CPU Public API Benchmark Results

Suite: cpu/public_api
Target profile: mac-cpu
Suite file: benchmarks/cpu/public_api.yaml
Public API coverage manifest: benchmarks/cpu/public_api_coverage.yaml
Run metadata: data/results/mac-cpu/cpu/public_api/20260923_210012/run.yaml
Timestamp: 20260923_210012

Latest run: PUBLICATION_GATE_PROFILE=full ./scripts/run_cpu_public_api.sh 1 4.

Sampling: full profile, 15 measured runs, 3 warmups per row

This file is generated from sequential CPU public API runs under data/results/mac-cpu/cpu/public_api/20260923_210012.

tenferro-rs commit: 8a1839febeb3c868a502e26397ca10761bbc568d

CPU Information

Model: Apple M5 Max
Vendor: Apple
Logical CPUs: 18
Physical CPUs: 18
Sockets: 1
Cores per socket: 18
Threads per core: 1
NUMA nodes: 1
Performance levels: Super: 6 physical / 6 logical (L1i 192 KiB, L1d 128 KiB, L2 16 MiB, 6 CPUs/L2); Performance: 12 physical / 12 logical (L1i 128 KiB, L1d 64 KiB, L2 8 MiB, 6 CPUs/L2)
Python platform: macOS-26.5.1-arm64-arm-64bit-Mach-O

Thread Environments

Threads: 1

Run metadata: data/results/mac-cpu/cpu/public_api/20260923_210012/run_t1.yaml
OMP_NUM_THREADS: 1
OMP_THREAD_LIMIT: 1
OMP_DYNAMIC: FALSE
RAYON_NUM_THREADS: 1
OPENBLAS_NUM_THREADS: 1
GOTO_NUM_THREADS: 1
MKL_NUM_THREADS: 1
VECLIB_MAXIMUM_THREADS: 1
VECLIB_NUM_THREADS: 1
NUMEXPR_NUM_THREADS: 1
BLIS_NUM_THREADS: 1
XLA_FLAGS: --xla_cpu_multi_thread_eigen=false intra_op_parallelism_threads=1
JULIA_NUM_THREADS: 1

Threads: 4

Run metadata: data/results/mac-cpu/cpu/public_api/20260923_210012/run_t4.yaml
OMP_NUM_THREADS: 4
OMP_THREAD_LIMIT: 4
OMP_DYNAMIC: FALSE
RAYON_NUM_THREADS: 4
OPENBLAS_NUM_THREADS: 4
GOTO_NUM_THREADS: 4
MKL_NUM_THREADS: 4
VECLIB_MAXIMUM_THREADS: 4
VECLIB_NUM_THREADS: 4
NUMEXPR_NUM_THREADS: 4
BLIS_NUM_THREADS: 4
XLA_FLAGS: --xla_cpu_multi_thread_eigen=true intra_op_parallelism_threads=4
JULIA_NUM_THREADS: 4

Timing Discipline

Input fixture tensors are created during warmup and outside the measured region for tenferro-rs, PyTorch, and JAX.
The tenferro-rs direct column measures immediate public operations (normally concrete Tensor + CpuBackend; lstsq/svd_full use EagerTensor because no concrete spelling exists). It is not labeled as the EagerTensor call layer.
tenferro-rs trace graphs are constructed and compiled outside the measured region; each compiled graph is reused for every warmup and timed run.
JAX functions are compiled with jax.jit during warmup, outside the measured region; timed calls include dispatch through jax.block_until_ready.
Allocation-returning API rows create their output tensor inside each timed call.
cpu/output_reuse rows allocate the destination during warmup and reuse it; tenferro-rs *_into is compared with PyTorch out=/copy_.
Trace mode is unsupported for caller-output rows because compiled tenferro-rs graphs own their output tensors; JAX is shown as missing because it has no equivalent mutable out= API.
PyTorch view-producing indexing operations are cloned inside the timed region to match tenferro-rs owned, materialized outputs.
reshape compares materialized outputs: PyTorch clones its reshape view inside timing to match tenferro-rs' output-sized write; JAX has value semantics and no public strided-view contract.
cpu/view_metadata separately compares concrete tenferro-rs, PyTorch, and Julia (julia-base) view creation without an output-sized copy; trace mode is unsupported and JAX is missing because neither exposes the same concrete strided-view contract.
Julia cpu/view_metadata rows are reshape/transpose/@view lazy wrappers with no output-sized copy; broadcast_in_dim_view has no natural Base spelling and stays missing for Julia.
Julia cpu/output_reuse rows use broadcast-into (.=), mul!, and copyto! with destinations allocated during warmup and reused, the same reuse discipline as the tenferro-rs _into/PyTorch out= rows above.
Rust, PyTorch, and JAX fixtures contain identical logical values. Python/JAX reconstruct the Rust column-major fixture in each framework's native layout before timing.
PyTorch complex conjugation uses torch.conj_physical to match tenferro-rs physical output rather than the lazy conjugate view from torch.conj.
dot_general_with_conj instead uses PyTorch's lazy conjugate view so conjugation can be handled by the contraction, matching tenferro-rs' conjugation flags; trace is unsupported because there is no equivalent public traced API. Julia's dot_general_with_conj row materializes the conjugate before the GEMM instead, since Julia has no lazy conj-without-transpose spelling that BLAS can fuse.
pad has no natural Base spelling and stays missing for Julia.
dynamic_update_slice reports trace mode as unsupported because tenferro-rs does not currently expose a corresponding TracedTensor API.
full_piv_lu and full_piv_lu_solve are excluded because PyTorch has no direct public full-pivot equivalent; substituting torch.linalg.solve would compare different algorithms.
cpu/linalg_batched rows use a batch of 1024 matrices with one rhs column. batched_lu_factor times the packed LU factorization alone. batched_lu_solve reuses LU factors prepared during warmup, outside the measured region, and times only the solve (tenferro-rs LinalgBackend::lu_solve_prepared, PyTorch torch.linalg.lu_solve, JAX jax.scipy.linalg.lu_solve, Julia LAPACK.getrs!). batched_triangular_solve times a lower-triangular solve.
Trace mode is unsupported for batched_lu_factor and batched_lu_solve because LinalgOp is not public, so a trace cannot hold a bare LU factor or prepared solve. The traced solve (LU factor plus prepared solve) and its backward are measured by the cpu/cpu_ops batched_solve and grad_sum_batched_solve_backward rows.
Julia has no batched LAPACK entry point, so the Julia cpu/linalg_batched rows loop the per-matrix LAPACK call over the batch axis and allocate their outputs inside the timed call.
The tenferro-rs runner builds its direct CpuBackend, the trace runtime, and the eager runtime with exactly --num-threads workers, and it fails at startup when a thread environment variable disagrees with that count or when the backend execution scope reports a different Rayon thread count.
svd_full remains in the table even when the selected tenferro-rs provider reports it as unsupported.
Julia is column-major, like tenferro-rs, so the julia-base/strided-jl columns need no PyTorch/JAX-style layout reconstruction to keep the same logical fixture values.
Julia warmup runs move JIT compilation outside the measured region, the same way PyTorch/JAX warmups do.
Julia factorization rows materialize their factors inside the timed call (cholesky returns the factor matrix, lu returns P/L/U, qr returns Q/R). A Julia Factorization keeps its factors packed in LAPACK's working storage, so timing the compact object would compare strictly less work than the tenferro-rs and PyTorch columns, which return separate materialized tensors.
Julia dense linalg rows run through Julia's own BLAS/LAPACK (libblastrampoline, by default OpenBLAS), recorded as julia.blas_provider in the run metadata. When that differs from the provider tenferro-rs and PyTorch link against (Accelerate on macOS), those rows partly compare BLAS implementations rather than framework overhead; read them together with the recorded providers.
The Julia lstsq row uses qr(a) \ rhs rather than a \ rhs: the bare backslash runs a column-pivoted, rank-revealing QR (the LAPACK gelsy algorithm), while the PyTorch row selects the gels driver, so the unpivoted spelling is the like-for-like comparison.
julia-base uses the natural Base/LinearAlgebra spelling and strided-jl the natural Strided.jl (@strided) spelling; each is populated only for rows where that spelling naturally applies (reductions and dense linalg have no natural Strided.jl spelling, so strided-jl covers elementwise/chain/transpose rows, the elementwise cpu/output_reuse _into rows, and the elementwise cpu/complex rows conj/mul/div/exp/log).
Strided.jl (https://github.com/Jutho/Strided.jl) is prior art for tenferro-rs' strided-rs kernel layer; the strided-jl column credits that lineage directly in the report.

