tiles",
                "block_swizzle",
                "fold_constants"
              ],
              "loops": [
                {
                  "induction_variable": "kb",
                  "kind": "loop",
                  "lanes": 128,
                  "elements_per_lane": 1,
                  "iteration_step": 16
                },
                {
                  "induction_variable": "kk",
                  "kind": "loop",
                  "lanes": 128,
                  "elements_per_lane": 1,
                  "iteration_step": 8
                }
              ],
              "allocations": [
                {
                  "name": "shared_a_0",
                  "address_space": "threadgroup",
                  "element_type": "float",
                  "elements": 1088,
                  "bytes": 4352
                },
                {
                  "name": "shared_a_1",
                  "address_space": "threadgroup",
                  "element_type": "float",
                  "elements": 1088,
                  "bytes": 4352
                },
                {
                  "name": "shared_b_0",
                  "address_space": "threadgroup",
                  "element_type": "float",
                  "elements": 1040,
                  "bytes": 4160
                },
                {
                  "name": "shared_b_1",
                  "address_space": "threadgroup",
                  "element_type": "float",
                  "elements": 1040,
                  "bytes": 4160
                }
              ],
              "double_buffered": true,
              "vectorized_loads": 0,
              "epilogue_regions": 0,
              "notes": [
                "Layout widths describe emitted Metal operations, not final machine instructions.",
                "Masked tails may use scalar accesses even when aligned interiors are vectorized."
              ]
            },
            "timing": {
              "samples": 1546,
              "gpu_us": 57.64584057033062,
              "wall_us": 275.64549999999997,
              "gpu_min_max_us": [
                45.58329237625003,
                241.0417073406279
              ],
              "wall_min_max_us": [
                140.625,
                572.2090000000001
              ]
            },
            "status": "ok"
          }
        ]
      }
    ],
    "current": [
      {
        "root": "/Users/andreslavescu/Documents/projects/meTile",
        "compiler_implementation_sha256": "d258683dcf0a92130bc92c14d306b75dfdb1194f300bbdc9aafe671cb6ffff65",
        "device": "Apple M5",
        "metal_compiler": "Apple metal version 32023.864 (metalfe-32023.864)\nTarget: air64-apple-darwin25.2.0\nThread model: posix\nInstalledDir: /private/var/run/com.apple.security.cryptexd/mnt/com.apple.MobileAsset.MetalToolchain-v17.3.7003.10.GzPOjD/Metal.xctoolchain/usr/metal/current/bin",
        "platform": "macOS-26.2-arm64-arm-64bit",
        "cases": [
          {
            "name": "float16_64x64x64",
            "dtype": "float16",
            "shape": [
              64,
              64,
              64
            ],
            "seed": 431,
            "schedule": {
              "backend": "simdgroup",
              "double_buffer": true,
              "BLOCK_M": 64,
              "BLOCK_N": 64,
              "BLOCK_K": 16,
              "RELAXED_PRECISION": false
            },
            "input_sha256": "f7743c34dfc78564a28e726c1924c410fbdb76f4158beba809e487c7fdc4d8b3",
            "correctness": {
              "reference": "NumPy FP32 matmul rounded to the output storage dtype",
              "max_absolute_error": 0.0,
              "rtol": 0.002,
              "atol": 0.002
            },
            "source_sha256": "775bf51864f7fadf5c0a51035e57a2f85c7857b382291cefd60dd69bf86f92d1",
            "execution_report": {
              "plan": {
                "backend": "simdgroup",
                "threadgroup_size": [
                  128,
                  1,
                  1
                ],
                "simdgroup_grid": [
                  2,
                  2
                ],
                "tile_shape": [
                  64,
                  64,
                  16
                ],
                "staging": "threadgroup",
                "vector_width": null,
                "double_buffer": true,
                "reasons": [
                  "The selected SIMDgroup grid partitions 8x8 accumulator fragments without overlap.",
                  "Cooperative loads stage operand tiles in threadgroup memory."
                ],
                "cooperative_layout": "8x8 simdgroup_matrix fragments",
                "outer_bounds_proven": true
              },
              "passes": [
                "pad_shared_memory",
                "double_buffer_k_loop",
                "vectorize_loads",
                "serpentine_mma",
                "preload_mma_tiles",
                "block_swizzle",
                "fold_constants"
              ],
              "loops": [
                {
                  "induction_variable": "kb",
                  "kind": "loop",
                  "lanes": 128,
                  "elements_per_lane": 1,
                  "iteration_step": 16
                },
                {
                  "induction_variable": "kk",
                  "kind": "loop",
                  "lanes": 128,
                  "elements_per_lane": 1,
                  "iteration_step": 8
                }
              ],
              "allocations": [
                {
                  "name": "shared_a_0",
                  "address_space": "threadgroup",
                  "element_type": "half",
                  "elements": 1088,
                  "bytes": 2176
                },
                {
                  "name": "shared_a_1",
                  "address_space": "threadgroup",
                  "element_type": "half",
                  "elements": 1088,
                  "bytes": 2176
                },
                {
                  "name": "shared_b_0",
                  "address_space": "threadgroup",
                  "element_type": "half",
                  "elements": 1040,
                  "bytes": 2080
                },
                {
                  "name": "shared_b_1",
                  "address_space": "threadgroup",
                  "element_type": "half",
                  "elements": 1040,
                  "bytes": 2080
                }
              ],
              "double_buffered": true,
              "vectorized_loads": 0,
              "epilogue_regions": 0,
              "notes": [
                "Layout widths describe emitted Metal operations, not final machine instructions.",
                "Masked tails may use scalar accesses even when aligned interiors are vectorized."
              ],
              "value_layouts": [],
              "layout_conversions": [],
              "pipelines": [
                {
                  "buffers": [
                    {
                      "logical_name": "shared_a",
                      "slots": [
                        "shared_a_0",
                        "shared_a_1"
                      ],
                      "element_type": "half",
                      "elements": 1088,
                      "current_pointer": "sa_curr",
                      "next_pointer": "sa_next"
                    },
                    {
                      "logical_name": "shared_b",
                      "slots": [
                        "shared_b_0",
                        "shared_b_1"
                      ],
                      "element_type": "half",
                      "elements": 1040,
                      "current_pointer": "sb_curr",
                      "next_pointer": "sb_next"
                    }
                  ],
                  "phases": [
                    {
                      "name": "load_first",
                      "region": "prologue",
                      "kind": "copy",
                      "reads": [],
                      "writes": [
                        {
                          "buffer": "shared_a",
                          "slot": "current"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "current"
                        }
                      ],
                      "publishes": [],
                      "recycles": [],
                      "rotates": [],
                      "barrier_scope": null,
                      "barrier_flags": null
                    },
                    {
                      "name": "publish_first",
                      "region": "prologue",
                      "kind": "barrier",
                      "reads": [],
                      "writes": [],
                      "publishes": [
                        {
                          "buffer": "shared_a",
                          "slot": "current"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "current"
                        }
                      ],
                      "recycles": [],
                      "rotates": [],
                      "barrier_scope": "threadgroup",
                      "barrier_flags": "mem_threadgroup"
                    },
                    {
                      "name": "load_next",
                      "region": "steady",
                      "kind": "copy",
                      "reads": [],
                      "writes": [
                        {
                          "buffer": "shared_a",
                          "slot": "next"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "next"
                        }
                      ],
                      "publishes": [],
                      "recycles": [],
                      "rotates": [],
                      "barrier_scope": null,
                      "barrier_flags": null
                    },
                    {
                      "name": "consume_current",
                      "region": "steady",
                      "kind": "compute",
                      "reads": [
                        {
                          "buffer": "shared_a",
                          "slot": "current"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "current"
                        }
                      ],
                      "writes": [],
                      "publishes": [],
                      "recycles": [],
                      "rotates": [],
                      "barrier_scope": null,
                      "barrier_flags": null
                    },
                    {
                      "name": "publish_and_recycle",
                      "region": "steady",
                      "kind": "barrier",
                      "reads": [],
                      "writes": [],
                      "publishes": [
                        {
                          "buffer": "shared_a",
                          "slot": "next"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "next"
                        }
                      ],
                      "recycles": [
                        {
                          "buffer": "shared_a",
                          "slot": "current"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "current"
                        }
                      ],
                      "rotates": [],
                      "barrier_scope": "threadgroup",
                      "barrier_flags": "mem_threadgroup"
                    },
                    {
                      "name": "rotate_slots",
                      "region": "steady",
                      "kind": "rotate",
                      "reads": [],
                      "writes": [],
                      "publishes": [],
                      "recycles": [],
                      "rotates": [
                        "shared_a",
                        "shared_b"
                      ],
                      "barrier_scope": null,
                      "barrier_flags": null
                    },
                    {
                      "name": "consume_last",
                      "region": "drain",
                      "kind": "compute",
                      "reads": [
                        {
                          "buffer": "shared_a",
                          "slot": "current"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "current"
                        }
                      ],
                      "writes": [],
                      "publishes": [],
                      "recycles": [],
                      "rotates": [],
                      "barrier_scope": null,
                      "barrier_flags": null
                    },
                    {
                      "name": "release_last",
                      "region": "drain",
                      "kind": "barrier",
                      "reads": [],
                      "writes": [],
                      "publishes": [],
                      "recycles": [
                        {
                          "buffer": "shared_a",
                          "slot": "current"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "current"
                        }
                      ],
                      "rotates": [],
                      "barrier_scope": "threadgroup",
                      "barrier_flags": "mem_threadgroup"
                    }
                  ],
                  "stages": 2,
                  "mechanism": "software"
                }
              ]
            },
            "timing": {
              "samples": 1309,
              "gpu_us": 65.33332634717226,
              "wall_us": 367.41700000000003,
              "gpu_min_max_us": [
                64.62499732151628,
                209.83332069590688
              ],
              "wall_min_max_us": [
                142.958,
                10539.292
              ]
            },
            "status": "ok"
          },
          {
            "name": "float16_256x256x256",
            "dtype": "float16",
            "shape": [
              256,
              256,
              256
            ],
            "seed": 432,
            "schedule": {
              "backend": "simdgroup",
              "double_buffer": true,
              "BLOCK_M": 64,
              "BLOCK_N": 64,
              "BLOCK_K": 16,
              "RELAXED_PRECISION": false
            },
            "input_sha256": "93ab6d6120e1756849446ff813e60fbd0616fa9eec32fbbd8c515ecaa3488b3d",
            "correctness": {
              "reference": "NumPy FP32 matmul rounded to the output storage dtype",
              "max_absolute_error": 0.0,
              "rtol": 0.002,
              "atol": 0.002
            },
            "source_sha256": "775bf51864f7fadf5c0a51035e57a2f85c7857b382291cefd60dd69bf86f92d1",
            "execution_report": {
              "plan": {
                "backend": "simdgroup",
                "threadgroup_size": [
                  128,
                  1,
                  1
                ],
                "simdgroup_grid": [
                  2,
                  2
                ],
                "tile_shape": [
                  64,
                  64,
                  16
                ],
                "staging": "threadgroup",
                "vector_width": null,
                "double_buffer": true,
                "reasons": [
                  "The selected SIMDgroup grid partitions 8x8 accumulator fragments without overlap.",
                  "Cooperative loads stage operand tiles in threadgroup memory."
                ],
                "cooperative_layout": "8x8 simdgroup_matrix fragments",
                "outer_bounds_proven": true
              },
              "passes": [
                "pad_shared_memory",
                "double_buffer_k_loop",
                "vectorize_loads",
                "serpentine_mma",
                "preload_mma_tiles",
                "block_swizzle",
                "fold_constants"
              ],
              "loops": [
                {
                  "induction_variable": "kb",
                  "kind": "loop",
                  "lanes": 128,
                  "elements_per_lane": 1,
                  "iteration_step": 16
                },
                {
                  "induction_variable": "kk",
                  "kind": "loop",
                  "lanes": 128,
                  "elements_per_lane": 1,
                  "iteration_step": 8
                }
              ],
              "allocations": [
                {
                  "name": "shared_a_0",
                  "address_space": "threadgroup",
                  "element_type": "half",
                  "elements": 1088,
                  "bytes": 2176
                },
                {
                  "name": "shared_a_1",
                  "address_space": "threadgroup",
                  "element_type": "half",
                  "elements": 1088,
                  "bytes": 2176
                },
                {
                  "name": "shared_b_0",
                  "address_space": "threadgroup",
                  "element_type": "half",
                  "elements": 1040,
                  "bytes": 2080
                },
                {
                  "name": "shared_b_1",
                  "address_space": "threadgroup",
                  "element_type": "half",
                  "elements": 1040,
                  "bytes": 2080
                }
              ],
              "double_buffered": true,
              "vectorized_loads": 0,
              "epilogue_regions": 0,
              "notes": [
                "Layout widths describe emitted Metal operations, not final machine instructions.",
                "Masked tails may use scalar accesses even when aligned interiors are vectorized."
              ],
              "value_layouts": [],
              "layout_conversions": [],
              "pipelines": [
                {
                  "buffers": [
                    {
                      "logical_name": "shared_a",
                      "slots": [
                        "shared_a_0",
                        "shared_a_1"
                      ],
                      "element_type": "half",
                      "elements": 1088,
                      "current_pointer": "sa_curr",
                      "next_pointer": "sa_next"
                    },
                    {
                      "logical_name": "shared_b",
                      "slots": [
                        "shared_b_0",
                        "shared_b_1"
                      ],
                      "element_type": "half",
                      "elements": 1040,
                      "current_pointer": "sb_curr",
                      "next_pointer": "sb_next"
                    }
                  ],
                  "phases": [
                    {
                      "name": "load_first",
                      "region": "prologue",
                      "kind": "copy",
                      "reads": [],
                      "writes": [
                        {
                          "buffer": "shared_a",
                          "slot": "current"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "current"
                        }
                      ],
                      "publishes": [],
                      "recycles": [],
                      "rotates": [],
                      "barrier_scope": null,
                      "barrier_flags": null
                    },
                    {
                      "name": "publish_first",
                      "region": "prologue",
                      "kind": "barrier",
                      "reads": [],
                      "writes": [],
                      "publishes": [
                        {
                          "buffer": "shared_a",
                          "slot": "current"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "current"
                        }
                      ],
                      "recycles": [],
                      "rotates": [],
                      "barrier_scope": "threadgroup",
                      "barrier_flags": "mem_threadgroup"
                    },
                    {
                      "name": "load_next",
                      "region": "steady",
                      "kind": "copy",
                      "reads": [],
                      "writes": [
                        {
                          "buffer": "shared_a",
                          "slot": "next"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "next"
                        }
                      ],
                      "publishes": [],
                      "recycles": [],
                      "rotates": [],
                      "barrier_scope": null,
                      "barrier_flags": null
                    },
                    {
                      "name": "consume_current",
                      "region": "steady",
                      "kind": "compute",
                      "reads": [
                        {
                          "buffer": "shared_a",
                          "slot": "current"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "current"
                        }
                      ],
                      "writes": [],
                      "publishes": [],
                      "recycles": [],
                      "rotates": [],
                      "barrier_scope": null,
                      "barrier_flags": null
                    },
                    {
                      "name": "publish_and_recycle",
                      "region": "steady",
                      "kind": "barrier",
                      "reads": [],
                      "writes": [],
                      "publishes": [
                        {
                          "buffer": "shared_a",
                          "slot": "next"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "next"
                        }
                      ],
                      "recycles": [
                        {
                          "buffer": "shared_a",
                          "slot": "current"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "current"
                        }
                      ],
                      "rotates": [],
                      "barrier_scope": "threadgroup",
                      "barrier_flags": "mem_threadgroup"
                    },
                    {
                      "name": "rotate_slots",
                      "region": "steady",
                      "kind": "rotate",
                      "reads": [],
                      "writes": [],
                      "publishes": [],
                      "recycles": [],
                      "rotates": [
                        "shared_a",
                        "shared_b"
                      ],
                      "barrier_scope": null,
                      "barrier_flags": null
                    },
                    {
                      "name": "consume_last",
                      "region": "drain",
                      "kind": "compute",
                      "reads": [
                        {
                          "buffer": "shared_a",
                          "slot": "current"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "current"
                        }
                      ],
                      "writes": [],
                      "publishes": [],
                      "recycles": [],
                      "rotates": [],
                      "barrier_scope": null,
                      "barrier_flags": null
                    },
                    {
                      "name": "release_last",
                      "region": "drain",
                      "kind": "barrier",
                      "reads": [],
                      "writes": [],
                      "publishes": [],
                      "recycles": [
                        {
                          "buffer": "shared_a",
                          "slot": "current"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "current"
                        }
                      ],
                      "rotates": [],
                      "barrier_scope": "threadgroup",
                      "barrier_flags": "mem_threadgroup"
                    }
                  ],
                  "stages": 2,
                  "mechanism": "software"
                }
              ]
            },
            "timing": {
              "samples": 1003,
              "gpu_us": 192.16665532439947,
              "wall_us": 501.875,
              "gpu_min_max_us": [
                189.33333922177553,
                221.2083782069385
              ],
              "wall_min_max_us": [
                283.708,
                600.375
              ]
            },
            "status": "ok"
          },
          {
            "name": "float16_1024x1024x1024",
            "dtype": "float16",
            "shape": [
              1024,
              1024,
              1024
            ],
            "seed": 433,
            "schedule": {
              "backend": "simdgroup",
              "double_buffer": true,
              "BLOCK_M": 64,
              "BLOCK_N": 64,
              "BLOCK_K": 16,
              "RELAXED_PRECISION": false
            },
            "input_sha256": "a3cdef8bbc69c848e84c524701f359db6268c696607cea04283a35e3be9e32c1",
            "correctness": {
              "reference": "NumPy FP32 matmul rounded to the output storage dtype",
              "max_absolute_error": 0.0,
              "rtol": 0.002,
              "atol": 0.002
            },
            "source_sha256": "775bf51864f7fadf5c0a51035e57a2f85c7857b382291cefd60dd69bf86f92d1",
            "execution_report": {
              "plan": {
                "backend": "simdgroup",
                "threadgroup_size": [
                  128,
                  1,
                  1
                ],
                "simdgroup_grid": [
                  2,
                  2
                ],
                "tile_shape": [
                  64,
                  64,
                  16
                ],
                "staging": "threadgroup",
                "vector_width": null,
                "double_buffer": true,
                "reasons": [
                  "The selected SIMDgroup grid partitions 8x8 accumulator fragments without overlap.",
                  "Cooperative loads stage operand tiles in threadgroup memory."
