WP40 RAID: Phase 3 gate — primitives benchmark records, summary, figure; status/progress updated
Co-Authored-By: Claude Fable 5.1 <noreply@anthropic.com>
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RESEARCH_STATUS.md
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| 1 | 1 | # RESEARCH_STATUS.md — RAID (UQO WP 40) |
| 2 | 2 | |
| 3 | −Last update: 2026-11-02 (Phase 2 passed). Legend: ✅ verified by tests/artifacts · 🧪 implemented, validation pending · | |
| 3 | +Last update: 2026-11-02 (Phase 3 passed). Legend: ✅ verified by tests/artifacts · 🧪 implemented, validation pending · | |
| 4 | 4 | 🧭 experimental · ⛔ blocked · ⏳ planned · ✖ not implemented (deliberately). |
| 5 | 5 | |
| 6 | 6 | ## Phases |
@@ -9,7 +9,7 @@ Last update: 2026-11-02 (Phase 2 passed). Legend: ✅ verified by tests/artifact | ||
| 9 | 9 | | 0 Audit | scope & feasibility memo | ✅ passed 2026-11-02 | `docs/audit.md`, `docs/capabilities.md`, `docs/novelty_matrix.md`, `docs/risks.md`, `docs/PROGRESS.md` | |
| 10 | 10 | | 1 Foundation | clean build + tests + docs | ✅ passed 2026-11-02 | `ctest` 26/26 (314 assertions), `pytest` 7/7, `docs/PROGRESS.md` Phase 1 | |
| 11 | 11 | | 2 Data | offline synthetic tests + opt-in live tests | ✅ passed 2026-11-02 | offline `[findata]` 4/4, live `[live]` 2/2 (60 assertions), `docs/operations/findata.md` | |
| 12 | −| 3 Numerical primitives | accuracy + measured break-even | ⏳ | — | | |
| 12 | +| 3 Numerical primitives | accuracy + measured break-even | ✅ passed 2026-11-02 | `[metal]` 6 cases / 6 411 assertions; `experiments/results/bench_primitives_summary.json` (Metal wins: fused realized ≥ 39 k elements up to 3.4×, GARCH NLL P=64 up to 7.9×; CPU wins: rolling sums, GARCH P=1, small panels) | | |
| 13 | 13 | | 4 Econometrics (Tier A) | references + Monte Carlo | ⏳ | — | |
| 14 | 14 | | 5 Extensions (Tier B) | per-feature specs + tests | ⏳ | — | |
| 15 | 15 | | 6 Benchmarking E1–E7 | every claim traceable | ⏳ | — | |
@@ -20,10 +20,10 @@ Last update: 2026-11-02 (Phase 2 passed). Legend: ✅ verified by tests/artifact | ||
| 20 | 20 | | Method | Tier | CPU FP64 | Metal FP32 | Reference software | Status | |
| 21 | 21 | |---|---|---|---|---|---| |
| 22 | 22 | | returns (log/arith), lag/lead, rolling windows, calendar-aware aggregation | A | ✅ | ⏳ (Phase 3) | numpy; exchange_calendars (calendar exact 2000–2026) | ✅ CPU | |
| 23 | −| RV, BPV, RSV±, RQ, jump proxy, TriPV, rCov/rCorr | A | ✅ (numpy truth 1e−12) | ⏳ (Phase 3) | highfrequency 1.0.3 (R comparison Phase 4) | ✅ CPU | | |
| 24 | −| OLS/WLS/ridge, HC0–3, HAC, cluster, rolling OLS | A | ✅ (statsmodels 1e−9) | ⏳ (sufficient stats, Phase 3) | statsmodels 0.15, scipy 1.18 | ✅ CPU | | |
| 23 | +| RV, BPV, RSV±, RQ, jump proxy, TriPV, rCov/rCorr | A | ✅ (numpy truth 1e−12) | ✅ fused kernel 1e−6 vs FP64 | highfrequency 1.0.3 (R comparison Phase 4) | ✅ CPU | | |