Threads: 1 4

CSV: data/results/mac-cpu/cpu/public_api/20260923_210012/cpu_public_api_t1_20260923_210012.csv
CSV: data/results/mac-cpu/cpu/public_api/20260923_210012/cpu_public_api_t4_20260923_210012.csv
Source table: data/results/mac-cpu/cpu/public_api/20260923_210012/cpu_public_api_20260923_210012.md

CPU Benchmark Items

Median ± IQR (ms). Missing backends are shown as -.

suite	benchmark	dtype	threads	shape	tenferro-rs direct API (ms)	tenferro-rs eager mode (ms)	tenferro-rs trace mode (ms)	PyTorch Python (ms)	JAX Python (XLA CPU) (ms)	Julia (Base/LinearAlgebra) (ms)	Julia (Strided.jl) (ms)
cpu/complex	`cholesky`	c64	1	`448x448`	2.422 ± 0.039	-	2.458 ± 0.094	2.851 ± 0.110	0.952 ± 0.024	2.920 ± 0.354	-
cpu/complex	`cholesky`	c64	4	`448x448`	2.498 ± 0.104	-	2.511 ± 0.086	2.493 ± 0.037	0.753 ± 0.024	1.203 ± 0.395	-
cpu/complex	`conj`	c64	1	`16777216`	4.472 ± 0.129	-	4.434 ± 0.208	4.525 ± 0.034	4.467 ± 0.065	4.435 ± 0.036	4.475 ± 0.151
cpu/complex	`conj`	c64	4	`16777216`	1.658 ± 0.073	-	1.616 ± 0.069	1.564 ± 0.043	1.619 ± 0.094	4.458 ± 0.070	5.398 ± 6.306
cpu/complex	`div`	c64	1	`8388608`	5.672 ± 0.078	-	5.735 ± 0.121	8.328 ± 0.318	23.349 ± 0.913	19.351 ± 0.296	18.203 ± 0.154
cpu/complex	`div`	c64	4	`8388608`	1.576 ± 0.061	-	1.801 ± 0.210	2.796 ± 0.061	7.702 ± 0.073	18.569 ± 0.034	8.572 ± 8.821
cpu/complex	`dot_general`	c64	1	`640x640`	5.701 ± 1.293	-	5.658 ± 0.213	5.428 ± 0.194	37.021 ± 0.145	40.291 ± 0.486	-
cpu/complex	`dot_general`	c64	4	`640x640`	6.032 ± 1.307	-	6.114 ± 0.278	5.517 ± 0.181	9.590 ± 0.253	10.982 ± 0.309	-
cpu/complex	`dot_general_with_conj`	c64	1	`640x640`	5.870 ± 0.194	-	unsupported	5.703 ± 0.216	36.640 ± 0.209	40.452 ± 0.657	-
cpu/complex	`dot_general_with_conj`	c64	4	`640x640`	5.831 ± 0.420	-	unsupported	5.658 ± 0.167	9.892 ± 0.111	10.923 ± 0.528	-
cpu/complex	`eig`	c64	1	`112x112`	5.875 ± 0.043	-	5.891 ± 0.061	5.887 ± 0.066	9.927 ± 0.011	5.163 ± 0.060	-
cpu/complex	`eig`	c64	4	`112x112`	5.853 ± 0.075	-	5.976 ± 0.083	5.881 ± 0.037	9.968 ± 0.086	4.860 ± 0.024	-
cpu/complex	`exp`	c64	1	`4194304`	20.508 ± 0.560	-	20.471 ± 0.602	20.121 ± 0.319	24.472 ± 0.648	26.073 ± 0.708	24.998 ± 1.395
cpu/complex	`exp`	c64	4	`4194304`	5.596 ± 0.407	-	5.668 ± 0.039	5.972 ± 0.094	6.354 ± 0.074	25.139 ± 0.941	6.454 ± 0.868
cpu/complex	`log`	c64	1	`4194304`	23.642 ± 0.167	-	23.632 ± 0.154	25.705 ± 0.345	50.111 ± 3.730	35.556 ± 0.471	34.486 ± 0.286
cpu/complex	`log`	c64	4	`4194304`	6.651 ± 0.220	-	6.595 ± 0.301	7.164 ± 0.296	13.738 ± 0.227	35.216 ± 0.147	9.673 ± 2.411
cpu/complex	`mul`	c64	1	`8388608`	4.057 ± 0.214	-	4.000 ± 0.066	4.238 ± 0.057	3.583 ± 0.138	3.685 ± 0.146	3.749 ± 0.135
cpu/complex	`mul`	c64	4	`8388608`	1.374 ± 0.063	-	1.378 ± 0.050	1.452 ± 0.020	1.304 ± 0.082	3.677 ± 0.655	3.588 ± 9.165
cpu/complex	`norm_fro`	c64	1	`2048x1536`	4.793 ± 0.041	-	3.970 ± 0.071	3.700 ± 0.060	1.954 ± 0.015	5.710 ± 0.130	-
cpu/complex	`norm_fro`	c64	4	`2048x1536`	1.987 ± 0.105	-	1.248 ± 0.197	0.936 ± 0.014	0.730 ± 0.048	5.885 ± 0.011	-
cpu/complex	`qr`	c64	1	`256x256`	4.780 ± 0.013	-	4.757 ± 0.026	5.020 ± 0.036	3.640 ± 0.026	6.151 ± 0.156	-
cpu/complex	`qr`	c64	4	`256x256`	4.705 ± 0.034	-	4.838 ± 0.041	4.859 ± 0.033	3.606 ± 0.033	2.793 ± 0.090	-
cpu/complex	`solve`	c64	1	`384x384,rhs=8`	3.001 ± 0.030	-	3.062 ± 0.032	3.171 ± 0.036	1.434 ± 0.007	3.638 ± 0.118	-
cpu/complex	`solve`	c64	4	`384x384,rhs=8`	3.232 ± 0.081	-	3.307 ± 0.156	3.301 ± 0.083	1.327 ± 0.039	1.500 ± 0.024	-
cpu/complex	`svd`	c64	1	`160x160`	3.852 ± 0.051	-	3.971 ± 0.026	3.840 ± 0.063	2.755 ± 0.018	4.566 ± 0.177	-
cpu/complex	`svd`	c64	4	`160x160`	3.950 ± 0.075	-	3.983 ± 0.106	3.838 ± 0.085	2.759 ± 0.034	2.871 ± 0.157	-
cpu/complex	`tensordot`	c64	1	`640x640`	5.564 ± 0.202	-	5.804 ± 0.191	5.387 ± 0.132	36.779 ± 0.526	40.028 ± 0.194	-
cpu/complex	`tensordot`	c64	4	`640x640`	5.639 ± 0.220	-	5.906 ± 0.498	5.667 ± 0.147	9.907 ± 0.240	10.539 ± 0.306	-
cpu/einsum_concrete	`einsum_ij_jk_ik`	f64	1	`1024x1024`	4.972 ± 0.937	-	unsupported	5.064 ± 0.198	32.420 ± 0.124	-	-
cpu/einsum_concrete	`einsum_ij_jk_ik`	f64	4	`1024x1024`	5.341 ± 0.834	-	unsupported	4.942 ± 0.560	9.091 ± 0.097	-	-
cpu/elementwise_reduction	`abs`	f64	1	`33554432`	4.387 ± 0.058	-	4.380 ± 0.075	4.340 ± 0.035	8.534 ± 0.753	4.334 ± 0.092	7.851 ± 0.101
cpu/elementwise_reduction	`abs`	f64	4	`33554432`	1.563 ± 0.036	-	1.598 ± 0.082	1.656 ± 0.081	2.486 ± 0.024	4.449 ± 0.135	2.852 ± 2.904
cpu/elementwise_reduction	`add`	f64	1	`33554432`	6.725 ± 0.248	-	6.429 ± 0.090	6.555 ± 0.385	11.712 ± 0.433	6.562 ± 0.402	8.504 ± 0.531
cpu/elementwise_reduction	`add`	f64	4	`33554432`	4.546 ± 0.152	-	4.255 ± 0.825	2.548 ± 0.164	3.758 ± 0.317	6.639 ± 0.128	7.647 ± 9.189
cpu/elementwise_reduction	`chain_log1p_exp_mul`	f64	1	`4194304`	16.658 ± 0.072	-	42.073 ± 1.059	17.869 ± 0.110	17.962 ± 0.399	21.057 ± 1.792	21.530 ± 1.190
cpu/elementwise_reduction	`chain_log1p_exp_mul`	f64	4	`4194304`	5.538 ± 0.152	-	17.371 ± 0.705	5.122 ± 0.130	4.744 ± 0.053	20.930 ± 0.147	5.972 ± 0.404
cpu/elementwise_reduction	`clamp`	f64	1	`8388608`	2.719 ± 0.030	-	2.746 ± 0.049	2.214 ± 0.058	3.796 ± 0.012	2.302 ± 0.165	3.111 ± 0.207
cpu/elementwise_reduction	`clamp`	f64	4	`8388608`	1.533 ± 0.120	-	1.554 ± 0.018	0.923 ± 0.070	1.912 ± 0.027	2.271 ± 0.135	1.254 ± 1.491
cpu/elementwise_reduction	`compare_lt`	f64	1	`33554432`	5.117 ± 0.036	-	5.135 ± 0.049	8.509 ± 0.102	8.687 ± 0.048	5.830 ± 0.063	-
cpu/elementwise_reduction	`compare_lt`	f64	4	`33554432`	2.057 ± 0.032	-	2.059 ± 0.023	2.989 ± 0.121	2.699 ± 0.050	5.799 ± 0.078	-
cpu/elementwise_reduction	`cos`	f64	1	`8388608`	16.116 ± 0.427	-	16.093 ± 1.042	16.904 ± 0.071	12.474 ± 0.137	20.372 ± 0.203	20.513 ± 0.289