                ],
                "cooperative_layout": "8x8 simdgroup_matrix fragments",
                "outer_bounds_proven": true
              },
              "passes": [
                "pad_shared_memory",
                "double_buffer_k_loop",
                "vectorize_loads",
                "serpentine_mma",
                "preload_mma_tiles",
                "block_swizzle",
                "fold_constants"
              ],
              "loops": [
                {
                  "induction_variable": "kb",
                  "kind": "loop",
                  "lanes": 128,
                  "elements_per_lane": 1,
                  "iteration_step": 16
                },
                {
                  "induction_variable": "kk",
                  "kind": "loop",
                  "lanes": 128,
                  "elements_per_lane": 1,
                  "iteration_step": 8
                }
              ],
              "allocations": [
                {
                  "name": "shared_a_0",
                  "address_space": "threadgroup",
                  "element_type": "half",
                  "elements": 1088,
                  "bytes": 2176
                },
                {
                  "name": "shared_a_1",
                  "address_space": "threadgroup",
                  "element_type": "half",
                  "elements": 1088,
                  "bytes": 2176
                },
                {
                  "name": "shared_b_0",
                  "address_space": "threadgroup",
                  "element_type": "half",
                  "elements": 1040,
                  "bytes": 2080
                },
                {
                  "name": "shared_b_1",
                  "address_space": "threadgroup",
                  "element_type": "half",
                  "elements": 1040,
                  "bytes": 2080
                }
              ],
              "double_buffered": true,
              "vectorized_loads": 0,
              "epilogue_regions": 0,
              "notes": [
                "Layout widths describe emitted Metal operations, not final machine instructions.",
                "Masked tails may use scalar accesses even when aligned interiors are vectorized."
              ],
              "value_layouts": [],
              "layout_conversions": [],
              "pipelines": [
                {
                  "buffers": [
                    {
                      "logical_name": "shared_a",
                      "slots": [
                        "shared_a_0",
                        "shared_a_1"
                      ],
                      "element_type": "half",
                      "elements": 1088,
                      "current_pointer": "sa_curr",
                      "next_pointer": "sa_next"
                    },
                    {
                      "logical_name": "shared_b",
                      "slots": [
                        "shared_b_0",
                        "shared_b_1"
                      ],
                      "element_type": "half",
                      "elements": 1040,
                      "current_pointer": "sb_curr",
                      "next_pointer": "sb_next"
                    }
                  ],
                  "phases": [
                    {
                      "name": "load_first",
                      "region": "prologue",
                      "kind": "copy",
                      "reads": [],
                      "writes": [
                        {
                          "buffer": "shared_a",
                          "slot": "current"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "current"
                        }
                      ],
                      "publishes": [],
                      "recycles": [],
                      "rotates": [],
                      "barrier_scope": null,
                      "barrier_flags": null
                    },
                    {
                      "name": "publish_first",
                      "region": "prologue",
                      "kind": "barrier",
                      "reads": [],
                      "writes": [],
                      "publishes": [
                        {
                          "buffer": "shared_a",
                          "slot": "current"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "current"
                        }
                      ],
                      "recycles": [],
                      "rotates": [],
                      "barrier_scope": "threadgroup",
                      "barrier_flags": "mem_threadgroup"
                    },
                    {
                      "name": "load_next",
                      "region": "steady",
                      "kind": "copy",
                      "reads": [],
                      "writes": [
                        {
                          "buffer": "shared_a",
                          "slot": "next"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "next"
                        }
                      ],
                      "publishes": [],
                      "recycles": [],
                      "rotates": [],
                      "barrier_scope": null,
                      "barrier_flags": null
                    },
                    {
                      "name": "consume_current",
                      "region": "steady",
                      "kind": "compute",
                      "reads": [
                        {
                          "buffer": "shared_a",
                          "slot": "current"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "current"
                        }
                      ],
                      "writes": [],
                      "publishes": [],
                      "recycles": [],
                      "rotates": [],
                      "barrier_scope": null,
                      "barrier_flags": null
                    },
                    {
                      "name": "publish_and_recycle",
                      "region": "steady",
                      "kind": "barrier",
                      "reads": [],
                      "writes": [],
                      "publishes": [
                        {
                          "buffer": "shared_a",
                          "slot": "next"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "next"
                        }
                      ],
                      "recycles": [
                        {
                          "buffer": "shared_a",
                          "slot": "current"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "current"
                        }
                      ],
                      "rotates": [],
                      "barrier_scope": "threadgroup",
                      "barrier_flags": "mem_threadgroup"
                    },
                    {
                      "name": "rotate_slots",
                      "region": "steady",
                      "kind": "rotate",
                      "reads": [],
                      "writes": [],
                      "publishes": [],
                      "recycles": [],
                      "rotates": [
                        "shared_a",
                        "shared_b"
                      ],
                      "barrier_scope": null,
                      "barrier_flags": null
                    },
                    {
                      "name": "consume_last",
                      "region": "drain",
                      "kind": "compute",
                      "reads": [
                        {
                          "buffer": "shared_a",
                          "slot": "current"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "current"
                        }
                      ],
                      "writes": [],
                      "publishes": [],
                      "recycles": [],
                      "rotates": [],
                      "barrier_scope": null,
                      "barrier_flags": null
                    },
                    {
                      "name": "release_last",
                      "region": "drain",
                      "kind": "barrier",
                      "reads": [],
                      "writes": [],
                      "publishes": [],
                      "recycles": [
                        {
                          "buffer": "shared_a",
                          "slot": "current"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "current"
                        }
                      ],
                      "rotates": [],
                      "barrier_scope": "threadgroup",
                      "barrier_flags": "mem_threadgroup"
                    }
                  ],
                  "stages": 2,
                  "mechanism": "software"
                }
              ]
            },
            "timing": {
              "samples": 471,
              "gpu_us": 850.9583421982825,
              "wall_us": 1058.583,
              "gpu_min_max_us": [
                810.9583286568522,
                931.1250178143382
              ],
              "wall_min_max_us": [
                919.708,
                1179.833
              ]
            },
            "status": "ok"
          },
          {
            "name": "float16_257x255x259",
            "dtype": "float16",
            "shape": [
              257,
              255,
              259
            ],
            "seed": 434,
            "schedule": {
              "backend": "simdgroup",
              "double_buffer": true,
              "BLOCK_M": 64,
              "BLOCK_N": 64,
              "BLOCK_K": 16,
              "RELAXED_PRECISION": false
            },
            "input_sha256": "9b256a8e5e5aa03086c616dbb685bfb3b2a3838b8a2de16524f12307645110ef",
            "correctness": {
              "reference": "NumPy FP32 matmul rounded to the output storage dtype",
              "max_absolute_error": 0.0,
              "rtol": 0.002,
              "atol": 0.002
            },
            "source_sha256": "775bf51864f7fadf5c0a51035e57a2f85c7857b382291cefd60dd69bf86f92d1",
            "execution_report": {
              "plan": {
                "backend": "simdgroup",
                "threadgroup_size": [
                  128,
                  1,
                  1
                ],
                "simdgroup_grid": [
                  2,
                  2
                ],
                "tile_shape": [
                  64,
                  64,
                  16
                ],
                "staging": "threadgroup",
                "vector_width": null,
                "double_buffer": true,
                "reasons": [
                  "The selected SIMDgroup grid partitions 8x8 accumulator fragments without overlap.",
                  "Cooperative loads stage operand tiles in threadgroup memory."
                ],
                "cooperative_layout": "8x8 simdgroup_matrix fragments",
                "outer_bounds_proven": false
              },
              "passes": [
                "pad_shared_memory",
                "double_buffer_k_loop",
                "vectorize_loads",
                "serpentine_mma",
                "preload_mma_tiles",
                "block_swizzle",
                "fold_constants"
              ],
              "loops": [
                {
                  "induction_variable": "kb",
                  "kind": "loop",
                  "lanes": 128,
                  "elements_per_lane": 1,
                  "iteration_step": 16
                },
                {
                  "induction_variable": "kk",
                  "kind": "loop",
                  "lanes": 128,
                  "elements_per_lane": 1,
                  "iteration_step": 8
                }
              ],
              "allocations": [
                {
                  "name": "shared_a_0",
                  "address_space": "threadgroup",
                  "element_type": "half",
                  "elements": 1088,
                  "bytes": 2176
                },
                {
                  "name": "shared_a_1",
                  "address_space": "threadgroup",
                  "element_type": "half",
                  "elements": 1088,
                  "bytes": 2176
                },
                {
                  "name": "shared_b_0",
                  "address_space": "threadgroup",
                  "element_type": "half",
                  "elements": 1040,
                  "bytes": 2080
                },
                {
                  "name": "shared_b_1",
                  "address_space": "threadgroup",
                  "element_type": "half",
                  "elements": 1040,
                  "bytes": 2080
                }
              ],
              "double_buffered": true,
              "vectorized_loads": 0,
              "epilogue_regions": 0,
              "notes": [
                "Layout widths describe emitted Metal operations, not final machine instructions.",
                "Masked tails may use scalar accesses even when aligned interiors are vectorized."
              ],
              "value_layouts": [],
              "layout_conversions": [],
              "pipelines": [
                {
                  "buffers": [
                    {
                      "logical_name": "shared_a",
                      "slots": [
                        "shared_a_0",
                        "shared_a_1"
                      ],
                      "element_type": "half",
                      "elements": 1088,
                      "current_pointer": "sa_curr",
                      "next_pointer": "sa_next"
                    },
                    {
                      "logical_name": "shared_b",
                      "slots": [
                        "shared_b_0",
                        "shared_b_1"
                      ],
                      "element_type": "half",
                      "elements": 1040,
                      "current_pointer": "sb_curr",
                      "next_pointer": "sb_next"
                    }
                  ],
                  "phases": [
                    {
                      "name": "load_first",
                      "region": "prologue",
                      "kind": "copy",
                      "reads": [],
                      "writes": [
                        {
                          "buffer": "shared_a",
                          "slot": "current"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "current"
                        }
                      ],
                      "publishes": [],
                      "recycles": [],
                      "rotates": [],
                      "barrier_scope": null,
                      "barrier_flags": null
                    },
                    {
                      "name": "publish_first",
                      "region": "prologue",
                      "kind": "barrier",
                      "reads": [],
                      "writes": [],
                      "publishes": [
                        {
                          "buffer": "shared_a",
                          "slot": "current"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "current"
                        }
                      ],
                      "recycles": [],
                      "rotates": [],
                      "barrier_scope": "threadgroup",
                      "barrier_flags": "mem_threadgroup"
                    },
                    {
                      "name": "load_next",
                      "region": "steady",
                      "kind": "copy",
                      "reads": [],
                      "writes": [
                        {
                          "buffer": "shared_a",
                          "slot": "next"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "next"
                        }
                      ],
                      "publishes": [],
                      "recycles": [],
                      "rotates": [],
                      "barrier_scope": null,
                      "barrier_flags": null
                    },
                    {
                      "name": "consume_current",
                      "region": "steady",
                      "kind": "compute",
                      "reads": [
                        {
                          "buffer": "shared_a",
                          "slot": "current"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "current"
                        }
                      ],
                      "writes": [],
                      "publishes": [],
                      "recycles": [],
                      "rotates": [],
                      "barrier_scope": null,
                      "barrier_flags": null
                    },
                    {
                      "name": "publish_and_recycle",
                      "region": "steady",
                      "kind": "barrier",
                      "reads": [],
                      "writes": [],
                      "publishes": [
                        {
                          "buffer": "shared_a",
                          "slot": "next"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "next"
                        }
                      ],
                      "recycles": [
                        {
                          "buffer": "shared_a",
                          "slot": "current"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "current"
                        }
                      ],
                      "rotates": [],
                      "barrier_scope": "threadgroup",
                      "barrier_flags": "mem_threadgroup"
                    },
                    {
                      "name": "rotate_slots",
                      "region": "steady",
                      "kind": "rotate",
                      "reads": [],
                      "writes": [],
                      "publishes": [],
                      "recycles": [],
                      "rotates": [
                        "shared_a",
                        "shared_b"
                      ],
                      "barrier_scope": null,
                      "barrier_flags": null
                    },
                    {
                      "name": "consume_last",
                      "region": "drain",
                      "kind": "compute",
                      "reads": [
                        {
                          "buffer": "shared_a",
                          "slot": "current"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "current"
                        }
                      ],
                      "writes": [],
                      "publishes": [],
                      "recycles": [],
                      "rotates": [],
                      "barrier_scope": null,
                      "barrier_flags": null
                    },
                    {
                      "name": "release_last",
                      "region": "drain",
                      "kind": "barrier",
                      "reads": [],
                      "writes": [],
                      "publishes": [],
                      "recycles": [
                        {
                          "buffer": "shared_a",
                          "slot": "current"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "current"
                        }
                      ],
                      "rotates": [],
                      "barrier_scope": "threadgroup",
                      "barrier_flags": "mem_threadgroup"
                    }
                  ],
                  "stages": 2,
                  "mechanism": "software"
                }
              ]
            },
            "timing": {
              "samples": 1500,
              "gpu_us": 57.999975979328156,
              "wall_us": 279.833,
              "gpu_min_max_us": [
                42.12500061839819,
                219.2499814555049
              ],
              "wall_min_max_us": [
                126.291,
                555.25
              ]
            },
            "status": "ok"
          },
          {
            "name": "float32_64x64x64",
            "dtype": "float32",
            "shape": [
              64,
              64,
              64
            ],
            "seed": 435,
            "schedule": {
              "backend": "simdgroup",
              "double_buffer": true,
              "BLOCK_M": 64,
              "BLOCK_N": 64,
              "BLOCK_K": 16,
              "RELAXED_PRECISION": false
            },
            "input_sha256": "5daffc014e3bf6c7425a716bc5a36f0a9f5ac3d06a994a5e9e8084b7cfb9cd1b",
            "correctness": {
              "reference": "NumPy FP32 matmul rounded to the output storage dtype",
              "max_absolute_error": 0.0,
              "rtol": 0.0003,
              "atol": 3e-05
            },
            "source_sha256": "4be0fb2e516dd502b4eab90ce5d42bc755710fb3331f6f7e4ea2f7c96e11e724",
            "execution_report": {
              "plan": {
                "backend": "simdgroup",
                "threadgroup_size": [
                  128,
                  1,
                  1
                ],
                "simdgroup_grid": [
                  2,
                  2
                ],
                "tile_shape": [
                  64,
                  64,
                  16
                ],
                "staging": "threadgroup",
                "vector_width": null,
                "double_buffer": true,
                "reasons": [
                  "The selected SIMDgroup grid partitions 8x8 accumulator fragments without overlap.",
                  "Cooperative loads stage operand tiles in threadgroup memory."