| 24 | +| OLS/WLS/ridge, HC0–3, HAC, cluster, rolling OLS | A | ✅ (statsmodels 1e−9) | ✅ sufficient statistics 1e−6 (k ≤ 8) | statsmodels 0.15, scipy 1.18 | ✅ CPU | | |
| 25 | 25 | | HAR-RV, log-HAR, HAR-X, HARQ | A | ⏳ | ⏳ | highfrequency `HARmodel`, statsmodels | ⏳ | |
| 26 | −| GARCH(1,1), GJR, EGARCH (N, t), QMLE/Hessian/OPG SE, forecasts | A | ✅ (arch 8.0: loglik 5e−4, params 5 %) | ⏳ (batched likelihood, Phase 3) | arch 8.0 ✅, rugarch 1.5.6 (Phase 4) | ✅ CPU | | |
| 26 | +| GARCH(1,1), GJR, EGARCH (N, t), QMLE/Hessian/OPG SE, forecasts | A | ✅ (arch 8.0: loglik 5e−4, params 5 %) | ✅ batched NLL 2e−5 (grids) | arch 8.0 ✅, rugarch 1.5.6 (Phase 4) | ✅ CPU | | |
| 27 | 27 | | Bootstrap (stationary / circular block), Monte Carlo | A | ⏳ | ⏳ | arch.bootstrap | ⏳ | |
| 28 | 28 | | VAR, GFEVD, Diebold–Yilmaz | B | ⏳ | ⏳ | statsmodels VAR | ⏳ | |
| 29 | 29 | | Realized GARCH, HEAVY, DCC, PCA/shrinkage, Kalman | B | ✖ until Tier A passes | | | ⏳ | |
@@ -35,6 +35,5 @@ Last update: 2026-11-02 (Phase 2 passed). Legend: ✅ verified by tests/artifact | ||
| 35 | 35 | not tested unless they come back. |
| 36 | 36 | |
| 37 | 37 | ## Next safe action |
| 38 | −Phase 3: Metal backend (device discovery, runtime + prebuilt shader library, buffer pool, batched reductions, | |
| 39 | −rolling sums, regression sufficient statistics, GARCH likelihood batch), FP32-vs-FP64 accuracy tests, first break-even | |
| 40 | −microbenchmarks (bench_reductions) with manifests. | |
| 38 | +Phase 4: HAR family (fit, rolling, batched via GPU sufficient statistics), block bootstrap, R references | |
| 39 | +(highfrequency / rugarch), Monte Carlo (bias/RMSE/coverage), gradient checks, registry completion. | |
modified
docs/PROGRESS.md
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@@ -81,3 +81,42 @@ Executed: | ||
| 81 | 81 | |
| 82 | 82 | Gate evidence: offline tests in `ctest`; live run transcript above; no vendor data in git (`scripts/check_no_secrets.sh`). |
| 83 | 83 | Open: least-privilege key for benchmarks (needs `findata create-key` on M3U96a — owner action, optional). |
| 84 | + | |
| 85 | +## Phase 3 — Numerical primitives (2026-11-02, 15:40–16:30 ET) — GATE PASSED | |
| 86 | +Plan: Metal backend with FP32 "double-float" (error-free-transform) accumulation, fused realized kernel, rolling sums, | |
| 87 | +regression sufficient statistics, batched GARCH likelihood; CPU/GPU agreement tests; measured break-even analysis. | |
| 88 | + | |
| 89 | +Executed: | |
| 90 | +- `backends/metal/shaders/raid_kernels.metal` (TwoSum/Fast2Sum double-float, deterministic threadgroup tree reductions, | |
| 91 | + chunked partial sums combined in FP64 on the CPU) and `backends/metal/host/metal_backend.mm` (device discovery, | |
| 92 | + prebuilt `raid.metallib` with runtime-MSL fallback, pipeline cache, buffer pool by power-of-two size class, GPU | |
| 93 | + timing from `GPUStartTime/GPUEndTime`, `-fno-fast-math` / `fastMathEnabled = NO` so the compensation is not optimised | |