cpu/elementwise_reduction	`cos`	f64	4	`8388608`	4.275 ± 0.196	-	4.258 ± 0.112	4.590 ± 0.331	3.527 ± 0.152	20.298 ± 0.327	5.310 ± 0.425
cpu/elementwise_reduction	`div`	f64	1	`33554432`	6.506 ± 0.079	-	6.627 ± 0.250	6.561 ± 0.131	13.051 ± 1.290	6.389 ± 0.126	8.444 ± 0.627
cpu/elementwise_reduction	`div`	f64	4	`33554432`	2.537 ± 0.214	-	2.520 ± 0.327	2.691 ± 0.143	3.472 ± 0.143	6.580 ± 0.086	3.638 ± 3.229
cpu/elementwise_reduction	`exp`	f64	1	`8388608`	15.938 ± 0.348	-	15.861 ± 0.489	12.192 ± 0.057	10.300 ± 0.034	17.271 ± 0.821	17.181 ± 0.489
cpu/elementwise_reduction	`exp`	f64	4	`8388608`	4.014 ± 0.046	-	4.148 ± 0.169	4.461 ± 0.086	2.835 ± 0.318	17.266 ± 0.428	5.861 ± 0.371
cpu/elementwise_reduction	`expm1`	f64	1	`4194304`	8.485 ± 0.302	-	8.620 ± 0.315	14.606 ± 0.045	10.921 ± 0.050	12.732 ± 0.268	12.762 ± 0.339
cpu/elementwise_reduction	`expm1`	f64	4	`4194304`	2.211 ± 0.055	-	2.214 ± 0.032	4.036 ± 0.405	2.923 ± 0.176	12.638 ± 0.061	3.233 ± 0.348
cpu/elementwise_reduction	`log`	f64	1	`8388608`	15.367 ± 1.625	-	15.409 ± 0.192	20.777 ± 0.169	14.043 ± 0.045	22.423 ± 0.182	22.618 ± 0.435
cpu/elementwise_reduction	`log`	f64	4	`8388608`	4.200 ± 0.150	-	4.315 ± 0.084	7.026 ± 0.134	4.172 ± 0.251	22.442 ± 0.130	6.500 ± 0.625
cpu/elementwise_reduction	`log1p`	f64	1	`4194304`	10.305 ± 0.441	-	10.298 ± 0.178	10.902 ± 0.029	9.912 ± 0.037	12.203 ± 0.272	12.192 ± 0.098
cpu/elementwise_reduction	`log1p`	f64	4	`4194304`	2.743 ± 0.076	-	2.815 ± 0.095	2.944 ± 0.165	2.829 ± 0.132	12.195 ± 0.036	3.137 ± 0.655
cpu/elementwise_reduction	`maximum`	f64	1	`33554432`	6.914 ± 0.228	-	6.888 ± 0.258	6.481 ± 0.073	11.436 ± 0.143	6.461 ± 0.170	8.775 ± 0.319
cpu/elementwise_reduction	`maximum`	f64	4	`33554432`	2.511 ± 0.061	-	2.421 ± 0.030	2.949 ± 0.245	3.453 ± 0.099	6.562 ± 0.058	3.249 ± 2.405
cpu/elementwise_reduction	`minimum`	f64	1	`33554432`	7.003 ± 0.387	-	6.610 ± 0.086	6.423 ± 0.064	11.503 ± 0.112	6.545 ± 0.092	8.903 ± 0.261
cpu/elementwise_reduction	`minimum`	f64	4	`33554432`	2.494 ± 0.010	-	2.522 ± 0.042	3.015 ± 0.591	3.398 ± 0.124	6.573 ± 0.090	3.095 ± 2.659
cpu/elementwise_reduction	`mul`	f64	1	`33554432`	6.709 ± 0.182	-	6.593 ± 0.103	6.582 ± 0.198	11.720 ± 0.219	6.481 ± 0.103	8.723 ± 0.962
cpu/elementwise_reduction	`mul`	f64	4	`33554432`	2.508 ± 0.087	-	2.491 ± 0.133	2.676 ± 0.140	3.429 ± 0.178	6.606 ± 0.084	3.537 ± 9.086
cpu/elementwise_reduction	`neg`	f64	1	`33554432`	4.303 ± 0.031	-	4.298 ± 0.070	4.327 ± 0.027	9.283 ± 1.215	4.379 ± 0.097	7.809 ± 0.046
cpu/elementwise_reduction	`neg`	f64	4	`33554432`	1.559 ± 0.022	-	1.579 ± 0.015	1.671 ± 0.174	2.522 ± 0.076	4.450 ± 0.095	3.152 ± 2.774
cpu/elementwise_reduction	`pow`	f64	1	`4194304`	18.044 ± 0.075	-	17.780 ± 0.116	38.118 ± 0.260	17.545 ± 0.054	31.856 ± 2.761	31.379 ± 0.581
cpu/elementwise_reduction	`pow`	f64	4	`4194304`	5.015 ± 0.547	-	4.977 ± 0.102	11.319 ± 1.706	4.985 ± 0.259	31.913 ± 1.508	8.502 ± 0.609
cpu/elementwise_reduction	`reduce_max_all`	f64	1	`8192x4096`	4.233 ± 0.184	-	4.100 ± 0.045	7.538 ± 0.230	10.131 ± 0.142	2.922 ± 0.047	-
cpu/elementwise_reduction	`reduce_max_all`	f64	4	`8192x4096`	1.721 ± 0.213	-	1.685 ± 0.162	1.996 ± 0.007	2.990 ± 0.013	2.986 ± 0.101	-
cpu/elementwise_reduction	`reduce_max_axis0`	f64	1	`2048x2048`	0.882 ± 0.042	-	0.723 ± 0.059	9.755 ± 1.479	0.954 ± 0.078	0.455 ± 0.180	-
cpu/elementwise_reduction	`reduce_max_axis0`	f64	4	`2048x2048`	0.293 ± 0.021	-	0.268 ± 0.034	4.837 ± 0.488	0.343 ± 0.042	0.382 ± 0.020	-
cpu/elementwise_reduction	`reduce_max_axis1`	f64	1	`2048x2048`	0.679 ± 0.078	-	0.677 ± 0.037	0.974 ± 0.038	0.388 ± 0.013	0.486 ± 0.005	-
cpu/elementwise_reduction	`reduce_max_axis1`	f64	4	`2048x2048`	0.245 ± 0.045	-	0.260 ± 0.017	0.296 ± 0.020	0.238 ± 0.010	0.498 ± 0.013	-
cpu/elementwise_reduction	`reduce_min_all`	f64	1	`8192x4096`	4.149 ± 0.030	-	4.180 ± 0.071	7.469 ± 0.142	10.145 ± 0.192	2.886 ± 0.020	-
cpu/elementwise_reduction	`reduce_min_all`	f64	4	`8192x4096`	1.513 ± 0.101	-	1.591 ± 0.262	1.996 ± 0.012	3.017 ± 0.048	2.986 ± 0.113	-
cpu/elementwise_reduction	`reduce_min_axis0`	f64	1	`2048x2048`	0.544 ± 0.019	-	0.535 ± 0.012	8.845 ± 0.061	1.033 ± 0.111	0.364 ± 0.009	-
cpu/elementwise_reduction	`reduce_min_axis0`	f64	4	`2048x2048`	0.161 ± 0.018	-	0.168 ± 0.011	4.634 ± 0.041	0.356 ± 0.039	0.360 ± 0.008	-
cpu/elementwise_reduction	`reduce_min_axis1`	f64	1	`4096x4096`	2.645 ± 0.108	-	2.569 ± 0.092	3.891 ± 0.225	1.560 ± 0.021	1.922 ± 0.030	-
cpu/elementwise_reduction	`reduce_min_axis1`	f64	4	`4096x4096`	1.067 ± 0.095	-	0.970 ± 0.052	1.056 ± 0.032	0.881 ± 0.059	1.910 ± 0.075	-
cpu/elementwise_reduction	`reduce_prod_all`	f64	1	`8192x4096`	3.305 ± 0.272	-	3.363 ± 0.052	3.159 ± 0.019	18.148 ± 0.307	3.022 ± 0.022	-
cpu/elementwise_reduction	`reduce_prod_all`	f64	4	`8192x4096`	1.560 ± 0.346	-	1.452 ± 0.271	1.110 ± 0.147	5.392 ± 0.044	3.134 ± 0.152	-
cpu/elementwise_reduction	`reduce_prod_axis0`	f64	1	`2048x2048`	0.370 ± 0.004	-	0.382 ± 0.003	1.513 ± 0.108	1.005 ± 0.064	0.404 ± 0.018	-
cpu/elementwise_reduction	`reduce_prod_axis0`	f64	4	`2048x2048`	0.128 ± 0.007	-	0.138 ± 0.011	0.676 ± 0.019	0.313 ± 0.086	0.377 ± 0.014	-
cpu/elementwise_reduction	`reduce_prod_axis1`	f64	1	`2048x2048`	0.453 ± 0.018	-	0.474 ± 0.016	0.341 ± 0.002	0.386 ± 0.006	0.625 ± 0.342	-
cpu/elementwise_reduction	`reduce_prod_axis1`	f64	4	`2048x2048`	0.179 ± 0.006	-	0.206 ± 0.012	0.123 ± 0.015	0.246 ± 0.016	0.498 ± 0.010	-
cpu/elementwise_reduction	`reduce_sum_all`	f64	1	`8192x4096`	3.295 ± 0.207	-	3.146 ± 0.072	2.920 ± 0.022	13.890 ± 0.266	2.911 ± 0.043	-