                ],
                "cooperative_layout": "8x8 simdgroup_matrix fragments",
                "outer_bounds_proven": true
              },
              "passes": [
                "pad_shared_memory",
                "double_buffer_k_loop",
                "vectorize_loads",
                "serpentine_mma",
                "preload_mma_tiles",
                "block_swizzle",
                "fold_constants"
              ],
              "loops": [
                {
                  "induction_variable": "kb",
                  "kind": "loop",
                  "lanes": 128,
                  "elements_per_lane": 1,
                  "iteration_step": 16
                },
                {
                  "induction_variable": "kk",
                  "kind": "loop",
                  "lanes": 128,
                  "elements_per_lane": 1,
                  "iteration_step": 8
                }
              ],
              "allocations": [
                {
                  "name": "shared_a_0",
                  "address_space": "threadgroup",
                  "element_type": "float",
                  "elements": 1088,
                  "bytes": 4352
                },
                {
                  "name": "shared_a_1",
                  "address_space": "threadgroup",
                  "element_type": "float",
                  "elements": 1088,
                  "bytes": 4352
                },
                {
                  "name": "shared_b_0",
                  "address_space": "threadgroup",
                  "element_type": "float",
                  "elements": 1040,
                  "bytes": 4160
                },
                {
                  "name": "shared_b_1",
                  "address_space": "threadgroup",
                  "element_type": "float",
                  "elements": 1040,
                  "bytes": 4160
                }
              ],
              "double_buffered": true,
              "vectorized_loads": 0,
              "epilogue_regions": 0,
              "notes": [
                "Layout widths describe emitted Metal operations, not final machine instructions.",
                "Masked tails may use scalar accesses even when aligned interiors are vectorized."
              ],
              "value_layouts": [],
              "layout_conversions": [],
              "pipelines": [
                {
                  "buffers": [
                    {
                      "logical_name": "shared_a",
                      "slots": [
                        "shared_a_0",
                        "shared_a_1"
                      ],
                      "element_type": "float",
                      "elements": 1088,
                      "current_pointer": "sa_curr",
                      "next_pointer": "sa_next"
                    },
                    {
                      "logical_name": "shared_b",
                      "slots": [
                        "shared_b_0",
                        "shared_b_1"
                      ],
                      "element_type": "float",
                      "elements": 1040,
                      "current_pointer": "sb_curr",
                      "next_pointer": "sb_next"
                    }
                  ],
                  "phases": [
                    {
                      "name": "load_first",
                      "region": "prologue",
                      "kind": "copy",
                      "reads": [],
                      "writes": [
                        {
                          "buffer": "shared_a",
                          "slot": "current"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "current"
                        }
                      ],
                      "publishes": [],
                      "recycles": [],
                      "rotates": [],
                      "barrier_scope": null,
                      "barrier_flags": null
                    },
                    {
                      "name": "publish_first",
                      "region": "prologue",
                      "kind": "barrier",
                      "reads": [],
                      "writes": [],
                      "publishes": [
                        {
                          "buffer": "shared_a",
                          "slot": "current"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "current"
                        }
                      ],
                      "recycles": [],
                      "rotates": [],
                      "barrier_scope": "threadgroup",
                      "barrier_flags": "mem_threadgroup"
                    },
                    {
                      "name": "load_next",
                      "region": "steady",
                      "kind": "copy",
                      "reads": [],
                      "writes": [
                        {
                          "buffer": "shared_a",
                          "slot": "next"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "next"
                        }
                      ],
                      "publishes": [],
                      "recycles": [],
                      "rotates": [],
                      "barrier_scope": null,
                      "barrier_flags": null
                    },
                    {
                      "name": "consume_current",
                      "region": "steady",
                      "kind": "compute",
                      "reads": [
                        {
                          "buffer": "shared_a",
                          "slot": "current"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "current"
                        }
                      ],
                      "writes": [],
                      "publishes": [],
                      "recycles": [],
                      "rotates": [],
                      "barrier_scope": null,
                      "barrier_flags": null
                    },
                    {
                      "name": "publish_and_recycle",
                      "region": "steady",
                      "kind": "barrier",
                      "reads": [],
                      "writes": [],
                      "publishes": [
                        {
                          "buffer": "shared_a",
                          "slot": "next"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "next"
                        }
                      ],
                      "recycles": [
                        {
                          "buffer": "shared_a",
                          "slot": "current"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "current"
                        }
                      ],
                      "rotates": [],
                      "barrier_scope": "threadgroup",
                      "barrier_flags": "mem_threadgroup"
                    },
                    {
                      "name": "rotate_slots",
                      "region": "steady",
                      "kind": "rotate",
                      "reads": [],
                      "writes": [],
                      "publishes": [],
                      "recycles": [],
                      "rotates": [
                        "shared_a",
                        "shared_b"
                      ],
                      "barrier_scope": null,
                      "barrier_flags": null
                    },
                    {
                      "name": "consume_last",
                      "region": "drain",
                      "kind": "compute",
                      "reads": [
                        {
                          "buffer": "shared_a",
                          "slot": "current"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "current"
                        }
                      ],
                      "writes": [],
                      "publishes": [],
                      "recycles": [],
                      "rotates": [],
                      "barrier_scope": null,
                      "barrier_flags": null
                    },
                    {
                      "name": "release_last",
                      "region": "drain",
                      "kind": "barrier",
                      "reads": [],
                      "writes": [],
                      "publishes": [],
                      "recycles": [
                        {
                          "buffer": "shared_a",
                          "slot": "current"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "current"
                        }
                      ],
                      "rotates": [],
                      "barrier_scope": "threadgroup",
                      "barrier_flags": "mem_threadgroup"
                    }
                  ],
                  "stages": 2,
                  "mechanism": "software"
                }
              ]
            },
            "timing": {
              "samples": 1351,
              "gpu_us": 68.62496957182884,
              "wall_us": 376.709,
              "gpu_min_max_us": [
                68.41664435341954,
                85.99995635449886
              ],
              "wall_min_max_us": [
                146.0,
                482.625
              ]
            },
            "status": "ok"
          },
          {
            "name": "float32_256x256x256",
            "dtype": "float32",
            "shape": [
              256,
              256,
              256
            ],
            "seed": 436,
            "schedule": {
              "backend": "simdgroup",
              "double_buffer": true,
              "BLOCK_M": 64,
              "BLOCK_N": 64,
              "BLOCK_K": 16,
              "RELAXED_PRECISION": false
            },
            "input_sha256": "ceba1209c2607c35efa378403bf1bd3a583a3330944ee09239152ee064143b95",
            "correctness": {
              "reference": "NumPy FP32 matmul rounded to the output storage dtype",
              "max_absolute_error": 0.0,
              "rtol": 0.0003,
              "atol": 3e-05
            },
            "source_sha256": "4be0fb2e516dd502b4eab90ce5d42bc755710fb3331f6f7e4ea2f7c96e11e724",
            "execution_report": {
              "plan": {
                "backend": "simdgroup",
                "threadgroup_size": [
                  128,
                  1,
                  1
                ],
                "simdgroup_grid": [
                  2,
                  2
                ],
                "tile_shape": [
                  64,
                  64,
                  16
                ],
                "staging": "threadgroup",
                "vector_width": null,
                "double_buffer": true,
                "reasons": [
                  "The selected SIMDgroup grid partitions 8x8 accumulator fragments without overlap.",
                  "Cooperative loads stage operand tiles in threadgroup memory."
                ],
                "cooperative_layout": "8x8 simdgroup_matrix fragments",
                "outer_bounds_proven": true
              },
              "passes": [
                "pad_shared_memory",
                "double_buffer_k_loop",
                "vectorize_loads",
                "serpentine_mma",
                "preload_mma_tiles",
                "block_swizzle",
                "fold_constants"
              ],
              "loops": [
                {
                  "induction_variable": "kb",
                  "kind": "loop",
                  "lanes": 128,
                  "elements_per_lane": 1,
                  "iteration_step": 16
                },
                {
                  "induction_variable": "kk",
                  "kind": "loop",
                  "lanes": 128,
                  "elements_per_lane": 1,
                  "iteration_step": 8
                }
              ],
              "allocations": [
                {
                  "name": "shared_a_0",
                  "address_space": "threadgroup",
                  "element_type": "float",
                  "elements": 1088,
                  "bytes": 4352
                },
                {
                  "name": "shared_a_1",
                  "address_space": "threadgroup",
                  "element_type": "float",
                  "elements": 1088,
                  "bytes": 4352
                },
                {
                  "name": "shared_b_0",
                  "address_space": "threadgroup",
                  "element_type": "float",
                  "elements": 1040,
                  "bytes": 4160
                },
                {
                  "name": "shared_b_1",
                  "address_space": "threadgroup",
                  "element_type": "float",
                  "elements": 1040,
                  "bytes": 4160
                }
              ],
              "double_buffered": true,
              "vectorized_loads": 0,
              "epilogue_regions": 0,
              "notes": [
                "Layout widths describe emitted Metal operations, not final machine instructions.",
                "Masked tails may use scalar accesses even when aligned interiors are vectorized."
              ],
              "value_layouts": [],
              "layout_conversions": [],
              "pipelines": [
                {
                  "buffers": [
                    {
                      "logical_name": "shared_a",
                      "slots": [
                        "shared_a_0",
                        "shared_a_1"
                      ],
                      "element_type": "float",
                      "elements": 1088,
                      "current_pointer": "sa_curr",
                      "next_pointer": "sa_next"
                    },
                    {
                      "logical_name": "shared_b",
                      "slots": [
                        "shared_b_0",
                        "shared_b_1"
                      ],
                      "element_type": "float",
                      "elements": 1040,
                      "current_pointer": "sb_curr",
                      "next_pointer": "sb_next"
                    }
                  ],
                  "phases": [
                    {
                      "name": "load_first",
                      "region": "prologue",
                      "kind": "copy",
                      "reads": [],
                      "writes": [
                        {
                          "buffer": "shared_a",
                          "slot": "current"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "current"
                        }
                      ],
                      "publishes": [],
                      "recycles": [],
                      "rotates": [],
                      "barrier_scope": null,
                      "barrier_flags": null
                    },
                    {
                      "name": "publish_first",
                      "region": "prologue",
                      "kind": "barrier",
                      "reads": [],
                      "writes": [],
                      "publishes": [
                        {
                          "buffer": "shared_a",
                          "slot": "current"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "current"
                        }
                      ],
                      "recycles": [],
                      "rotates": [],
                      "barrier_scope": "threadgroup",
                      "barrier_flags": "mem_threadgroup"
                    },
                    {
                      "name": "load_next",
                      "region": "steady",
                      "kind": "copy",
                      "reads": [],
                      "writes": [
                        {
                          "buffer": "shared_a",
                          "slot": "next"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "next"
                        }
                      ],
                      "publishes": [],
                      "recycles": [],
                      "rotates": [],
                      "barrier_scope": null,
                      "barrier_flags": null
                    },
                    {
                      "name": "consume_current",
                      "region": "steady",
                      "kind": "compute",
                      "reads": [
                        {
                          "buffer": "shared_a",
                          "slot": "current"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "current"
                        }
                      ],
                      "writes": [],
                      "publishes": [],
                      "recycles": [],
                      "rotates": [],
                      "barrier_scope": null,
                      "barrier_flags": null
                    },
                    {
                      "name": "publish_and_recycle",
                      "region": "steady",
                      "kind": "barrier",
                      "reads": [],
                      "writes": [],
                      "publishes": [
                        {
                          "buffer": "shared_a",
                          "slot": "next"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "next"
                        }
                      ],
                      "recycles": [
                        {
                          "buffer": "shared_a",
                          "slot": "current"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "current"
                        }
                      ],
                      "rotates": [],
                      "barrier_scope": "threadgroup",
                      "barrier_flags": "mem_threadgroup"
                    },
                    {
                      "name": "rotate_slots",
                      "region": "steady",
                      "kind": "rotate",
                      "reads": [],
                      "writes": [],
                      "publishes": [],
                      "recycles": [],
                      "rotates": [
                        "shared_a",
                        "shared_b"
                      ],
                      "barrier_scope": null,
                      "barrier_flags": null
                    },
                    {
                      "name": "consume_last",
                      "region": "drain",
                      "kind": "compute",
                      "reads": [
                        {
                          "buffer": "shared_a",
                          "slot": "current"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "current"
                        }
                      ],
                      "writes": [],
                      "publishes": [],
                      "recycles": [],
                      "rotates": [],
                      "barrier_scope": null,
                      "barrier_flags": null
                    },
                    {
                      "name": "release_last",
                      "region": "drain",
                      "kind": "barrier",
                      "reads": [],
                      "writes": [],
                      "publishes": [],
                      "recycles": [
                        {
                          "buffer": "shared_a",
                          "slot": "current"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "current"
                        }
                      ],
                      "rotates": [],
                      "barrier_scope": "threadgroup",
                      "barrier_flags": "mem_threadgroup"
                    }
                  ],
                  "stages": 2,
                  "mechanism": "software"
                }
              ]
            },
            "timing": {
              "samples": 917,
              "gpu_us": 212.9583153873682,
              "wall_us": 519.708,
              "gpu_min_max_us": [
                210.5833264067769,
                236.37496633455157
              ],
              "wall_min_max_us": [
                300.208,
                6823.292
              ]
            },
            "status": "ok"
          },
          {
            "name": "float32_1024x1024x1024",
            "dtype": "float32",
            "shape": [
              1024,
              1024,
              1024
            ],
            "seed": 437,
            "schedule": {
              "backend": "simdgroup",
              "double_buffer": true,
              "BLOCK_M": 64,
              "BLOCK_N": 64,
              "BLOCK_K": 16,
              "RELAXED_PRECISION": false
            },
            "input_sha256": "16ed3544359adfe6ed4ecc94e89ed08c70fd5aeef3243f80b2009c2096d05f8c",
            "correctness": {
              "reference": "NumPy FP32 matmul rounded to the output storage dtype",
              "max_absolute_error": 0.0,
              "rtol": 0.0003,
              "atol": 3e-05
            },
            "source_sha256": "4be0fb2e516dd502b4eab90ce5d42bc755710fb3331f6f7e4ea2f7c96e11e724",
            "execution_report": {
              "plan": {
                "backend": "simdgroup",
                "threadgroup_size": [
                  128,
                  1,
                  1
                ],
                "simdgroup_grid": [
                  2,
                  2
                ],
                "tile_shape": [
                  64,
                  64,
                  16
                ],
                "staging": "threadgroup",
                "vector_width": null,
                "double_buffer": true,
                "reasons": [
                  "The selected SIMDgroup grid partitions 8x8 accumulator fragments without overlap.",
                  "Cooperative loads stage operand tiles in threadgroup memory."