| 94 | + away). Metal has no `lgamma`/`log1p`: Student-t constants are computed in FP64 on the host and passed per parameter | |
| 95 | + vector. | |
| 96 | +- Tests `[metal]` (6 cases, 6 411 assertions): fused and single-statistic accumulators vs CPU FP64 within 1e−6 | |
| 97 | + (Σx⁴ 1e−5) for n = 390/3 900/39 000 across chunk boundaries (4 096); bitwise determinism across runs; rolling sums | |
| 98 | + 1e−5; regression statistics 1e−6 (and the solve from GPU statistics agrees with CPU QR to 1e−5); batched GARCH NLL | |
| 99 | + 2e−5 relative (GJR + Student-t fixed ν 5e−5), argmin over a 16-point grid identical; +inf on invalid parameters. | |
| 100 | + Full suite: `ctest` 38/38 (2 live skipped), `pytest` 7/7. | |
| 101 | +- `bench_bench_primitives` (laptop M5 Max 40-core GPU, 18 CPU threads, load ≈ 3–4 from other sessions, no thermal | |
| 102 | + warning, 5 repetitions, shuffled order, 2 warm-ups; raw records `experiments/results/raw/bench_primitives.jsonl` | |
| 103 | + + manifest; summary `experiments/results/bench_primitives_summary.{json,csv}`, figure | |
| 104 | + `fig_bench_primitives_throughput.pdf`). Medians of wall-clock including FP64→FP32 conversion and buffer traffic; | |
| 105 | + verdicts use non-overlapping bootstrap 95 % CIs of the median: | |
| 106 | + - realized_fused: Metal wins from 39 000 elements (100 × 390: 2.4×), 2.0–3.4× vs 18-thread CPU at 3.9 M–39 M | |
| 107 | + elements (max 3.4× at 1 000 × 39 000); ties at 390 000 for 10 × 39 000 and 100 × 3 900 shapes; CPU 1 thread is | |
| 108 | + 27–40× slower than Metal at 39 M. | |
| 109 | + - regression_stats (k = 4): break-even ≈ 390 000 elements for a single long series (3.9×); ties for most shapes | |
| 110 | + between 390 k and 3.9 M; 1.1–1.4× at 39 M. CPU wins below 39 000 elements. | |
| 111 | + - rolling_sumsq (w = 22, direct O(w) kernel): **CPU wins at every size** (Metal 0.4–0.9× of CPU-MT); the GPU kernel | |
| 112 | + is memory/arithmetic-bound by its O(w) design and the CPU running sum is O(1) per element — a negative result kept | |
| 113 | + for the paper (a scan-based kernel is future work). | |
| 114 | + - garch_nll: with one parameter vector per series (P = 1) the **CPU wins everywhere** (0.01–0.33×; the recursion is | |
| 115 | + sequential and the GPU is launch-bound); with P = 64 parameter vectors per series Metal wins from 100 series | |
| 116 | + (1.9×) up to 7.9× at 1 000 × 3 900 — batched likelihood evaluation is where the GPU pays off. | |
| 117 | + - Device time is 5–20× smaller than wall time for the reductions: FP64→FP32 conversion and buffer fills dominate | |
| 118 | + ("unified memory is not free computation"); E6 will add the FP32-resident ablation. | |
| 119 | + - Shader library: prebuilt metallib loaded in 0.23 ms; first kernel call 14 ms (pipeline creation); runtime MSL | |
| 120 | + compilation of the bundle is measured separately in E7 (toolchain-less nodes). | |
| 121 | + | |