cpu/elementwise_reduction	`reduce_sum_all`	f64	4	`8192x4096`	1.722 ± 0.156	-	1.832 ± 0.135	1.065 ± 0.040	4.478 ± 0.024	3.058 ± 0.052	-
cpu/elementwise_reduction	`reduce_sum_axis0`	f64	1	`2048x2048`	0.377 ± 0.012	-	0.365 ± 0.007	1.276 ± 0.037	0.829 ± 0.030	0.385 ± 0.027	-
cpu/elementwise_reduction	`reduce_sum_axis0`	f64	4	`2048x2048`	0.167 ± 0.011	-	0.144 ± 0.006	0.621 ± 0.009	0.342 ± 0.037	0.382 ± 0.013	-
cpu/elementwise_reduction	`reduce_sum_axis1`	f64	1	`2048x2048`	0.473 ± 0.022	-	0.474 ± 0.030	0.305 ± 0.004	0.375 ± 0.006	0.494 ± 0.028	-
cpu/elementwise_reduction	`reduce_sum_axis1`	f64	4	`2048x2048`	0.168 ± 0.008	-	0.202 ± 0.015	0.120 ± 0.015	0.249 ± 0.040	0.485 ± 0.009	-
cpu/elementwise_reduction	`rem`	f64	1	`8388608`	16.070 ± 0.671	-	15.765 ± 0.739	19.250 ± 0.091	14.658 ± 0.358	13.568 ± 3.444	13.580 ± 1.011
cpu/elementwise_reduction	`rem`	f64	4	`8388608`	4.404 ± 0.830	-	4.251 ± 1.962	6.432 ± 0.082	6.506 ± 1.816	13.710 ± 0.975	3.853 ± 1.607
cpu/elementwise_reduction	`rsqrt`	f64	1	`33554432`	12.206 ± 0.130	-	12.138 ± 0.316	11.301 ± 0.052	22.960 ± 0.397	24.291 ± 0.351	23.263 ± 0.828
cpu/elementwise_reduction	`rsqrt`	f64	4	`33554432`	3.077 ± 0.031	-	3.068 ± 0.013	3.137 ± 0.101	6.154 ± 0.039	23.506 ± 0.220	6.571 ± 2.512
cpu/elementwise_reduction	`select`	f64	1	`33554432`	8.388 ± 1.905	-	8.384 ± 0.060	9.094 ± 0.159	14.040 ± 0.056	7.842 ± 0.179	-
cpu/elementwise_reduction	`select`	f64	4	`33554432`	3.719 ± 0.115	-	3.749 ± 0.107	3.686 ± 0.086	5.928 ± 1.504	7.826 ± 0.068	-
cpu/elementwise_reduction	`sign`	f64	1	`33554432`	5.220 ± 0.115	-	5.252 ± 0.281	5.028 ± 0.073	9.917 ± 0.122	4.424 ± 0.082	11.769 ± 0.147
cpu/elementwise_reduction	`sign`	f64	4	`33554432`	3.204 ± 0.047	-	3.200 ± 0.072	1.796 ± 0.074	3.294 ± 0.032	4.459 ± 0.125	3.261 ± 2.418
cpu/elementwise_reduction	`sin`	f64	1	`8388608`	14.688 ± 0.119	-	14.747 ± 1.510	14.137 ± 0.030	11.180 ± 0.234	17.361 ± 0.210	17.620 ± 0.276
cpu/elementwise_reduction	`sin`	f64	4	`8388608`	3.969 ± 0.122	-	4.082 ± 0.207	5.036 ± 0.029	3.337 ± 0.394	17.291 ± 0.337	4.401 ± 0.435
cpu/elementwise_reduction	`sqrt`	f64	1	`33554432`	8.015 ± 0.268	-	7.948 ± 0.071	7.565 ± 0.128	8.487 ± 1.129	15.838 ± 0.356	15.902 ± 0.180
cpu/elementwise_reduction	`sqrt`	f64	4	`33554432`	2.018 ± 0.027	-	2.037 ± 0.047	2.036 ± 0.049	2.483 ± 0.067	15.638 ± 0.065	4.129 ± 2.698
cpu/elementwise_reduction	`sub`	f64	1	`33554432`	6.470 ± 0.081	-	6.502 ± 0.044	6.493 ± 0.060	11.602 ± 0.094	6.467 ± 0.150	8.622 ± 0.506
cpu/elementwise_reduction	`sub`	f64	4	`33554432`	2.506 ± 0.086	-	2.524 ± 0.099	2.603 ± 0.355	3.533 ± 0.260	6.600 ± 0.119	3.260 ± 2.618
cpu/elementwise_reduction	`tanh`	f64	1	`8388608`	21.278 ± 0.083	-	21.207 ± 0.077	35.378 ± 0.087	8.376 ± 0.055	23.354 ± 0.206	23.374 ± 0.232
cpu/elementwise_reduction	`tanh`	f64	4	`8388608`	5.495 ± 0.150	-	5.519 ± 0.106	9.505 ± 0.325	2.470 ± 0.474	23.838 ± 0.122	6.508 ± 0.641
cpu/indexing_layout	`concatenate`	f64	1	`1048576+1048576`	0.282 ± 0.022	-	0.560 ± 0.020	0.215 ± 0.017	0.223 ± 0.006	0.290 ± 0.015	-
cpu/indexing_layout	`concatenate`	f64	4	`1048576+1048576`	0.108 ± 0.017	-	0.293 ± 0.021	0.122 ± 0.047	0.232 ± 0.008	0.300 ± 0.075	-
cpu/indexing_layout	`dynamic_slice`	f64	1	`4194304 -> 2097152`	0.259 ± 0.051	-	0.864 ± 0.083	0.266 ± 0.014	0.264 ± 0.004	0.280 ± 0.014	-
cpu/indexing_layout	`dynamic_slice`	f64	4	`4194304 -> 2097152`	0.150 ± 0.014	-	0.474 ± 0.010	0.083 ± 0.002	0.123 ± 0.038	0.295 ± 0.008	-
cpu/indexing_layout	`dynamic_update_slice`	f64	1	`2097152`	0.402 ± 0.096	-	unsupported	0.407 ± 0.020	0.372 ± 0.007	0.411 ± 0.179	-
cpu/indexing_layout	`dynamic_update_slice`	f64	4	`2097152`	0.177 ± 0.009	-	unsupported	0.156 ± 0.001	0.302 ± 0.009	0.405 ± 0.004	-
cpu/indexing_layout	`gather`	f64	1	`262144`	0.338 ± 0.174	-	0.336 ± 0.152	0.161 ± 0.006	0.183 ± 0.009	0.282 ± 0.019	-
cpu/indexing_layout	`gather`	f64	4	`262144`	0.278 ± 0.018	-	0.311 ± 0.034	0.176 ± 0.001	0.080 ± 0.011	0.286 ± 0.148	-
cpu/indexing_layout	`pad`	f64	1	`2097152`	0.359 ± 0.024	-	0.671 ± 0.106	0.399 ± 0.006	0.284 ± 0.001	-	-
cpu/indexing_layout	`pad`	f64	4	`2097152`	0.172 ± 0.016	-	0.365 ± 0.018	0.170 ± 0.002	0.149 ± 0.034	-	-
cpu/indexing_layout	`reverse`	f64	1	`2097152`	0.279 ± 0.011	-	0.587 ± 0.123	0.276 ± 0.062	0.269 ± 0.010	0.729 ± 0.227	-
cpu/indexing_layout	`reverse`	f64	4	`2097152`	0.098 ± 0.004	-	0.282 ± 0.016	0.113 ± 0.011	0.114 ± 0.015	0.618 ± 0.009	-
cpu/indexing_layout	`scatter`	f64	1	`262144`	0.355 ± 0.040	-	0.474 ± 0.033	0.230 ± 0.005	0.230 ± 0.008	0.229 ± 0.037	-
cpu/indexing_layout	`scatter`	f64	4	`262144`	0.489 ± 0.011	-	0.551 ± 0.027	0.344 ± 0.007	0.216 ± 0.006	0.220 ± 0.053	-
cpu/indexing_layout	`slice`	f64	1	`4194304 -> 2096128`	0.513 ± 0.021	-	1.091 ± 0.145	0.419 ± 0.003	0.417 ± 0.003	0.676 ± 0.046	-
cpu/indexing_layout	`slice`	f64	4	`4194304 -> 2096128`	0.220 ± 0.015	-	0.581 ± 0.031	0.141 ± 0.040	0.287 ± 0.029	0.666 ± 0.019	-
cpu/linalg_batched	`batched_lu_factor`	f64	1	`1024x16x16,rhs=1`	0.792 ± 0.046	-	unsupported	0.473 ± 0.008	0.563 ± 0.016	1.087 ± 0.054	-
cpu/linalg_batched	`batched_lu_factor`	f64	1	`1024x2x2,rhs=1`	0.032 ± 0.001	-	unsupported	0.034 ± 0.001	0.070 ± 0.003	0.041 ± 0.003	-
cpu/linalg_batched	`batched_lu_factor`	f64	1	`1024x4x4,rhs=1`	0.067 ± 0.001	-	unsupported	0.060 ± 0.003	0.095 ± 0.003	0.071 ± 0.012	-
cpu/linalg_batched	`batched_lu_factor`	f64	1	`1024x8x8,rhs=1`	0.274 ± 0.140	-	unsupported	0.159 ± 0.004	0.198 ± 0.004	0.246 ± 0.007	-
cpu/linalg_batched	`batched_lu_factor`	f64	4	`1024x16x16,rhs=1`	0.695 ± 0.059	-	unsupported	0.200 ± 0.014	0.301 ± 0.010	1.009 ± 0.147	-
cpu/linalg_batched	`batched_lu_factor`	f64	4	`1024x2x2,rhs=1`	0.046 ± 0.000	-	unsupported	0.108 ± 0.038	0.067 ± 0.002	0.043 ± 0.002	-