                ],
                "cooperative_layout": "8x8 simdgroup_matrix fragments",
                "outer_bounds_proven": true
              },
              "passes": [
                "pad_shared_memory",
                "double_buffer_k_loop",
                "vectorize_loads",
                "serpentine_mma",
                "preload_mma_tiles",
                "block_swizzle",
                "fold_constants"
              ],
              "loops": [
                {
                  "induction_variable": "kb",
                  "kind": "loop",
                  "lanes": 128,
                  "elements_per_lane": 1,
                  "iteration_step": 16
                },
                {
                  "induction_variable": "kk",
                  "kind": "loop",
                  "lanes": 128,
                  "elements_per_lane": 1,
                  "iteration_step": 8
                }
              ],
              "allocations": [
                {
                  "name": "shared_a_0",
                  "address_space": "threadgroup",
                  "element_type": "float",
                  "elements": 1088,
                  "bytes": 4352
                },
                {
                  "name": "shared_a_1",
                  "address_space": "threadgroup",
                  "element_type": "float",
                  "elements": 1088,
                  "bytes": 4352
                },
                {
                  "name": "shared_b_0",
                  "address_space": "threadgroup",
                  "element_type": "float",
                  "elements": 1040,
                  "bytes": 4160
                },
                {
                  "name": "shared_b_1",
                  "address_space": "threadgroup",
                  "element_type": "float",
                  "elements": 1040,
                  "bytes": 4160
                }
              ],
              "double_buffered": true,
              "vectorized_loads": 0,
              "epilogue_regions": 0,
              "notes": [
                "Layout widths describe emitted Metal operations, not final machine instructions.",
                "Masked tails may use scalar accesses even when aligned interiors are vectorized."
              ],
              "value_layouts": [],
              "layout_conversions": [],
              "pipelines": [
                {
                  "buffers": [
                    {
                      "logical_name": "shared_a",
                      "slots": [
                        "shared_a_0",
                        "shared_a_1"
                      ],
                      "element_type": "float",
                      "elements": 1088,
                      "current_pointer": "sa_curr",
                      "next_pointer": "sa_next"
                    },
                    {
                      "logical_name": "shared_b",
                      "slots": [
                        "shared_b_0",
                        "shared_b_1"
                      ],
                      "element_type": "float",
                      "elements": 1040,
                      "current_pointer": "sb_curr",
                      "next_pointer": "sb_next"
                    }
                  ],
                  "phases": [
                    {
                      "name": "load_first",
                      "region": "prologue",
                      "kind": "copy",
                      "reads": [],
                      "writes": [
                        {
                          "buffer": "shared_a",
                          "slot": "current"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "current"
                        }
                      ],
                      "publishes": [],
                      "recycles": [],
                      "rotates": [],
                      "barrier_scope": null,
                      "barrier_flags": null
                    },
                    {
                      "name": "publish_first",
                      "region": "prologue",
                      "kind": "barrier",
                      "reads": [],
                      "writes": [],
                      "publishes": [
                        {
                          "buffer": "shared_a",
                          "slot": "current"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "current"
                        }
                      ],
                      "recycles": [],
                      "rotates": [],
                      "barrier_scope": "threadgroup",
                      "barrier_flags": "mem_threadgroup"
                    },
                    {
                      "name": "load_next",
                      "region": "steady",
                      "kind": "copy",
                      "reads": [],
                      "writes": [
                        {
                          "buffer": "shared_a",
                          "slot": "next"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "next"
                        }
                      ],
                      "publishes": [],
                      "recycles": [],
                      "rotates": [],
                      "barrier_scope": null,
                      "barrier_flags": null
                    },
                    {
                      "name": "consume_current",
                      "region": "steady",
                      "kind": "compute",
                      "reads": [
                        {
                          "buffer": "shared_a",
                          "slot": "current"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "current"
                        }
                      ],
                      "writes": [],
                      "publishes": [],
                      "recycles": [],
                      "rotates": [],
                      "barrier_scope": null,
                      "barrier_flags": null
                    },
                    {
                      "name": "publish_and_recycle",
                      "region": "steady",
                      "kind": "barrier",
                      "reads": [],
                      "writes": [],
                      "publishes": [
                        {
                          "buffer": "shared_a",
                          "slot": "next"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "next"
                        }
                      ],
                      "recycles": [
                        {
                          "buffer": "shared_a",
                          "slot": "current"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "current"
                        }
                      ],
                      "rotates": [],
                      "barrier_scope": "threadgroup",
                      "barrier_flags": "mem_threadgroup"
                    },
                    {
                      "name": "rotate_slots",
                      "region": "steady",
                      "kind": "rotate",
                      "reads": [],
                      "writes": [],
                      "publishes": [],
                      "recycles": [],
                      "rotates": [
                        "shared_a",
                        "shared_b"
                      ],
                      "barrier_scope": null,
                      "barrier_flags": null
                    },
                    {
                      "name": "consume_last",
                      "region": "drain",
                      "kind": "compute",
                      "reads": [
                        {
                          "buffer": "shared_a",
                          "slot": "current"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "current"
                        }
                      ],
                      "writes": [],
                      "publishes": [],
                      "recycles": [],
                      "rotates": [],
                      "barrier_scope": null,
                      "barrier_flags": null
                    },
                    {
                      "name": "release_last",
                      "region": "drain",
                      "kind": "barrier",
                      "reads": [],
                      "writes": [],
                      "publishes": [],
                      "recycles": [
                        {
                          "buffer": "shared_a",
                          "slot": "current"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "current"
                        }
                      ],
                      "rotates": [],
                      "barrier_scope": "threadgroup",
                      "barrier_flags": "mem_threadgroup"
                    }
                  ],
                  "stages": 2,
                  "mechanism": "software"
                }
              ]
            },
            "timing": {
              "samples": 396,
              "gpu_us": 987.1041984297335,
              "wall_us": 1200.979,
              "gpu_min_max_us": [
                970.5416741780937,
                1175.4999868571758
              ],
              "wall_min_max_us": [
                1071.666,
                10793.042
              ]
            },
            "status": "ok"
          },
          {
            "name": "float32_257x255x259",
            "dtype": "float32",
            "shape": [
              257,
              255,
              259
            ],
            "seed": 438,
            "schedule": {
              "backend": "simdgroup",
              "double_buffer": true,
              "BLOCK_M": 64,
              "BLOCK_N": 64,
              "BLOCK_K": 16,
              "RELAXED_PRECISION": false
            },
            "input_sha256": "acff8f3e2b353c103ecee705731d3d2c8c26b98f0a80634d1fd4a06c38113a26",
            "correctness": {
              "reference": "NumPy FP32 matmul rounded to the output storage dtype",
              "max_absolute_error": 0.0,
              "rtol": 0.0003,
              "atol": 3e-05
            },
            "source_sha256": "4be0fb2e516dd502b4eab90ce5d42bc755710fb3331f6f7e4ea2f7c96e11e724",
            "execution_report": {
              "plan": {
                "backend": "simdgroup",
                "threadgroup_size": [
                  128,
                  1,
                  1
                ],
                "simdgroup_grid": [
                  2,
                  2
                ],
                "tile_shape": [
                  64,
                  64,
                  16
                ],
                "staging": "threadgroup",
                "vector_width": null,
                "double_buffer": true,
                "reasons": [
                  "The selected SIMDgroup grid partitions 8x8 accumulator fragments without overlap.",
                  "Cooperative loads stage operand tiles in threadgroup memory."
                ],
                "cooperative_layout": "8x8 simdgroup_matrix fragments",
                "outer_bounds_proven": false
              },
              "passes": [
                "pad_shared_memory",
                "double_buffer_k_loop",
                "vectorize_loads",
                "serpentine_mma",
                "preload_mma_tiles",
                "block_swizzle",
                "fold_constants"
              ],
              "loops": [
                {
                  "induction_variable": "kb",
                  "kind": "loop",
                  "lanes": 128,
                  "elements_per_lane": 1,
                  "iteration_step": 16
                },
                {
                  "induction_variable": "kk",
                  "kind": "loop",
                  "lanes": 128,
                  "elements_per_lane": 1,
                  "iteration_step": 8
                }
              ],
              "allocations": [
                {
                  "name": "shared_a_0",
                  "address_space": "threadgroup",
                  "element_type": "float",
                  "elements": 1088,
                  "bytes": 4352
                },
                {
                  "name": "shared_a_1",
                  "address_space": "threadgroup",
                  "element_type": "float",
                  "elements": 1088,
                  "bytes": 4352
                },
                {
                  "name": "shared_b_0",
                  "address_space": "threadgroup",
                  "element_type": "float",
                  "elements": 1040,
                  "bytes": 4160
                },
                {
                  "name": "shared_b_1",
                  "address_space": "threadgroup",
                  "element_type": "float",
                  "elements": 1040,
                  "bytes": 4160
                }
              ],
              "double_buffered": true,
              "vectorized_loads": 0,
              "epilogue_regions": 0,
              "notes": [
                "Layout widths describe emitted Metal operations, not final machine instructions.",
                "Masked tails may use scalar accesses even when aligned interiors are vectorized."
              ],
              "value_layouts": [],
              "layout_conversions": [],
              "pipelines": [
                {
                  "buffers": [
                    {
                      "logical_name": "shared_a",
                      "slots": [
                        "shared_a_0",
                        "shared_a_1"
                      ],
                      "element_type": "float",
                      "elements": 1088,
                      "current_pointer": "sa_curr",
                      "next_pointer": "sa_next"
                    },
                    {
                      "logical_name": "shared_b",
                      "slots": [
                        "shared_b_0",
                        "shared_b_1"
                      ],
                      "element_type": "float",
                      "elements": 1040,
                      "current_pointer": "sb_curr",
                      "next_pointer": "sb_next"
                    }
                  ],
                  "phases": [
                    {
                      "name": "load_first",
                      "region": "prologue",
                      "kind": "copy",
                      "reads": [],
                      "writes": [
                        {
                          "buffer": "shared_a",
                          "slot": "current"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "current"
                        }
                      ],
                      "publishes": [],
                      "recycles": [],
                      "rotates": [],
                      "barrier_scope": null,
                      "barrier_flags": null
                    },
                    {
                      "name": "publish_first",
                      "region": "prologue",
                      "kind": "barrier",
                      "reads": [],
                      "writes": [],
                      "publishes": [
                        {
                          "buffer": "shared_a",
                          "slot": "current"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "current"
                        }
                      ],
                      "recycles": [],
                      "rotates": [],
                      "barrier_scope": "threadgroup",
                      "barrier_flags": "mem_threadgroup"
                    },
                    {
                      "name": "load_next",
                      "region": "steady",
                      "kind": "copy",
                      "reads": [],
                      "writes": [
                        {
                          "buffer": "shared_a",
                          "slot": "next"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "next"
                        }
                      ],
                      "publishes": [],
                      "recycles": [],
                      "rotates": [],
                      "barrier_scope": null,
                      "barrier_flags": null
                    },
                    {
                      "name": "consume_current",
                      "region": "steady",
                      "kind": "compute",
                      "reads": [
                        {
                          "buffer": "shared_a",
                          "slot": "current"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "current"
                        }
                      ],
                      "writes": [],
                      "publishes": [],
                      "recycles": [],
                      "rotates": [],
                      "barrier_scope": null,
                      "barrier_flags": null
                    },
                    {
                      "name": "publish_and_recycle",
                      "region": "steady",
                      "kind": "barrier",
                      "reads": [],
                      "writes": [],
                      "publishes": [
                        {
                          "buffer": "shared_a",
                          "slot": "next"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "next"
                        }
                      ],
                      "recycles": [
                        {
                          "buffer": "shared_a",
                          "slot": "current"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "current"
                        }
                      ],
                      "rotates": [],
                      "barrier_scope": "threadgroup",
                      "barrier_flags": "mem_threadgroup"
                    },
                    {
                      "name": "rotate_slots",
                      "region": "steady",
                      "kind": "rotate",
                      "reads": [],
                      "writes": [],
                      "publishes": [],
                      "recycles": [],
                      "rotates": [
                        "shared_a",
                        "shared_b"
                      ],
                      "barrier_scope": null,
                      "barrier_flags": null
                    },
                    {
                      "name": "consume_last",
                      "region": "drain",
                      "kind": "compute",
                      "reads": [
                        {
                          "buffer": "shared_a",
                          "slot": "current"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "current"
                        }
                      ],
                      "writes": [],
                      "publishes": [],
                      "recycles": [],
                      "rotates": [],
                      "barrier_scope": null,
                      "barrier_flags": null
                    },
                    {
                      "name": "release_last",
                      "region": "drain",
                      "kind": "barrier",
                      "reads": [],
                      "writes": [],
                      "publishes": [],
                      "recycles": [
                        {
                          "buffer": "shared_a",
                          "slot": "current"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "current"
                        }
                      ],
                      "rotates": [],
                      "barrier_scope": "threadgroup",
                      "barrier_flags": "mem_threadgroup"
                    }
                  ],
                  "stages": 2,
                  "mechanism": "software"
                }
              ]
            },
            "timing": {
              "samples": 1502,
              "gpu_us": 58.85417340323329,
              "wall_us": 280.97950000000003,
              "gpu_min_max_us": [
                45.66670395433903,
                242.24998196586967
              ],
              "wall_min_max_us": [
                134.958,
                579.792
              ]
            },
            "status": "ok"
          }
        ]
      },
      {
        "root": "/Users/andreslavescu/Documents/projects/meTile",
        "compiler_implementation_sha256": "d258683dcf0a92130bc92c14d306b75dfdb1194f300bbdc9aafe671cb6ffff65",
        "device": "Apple M5",
        "metal_compiler": "Apple metal version 32023.864 (metalfe-32023.864)\nTarget: air64-apple-darwin25.2.0\nThread model: posix\nInstalledDir: /private/var/run/com.apple.security.cryptexd/mnt/com.apple.MobileAsset.MetalToolchain-v17.3.7003.10.GzPOjD/Metal.xctoolchain/usr/metal/current/bin",
        "platform": "macOS-26.2-arm64-arm-64bit",
        "cases": [
          {
            "name": "float16_64x64x64",
            "dtype": "float16",
            "shape": [
              64,
              64,
              64
            ],
            "seed": 431,
            "schedule": {
              "backend": "simdgroup",
              "double_buffer": true,
              "BLOCK_M": 64,
              "BLOCK_N": 64,
              "BLOCK_K": 16,
              "RELAXED_PRECISION": false
            },
            "input_sha256": "f7743c34dfc78564a28e726c1924c410fbdb76f4158beba809e487c7fdc4d8b3",
            "correctness": {
              "reference": "NumPy FP32 matmul rounded to the output storage dtype",
              "max_absolute_error": 0.0,
              "rtol": 0.002,
              "atol": 0.002
            },
            "source_sha256": "775bf51864f7fadf5c0a51035e57a2f85c7857b382291cefd60dd69bf86f92d1",
            "execution_report": {
              "plan": {
                "backend": "simdgroup",
                "threadgroup_size": [
                  128,
                  1,
                  1
                ],
                "simdgroup_grid": [
                  2,
                  2
                ],
                "tile_shape": [
                  64,
                  64,
                  16
                ],
                "staging": "threadgroup",
                "vector_width": null,
                "double_buffer": true,
                "reasons": [
                  "The selected SIMDgroup grid partitions 8x8 accumulator fragments without overlap.",
                  "Cooperative loads stage operand tiles in threadgroup memory."
                ],
                "cooperative_layout": "8x8 simdgroup_matrix fragments",
                "outer_bounds_proven": true
              },
              "passes": [
                "pad_shared_memory",
                "double_buffer_k_loop",
                "vectorize_loads",
                "serpentine_mma",
                "preload_mma_tiles",
                "block_swizzle",
                "fold_constants"
              ],
              "loops": [
                {
                  "induction_variable": "kb",
                  "kind": "loop",
                  "lanes": 128,
                  "elements_per_lane": 1,
                  "iteration_step": 16
                },
                {
                  "induction_variable": "kk",
                  "kind": "loop",
                  "lanes": 128,
                  "elements_per_lane": 1,
                  "iteration_step": 8
                }
              ],
              "allocations": [
                {
                  "name": "shared_a_0",
                  "address_space": "threadgroup",
                  "element_type": "half",
                  "elements": 1088,
                  "bytes": 2176
                },
                {
                  "name": "shared_a_1",
                  "address_space": "threadgroup",
                  "element_type": "half",
                  "elements": 1088,
                  "bytes": 2176
                },
                {
                  "name": "shared_b_0",
                  "address_space": "threadgroup",
                  "element_type": "half",
                  "elements": 1040,
                  "bytes": 2080
                },
                {
                  "name": "shared_b_1",
                  "address_space": "threadgroup",
                  "element_type": "half",
                  "elements": 1040,
                  "bytes": 2080
                }
              ],
              "double_buffered": true,
              "vectorized_loads": 0,
              "epilogue_regions": 0,
              "notes": [
                "Layout widths describe emitted Metal operations, not final machine instructions.",
                "Masked tails may use scalar accesses even when aligned interiors are vectorized."