| 122 | +Gate evidence: accuracy tests and the measured break-even table above; no claim beyond the tested shapes. | |
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experiments/results/bench_primitives_summary.csv
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| 1 | +kernel,S,n,elements,backend,threads,median_s,ci_lo,ci_hi,device_s,elements_per_s,reps,precision,peak_rss_mb | |
| 2 | +garch_nll_P1,1,390,390,cpu,1,1.7909333109855652e-06,1.7499551177024841e-06,1.8328428268432617e-06,0.0,217763552.44929796,5,fp64,3255.451648 | |
| 3 | +garch_nll_P1,1,390,390,cpu,18,1.7499551177024841e-06,1.6670674085617065e-06,1.8333084881305695e-06,0.0,222862858.62692922,5,fp64,3368.943616 | |
| 4 | +garch_nll_P1,1,390,390,metal,0,0.0009180000051856041,0.00044724997133016586,0.0009358339011669159,0.00032679166179150343,424836.59890736995,5,fp32,2962.440192 | |
| 5 | +garch_nll_P1,1,3900,3900,cpu,1,1.6250181943178177e-05,1.6207806766033173e-05,1.637497916817665e-05,0.0,239997312.86930108,5,fp64,2962.440192 | |
| 6 | +garch_nll_P1,1,3900,3900,cpu,18,1.695798709988594e-05,1.691700890660286e-05,1.9416213035583496e-05,0.0,229980125.41395503,5,fp64,3431.858176 | |
| 7 | +garch_nll_P1,1,3900,3900,metal,0,0.001348957885056734,0.0010095001198351383,0.0015331669710576534,0.0011987084290012717,2891120.6518771155,5,fp32,2962.440192 | |
| 8 | +garch_nll_P1,10,390,3900,cpu,1,2.1916814148426056e-05,2.1541956812143326e-05,7.208297029137611e-05,0.0,177945570.62847915,5,fp64,2962.440192 | |
| 9 | +garch_nll_P1,10,390,3900,cpu,18,2.929195761680603e-05,1.7000362277030945e-05,4.200031980872154e-05,0.0,133142347.50095384,5,fp64,2962.440192 | |
| 10 | +garch_nll_P1,10,390,3900,metal,0,0.0003432091325521469,0.0003193751908838749,0.0009956671856343746,0.00019762502051889896,11363333.98531415,5,fp32,2920.169472 | |
| 11 | +garch_nll_P1,10,3900,39000,cpu,1,0.0002155420370399952,0.00016279099509119987,0.00037720799446105957,0.0,180939182.60948467,5,fp64,576.782336 | |
| 12 | +garch_nll_P1,10,3900,39000,cpu,18,6.916606798768044e-05,6.245775148272514e-05,7.533328607678413e-05,0.0,563860302.2358668,5,fp64,781.43488 | |
| 13 | +garch_nll_P1,10,3900,39000,metal,0,0.0014300826005637646,0.0012115412391722202,0.0016847080551087856,0.0010766249615699053,27271152.019208886,5,fp32,3360.11264 | |
| 14 | +garch_nll_P1,100,390,39000,cpu,1,0.0001916671171784401,0.0001916252076625824,0.0002199173904955387,0.0,203477782.59580857,5,fp64,3431.87456 | |
| 15 | +garch_nll_P1,100,390,39000,cpu,18,0.00016116676852107048,0.00015066703781485558,0.00017320923507213593,0.0,241985369.30335766,5,fp64,3359.932416 | |
| 16 | +garch_nll_P1,100,390,39000,metal,0,0.0006238752976059914,0.0006115422584116459,0.0006384579464793205,0.0004310833755880594,62512492.720348835,5,fp32,3355.901952 | |
| 17 | +garch_nll_P1,100,3900,390000,cpu,1,0.0016154590994119644,0.0016071251593530178,0.0016200002282857895,0.0,241417439.87326083,5,fp64,3222.339584 | |