cpu/linalg_batched	`batched_lu_factor`	f64	4	`1024x4x4,rhs=1`	0.086 ± 0.002	-	unsupported	0.086 ± 0.032	0.098 ± 0.002	0.086 ± 0.009	-
cpu/linalg_batched	`batched_lu_factor`	f64	4	`1024x8x8,rhs=1`	0.316 ± 0.021	-	unsupported	0.139 ± 0.009	0.106 ± 0.005	0.247 ± 0.007	-
cpu/linalg_batched	`batched_lu_solve`	f64	1	`1024x16x16,rhs=1`	0.195 ± 0.004	-	unsupported	0.119 ± 0.005	0.268 ± 0.014	0.182 ± 0.006	-
cpu/linalg_batched	`batched_lu_solve`	f64	1	`1024x2x2,rhs=1`	0.049 ± 0.001	-	unsupported	0.023 ± 0.000	0.040 ± 0.001	0.026 ± 0.000	-
cpu/linalg_batched	`batched_lu_solve`	f64	1	`1024x4x4,rhs=1`	0.058 ± 0.000	-	unsupported	0.027 ± 0.000	0.050 ± 0.002	0.044 ± 0.001	-
cpu/linalg_batched	`batched_lu_solve`	f64	1	`1024x8x8,rhs=1`	0.086 ± 0.001	-	unsupported	0.050 ± 0.003	0.090 ± 0.008	0.092 ± 0.005	-
cpu/linalg_batched	`batched_lu_solve`	f64	4	`1024x16x16,rhs=1`	0.178 ± 0.004	-	unsupported	0.125 ± 0.018	0.228 ± 0.008	0.182 ± 0.001	-
cpu/linalg_batched	`batched_lu_solve`	f64	4	`1024x2x2,rhs=1`	0.038 ± 0.001	-	unsupported	0.024 ± 0.000	0.035 ± 0.003	0.026 ± 0.000	-
cpu/linalg_batched	`batched_lu_solve`	f64	4	`1024x4x4,rhs=1`	0.045 ± 0.004	-	unsupported	0.028 ± 0.000	0.046 ± 0.002	0.047 ± 0.002	-
cpu/linalg_batched	`batched_lu_solve`	f64	4	`1024x8x8,rhs=1`	0.069 ± 0.000	-	unsupported	0.048 ± 0.002	0.083 ± 0.002	0.081 ± 0.005	-
cpu/linalg_batched	`batched_triangular_solve`	f64	1	`1024x16x16,rhs=1`	0.062 ± 0.003	-	0.117 ± 0.002	0.048 ± 0.000	0.108 ± 0.002	0.113 ± 0.003	-
cpu/linalg_batched	`batched_triangular_solve`	f64	1	`1024x2x2,rhs=1`	0.025 ± 0.000	-	0.033 ± 0.002	0.012 ± 0.000	0.013 ± 0.000	0.021 ± 0.001	-
cpu/linalg_batched	`batched_triangular_solve`	f64	1	`1024x4x4,rhs=1`	0.026 ± 0.003	-	0.035 ± 0.000	0.015 ± 0.000	0.017 ± 0.000	0.033 ± 0.001	-
cpu/linalg_batched	`batched_triangular_solve`	f64	1	`1024x8x8,rhs=1`	0.031 ± 0.000	-	0.049 ± 0.000	0.020 ± 0.000	0.033 ± 0.001	0.058 ± 0.002	-
cpu/linalg_batched	`batched_triangular_solve`	f64	4	`1024x16x16,rhs=1`	0.057 ± 0.000	-	0.108 ± 0.019	0.048 ± 0.001	0.090 ± 0.008	0.112 ± 0.005	-
cpu/linalg_batched	`batched_triangular_solve`	f64	4	`1024x2x2,rhs=1`	0.022 ± 0.000	-	0.048 ± 0.009	0.017 ± 0.002	0.013 ± 0.001	0.022 ± 0.000	-
cpu/linalg_batched	`batched_triangular_solve`	f64	4	`1024x4x4,rhs=1`	0.023 ± 0.000	-	0.054 ± 0.006	0.014 ± 0.001	0.016 ± 0.000	0.035 ± 0.000	-
cpu/linalg_batched	`batched_triangular_solve`	f64	4	`1024x8x8,rhs=1`	0.028 ± 0.000	-	0.069 ± 0.008	0.019 ± 0.001	0.045 ± 0.007	0.061 ± 0.002	-
cpu/linalg_uncovered	`cholesky`	f64	1	`1536x1536`	4.264 ± 0.373	-	5.080 ± 0.483	14.805 ± 0.113	8.825 ± 0.201	26.077 ± 2.957	-
cpu/linalg_uncovered	`cholesky`	f64	4	`1536x1536`	4.474 ± 0.822	-	4.503 ± 0.226	10.602 ± 5.197	6.103 ± 0.181	10.802 ± 12.418	-
cpu/linalg_uncovered	`det`	f64	1	`1024x1024`	4.098 ± 0.041	-	4.119 ± 0.033	4.311 ± 0.105	4.076 ± 0.019	13.641 ± 0.418	-
cpu/linalg_uncovered	`det`	f64	4	`1024x1024`	4.380 ± 0.200	-	4.011 ± 0.190	3.966 ± 0.052	4.050 ± 0.649	5.050 ± 0.274	-
cpu/linalg_uncovered	`eig`	f64	1	`160x160`	4.462 ± 0.205	-	4.472 ± 0.432	4.471 ± 0.042	5.298 ± 0.064	4.013 ± 0.052	-
cpu/linalg_uncovered	`eig`	f64	4	`160x160`	4.460 ± 0.070	-	4.466 ± 0.048	4.439 ± 0.051	5.444 ± 0.097	4.133 ± 0.057	-
cpu/linalg_uncovered	`eigvals`	f64	1	`192x192`	4.616 ± 0.067	-	4.650 ± 0.127	4.614 ± 0.033	4.271 ± 0.062	4.431 ± 0.042	-
cpu/linalg_uncovered	`eigvals`	f64	4	`192x192`	4.623 ± 0.071	-	4.656 ± 0.041	4.661 ± 0.034	4.239 ± 0.036	4.506 ± 0.040	-
cpu/linalg_uncovered	`eigvalsh`	f64	1	`512x512`	14.927 ± 0.537	-	15.083 ± 0.194	14.115 ± 0.738	12.581 ± 0.099	10.840 ± 0.124	-
cpu/linalg_uncovered	`eigvalsh`	f64	4	`512x512`	14.005 ± 0.340	-	14.774 ± 0.362	14.918 ± 0.126	12.705 ± 0.615	6.516 ± 0.061	-
cpu/linalg_uncovered	`inv`	f64	1	`768x768`	6.073 ± 0.073	-	5.194 ± 0.218	6.439 ± 0.722	5.479 ± 0.031	19.096 ± 0.153	-
cpu/linalg_uncovered	`inv`	f64	4	`768x768`	6.202 ± 0.159	-	5.248 ± 0.124	5.472 ± 0.164	5.110 ± 0.136	6.448 ± 0.262	-
cpu/linalg_uncovered	`lstsq`	f64	1	`768x384,rhs=16`	-	5.635 ± 0.037	5.549 ± 0.049	3.241 ± 0.035	13.559 ± 0.035	5.208 ± 0.033	-
cpu/linalg_uncovered	`lstsq`	f64	4	`768x384,rhs=16`	-	5.695 ± 0.058	5.585 ± 0.029	3.165 ± 0.023	13.264 ± 0.184	3.082 ± 0.044	-
cpu/linalg_uncovered	`lu`	f64	1	`1024x1024`	4.154 ± 0.359	-	4.250 ± 0.235	7.101 ± 0.461	6.650 ± 0.051	15.499 ± 3.476	-
cpu/linalg_uncovered	`lu`	f64	4	`1024x1024`	4.180 ± 0.304	-	4.346 ± 0.326	5.171 ± 0.065	5.507 ± 0.544	7.396 ± 2.693	-
cpu/linalg_uncovered	`norm_fro`	f64	1	`2048x2048`	0.362 ± 0.003	-	0.366 ± 0.020	1.270 ± 0.043	2.858 ± 0.227	3.744 ± 0.111	-
cpu/linalg_uncovered	`norm_fro`	f64	4	`2048x2048`	0.156 ± 0.033	-	0.176 ± 0.036	1.273 ± 0.013	0.816 ± 0.045	3.920 ± 0.006	-
cpu/linalg_uncovered	`pinv`	f64	1	`512x256`	6.601 ± 0.046	-	6.504 ± 0.106	6.680 ± 0.650	7.319 ± 0.057	12.944 ± 0.201	-
cpu/linalg_uncovered	`pinv`	f64	4	`512x256`	6.674 ± 0.104	-	6.740 ± 0.105	6.683 ± 0.129	6.525 ± 0.103	9.479 ± 0.070	-
cpu/linalg_uncovered	`pinv_with_rtol`	f64	1	`512x256`	6.560 ± 0.025	-	6.445 ± 0.038	6.814 ± 0.402	7.294 ± 0.076	12.896 ± 0.066	-
cpu/linalg_uncovered	`pinv_with_rtol`	f64	4	`512x256`	6.580 ± 0.112	-	6.733 ± 0.063	6.486 ± 0.055	6.569 ± 0.122	9.411 ± 0.136	-
cpu/linalg_uncovered	`slogdet`	f64	1	`1024x1024`	4.111 ± 0.043	-	4.109 ± 0.036	4.476 ± 0.409	4.093 ± 0.016	13.485 ± 0.142	-
cpu/linalg_uncovered	`slogdet`	f64	4	`1024x1024`	4.272 ± 0.190	-	4.083 ± 0.192	3.972 ± 0.252	3.900 ± 0.186	5.127 ± 0.329	-
cpu/linalg_uncovered	`svd_full`	f64	1	`768x384`	-	18.337 ± 0.193	18.630 ± 0.179	18.578 ± 0.256	18.739 ± 0.041	44.442 ± 0.388	-