              ],
              "value_layouts": [],
              "layout_conversions": [],
              "pipelines": [
                {
                  "buffers": [
                    {
                      "logical_name": "shared_a",
                      "slots": [
                        "shared_a_0",
                        "shared_a_1"
                      ],
                      "element_type": "half",
                      "elements": 1088,
                      "current_pointer": "sa_curr",
                      "next_pointer": "sa_next"
                    },
                    {
                      "logical_name": "shared_b",
                      "slots": [
                        "shared_b_0",
                        "shared_b_1"
                      ],
                      "element_type": "half",
                      "elements": 1040,
                      "current_pointer": "sb_curr",
                      "next_pointer": "sb_next"
                    }
                  ],
                  "phases": [
                    {
                      "name": "load_first",
                      "region": "prologue",
                      "kind": "copy",
                      "reads": [],
                      "writes": [
                        {
                          "buffer": "shared_a",
                          "slot": "current"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "current"
                        }
                      ],
                      "publishes": [],
                      "recycles": [],
                      "rotates": [],
                      "barrier_scope": null,
                      "barrier_flags": null
                    },
                    {
                      "name": "publish_first",
                      "region": "prologue",
                      "kind": "barrier",
                      "reads": [],
                      "writes": [],
                      "publishes": [
                        {
                          "buffer": "shared_a",
                          "slot": "current"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "current"
                        }
                      ],
                      "recycles": [],
                      "rotates": [],
                      "barrier_scope": "threadgroup",
                      "barrier_flags": "mem_threadgroup"
                    },
                    {
                      "name": "load_next",
                      "region": "steady",
                      "kind": "copy",
                      "reads": [],
                      "writes": [
                        {
                          "buffer": "shared_a",
                          "slot": "next"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "next"
                        }
                      ],
                      "publishes": [],
                      "recycles": [],
                      "rotates": [],
                      "barrier_scope": null,
                      "barrier_flags": null
                    },
                    {
                      "name": "consume_current",
                      "region": "steady",
                      "kind": "compute",
                      "reads": [
                        {
                          "buffer": "shared_a",
                          "slot": "current"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "current"
                        }
                      ],
                      "writes": [],
                      "publishes": [],
                      "recycles": [],
                      "rotates": [],
                      "barrier_scope": null,
                      "barrier_flags": null
                    },
                    {
                      "name": "publish_and_recycle",
                      "region": "steady",
                      "kind": "barrier",
                      "reads": [],
                      "writes": [],
                      "publishes": [
                        {
                          "buffer": "shared_a",
                          "slot": "next"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "next"
                        }
                      ],
                      "recycles": [
                        {
                          "buffer": "shared_a",
                          "slot": "current"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "current"
                        }
                      ],
                      "rotates": [],
                      "barrier_scope": "threadgroup",
                      "barrier_flags": "mem_threadgroup"
                    },
                    {
                      "name": "rotate_slots",
                      "region": "steady",
                      "kind": "rotate",
                      "reads": [],
                      "writes": [],
                      "publishes": [],
                      "recycles": [],
                      "rotates": [
                        "shared_a",
                        "shared_b"
                      ],
                      "barrier_scope": null,
                      "barrier_flags": null
                    },
                    {
                      "name": "consume_last",
                      "region": "drain",
                      "kind": "compute",
                      "reads": [
                        {
                          "buffer": "shared_a",
                          "slot": "current"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "current"
                        }
                      ],
                      "writes": [],
                      "publishes": [],
                      "recycles": [],
                      "rotates": [],
                      "barrier_scope": null,
                      "barrier_flags": null
                    },
                    {
                      "name": "release_last",
                      "region": "drain",
                      "kind": "barrier",
                      "reads": [],
                      "writes": [],
                      "publishes": [],
                      "recycles": [
                        {
                          "buffer": "shared_a",
                          "slot": "current"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "current"
                        }
                      ],
                      "rotates": [],
                      "barrier_scope": "threadgroup",
                      "barrier_flags": "mem_threadgroup"
                    }
                  ],
                  "stages": 2,
                  "mechanism": "software"
                }
              ]
            },
            "timing": {
              "samples": 1370,
              "gpu_us": 64.9583525955677,
              "wall_us": 368.875,
              "gpu_min_max_us": [
                64.7500273771584,
                79.24996316432953
              ],
              "wall_min_max_us": [
                149.708,
                455.958
              ]
            },
            "status": "ok"
          },
          {
            "name": "float16_256x256x256",
            "dtype": "float16",
            "shape": [
              256,
              256,
              256
            ],
            "seed": 432,
            "schedule": {
              "backend": "simdgroup",
              "double_buffer": true,
              "BLOCK_M": 64,
              "BLOCK_N": 64,
              "BLOCK_K": 16,
              "RELAXED_PRECISION": false
            },
            "input_sha256": "93ab6d6120e1756849446ff813e60fbd0616fa9eec32fbbd8c515ecaa3488b3d",
            "correctness": {
              "reference": "NumPy FP32 matmul rounded to the output storage dtype",
              "max_absolute_error": 0.0,
              "rtol": 0.002,
              "atol": 0.002
            },
            "source_sha256": "775bf51864f7fadf5c0a51035e57a2f85c7857b382291cefd60dd69bf86f92d1",
            "execution_report": {
              "plan": {
                "backend": "simdgroup",
                "threadgroup_size": [
                  128,
                  1,
                  1
                ],
                "simdgroup_grid": [
                  2,
                  2
                ],
                "tile_shape": [
                  64,
                  64,
                  16
                ],
                "staging": "threadgroup",
                "vector_width": null,
                "double_buffer": true,
                "reasons": [
                  "The selected SIMDgroup grid partitions 8x8 accumulator fragments without overlap.",
                  "Cooperative loads stage operand tiles in threadgroup memory."
                ],
                "cooperative_layout": "8x8 simdgroup_matrix fragments",
                "outer_bounds_proven": true
              },
              "passes": [
                "pad_shared_memory",
                "double_buffer_k_loop",
                "vectorize_loads",
                "serpentine_mma",
                "preload_mma_tiles",
                "block_swizzle",
                "fold_constants"
              ],
              "loops": [
                {
                  "induction_variable": "kb",
                  "kind": "loop",
                  "lanes": 128,
                  "elements_per_lane": 1,
                  "iteration_step": 16
                },
                {
                  "induction_variable": "kk",
                  "kind": "loop",
                  "lanes": 128,
                  "elements_per_lane": 1,
                  "iteration_step": 8
                }
              ],
              "allocations": [
                {
                  "name": "shared_a_0",
                  "address_space": "threadgroup",
                  "element_type": "half",
                  "elements": 1088,
                  "bytes": 2176
                },
                {
                  "name": "shared_a_1",
                  "address_space": "threadgroup",
                  "element_type": "half",
                  "elements": 1088,
                  "bytes": 2176
                },
                {
                  "name": "shared_b_0",
                  "address_space": "threadgroup",
                  "element_type": "half",
                  "elements": 1040,
                  "bytes": 2080
                },
                {
                  "name": "shared_b_1",
                  "address_space": "threadgroup",
                  "element_type": "half",
                  "elements": 1040,
                  "bytes": 2080
                }
              ],
              "double_buffered": true,
              "vectorized_loads": 0,
              "epilogue_regions": 0,
              "notes": [
                "Layout widths describe emitted Metal operations, not final machine instructions.",
                "Masked tails may use scalar accesses even when aligned interiors are vectorized."
              ],
              "value_layouts": [],
              "layout_conversions": [],
              "pipelines": [
                {
                  "buffers": [
                    {
                      "logical_name": "shared_a",
                      "slots": [
                        "shared_a_0",
                        "shared_a_1"
                      ],
                      "element_type": "half",
                      "elements": 1088,
                      "current_pointer": "sa_curr",
                      "next_pointer": "sa_next"
                    },
                    {
                      "logical_name": "shared_b",
                      "slots": [
                        "shared_b_0",
                        "shared_b_1"
                      ],
                      "element_type": "half",
                      "elements": 1040,
                      "current_pointer": "sb_curr",
                      "next_pointer": "sb_next"
                    }
                  ],
                  "phases": [
                    {
                      "name": "load_first",
                      "region": "prologue",
                      "kind": "copy",
                      "reads": [],
                      "writes": [
                        {
                          "buffer": "shared_a",
                          "slot": "current"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "current"
                        }
                      ],
                      "publishes": [],
                      "recycles": [],
                      "rotates": [],
                      "barrier_scope": null,
                      "barrier_flags": null
                    },
                    {
                      "name": "publish_first",
                      "region": "prologue",
                      "kind": "barrier",
                      "reads": [],
                      "writes": [],
                      "publishes": [
                        {
                          "buffer": "shared_a",
                          "slot": "current"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "current"
                        }
                      ],
                      "recycles": [],
                      "rotates": [],
                      "barrier_scope": "threadgroup",
                      "barrier_flags": "mem_threadgroup"
                    },
                    {
                      "name": "load_next",
                      "region": "steady",
                      "kind": "copy",
                      "reads": [],
                      "writes": [
                        {
                          "buffer": "shared_a",
                          "slot": "next"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "next"
                        }
                      ],
                      "publishes": [],
                      "recycles": [],
                      "rotates": [],
                      "barrier_scope": null,
                      "barrier_flags": null
                    },
                    {
                      "name": "consume_current",
                      "region": "steady",
                      "kind": "compute",
                      "reads": [
                        {
                          "buffer": "shared_a",
                          "slot": "current"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "current"
                        }
                      ],
                      "writes": [],
                      "publishes": [],
                      "recycles": [],
                      "rotates": [],
                      "barrier_scope": null,
                      "barrier_flags": null
                    },
                    {
                      "name": "publish_and_recycle",
                      "region": "steady",
                      "kind": "barrier",
                      "reads": [],
                      "writes": [],
                      "publishes": [
                        {
                          "buffer": "shared_a",
                          "slot": "next"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "next"
                        }
                      ],
                      "recycles": [
                        {
                          "buffer": "shared_a",
                          "slot": "current"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "current"
                        }
                      ],
                      "rotates": [],
                      "barrier_scope": "threadgroup",
                      "barrier_flags": "mem_threadgroup"
                    },
                    {
                      "name": "rotate_slots",
                      "region": "steady",
                      "kind": "rotate",
                      "reads": [],
                      "writes": [],
                      "publishes": [],
                      "recycles": [],
                      "rotates": [
                        "shared_a",
                        "shared_b"
                      ],
                      "barrier_scope": null,
                      "barrier_flags": null
                    },
                    {
                      "name": "consume_last",
                      "region": "drain",
                      "kind": "compute",
                      "reads": [
                        {
                          "buffer": "shared_a",
                          "slot": "current"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "current"
                        }
                      ],
                      "writes": [],
                      "publishes": [],
                      "recycles": [],
                      "rotates": [],
                      "barrier_scope": null,
                      "barrier_flags": null
                    },
                    {
                      "name": "release_last",
                      "region": "drain",
                      "kind": "barrier",
                      "reads": [],
                      "writes": [],
                      "publishes": [],
                      "recycles": [
                        {
                          "buffer": "shared_a",
                          "slot": "current"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "current"
                        }
                      ],
                      "rotates": [],
                      "barrier_scope": "threadgroup",
                      "barrier_flags": "mem_threadgroup"
                    }
                  ],
                  "stages": 2,
                  "mechanism": "software"
                }
              ]
            },
            "timing": {
              "samples": 1004,
              "gpu_us": 191.95833010599017,
              "wall_us": 500.9585,
              "gpu_min_max_us": [
                189.12501400336623,
                216.95834584534168
              ],
              "wall_min_max_us": [
                284.625,
                592.9590000000001
              ]
            },
            "status": "ok"
          },
          {
            "name": "float16_1024x1024x1024",
            "dtype": "float16",
            "shape": [
              1024,
              1024,
              1024
            ],
            "seed": 433,
            "schedule": {
              "backend": "simdgroup",
              "double_buffer": true,
              "BLOCK_M": 64,
              "BLOCK_N": 64,
              "BLOCK_K": 16,
              "RELAXED_PRECISION": false
            },
            "input_sha256": "a3cdef8bbc69c848e84c524701f359db6268c696607cea04283a35e3be9e32c1",
            "correctness": {
              "reference": "NumPy FP32 matmul rounded to the output storage dtype",
              "max_absolute_error": 0.0,
              "rtol": 0.002,
              "atol": 0.002
            },
            "source_sha256": "775bf51864f7fadf5c0a51035e57a2f85c7857b382291cefd60dd69bf86f92d1",
            "execution_report": {
              "plan": {
                "backend": "simdgroup",
                "threadgroup_size": [
                  128,
                  1,
                  1
                ],
                "simdgroup_grid": [
                  2,
                  2
                ],
                "tile_shape": [
                  64,
                  64,
                  16
                ],
                "staging": "threadgroup",
                "vector_width": null,
                "double_buffer": true,
                "reasons": [
                  "The selected SIMDgroup grid partitions 8x8 accumulator fragments without overlap.",
                  "Cooperative loads stage operand tiles in threadgroup memory."
                ],
                "cooperative_layout": "8x8 simdgroup_matrix fragments",
                "outer_bounds_proven": true
              },
              "passes": [
                "pad_shared_memory",
                "double_buffer_k_loop",
                "vectorize_loads",
                "serpentine_mma",
                "preload_mma_tiles",
                "block_swizzle",
                "fold_constants"
              ],
              "loops": [
                {
                  "induction_variable": "kb",
                  "kind": "loop",
                  "lanes": 128,
                  "elements_per_lane": 1,
                  "iteration_step": 16
                },
                {
                  "induction_variable": "kk",
                  "kind": "loop",
                  "lanes": 128,
                  "elements_per_lane": 1,
                  "iteration_step": 8
                }
              ],
              "allocations": [
                {
                  "name": "shared_a_0",
                  "address_space": "threadgroup",
                  "element_type": "half",
                  "elements": 1088,
                  "bytes": 2176
                },
                {
                  "name": "shared_a_1",
                  "address_space": "threadgroup",
                  "element_type": "half",
                  "elements": 1088,
                  "bytes": 2176
                },
                {
                  "name": "shared_b_0",
                  "address_space": "threadgroup",
                  "element_type": "half",
                  "elements": 1040,
                  "bytes": 2080
                },
                {
                  "name": "shared_b_1",
                  "address_space": "threadgroup",
                  "element_type": "half",
                  "elements": 1040,
                  "bytes": 2080
                }
              ],
              "double_buffered": true,
              "vectorized_loads": 0,
              "epilogue_regions": 0,
              "notes": [
                "Layout widths describe emitted Metal operations, not final machine instructions.",
                "Masked tails may use scalar accesses even when aligned interiors are vectorized."