| 18 | +garch_nll_P1,100,3900,390000,cpu,18,0.00020695803686976433,0.00020262505859136581,0.0002222089096903801,0.0,1884439985.5098226,5,fp64,2962.440192 | |
| 19 | +garch_nll_P1,100,3900,390000,metal,0,0.0016493331640958786,0.0015722080133855343,0.004429208114743233,0.0009533748961985111,236459199.68740082,5,fp32,2962.440192 | |
| 20 | +garch_nll_P1,1000,390,390000,cpu,1,0.0016390001401305199,0.001627500168979168,0.0016581248492002487,0.0,237949949.14945084,5,fp64,3359.932416 | |
| 21 | +garch_nll_P1,1000,390,390000,cpu,18,0.0002765827812254429,0.00027295900508761406,0.00033191684633493423,0.0,1410066086.8042636,5,fp64,2962.440192 | |
| 22 | +garch_nll_P1,1000,390,390000,metal,0,0.0011531668715178967,0.0010962923988699913,0.0011774590238928795,0.00017799995839595795,338199101.65009224,5,fp32,3222.339584 | |
| 23 | +garch_nll_P1,1000,3900,3900000,cpu,1,0.018310166895389557,0.01771716633811593,0.019527375232428312,0.0,212996420.09172553,5,fp64,572.112896 | |
| 24 | +garch_nll_P1,1000,3900,3900000,cpu,18,0.0014978330582380295,0.001383374910801649,0.0015932917594909668,0.0,2603761466.306366,5,fp64,3432.742912 | |
| 25 | +garch_nll_P1,1000,3900,3900000,metal,0,0.0072068748995661736,0.007158916909247637,0.009398084133863449,0.0010924999369308352,541149951.171591,5,fp32,3360.11264 | |
| 26 | +garch_nll_P1,10000,390,3900000,cpu,1,0.017741417046636343,0.01734916679561138,0.017816499806940556,0.0,219824605.3146817,5,fp64,3355.901952 | |
| 27 | +garch_nll_P1,10000,390,3900000,cpu,18,0.0022433330304920673,0.002103041857481003,0.002292540855705738,0.0,1738484632.905596,5,fp64,2962.440192 | |
| 28 | +garch_nll_P1,10000,390,3900000,metal,0,0.00675466563552618,0.006540417205542326,0.007071124855428934,0.00046787504106760025,577378690.5880197,5,fp32,2962.440192 | |
| 29 | +garch_nll_P1,10000,3900,39000000,cpu,1,0.16226391727104783,0.16133012529462576,0.16484179068356752,0.0,240349183.3298581,5,fp64,3255.451648 | |
| 30 | +garch_nll_P1,10000,3900,39000000,cpu,18,0.01383341709151864,0.012941500172019005,0.014138792175799608,0.0,2819260038.3538756,5,fp64,3254.272 | |
| 31 | +garch_nll_P1,10000,3900,39000000,metal,0,0.06106641702353954,0.05950908316299319,0.0616582497023046,0.004054000019095838,638648899.0334327,5,fp32,3355.901952 | |
| 32 | +garch_nll_P64,1,390,390,cpu,1,8.287513628602028e-05,8.27503390610218e-05,8.458364754915237e-05,0.0,4705874.614239238,5,fp64,577.159168 | |
| 33 | +garch_nll_P64,1,390,390,cpu,18,0.00017224997282028198,0.00012754183262586594,0.0002139592543244362,0.0,2264151.3006617934,5,fp64,3431.514112 | |
| 34 | +garch_nll_P64,1,390,390,metal,0,0.0005012080073356628,0.00047737499698996544,0.0006123748607933521,0.0003255000337958336,778120.0505418383,5,fp32,3431.46496 | |
| 35 | +garch_nll_P64,1,3900,3900,cpu,1,0.0008078329265117645,0.0008031250908970833,0.0008203750476241112,0.0,4827730.923076213,5,fp64,3431.87456 | |
| 36 | +garch_nll_P64,1,3900,3900,cpu,18,0.00014187488704919815,0.000135000329464674,0.00021779071539640427,0.0,27489008.668937948,5,fp64,3222.339584 | |