cpu/linalg_uncovered	`svd_full`	f64	4	`768x384`	-	18.859 ± 0.261	18.920 ± 0.273	18.848 ± 0.337	18.683 ± 0.178	29.169 ± 0.155	-
cpu/linalg_uncovered	`triangular_solve`	f64	1	`4096x4096,rhs=64`	5.768 ± 0.438	-	7.797 ± 0.291	3.923 ± 0.052	24.834 ± 0.138	20.770 ± 0.135	-
cpu/linalg_uncovered	`triangular_solve`	f64	4	`4096x4096,rhs=64`	5.606 ± 0.336	-	7.142 ± 0.326	3.780 ± 0.023	12.516 ± 0.478	7.188 ± 0.223	-
cpu/output_reuse	`add_into`	f64	1	`33554432`	6.409 ± 0.105	-	unsupported	6.485 ± 0.069	-	6.518 ± 0.211	8.303 ± 0.618
cpu/output_reuse	`add_into`	f64	4	`33554432`	2.610 ± 0.178	-	unsupported	2.525 ± 0.145	-	6.471 ± 0.042	3.155 ± 0.245
cpu/output_reuse	`conj_into`	c64	1	`16777216`	4.341 ± 0.039	-	unsupported	4.498 ± 0.020	-	4.334 ± 0.032	4.336 ± 0.041
cpu/output_reuse	`conj_into`	c64	4	`16777216`	1.637 ± 0.051	-	unsupported	1.563 ± 0.046	-	4.332 ± 0.036	1.752 ± 0.184
cpu/output_reuse	`copy_read_into`	f64	1	`33554432`	3.878 ± 0.092	-	unsupported	4.337 ± 0.088	-	3.787 ± 0.081	-
cpu/output_reuse	`copy_read_into`	f64	4	`33554432`	1.556 ± 0.019	-	unsupported	1.528 ± 0.009	-	3.821 ± 0.044	-
cpu/output_reuse	`div_into`	f64	1	`33554432`	6.483 ± 0.119	-	unsupported	6.428 ± 0.076	-	6.421 ± 0.130	8.707 ± 0.544
cpu/output_reuse	`div_into`	f64	4	`33554432`	2.562 ± 0.288	-	unsupported	2.467 ± 0.023	-	6.458 ± 0.064	3.222 ± 0.120
cpu/output_reuse	`dot_general_read_into`	f64	1	`1024x1024`	4.444 ± 0.050	-	unsupported	4.620 ± 0.157	-	35.864 ± 0.208	-
cpu/output_reuse	`dot_general_read_into`	f64	4	`1024x1024`	4.512 ± 0.069	-	unsupported	4.630 ± 0.081	-	9.746 ± 0.277	-
cpu/output_reuse	`dot_general_read_into_accum`	f64	1	`1024x1024`	4.671 ± 0.017	-	unsupported	4.876 ± 0.135	-	35.790 ± 0.104	-
cpu/output_reuse	`dot_general_read_into_accum`	f64	4	`1024x1024`	4.917 ± 0.100	-	unsupported	5.107 ± 0.271	-	9.534 ± 0.252	-
cpu/output_reuse	`mul_into`	f64	1	`33554432`	6.510 ± 0.115	-	unsupported	6.443 ± 0.049	-	6.413 ± 0.096	8.333 ± 0.531
cpu/output_reuse	`mul_into`	f64	4	`33554432`	2.505 ± 0.143	-	unsupported	2.474 ± 0.016	-	6.455 ± 0.031	3.202 ± 0.129
cpu/output_reuse	`neg_into`	f64	1	`33554432`	4.321 ± 0.036	-	unsupported	4.333 ± 0.039	-	4.330 ± 0.040	7.947 ± 0.284
cpu/output_reuse	`neg_into`	f64	4	`33554432`	1.577 ± 0.056	-	unsupported	1.526 ± 0.009	-	4.377 ± 0.053	2.695 ± 0.763
cpu/output_reuse	`sub_into`	f64	1	`33554432`	6.394 ± 0.080	-	unsupported	6.513 ± 0.120	-	6.435 ± 0.110	8.341 ± 0.463
cpu/output_reuse	`sub_into`	f64	4	`33554432`	2.487 ± 0.106	-	unsupported	2.466 ± 0.022	-	6.462 ± 0.046	3.140 ± 0.069
cpu/structural_shape	`broadcast_in_dim`	f64	1	`8192x1 -> 8192x4096`	3.304 ± 0.075	-	2.021 ± 0.015	2.051 ± 0.086	1.929 ± 0.088	8.571 ± 0.105	-
cpu/structural_shape	`broadcast_in_dim`	f64	4	`8192x1 -> 8192x4096`	1.900 ± 0.026	-	1.974 ± 0.054	1.078 ± 0.008	0.931 ± 0.067	8.519 ± 0.115	-
cpu/structural_shape	`cast_f64_f32`	f64->f32	1	`33554432`	3.501 ± 0.021	-	7.863 ± 0.128	3.541 ± 0.019	4.858 ± 0.808	3.677 ± 0.428	-
cpu/structural_shape	`cast_f64_f32`	f64->f32	4	`33554432`	1.355 ± 0.071	-	2.898 ± 0.069	1.317 ± 0.059	1.386 ± 0.078	3.687 ± 0.076	-
cpu/structural_shape	`embed_diagonal`	f64	1	`8192 -> 8192x8192`	3.775 ± 0.053	-	3.768 ± 0.091	3.969 ± 0.042	5.980 ± 0.025	2.044 ± 0.108	-
cpu/structural_shape	`embed_diagonal`	f64	4	`8192 -> 8192x8192`	1.937 ± 0.342	-	2.260 ± 0.060	2.133 ± 0.015	2.118 ± 0.160	2.166 ± 0.221	-
cpu/structural_shape	`extract_diagonal`	f64	1	`8388608x2x2 -> 8388608x2`	2.138 ± 0.109	-	6.409 ± 0.091	5.506 ± 1.432	3.479 ± 0.029	-	-
cpu/structural_shape	`extract_diagonal`	f64	4	`8388608x2x2 -> 8388608x2`	2.187 ± 0.080	-	3.851 ± 0.080	1.744 ± 0.015	1.347 ± 0.046	-	-
cpu/structural_shape	`reshape`	f64	1	`33554432 -> 8192x4096`	3.785 ± 0.033	-	4.260 ± 0.142	4.306 ± 0.131	3.531 ± 0.071	3.875 ± 0.031	-
cpu/structural_shape	`reshape`	f64	4	`33554432 -> 8192x4096`	3.845 ± 0.090	-	1.607 ± 0.111	1.543 ± 0.079	1.783 ± 0.117	4.017 ± 0.131	-
cpu/structural_shape	`transpose`	f64	1	`4096x4096`	27.749 ± 0.472	-	22.984 ± 0.656	18.186 ± 0.474	13.189 ± 0.188	53.414 ± 2.983	30.703 ± 0.615
cpu/structural_shape	`transpose`	f64	4	`4096x4096`	12.162 ± 0.805	-	7.345 ± 0.329	18.511 ± 0.535	5.338 ± 0.282	50.858 ± 0.843	17.027 ± 7.444
cpu/structural_shape	`tril`	f64	1	`4096x4096`	3.131 ± 0.128	-	5.342 ± 0.057	3.563 ± 0.103	2.205 ± 0.018	4.208 ± 0.116	-
cpu/structural_shape	`tril`	f64	4	`4096x4096`	1.411 ± 0.102	-	2.473 ± 0.550	1.369 ± 0.027	0.866 ± 0.051	4.258 ± 0.158	-
cpu/structural_shape	`triu`	f64	1	`4096x4096`	2.939 ± 0.084	-	5.366 ± 0.086	3.187 ± 0.085	2.200 ± 0.009	3.888 ± 0.202	-
cpu/structural_shape	`triu`	f64	4	`4096x4096`	1.358 ± 0.059	-	2.807 ± 0.411	1.238 ± 0.020	0.905 ± 0.061	4.026 ± 0.127	-
cpu/view_metadata	`broadcast_in_dim_view`	f64	1	`8192x1 -> 8192x4096`	0.000 ± 0.000	-	unsupported	0.000 ± 0.000	-	-	-
cpu/view_metadata	`broadcast_in_dim_view`	f64	4	`8192x1 -> 8192x4096`	0.000 ± 0.000	-	unsupported	0.000 ± 0.000	-	-	-
cpu/view_metadata	`reshape_view`	f64	1	`33554432 -> 8192x4096`	0.000 ± 0.000	-	unsupported	0.000 ± 0.000	-	0.000 ± 0.000	-
cpu/view_metadata	`reshape_view`	f64	4	`33554432 -> 8192x4096`	0.000 ± 0.000	-	unsupported	0.000 ± 0.000	-	0.000 ± 0.000	-
cpu/view_metadata	`slice_view`	f64	1	`4194304 -> 2096128`	0.000 ± 0.000	-	unsupported	0.000 ± 0.000	-	0.000 ± 0.000	-
cpu/view_metadata	`slice_view`	f64	4	`4194304 -> 2096128`	0.000 ± 0.000	-	unsupported	0.000 ± 0.000	-	0.000 ± 0.000	-
cpu/view_metadata	`transpose_view`	f64	1	`4096x4096`	0.000 ± 0.000	-	unsupported	0.000 ± 0.000	-	0.000 ± 0.000	-
cpu/view_metadata	`transpose_view`	f64	4	`4096x4096`	0.000 ± 0.000	-	unsupported	0.000 ± 0.000	-	0.000 ± 0.000	-