              ],
              "value_layouts": [],
              "layout_conversions": [],
              "pipelines": [
                {
                  "buffers": [
                    {
                      "logical_name": "shared_a",
                      "slots": [
                        "shared_a_0",
                        "shared_a_1"
                      ],
                      "element_type": "half",
                      "elements": 1088,
                      "current_pointer": "sa_curr",
                      "next_pointer": "sa_next"
                    },
                    {
                      "logical_name": "shared_b",
                      "slots": [
                        "shared_b_0",
                        "shared_b_1"
                      ],
                      "element_type": "half",
                      "elements": 1040,
                      "current_pointer": "sb_curr",
                      "next_pointer": "sb_next"
                    }
                  ],
                  "phases": [
                    {
                      "name": "load_first",
                      "region": "prologue",
                      "kind": "copy",
                      "reads": [],
                      "writes": [
                        {
                          "buffer": "shared_a",
                          "slot": "current"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "current"
                        }
                      ],
                      "publishes": [],
                      "recycles": [],
                      "rotates": [],
                      "barrier_scope": null,
                      "barrier_flags": null
                    },
                    {
                      "name": "publish_first",
                      "region": "prologue",
                      "kind": "barrier",
                      "reads": [],
                      "writes": [],
                      "publishes": [
                        {
                          "buffer": "shared_a",
                          "slot": "current"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "current"
                        }
                      ],
                      "recycles": [],
                      "rotates": [],
                      "barrier_scope": "threadgroup",
                      "barrier_flags": "mem_threadgroup"
                    },
                    {
                      "name": "load_next",
                      "region": "steady",
                      "kind": "copy",
                      "reads": [],
                      "writes": [
                        {
                          "buffer": "shared_a",
                          "slot": "next"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "next"
                        }
                      ],
                      "publishes": [],
                      "recycles": [],
                      "rotates": [],
                      "barrier_scope": null,
                      "barrier_flags": null
                    },
                    {
                      "name": "consume_current",
                      "region": "steady",
                      "kind": "compute",
                      "reads": [
                        {
                          "buffer": "shared_a",
                          "slot": "current"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "current"
                        }
                      ],
                      "writes": [],
                      "publishes": [],
                      "recycles": [],
                      "rotates": [],
                      "barrier_scope": null,
                      "barrier_flags": null
                    },
                    {
                      "name": "publish_and_recycle",
                      "region": "steady",
                      "kind": "barrier",
                      "reads": [],
                      "writes": [],
                      "publishes": [
                        {
                          "buffer": "shared_a",
                          "slot": "next"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "next"
                        }
                      ],
                      "recycles": [
                        {
                          "buffer": "shared_a",
                          "slot": "current"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "current"
                        }
                      ],
                      "rotates": [],
                      "barrier_scope": "threadgroup",
                      "barrier_flags": "mem_threadgroup"
                    },
                    {
                      "name": "rotate_slots",
                      "region": "steady",
                      "kind": "rotate",
                      "reads": [],
                      "writes": [],
                      "publishes": [],
                      "recycles": [],
                      "rotates": [
                        "shared_a",
                        "shared_b"
                      ],
                      "barrier_scope": null,
                      "barrier_flags": null
                    },
                    {
                      "name": "consume_last",
                      "region": "drain",
                      "kind": "compute",
                      "reads": [
                        {
                          "buffer": "shared_a",
                          "slot": "current"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "current"
                        }
                      ],
                      "writes": [],
                      "publishes": [],
                      "recycles": [],
                      "rotates": [],
                      "barrier_scope": null,
                      "barrier_flags": null
                    },
                    {
                      "name": "release_last",
                      "region": "drain",
                      "kind": "barrier",
                      "reads": [],
                      "writes": [],
                      "publishes": [],
                      "recycles": [
                        {
                          "buffer": "shared_a",
                          "slot": "current"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "current"
                        }
                      ],
                      "rotates": [],
                      "barrier_scope": "threadgroup",
                      "barrier_flags": "mem_threadgroup"
                    }
                  ],
                  "stages": 2,
                  "mechanism": "software"
                }
              ]
            },
            "timing": {
              "samples": 471,
              "gpu_us": 849.9999530613422,
              "wall_us": 1057.709,
              "gpu_min_max_us": [
                807.3333301581442,
                953.9999882690609
              ],
              "wall_min_max_us": [
                922.0,
                1158.958
              ]
            },
            "status": "ok"
          },
          {
            "name": "float16_257x255x259",
            "dtype": "float16",
            "shape": [
              257,
              255,
              259
            ],
            "seed": 434,
            "schedule": {
              "backend": "simdgroup",
              "double_buffer": true,
              "BLOCK_M": 64,
              "BLOCK_N": 64,
              "BLOCK_K": 16,
              "RELAXED_PRECISION": false
            },
            "input_sha256": "9b256a8e5e5aa03086c616dbb685bfb3b2a3838b8a2de16524f12307645110ef",
            "correctness": {
              "reference": "NumPy FP32 matmul rounded to the output storage dtype",
              "max_absolute_error": 0.0,
              "rtol": 0.002,
              "atol": 0.002
            },
            "source_sha256": "775bf51864f7fadf5c0a51035e57a2f85c7857b382291cefd60dd69bf86f92d1",
            "execution_report": {
              "plan": {
                "backend": "simdgroup",
                "threadgroup_size": [
                  128,
                  1,
                  1
                ],
                "simdgroup_grid": [
                  2,
                  2
                ],
                "tile_shape": [
                  64,
                  64,
                  16
                ],
                "staging": "threadgroup",
                "vector_width": null,
                "double_buffer": true,
                "reasons": [
                  "The selected SIMDgroup grid partitions 8x8 accumulator fragments without overlap.",
                  "Cooperative loads stage operand tiles in threadgroup memory."
                ],
                "cooperative_layout": "8x8 simdgroup_matrix fragments",
                "outer_bounds_proven": false
              },
              "passes": [
                "pad_shared_memory",
                "double_buffer_k_loop",
                "vectorize_loads",
                "serpentine_mma",
                "preload_mma_tiles",
                "block_swizzle",
                "fold_constants"
              ],
              "loops": [
                {
                  "induction_variable": "kb",
                  "kind": "loop",
                  "lanes": 128,
                  "elements_per_lane": 1,
                  "iteration_step": 16
                },
                {
                  "induction_variable": "kk",
                  "kind": "loop",
                  "lanes": 128,
                  "elements_per_lane": 1,
                  "iteration_step": 8
                }
              ],
              "allocations": [
                {
                  "name": "shared_a_0",
                  "address_space": "threadgroup",
                  "element_type": "half",
                  "elements": 1088,
                  "bytes": 2176
                },
                {
                  "name": "shared_a_1",
                  "address_space": "threadgroup",
                  "element_type": "half",
                  "elements": 1088,
                  "bytes": 2176
                },
                {
                  "name": "shared_b_0",
                  "address_space": "threadgroup",
                  "element_type": "half",
                  "elements": 1040,
                  "bytes": 2080
                },
                {
                  "name": "shared_b_1",
                  "address_space": "threadgroup",
                  "element_type": "half",
                  "elements": 1040,
                  "bytes": 2080
                }
              ],
              "double_buffered": true,
              "vectorized_loads": 0,
              "epilogue_regions": 0,
              "notes": [
                "Layout widths describe emitted Metal operations, not final machine instructions.",
                "Masked tails may use scalar accesses even when aligned interiors are vectorized."
              ],
              "value_layouts": [],
              "layout_conversions": [],
              "pipelines": [
                {
                  "buffers": [
                    {
                      "logical_name": "shared_a",
                      "slots": [
                        "shared_a_0",
                        "shared_a_1"
                      ],
                      "element_type": "half",
                      "elements": 1088,
                      "current_pointer": "sa_curr",
                      "next_pointer": "sa_next"
                    },
                    {
                      "logical_name": "shared_b",
                      "slots": [
                        "shared_b_0",
                        "shared_b_1"
                      ],
                      "element_type": "half",
                      "elements": 1040,
                      "current_pointer": "sb_curr",
                      "next_pointer": "sb_next"
                    }
                  ],
                  "phases": [
                    {
                      "name": "load_first",
                      "region": "prologue",
                      "kind": "copy",
                      "reads": [],
                      "writes": [
                        {
                          "buffer": "shared_a",
                          "slot": "current"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "current"
                        }
                      ],
                      "publishes": [],
                      "recycles": [],
                      "rotates": [],
                      "barrier_scope": null,
                      "barrier_flags": null
                    },
                    {
                      "name": "publish_first",
                      "region": "prologue",
                      "kind": "barrier",
                      "reads": [],
                      "writes": [],
                      "publishes": [
                        {
                          "buffer": "shared_a",
                          "slot": "current"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "current"
                        }
                      ],
                      "recycles": [],
                      "rotates": [],
                      "barrier_scope": "threadgroup",
                      "barrier_flags": "mem_threadgroup"
                    },
                    {
                      "name": "load_next",
                      "region": "steady",
                      "kind": "copy",
                      "reads": [],
                      "writes": [
                        {
                          "buffer": "shared_a",
                          "slot": "next"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "next"
                        }
                      ],
                      "publishes": [],
                      "recycles": [],
                      "rotates": [],
                      "barrier_scope": null,
                      "barrier_flags": null
                    },
                    {
                      "name": "consume_current",
                      "region": "steady",
                      "kind": "compute",
                      "reads": [
                        {
                          "buffer": "shared_a",
                          "slot": "current"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "current"
                        }
                      ],
                      "writes": [],
                      "publishes": [],
                      "recycles": [],
                      "rotates": [],
                      "barrier_scope": null,
                      "barrier_flags": null
                    },
                    {
                      "name": "publish_and_recycle",
                      "region": "steady",
                      "kind": "barrier",
                      "reads": [],
                      "writes": [],
                      "publishes": [
                        {
                          "buffer": "shared_a",
                          "slot": "next"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "next"
                        }
                      ],
                      "recycles": [
                        {
                          "buffer": "shared_a",
                          "slot": "current"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "current"
                        }
                      ],
                      "rotates": [],
                      "barrier_scope": "threadgroup",
                      "barrier_flags": "mem_threadgroup"
                    },
                    {
                      "name": "rotate_slots",
                      "region": "steady",
                      "kind": "rotate",
                      "reads": [],
                      "writes": [],
                      "publishes": [],
                      "recycles": [],
                      "rotates": [
                        "shared_a",
                        "shared_b"
                      ],
                      "barrier_scope": null,
                      "barrier_flags": null
                    },
                    {
                      "name": "consume_last",
                      "region": "drain",
                      "kind": "compute",
                      "reads": [
                        {
                          "buffer": "shared_a",
                          "slot": "current"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "current"
                        }
                      ],
                      "writes": [],
                      "publishes": [],
                      "recycles": [],
                      "rotates": [],
                      "barrier_scope": null,
                      "barrier_flags": null
                    },
                    {
                      "name": "release_last",
                      "region": "drain",
                      "kind": "barrier",
                      "reads": [],
                      "writes": [],
                      "publishes": [],
                      "recycles": [
                        {
                          "buffer": "shared_a",
                          "slot": "current"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "current"
                        }
                      ],
                      "rotates": [],
                      "barrier_scope": "threadgroup",
                      "barrier_flags": "mem_threadgroup"
                    }
                  ],
                  "stages": 2,
                  "mechanism": "software"
                }
              ]
            },
            "timing": {
              "samples": 1394,
              "gpu_us": 62.62504030019045,
              "wall_us": 291.04150000000004,
              "gpu_min_max_us": [
                42.041647247970104,
                220.24998906999826
              ],
              "wall_min_max_us": [
                133.875,
                3756.583
              ]
            },
            "status": "ok"
          },
          {
            "name": "float32_64x64x64",
            "dtype": "float32",
            "shape": [
              64,
              64,
              64
            ],
            "seed": 435,
            "schedule": {
              "backend": "simdgroup",
              "double_buffer": true,
              "BLOCK_M": 64,
              "BLOCK_N": 64,
              "BLOCK_K": 16,
              "RELAXED_PRECISION": false
            },
            "input_sha256": "5daffc014e3bf6c7425a716bc5a36f0a9f5ac3d06a994a5e9e8084b7cfb9cd1b",
            "correctness": {
              "reference": "NumPy FP32 matmul rounded to the output storage dtype",
              "max_absolute_error": 0.0,
              "rtol": 0.0003,
              "atol": 3e-05
            },
            "source_sha256": "4be0fb2e516dd502b4eab90ce5d42bc755710fb3331f6f7e4ea2f7c96e11e724",
            "execution_report": {
              "plan": {
                "backend": "simdgroup",
                "threadgroup_size": [
                  128,
                  1,
                  1
                ],
                "simdgroup_grid": [
                  2,
                  2
                ],
                "tile_shape": [
                  64,
                  64,
                  16
                ],
                "staging": "threadgroup",
                "vector_width": null,
                "double_buffer": true,
                "reasons": [
                  "The selected SIMDgroup grid partitions 8x8 accumulator fragments without overlap.",
                  "Cooperative loads stage operand tiles in threadgroup memory."
                ],
                "cooperative_layout": "8x8 simdgroup_matrix fragments",
                "outer_bounds_proven": true
              },
              "passes": [
                "pad_shared_memory",
                "double_buffer_k_loop",
                "vectorize_loads",
                "serpentine_mma",
                "preload_mma_tiles",
                "block_swizzle",
                "fold_constants"
              ],
              "loops": [
                {
                  "induction_variable": "kb",
                  "kind": "loop",
                  "lanes": 128,
                  "elements_per_lane": 1,
                  "iteration_step": 16
                },
                {
                  "induction_variable": "kk",
                  "kind": "loop",
                  "lanes": 128,
                  "elements_per_lane": 1,
                  "iteration_step": 8
                }
              ],
              "allocations": [
                {
                  "name": "shared_a_0",
                  "address_space": "threadgroup",
                  "element_type": "float",
                  "elements": 1088,
                  "bytes": 4352
                },
                {
                  "name": "shared_a_1",
                  "address_space": "threadgroup",
                  "element_type": "float",
                  "elements": 1088,
                  "bytes": 4352
                },
                {
                  "name": "shared_b_0",
                  "address_space": "threadgroup",
                  "element_type": "float",
                  "elements": 1040,
                  "bytes": 4160
                },
                {
                  "name": "shared_b_1",
                  "address_space": "threadgroup",
                  "element_type": "float",
                  "elements": 1040,
                  "bytes": 4160
                }
              ],
              "double_buffered": true,
              "vectorized_loads": 0,
              "epilogue_regions": 0,
              "notes": [
                "Layout widths describe emitted Metal operations, not final machine instructions.",
                "Masked tails may use scalar accesses even when aligned interiors are vectorized."