Short-operation batches

Total batch duration and normalized ns/op are shown without rounding sub-microsecond calls to zero. Metadata views require no execution session.

Operation	Threads	Backend	Operations/batch	Median batch ms	Median ns/op
broadcast_in_dim_view	1	PyTorch Python (ms)	16	0.005625	351.56
broadcast_in_dim_view	1	tenferro-rs direct API (ms)	16	0.001375	85.94
broadcast_in_dim_view	4	PyTorch Python (ms)	16	0.005791	361.94
broadcast_in_dim_view	4	tenferro-rs direct API (ms)	16	0.001375	85.94
reshape_view	1	Julia (Base/LinearAlgebra) (ms)	16	0.000042	2.62
reshape_view	1	PyTorch Python (ms)	16	0.005291	330.69
reshape_view	1	tenferro-rs direct API (ms)	16	0.002625	164.06
reshape_view	4	Julia (Base/LinearAlgebra) (ms)	16	0.000042	2.62
reshape_view	4	PyTorch Python (ms)	16	0.005792	362.00
reshape_view	4	tenferro-rs direct API (ms)	16	0.002667	166.69
slice_view	1	Julia (Base/LinearAlgebra) (ms)	16	0.000042	2.62
slice_view	1	PyTorch Python (ms)	16	0.004708	294.25
slice_view	1	tenferro-rs direct API (ms)	16	0.002416	151.00
slice_view	4	Julia (Base/LinearAlgebra) (ms)	16	0.000042	2.62
slice_view	4	PyTorch Python (ms)	16	0.004917	307.31
slice_view	4	tenferro-rs direct API (ms)	16	0.002458	153.62
transpose_view	1	Julia (Base/LinearAlgebra) (ms)	16	0.000042	2.62
transpose_view	1	PyTorch Python (ms)	16	0.004666	291.62
transpose_view	1	tenferro-rs direct API (ms)	16	0.001708	106.75
transpose_view	4	Julia (Base/LinearAlgebra) (ms)	16	0.000042	2.62
transpose_view	4	PyTorch Python (ms)	16	0.004916	307.25
transpose_view	4	tenferro-rs direct API (ms)	16	0.001875	117.19

Cross-Backend Spread Audit

Rows with a successful cell more than 10x faster than the slowest successful cell are flagged for operation-specific review. This cross-backend spread check is a warning, not a correctness verdict.

cpu/complex/div (c64, threads=4, shape=8388608): tenferro-direct is 11.8x faster than the slowest successful cell (julia-base, 18.569 ms). Audit fixture semantics, synchronization, labels, and operation-specific bandwidth/FLOP bounds.
cpu/complex/div (c64, threads=4, shape=8388608): tenferro-trace is 10.3x faster than the slowest successful cell (julia-base, 18.569 ms). Audit fixture semantics, synchronization, labels, and operation-specific bandwidth/FLOP bounds.
cpu/elementwise_reduction/reduce_max_axis0 (f64, threads=1, shape=2048x2048): jax-cpu is 10.2x faster than the slowest successful cell (pytorch-cpu, 9.755 ms). Audit fixture semantics, synchronization, labels, and operation-specific bandwidth/FLOP bounds.
cpu/elementwise_reduction/reduce_max_axis0 (f64, threads=1, shape=2048x2048): julia-base is 21.5x faster than the slowest successful cell (pytorch-cpu, 9.755 ms). Audit fixture semantics, synchronization, labels, and operation-specific bandwidth/FLOP bounds.
cpu/elementwise_reduction/reduce_max_axis0 (f64, threads=1, shape=2048x2048): tenferro-direct is 11.1x faster than the slowest successful cell (pytorch-cpu, 9.755 ms). Audit fixture semantics, synchronization, labels, and operation-specific bandwidth/FLOP bounds.
cpu/elementwise_reduction/reduce_max_axis0 (f64, threads=1, shape=2048x2048): tenferro-trace is 13.5x faster than the slowest successful cell (pytorch-cpu, 9.755 ms). Audit fixture semantics, synchronization, labels, and operation-specific bandwidth/FLOP bounds.
cpu/elementwise_reduction/reduce_max_axis0 (f64, threads=4, shape=2048x2048): jax-cpu is 14.1x faster than the slowest successful cell (pytorch-cpu, 4.837 ms). Audit fixture semantics, synchronization, labels, and operation-specific bandwidth/FLOP bounds.
cpu/elementwise_reduction/reduce_max_axis0 (f64, threads=4, shape=2048x2048): julia-base is 12.7x faster than the slowest successful cell (pytorch-cpu, 4.837 ms). Audit fixture semantics, synchronization, labels, and operation-specific bandwidth/FLOP bounds.
cpu/elementwise_reduction/reduce_max_axis0 (f64, threads=4, shape=2048x2048): tenferro-direct is 16.5x faster than the slowest successful cell (pytorch-cpu, 4.837 ms). Audit fixture semantics, synchronization, labels, and operation-specific bandwidth/FLOP bounds.
cpu/elementwise_reduction/reduce_max_axis0 (f64, threads=4, shape=2048x2048): tenferro-trace is 18.1x faster than the slowest successful cell (pytorch-cpu, 4.837 ms). Audit fixture semantics, synchronization, labels, and operation-specific bandwidth/FLOP bounds.
cpu/elementwise_reduction/reduce_min_axis0 (f64, threads=1, shape=2048x2048): julia-base is 24.3x faster than the slowest successful cell (pytorch-cpu, 8.845 ms). Audit fixture semantics, synchronization, labels, and operation-specific bandwidth/FLOP bounds.
cpu/elementwise_reduction/reduce_min_axis0 (f64, threads=1, shape=2048x2048): tenferro-direct is 16.3x faster than the slowest successful cell (pytorch-cpu, 8.845 ms). Audit fixture semantics, synchronization, labels, and operation-specific bandwidth/FLOP bounds.
cpu/elementwise_reduction/reduce_min_axis0 (f64, threads=1, shape=2048x2048): tenferro-trace is 16.5x faster than the slowest successful cell (pytorch-cpu, 8.845 ms). Audit fixture semantics, synchronization, labels, and operation-specific bandwidth/FLOP bounds.
cpu/elementwise_reduction/reduce_min_axis0 (f64, threads=4, shape=2048x2048): jax-cpu is 13.0x faster than the slowest successful cell (pytorch-cpu, 4.634 ms). Audit fixture semantics, synchronization, labels, and operation-specific bandwidth/FLOP bounds.
cpu/elementwise_reduction/reduce_min_axis0 (f64, threads=4, shape=2048x2048): julia-base is 12.9x faster than the slowest successful cell (pytorch-cpu, 4.634 ms). Audit fixture semantics, synchronization, labels, and operation-specific bandwidth/FLOP bounds.
cpu/elementwise_reduction/reduce_min_axis0 (f64, threads=4, shape=2048x2048): tenferro-direct is 28.7x faster than the slowest successful cell (pytorch-cpu, 4.634 ms). Audit fixture semantics, synchronization, labels, and operation-specific bandwidth/FLOP bounds.
cpu/elementwise_reduction/reduce_min_axis0 (f64, threads=4, shape=2048x2048): tenferro-trace is 27.6x faster than the slowest successful cell (pytorch-cpu, 4.634 ms). Audit fixture semantics, synchronization, labels, and operation-specific bandwidth/FLOP bounds.
cpu/linalg_uncovered/norm_fro (f64, threads=1, shape=2048x2048): tenferro-direct is 10.4x faster than the slowest successful cell (julia-base, 3.744 ms). Audit fixture semantics, synchronization, labels, and operation-specific bandwidth/FLOP bounds.
cpu/linalg_uncovered/norm_fro (f64, threads=1, shape=2048x2048): tenferro-trace is 10.2x faster than the slowest successful cell (julia-base, 3.744 ms). Audit fixture semantics, synchronization, labels, and operation-specific bandwidth/FLOP bounds.
cpu/linalg_uncovered/norm_fro (f64, threads=4, shape=2048x2048): tenferro-direct is 25.2x faster than the slowest successful cell (julia-base, 3.920 ms). Audit fixture semantics, synchronization, labels, and operation-specific bandwidth/FLOP bounds.
cpu/linalg_uncovered/norm_fro (f64, threads=4, shape=2048x2048): tenferro-trace is 22.3x faster than the slowest successful cell (julia-base, 3.920 ms). Audit fixture semantics, synchronization, labels, and operation-specific bandwidth/FLOP bounds.
cpu/view_metadata/reshape_view (f64, threads=1, shape=33554432 -> 8192x4096): julia-base is 110.3x faster than the slowest successful cell (pytorch-cpu, 0.000 ms). Audit fixture semantics, synchronization, labels, and operation-specific bandwidth/FLOP bounds.
cpu/view_metadata/reshape_view (f64, threads=4, shape=33554432 -> 8192x4096): julia-base is 120.7x faster than the slowest successful cell (pytorch-cpu, 0.000 ms). Audit fixture semantics, synchronization, labels, and operation-specific bandwidth/FLOP bounds.
cpu/view_metadata/slice_view (f64, threads=1, shape=4194304 -> 2096128): julia-base is 98.0x faster than the slowest successful cell (pytorch-cpu, 0.000 ms). Audit fixture semantics, synchronization, labels, and operation-specific bandwidth/FLOP bounds.
cpu/view_metadata/slice_view (f64, threads=4, shape=4194304 -> 2096128): julia-base is 102.3x faster than the slowest successful cell (pytorch-cpu, 0.000 ms). Audit fixture semantics, synchronization, labels, and operation-specific bandwidth/FLOP bounds.
cpu/view_metadata/transpose_view (f64, threads=1, shape=4096x4096): julia-base is 97.3x faster than the slowest successful cell (pytorch-cpu, 0.000 ms). Audit fixture semantics, synchronization, labels, and operation-specific bandwidth/FLOP bounds.
cpu/view_metadata/transpose_view (f64, threads=4, shape=4096x4096): julia-base is 102.3x faster than the slowest successful cell (pytorch-cpu, 0.000 ms). Audit fixture semantics, synchronization, labels, and operation-specific bandwidth/FLOP bounds.

Physical Bound Audit

This independent check derives minimum logical bytes from dtype and shape for materializing public API operations, plus conservative operation FLOPs for reductions, Frobenius norms, matrix products, triangular solves, and recognized dense linalg families. Decorated shapes (->, rhs=, and +) are parsed explicitly. Operations whose touched region cannot be inferred conservatively from the reported shape are left unmodeled. It assumes at most 100 GB/s and 50 GFLOP/s per requested CPU thread, capped at 1000 GB/s and 3200 GFLOP/s. A cell more than 10x faster than the resulting lower bound is flagged. These deliberately generous ceilings are a sanity screen, not a performance gate.

No cell exceeded the conservative physical bound by more than 10x.