              ],
              "value_layouts": [],
              "layout_conversions": [],
              "pipelines": [
                {
                  "buffers": [
                    {
                      "logical_name": "shared_a",
                      "slots": [
                        "shared_a_0",
                        "shared_a_1"
                      ],
                      "element_type": "float",
                      "elements": 1088,
                      "current_pointer": "sa_curr",
                      "next_pointer": "sa_next"
                    },
                    {
                      "logical_name": "shared_b",
                      "slots": [
                        "shared_b_0",
                        "shared_b_1"
                      ],
                      "element_type": "float",
                      "elements": 1040,
                      "current_pointer": "sb_curr",
                      "next_pointer": "sb_next"
                    }
                  ],
                  "phases": [
                    {
                      "name": "load_first",
                      "region": "prologue",
                      "kind": "copy",
                      "reads": [],
                      "writes": [
                        {
                          "buffer": "shared_a",
                          "slot": "current"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "current"
                        }
                      ],
                      "publishes": [],
                      "recycles": [],
                      "rotates": [],
                      "barrier_scope": null,
                      "barrier_flags": null
                    },
                    {
                      "name": "publish_first",
                      "region": "prologue",
                      "kind": "barrier",
                      "reads": [],
                      "writes": [],
                      "publishes": [
                        {
                          "buffer": "shared_a",
                          "slot": "current"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "current"
                        }
                      ],
                      "recycles": [],
                      "rotates": [],
                      "barrier_scope": "threadgroup",
                      "barrier_flags": "mem_threadgroup"
                    },
                    {
                      "name": "load_next",
                      "region": "steady",
                      "kind": "copy",
                      "reads": [],
                      "writes": [
                        {
                          "buffer": "shared_a",
                          "slot": "next"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "next"
                        }
                      ],
                      "publishes": [],
                      "recycles": [],
                      "rotates": [],
                      "barrier_scope": null,
                      "barrier_flags": null
                    },
                    {
                      "name": "consume_current",
                      "region": "steady",
                      "kind": "compute",
                      "reads": [
                        {
                          "buffer": "shared_a",
                          "slot": "current"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "current"
                        }
                      ],
                      "writes": [],
                      "publishes": [],
                      "recycles": [],
                      "rotates": [],
                      "barrier_scope": null,
                      "barrier_flags": null
                    },
                    {
                      "name": "publish_and_recycle",
                      "region": "steady",
                      "kind": "barrier",
                      "reads": [],
                      "writes": [],
                      "publishes": [
                        {
                          "buffer": "shared_a",
                          "slot": "next"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "next"
                        }
                      ],
                      "recycles": [
                        {
                          "buffer": "shared_a",
                          "slot": "current"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "current"
                        }
                      ],
                      "rotates": [],
                      "barrier_scope": "threadgroup",
                      "barrier_flags": "mem_threadgroup"
                    },
                    {
                      "name": "rotate_slots",
                      "region": "steady",
                      "kind": "rotate",
                      "reads": [],
                      "writes": [],
                      "publishes": [],
                      "recycles": [],
                      "rotates": [
                        "shared_a",
                        "shared_b"
                      ],
                      "barrier_scope": null,
                      "barrier_flags": null
                    },
                    {
                      "name": "consume_last",
                      "region": "drain",
                      "kind": "compute",
                      "reads": [
                        {
                          "buffer": "shared_a",
                          "slot": "current"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "current"
                        }
                      ],
                      "writes": [],
                      "publishes": [],
                      "recycles": [],
                      "rotates": [],
                      "barrier_scope": null,
                      "barrier_flags": null
                    },
                    {
                      "name": "release_last",
                      "region": "drain",
                      "kind": "barrier",
                      "reads": [],
                      "writes": [],
                      "publishes": [],
                      "recycles": [
                        {
                          "buffer": "shared_a",
                          "slot": "current"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "current"
                        }
                      ],
                      "rotates": [],
                      "barrier_scope": "threadgroup",
                      "barrier_flags": "mem_threadgroup"
                    }
                  ],
                  "stages": 2,
                  "mechanism": "software"
                }
              ]
            },
            "timing": {
              "samples": 1411,
              "gpu_us": 68.91664816066623,
              "wall_us": 371.66700000000003,
              "gpu_min_max_us": [
                68.6667044647038,
                85.99995635449886
              ],
              "wall_min_max_us": [
                137.667,
                529.667
              ]
            },
            "status": "ok"
          },
          {
            "name": "float32_256x256x256",
            "dtype": "float32",
            "shape": [
              256,
              256,
              256
            ],
            "seed": 436,
            "schedule": {
              "backend": "simdgroup",
              "double_buffer": true,
              "BLOCK_M": 64,
              "BLOCK_N": 64,
              "BLOCK_K": 16,
              "RELAXED_PRECISION": false
            },
            "input_sha256": "ceba1209c2607c35efa378403bf1bd3a583a3330944ee09239152ee064143b95",
            "correctness": {
              "reference": "NumPy FP32 matmul rounded to the output storage dtype",
              "max_absolute_error": 0.0,
              "rtol": 0.0003,
              "atol": 3e-05
            },
            "source_sha256": "4be0fb2e516dd502b4eab90ce5d42bc755710fb3331f6f7e4ea2f7c96e11e724",
            "execution_report": {
              "plan": {
                "backend": "simdgroup",
                "threadgroup_size": [
                  128,
                  1,
                  1
                ],
                "simdgroup_grid": [
                  2,
                  2
                ],
                "tile_shape": [
                  64,
                  64,
                  16
                ],
                "staging": "threadgroup",
                "vector_width": null,
                "double_buffer": true,
                "reasons": [
                  "The selected SIMDgroup grid partitions 8x8 accumulator fragments without overlap.",
                  "Cooperative loads stage operand tiles in threadgroup memory."
                ],
                "cooperative_layout": "8x8 simdgroup_matrix fragments",
                "outer_bounds_proven": true
              },
              "passes": [
                "pad_shared_memory",
                "double_buffer_k_loop",
                "vectorize_loads",
                "serpentine_mma",
                "preload_mma_tiles",
                "block_swizzle",
                "fold_constants"
              ],
              "loops": [
                {
                  "induction_variable": "kb",
                  "kind": "loop",
                  "lanes": 128,
                  "elements_per_lane": 1,
                  "iteration_step": 16
                },
                {
                  "induction_variable": "kk",
                  "kind": "loop",
                  "lanes": 128,
                  "elements_per_lane": 1,
                  "iteration_step": 8
                }
              ],
              "allocations": [
                {
                  "name": "shared_a_0",
                  "address_space": "threadgroup",
                  "element_type": "float",
                  "elements": 1088,
                  "bytes": 4352
                },
                {
                  "name": "shared_a_1",
                  "address_space": "threadgroup",
                  "element_type": "float",
                  "elements": 1088,
                  "bytes": 4352
                },
                {
                  "name": "shared_b_0",
                  "address_space": "threadgroup",
                  "element_type": "float",
                  "elements": 1040,
                  "bytes": 4160
                },
                {
                  "name": "shared_b_1",
                  "address_space": "threadgroup",
                  "element_type": "float",
                  "elements": 1040,
                  "bytes": 4160
                }
              ],
              "double_buffered": true,
              "vectorized_loads": 0,
              "epilogue_regions": 0,
              "notes": [
                "Layout widths describe emitted Metal operations, not final machine instructions.",
                "Masked tails may use scalar accesses even when aligned interiors are vectorized."
              ],
              "value_layouts": [],
              "layout_conversions": [],
              "pipelines": [
                {
                  "buffers": [
                    {
                      "logical_name": "shared_a",
                      "slots": [
                        "shared_a_0",
                        "shared_a_1"
                      ],
                      "element_type": "float",
                      "elements": 1088,
                      "current_pointer": "sa_curr",
                      "next_pointer": "sa_next"
                    },
                    {
                      "logical_name": "shared_b",
                      "slots": [
                        "shared_b_0",
                        "shared_b_1"
                      ],
                      "element_type": "float",
                      "elements": 1040,
                      "current_pointer": "sb_curr",
                      "next_pointer": "sb_next"
                    }
                  ],
                  "phases": [
                    {
                      "name": "load_first",
                      "region": "prologue",
                      "kind": "copy",
                      "reads": [],
                      "writes": [
                        {
                          "buffer": "shared_a",
                          "slot": "current"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "current"
                        }
                      ],
                      "publishes": [],
                      "recycles": [],
                      "rotates": [],
                      "barrier_scope": null,
                      "barrier_flags": null
                    },
                    {
                      "name": "publish_first",
                      "region": "prologue",
                      "kind": "barrier",
                      "reads": [],
                      "writes": [],
                      "publishes": [
                        {
                          "buffer": "shared_a",
                          "slot": "current"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "current"
                        }
                      ],
                      "recycles": [],
                      "rotates": [],
                      "barrier_scope": "threadgroup",
                      "barrier_flags": "mem_threadgroup"
                    },
                    {
                      "name": "load_next",
                      "region": "steady",
                      "kind": "copy",
                      "reads": [],
                      "writes": [
                        {
                          "buffer": "shared_a",
                          "slot": "next"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "next"
                        }
                      ],
                      "publishes": [],
                      "recycles": [],
                      "rotates": [],
                      "barrier_scope": null,
                      "barrier_flags": null
                    },
                    {
                      "name": "consume_current",
                      "region": "steady",
                      "kind": "compute",
                      "reads": [
                        {
                          "buffer": "shared_a",
                          "slot": "current"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "current"
                        }
                      ],
                      "writes": [],
                      "publishes": [],
                      "recycles": [],
                      "rotates": [],
                      "barrier_scope": null,
                      "barrier_flags": null
                    },
                    {
                      "name": "publish_and_recycle",
                      "region": "steady",
                      "kind": "barrier",
                      "reads": [],
                      "writes": [],
                      "publishes": [
                        {
                          "buffer": "shared_a",
                          "slot": "next"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "next"
                        }
                      ],
                      "recycles": [
                        {
                          "buffer": "shared_a",
                          "slot": "current"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "current"
                        }
                      ],
                      "rotates": [],
                      "barrier_scope": "threadgroup",
                      "barrier_flags": "mem_threadgroup"
                    },
                    {
                      "name": "rotate_slots",
                      "region": "steady",
                      "kind": "rotate",
                      "reads": [],
                      "writes": [],
                      "publishes": [],
                      "recycles": [],
                      "rotates": [
                        "shared_a",
                        "shared_b"
                      ],
                      "barrier_scope": null,
                      "barrier_flags": null
                    },
                    {
                      "name": "consume_last",
                      "region": "drain",
                      "kind": "compute",
                      "reads": [
                        {
                          "buffer": "shared_a",
                          "slot": "current"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "current"
                        }
                      ],
                      "writes": [],
                      "publishes": [],
                      "recycles": [],
                      "rotates": [],
                      "barrier_scope": null,
                      "barrier_flags": null
                    },
                    {
                      "name": "release_last",
                      "region": "drain",
                      "kind": "barrier",
                      "reads": [],
                      "writes": [],
                      "publishes": [],
                      "recycles": [
                        {
                          "buffer": "shared_a",
                          "slot": "current"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "current"
                        }
                      ],
                      "rotates": [],
                      "barrier_scope": "threadgroup",
                      "barrier_flags": "mem_threadgroup"
                    }
                  ],
                  "stages": 2,
                  "mechanism": "software"
                }
              ]
            },
            "timing": {
              "samples": 930,
              "gpu_us": 212.7499901689589,
              "wall_us": 521.979,
              "gpu_min_max_us": [
                210.20829444751143,
                234.9583082832396
              ],
              "wall_min_max_us": [
                307.834,
                2700.0
              ]
            },
            "status": "ok"
          },
          {
            "name": "float32_1024x1024x1024",
            "dtype": "float32",
            "shape": [
              1024,
              1024,
              1024
            ],
            "seed": 437,
            "schedule": {
              "backend": "simdgroup",
              "double_buffer": true,
              "BLOCK_M": 64,
              "BLOCK_N": 64,
              "BLOCK_K": 16,
              "RELAXED_PRECISION": false
            },
            "input_sha256": "16ed3544359adfe6ed4ecc94e89ed08c70fd5aeef3243f80b2009c2096d05f8c",
            "correctness": {
              "reference": "NumPy FP32 matmul rounded to the output storage dtype",
              "max_absolute_error": 0.0,
              "rtol": 0.0003,
              "atol": 3e-05
            },
            "source_sha256": "4be0fb2e516dd502b4eab90ce5d42bc755710fb3331f6f7e4ea2f7c96e11e724",
            "execution_report": {
              "plan": {
                "backend": "simdgroup",
                "threadgroup_size": [
                  128,
                  1,
                  1
                ],
                "simdgroup_grid": [
                  2,
                  2
                ],
                "tile_shape": [
                  64,
                  64,
                  16
                ],
                "staging": "threadgroup",
                "vector_width": null,
                "double_buffer": true,
                "reasons": [
                  "The selected SIMDgroup grid partitions 8x8 accumulator fragments without overlap.",
                  "Cooperative loads stage operand tiles in threadgroup memory."
                ],
                "cooperative_layout": "8x8 simdgroup_matrix fragments",
                "outer_bounds_proven": true
              },
              "passes": [
                "pad_shared_memory",
                "double_buffer_k_loop",
                "vectorize_loads",
                "serpentine_mma",
                "preload_mma_tiles",
                "block_swizzle",
                "fold_constants"
              ],
              "loops": [
                {
                  "induction_variable": "kb",
                  "kind": "loop",
                  "lanes": 128,
                  "elements_per_lane": 1,
                  "iteration_step": 16
                },
                {
                  "induction_variable": "kk",
                  "kind": "loop",
                  "lanes": 128,
                  "elements_per_lane": 1,
                  "iteration_step": 8
                }
              ],
              "allocations": [
                {
                  "name": "shared_a_0",
                  "address_space": "threadgroup",
                  "element_type": "float",
                  "elements": 1088,
                  "bytes": 4352
                },
                {
                  "name": "shared_a_1",
                  "address_space": "threadgroup",
                  "element_type": "float",
                  "elements": 1088,
                  "bytes": 4352
                },
                {
                  "name": "shared_b_0",
                  "address_space": "threadgroup",
                  "element_type": "float",
                  "elements": 1040,
                  "bytes": 4160
                },
                {
                  "name": "shared_b_1",
                  "address_space": "threadgroup",
                  "element_type": "float",
                  "elements": 1040,
                  "bytes": 4160
                }
              ],
              "double_buffered": true,
              "vectorized_loads": 0,
              "epilogue_regions": 0,
              "notes": [
                "Layout widths describe emitted Metal operations, not final machine instructions.",
                "Masked tails may use scalar accesses even when aligned interiors are vectorized."
              ],
              "value_layouts": [],
              "layout_conversions": [],
              "pipelines": [
                {
                  "buffers": [
                    {
                      "logical_name": "shared_a",
                      "slots": [
                        "shared_a_0",
                        "shared_a_1"
                      ],
                      "element_type": "float",
                      "elements": 1088,
                      "current_pointer": "sa_curr",
                      "next_pointer": "sa_next"
                    },
                    {
                      "logical_name": "shared_b",
                      "slots": [
                        "shared_b_0",
                        "shared_b_1"
                      ],
                      "element_type": "float",
                      "elements": 1040,
                      "current_pointer": "sb_curr",
                      "next_pointer": "sb_next"
                    }
                  ],
                  "phases": [
                    {
                      "name": "load_first",
                      "region": "prologue",
                      "kind": "copy",
                      "reads": [],
                      "writes": [
                        {
                          "buffer": "shared_a",
                          "slot": "current"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "current"
                        }
                      ],
                      "publishes": [],
                      "recycles": [],
                      "rotates": [],
                      "barrier_scope": null,
                      "barrier_flags": null
                    },
                    {
                      "name": "publish_first",
                      "region": "prologue",
                      "kind": "barrier",
                      "reads": [],
                      "writes": [],
                      "publishes": [
                        {
                          "buffer": "shared_a",
                          "slot": "current"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "current"
                        }
                      ],
                      "recycles": [],
                      "rotates": [],
                      "barrier_scope": "threadgroup",
                      "barrier_flags": "mem_threadgroup"
                    },
                    {
                      "name": "load_next",
                      "region": "steady",
                      "kind": "copy",
                      "reads": [],
                      "writes": [
                        {
                          "buffer": "shared_a",
                          "slot": "next"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "next"
                        }
                      ],
                      "publishes": [],
                      "recycles": [],
                      "rotates": [],
                      "barrier_scope": null,
                      "barrier_flags": null
                    },
                    {
                      "name": "consume_current",
                      "region": "steady",
                      "kind": "compute",
                      "reads": [
                        {
                          "buffer": "shared_a",
                          "slot": "current"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "current"
                        }
                      ],
                      "writes": [],
                      "publishes": [],
                      "recycles": [],
                      "rotates": [],
                      "barrier_scope": null,
                      "barrier_flags": null
                    },
                    {
                      "name": "publish_and_recycle",
                      "region": "steady",
                      "kind": "barrier",
                      "reads": [],
                      "writes": [],
                      "publishes": [
                        {
                          "buffer": "shared_a",
                          "slot": "next"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "next"
                        }
                      ],
                      "recycles": [
                        {
                          "buffer": "shared_a",
                          "slot": "current"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "current"
                        }
                      ],
                      "rotates": [],
                      "barrier_scope": "threadgroup",
                      "barrier_flags": "mem_threadgroup"
                    },
                    {
                      "name": "rotate_slots",
                      "region": "steady",
                      "kind": "rotate",
                      "reads": [],
                      "writes": [],
                      "publishes": [],
                      "recycles": [],
                      "rotates": [
                        "shared_a",
                        "shared_b"
                      ],
                      "barrier_scope": null,
                      "barrier_flags": null
                    },
                    {
                      "name": "consume_last",
                      "region": "drain",
                      "kind": "compute",
                      "reads": [
                        {
                          "buffer": "shared_a",
                          "slot": "current"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "current"
                        }
                      ],
                      "writes": [],
                      "publishes": [],
                      "recycles": [],
                      "rotates": [],
                      "barrier_scope": null,
                      "barrier_flags": null
                    },
                    {
                      "name": "release_last",
                      "region": "drain",
                      "kind": "barrier",
                      "reads": [],
                      "writes": [],
                      "publishes": [],
                      "recycles": [
                        {
                          "buffer": "shared_a",
                          "slot": "current"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "current"
                        }
                      ],
                      "rotates": [],
                      "barrier_scope": "threadgroup",
                      "barrier_flags": "mem_threadgroup"
                    }
                  ],
                  "stages": 2,
                  "mechanism": "software"
                }
              ]
            },
            "timing": {
              "samples": 415,
              "gpu_us": 976.9166354089975,
              "wall_us": 1198.625,
              "gpu_min_max_us": [
                967.8333881311119,
                1122.9583178646863
              ],
              "wall_min_max_us": [
                1100.625,
                1354.584
              ]
            },
            "status": "ok"
          },
          {
            "name": "float32_257x255x259",
            "dtype": "float32",
            "shape": [
              257,
              255,
              259
            ],
            "seed": 438,
            "schedule": {
              "backend": "simdgroup",
              "double_buffer": true,
              "BLOCK_M": 64,
              "BLOCK_N": 64,
              "BLOCK_K": 16,
              "RELAXED_PRECISION": false
            },
            "input_sha256": "acff8f3e2b353c103ecee705731d3d2c8c26b98f0a80634d1fd4a06c38113a26",
            "correctness": {
              "reference": "NumPy FP32 matmul rounded to the output storage dtype",
              "max_absolute_error": 0.0,
              "rtol": 0.0003,
              "atol": 3e-05
            },
            "source_sha256": "4be0fb2e516dd502b4eab90ce5d42bc755710fb3331f6f7e4ea2f7c96e11e724",
            "execution_report": {
              "plan": {
                "backend": "simdgroup",
                "threadgroup_size": [
                  128,
                  1,
                  1
                ],
                "simdgroup_grid": [
                  2,
                  2
                ],
                "tile_shape": [
                  64,
                  64,
                  16
                ],
                "staging": "threadgroup",
                "vector_width": null,
                "double_buffer": true,
                "reasons": [
                  "The selected SIMDgroup grid partitions 8x8 accumulator fragments without overlap.",
                  "Cooperative loads stage operand tiles in threadgroup memory."
                ],
                "cooperative_layout": "8x8 simdgroup_matrix fragments",
                "outer_bounds_proven": false
              },
              "passes": [
                "pad_shared_memory",
                "double_buffer_k_loop",
                "vectorize_loads",
                "serpentine_mma",
                "preload_mma_tiles",
                "block_swizzle",
                "fold_constants"
              ],
              "loops": [
                {
                  "induction_variable": "kb",
                  "kind": "loop",
                  "lanes": 128,
                  "elements_per_lane": 1,
                  "iteration_step": 16
                },
                {
                  "induction_variable": "kk",
                  "kind": "loop",
                  "lanes": 128,
                  "elements_per_lane": 1,
                  "iteration_step": 8
                }
              ],
              "allocations": [
                {
                  "name": "shared_a_0",
                  "address_space": "threadgroup",
                  "element_type": "float",
                  "elements": 1088,
                  "bytes": 4352
                },
                {
                  "name": "shared_a_1",
                  "address_space": "threadgroup",
                  "element_type": "float",
                  "elements": 1088,
                  "bytes": 4352
                },
                {
                  "name": "shared_b_0",
                  "address_space": "threadgroup",
                  "element_type": "float",
                  "elements": 1040,
                  "bytes": 4160
                },
                {
                  "name": "shared_b_1",
                  "address_space": "threadgroup",
                  "element_type": "float",
                  "elements": 1040,
                  "bytes": 4160
                }
              ],
              "double_buffered": true,
              "vectorized_loads": 0,
              "epilogue_regions": 0,
              "notes": [
                "Layout widths describe emitted Metal operations, not final machine instructions.",
                "Masked tails may use scalar accesses even when aligned interiors are vectorized."
              ],
              "value_layouts": [],
              "layout_conversions": [],
              "pipelines": [
                {
                  "buffers": [
                    {
                      "logical_name": "shared_a",
                      "slots": [
                        "shared_a_0",
                        "shared_a_1"
                      ],
                      "element_type": "float",
                      "elements": 1088,
                      "current_pointer": "sa_curr",
                      "next_pointer": "sa_next"
                    },
                    {
                      "logical_name": "shared_b",
                      "slots": [
                        "shared_b_0",
                        "shared_b_1"
                      ],
                      "element_type": "float",
                      "elements": 1040,
                      "current_pointer": "sb_curr",
                      "next_pointer": "sb_next"
                    }
                  ],
                  "phases": [
                    {
                      "name": "load_first",
                      "region": "prologue",
                      "kind": "copy",
                      "reads": [],
                      "writes": [
                        {
                          "buffer": "shared_a",
                          "slot": "current"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "current"
                        }
                      ],
                      "publishes": [],
                      "recycles": [],
                      "rotates": [],
                      "barrier_scope": null,
                      "barrier_flags": null
                    },
                    {
                      "name": "publish_first",
                      "region": "prologue",
                      "kind": "barrier",
                      "reads": [],
                      "writes": [],
                      "publishes": [
                        {
                          "buffer": "shared_a",
                          "slot": "current"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "current"
                        }
                      ],
                      "recycles": [],
                      "rotates": [],
                      "barrier_scope": "threadgroup",
                      "barrier_flags": "mem_threadgroup"
                    },
                    {
                      "name": "load_next",
                      "region": "steady",
                      "kind": "copy",
                      "reads": [],
                      "writes": [
                        {
                          "buffer": "shared_a",
                          "slot": "next"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "next"
                        }
                      ],
                      "publishes": [],
                      "recycles": [],
                      "rotates": [],
                      "barrier_scope": null,
                      "barrier_flags": null
                    },
                    {
                      "name": "consume_current",
                      "region": "steady",
                      "kind": "compute",
                      "reads": [
                        {
                          "buffer": "shared_a",
                          "slot": "current"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "current"
                        }
                      ],
                      "writes": [],
                      "publishes": [],
                      "recycles": [],
                      "rotates": [],
                      "barrier_scope": null,
                      "barrier_flags": null
                    },
                    {
                      "name": "publish_and_recycle",
                      "region": "steady",
                      "kind": "barrier",
                      "reads": [],
                      "writes": [],
                      "publishes": [
                        {
                          "buffer": "shared_a",
                          "slot": "next"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "next"
                        }
                      ],
                      "recycles": [
                        {
                          "buffer": "shared_a",
                          "slot": "current"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "current"
                        }
                      ],
                      "rotates": [],
                      "barrier_scope": "threadgroup",
                      "barrier_flags": "mem_threadgroup"
                    },
                    {
                      "name": "rotate_slots",
                      "region": "steady",
                      "kind": "rotate",
                      "reads": [],
                      "writes": [],
                      "publishes": [],
                      "recycles": [],
                      "rotates": [
                        "shared_a",
                        "shared_b"
                      ],
                      "barrier_scope": null,
                      "barrier_flags": null
                    },
                    {
                      "name": "consume_last",
                      "region": "drain",
                      "kind": "compute",
                      "reads": [
                        {
                          "buffer": "shared_a",
                          "slot": "current"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "current"
                        }
                      ],
                      "writes": [],
                      "publishes": [],
                      "recycles": [],
                      "rotates": [],
                      "barrier_scope": null,
                      "barrier_flags": null
                    },
                    {
                      "name": "release_last",
                      "region": "drain",
                      "kind": "barrier",
                      "reads": [],
                      "writes": [],
                      "publishes": [],
                      "recycles": [
                        {
                          "buffer": "shared_a",
                          "slot": "current"
                        },
                        {
                          "buffer": "shared_b",
                          "slot": "current"
                        }
                      ],
                      "rotates": [],
                      "barrier_scope": "threadgroup",
                      "barrier_flags": "mem_threadgroup"
                    }
                  ],
                  "stages": 2,
                  "mechanism": "software"
                }
              ]
            },
            "timing": {
              "samples": 1554,
              "gpu_us": 55.145821534097195,
              "wall_us": 277.60400000000004,
              "gpu_min_max_us": [
                45.874970965087414,
                245.95833383500576
              ],
              "wall_min_max_us": [
                142.167,
                603.708
              ]
            },
            "status": "ok"
          }
        ]
      }
    ]
  },
  "comparisons": [
    {
      "name": "float16_64x64x64",
      "shape": [
        64,
        64,
        64
      ],
      "dtype": "float16",
      "status": "ok",
      "gpu_us": {
        "baseline": 64.58269121238443,
        "current": 65.14556968129843,
        "speedup": 0.9913596815306447,
        "samples": {
          "baseline": [
            64.29170025512576,
            64.87499922513962
          ],
          "current": [
            65.33332634717226,
            64.9583525955677
          ]
        }
      },
      "wall_us": {
        "baseline": 367.0158885824973,
        "current": 368.14527821907484,
        "speedup": 0.9969322175146698,
        "samples": {
          "baseline": [
            365.084,
            368.958
          ],
          "current": [
            367.41700000000003,
            368.875
          ]
        }
      },
      "source_sha256": {
        "baseline": "925bd354b757114e81e8fe33b26e1821d01d90e9e0e26ac3dc4207f5dfc30f3b",
        "current": "775bf51864f7fadf5c0a51035e57a2f85c7857b382291cefd60dd69bf86f92d1"
      }
    },
    {
      "name": "float16_256x256x256",
      "shape": [
        256,
        256,
        256
      ],
      "dtype": "float16",
      "status": "ok",
      "gpu_us": {
        "baseline": 191.9374815826498,
        "current": 192.0624644695707,
        "speedup": 0.9993492591732275,
        "samples": {
          "baseline": [
            191.8749767355621,
            192.0000067912042
          ],
          "current": [
            192.16665532439947,
            191.95833010599017
          ]
        }
      },
      "wall_us": {
        "baseline": 502.5178059034324,
        "current": 501.41654060022813,
        "speedup": 1.0021963082866912,
        "samples": {
          "baseline": [
            500.875,
            504.166
          ],
          "current": [
            501.875,
            500.9585
          ]
        }
      },
      "source_sha256": {
        "baseline": "925bd354b757114e81e8fe33b26e1821d01d90e9e0e26ac3dc4207f5dfc30f3b",
        "current": "775bf51864f7fadf5c0a51035e57a2f85c7857b382291cefd60dd69bf86f92d1"
      }
    },
    {
      "name": "float16_1024x1024x1024",
      "shape": [
        1024,
        1024,
        1024
      ],
      "dtype": "float16",
      "status": "ok",
      "gpu_us": {
        "baseline": 817.3958025249793,
        "current": 850.4790126309393,
        "speedup": 0.9611004979374884,
        "samples": {
          "baseline": [
            817.4583199433982,
            817.3332898877561
          ],
          "current": [
            850.9583421982825,
            849.9999530613422
          ]
        }
      },
      "wall_us": {
        "baseline": 1031.083334895875,
        "current": 1058.145909762448,
        "speedup": 0.9744245338786515,
        "samples": {
          "baseline": [
            1031.667,
            1030.5
          ],
          "current": [
            1058.583,
            1057.709
          ]
        }
      },
      "source_sha256": {
        "baseline": "925bd354b757114e81e8fe33b26e1821d01d90e9e0e26ac3dc4207f5dfc30f3b",
        "current": "775bf51864f7fadf5c0a51035e57a2f85c7857b382291cefd60dd69bf86f92d1"
      }
    },
    {
      "name": "float16_257x255x259",
      "shape": [
        257,
        255,
        259
      ],
      "dtype": "float16",
      "status": "ok",
      "gpu_us": {
        "baseline": 57.854072072102824,
        "current": 60.26815770467437,
        "speedup": 0.9599442603770795,
        "samples": {
          "baseline": [
            57.95829929411411,
            57.75003228336573
          ],
          "current": [
            57.999975979328156,
            62.62504030019045
          ]
        }
      },
      "wall_us": {
        "baseline": 280.1130331990998,
        "current": 285.3822280197211,
        "speedup": 0.9815363596493571,
        "samples": {
          "baseline": [
            281.021,
            279.208
          ],
          "current": [
            279.833,
            291.04150000000004
          ]
        }
      },
      "source_sha256": {
        "baseline": "925bd354b757114e81e8fe33b26e1821d01d90e9e0e26ac3dc4207f5dfc30f3b",
        "current": "775bf51864f7fadf5c0a51035e57a2f85c7857b382291cefd60dd69bf86f92d1"
      }
    },
    {
      "name": "float32_64x64x64",
      "shape": [
        64,
        64,
        64
      ],
      "dtype": "float32",
      "status": "ok",
      "gpu_us": {
        "baseline": 68.39572664981074,
        "current": 68.77065422851635,
        "speedup": 0.9945481458201667,
        "samples": {
          "baseline": [
            68.49999772384763,
            68.29161429777741
          ],
          "current": [
            68.62496957182884,
            68.91664816066623
          ]
        }
      },
      "wall_us": {
        "baseline": 372.80972861501346,
        "current": 374.1795075936147,
        "speedup": 0.9963392464023206,
        "samples": {
          "baseline": [
            371.375,
            374.25
          ],
          "current": [
            376.709,
            371.66700000000003
          ]
        }
      },
      "source_sha256": {
        "baseline": "f3f104bd99ff3f71a2487b1d00cfd450cf4ed9085888a27b979798e443a98808",
        "current": "4be0fb2e516dd502b4eab90ce5d42bc755710fb3331f6f7e4ea2f7c96e11e724"
      }
    },
    {
      "name": "float32_256x256x256",
      "shape": [
        256,
        256,
        256
      ],
      "dtype": "float32",
      "status": "ok",
      "gpu_us": {
        "baseline": 212.87495442026582,
        "current": 212.8541272915813,
        "speedup": 1.0000978469572075,
        "samples": {
          "baseline": [
            212.7499901689589,
            212.99999207258224
          ],
          "current": [
            212.9583153873682,
            212.7499901689589
          ]
        }
      },
      "wall_us": {
        "baseline": 520.9370463405346,
        "current": 520.8422622368504,
        "speedup": 1.0001819823592601,
        "samples": {
          "baseline": [
            520.25,
            521.625
          ],
          "current": [
            519.708,
            521.979
          ]
        }
      },
      "source_sha256": {
        "baseline": "f3f104bd99ff3f71a2487b1d00cfd450cf4ed9085888a27b979798e443a98808",
        "current": "4be0fb2e516dd502b4eab90ce5d42bc755710fb3331f6f7e4ea2f7c96e11e724"
      }
    },
    {
      "name": "float32_1024x1024x1024",
      "shape": [
        1024,
        1024,
        1024
      ],
      "dtype": "float32",
      "status": "ok",
      "gpu_us": {
        "baseline": 983.0817260883854,
        "current": 981.9972058657142,
        "speedup": 1.0011044025545013,
        "samples": {
          "baseline": [
            981.2916978262365,
            984.8750196397305
          ],
          "current": [
            987.1041984297335,
            976.9166354089975
          ]
        }
      },
      "wall_us": {
        "baseline": 1200.8528150223067,
        "current": 1199.8014226841874,
        "speedup": 1.000876305293727,
        "samples": {
          "baseline": [
            1199.167,
            1202.541
          ],
          "current": [
            1200.979,
            1198.625
          ]
        }
      },
      "source_sha256": {
        "baseline": "f3f104bd99ff3f71a2487b1d00cfd450cf4ed9085888a27b979798e443a98808",
        "current": "4be0fb2e516dd502b4eab90ce5d42bc755710fb3331f6f7e4ea2f7c96e11e724"
      }
    },
    {
      "name": "float32_257x255x259",
      "shape": [
        257,
        255,
        259
      ],
      "dtype": "float32",
      "status": "ok",
      "gpu_us": {
        "baseline": 57.94712191529367,
        "current": 56.96983186767813,
        "speedup": 1.017154518726428,
        "samples": {
          "baseline": [
            58.2499778829515,
            57.64584057033062
          ],
          "current": [
            58.85417340323329,
            55.145821534097195
          ]
        }
      },
      "wall_us": {
        "baseline": 277.95879310295254,
        "current": 279.2866504471703,
        "speedup": 0.9952455395125699,
        "samples": {
          "baseline": [
            280.29150000000004,
            275.64549999999997
          ],
          "current": [
            280.97950000000003,
            277.60400000000004
          ]
        }
      },
      "source_sha256": {
        "baseline": "f3f104bd99ff3f71a2487b1d00cfd450cf4ed9085888a27b979798e443a98808",
        "current": "4be0fb2e516dd502b4eab90ce5d42bc755710fb3331f6f7e4ea2f7c96e11e724"
      }
    }
  ]
}