| 37 | +garch_nll_P64,1,3900,3900,metal,0,0.0014235423877835274,0.00134983379393816,0.0033927499316632748,0.00122337497305125,2739644.4485733556,5,fp32,3431.87456 | |
| 38 | +garch_nll_P64,10,390,3900,cpu,1,0.0008257082663476467,0.000809917226433754,0.0008320827037096024,0.0,4723217.8227436915,5,fp64,3432.742912 | |
| 39 | +garch_nll_P64,10,390,3900,cpu,18,0.0002438751980662346,0.00013074977323412895,0.0002598753198981285,0.0,15991786.089460358,5,fp64,3368.943616 | |
| 40 | +garch_nll_P64,10,390,3900,metal,0,0.0010179998353123665,0.0004632081836462021,0.0010751672089099884,0.00032300001475960016,3831041.877136759,5,fp32,3431.530496 | |
| 41 | +garch_nll_P64,10,3900,39000,cpu,1,0.008083874825388193,0.008056249935179949,0.00812424998730421,0.0,4824419.086440666,5,fp64,3355.901952 | |
| 42 | +garch_nll_P64,10,3900,39000,cpu,18,0.000775500200688839,0.0006874999962747097,0.0008766250684857368,0.0,50290122.38211957,5,fp64,3432.742912 | |
| 43 | +garch_nll_P64,10,3900,39000,metal,0,0.0013822498731315136,0.0008970410563051701,0.0033571659587323666,0.0006641249638050795,28214869.654243305,5,fp32,3431.530496 | |
| 44 | +garch_nll_P64,100,390,39000,cpu,1,0.008346542250365019,0.008285791147500277,0.008543540723621845,0.0,4672593.611839012,5,fp64,3431.514112 | |
| 45 | +garch_nll_P64,100,390,39000,cpu,18,0.001005750149488449,0.0009415419772267342,0.0010966667905449867,0.0,38777026.30204572,5,fp64,781.484032 | |
| 46 | +garch_nll_P64,100,390,39000,metal,0,0.0005332920700311661,0.0005230000242590904,0.0005429168231785297,0.00033650000113993883,73130658.02332444,5,fp32,2962.440192 | |
| 47 | +garch_nll_P64,100,3900,390000,cpu,1,0.0801338329911232,0.07999316696077585,0.08033083425834775,0.0,4866858.172667244,5,fp64,3359.932416 | |
| 48 | +garch_nll_P64,100,3900,390000,cpu,18,0.006173874717205763,0.005890249740332365,0.006268457975238562,0.0,63169406.22606451,5,fp64,3432.742912 | |
| 49 | +garch_nll_P64,100,3900,390000,metal,0,0.0021704169921576977,0.0018634586594998837,0.0022297906689345837,0.0010580417001619935,179688972.86059555,5,fp32,3431.858176 | |
| 50 | +garch_nll_P64,1000,390,390000,cpu,1,0.09679854195564985,0.08949454175308347,0.10223195794969797,0.0,4028986.306205791,5,fp64,2962.440192 | |
| 51 | +garch_nll_P64,1000,390,390000,cpu,18,0.00848708301782608,0.008417499717324972,0.008939292281866074,0.0,45952183.94598623,5,fp64,2962.440192 | |
| 52 | +garch_nll_P64,1000,390,390000,metal,0,0.002336665987968445,0.002312499564141035,0.0027117920108139515,0.001452916651032865,166904470.73228282,5,fp32,3359.932416 | |
| 53 | +garch_nll_P64,1000,3900,3900000,cpu,1,0.8561791670508683,0.8505779169499874,0.9446879159659147,0.0,4555121.34619399,5,fp64,2962.440192 | |
| 54 | +garch_nll_P64,1000,3900,3900000,cpu,18,0.08150566695258021,0.0744811249896884,0.10778554202988744,0.0,47849433.61384933,5,fp64,3255.451648 | |
| 55 | +garch_nll_P64,1000,3900,3900000,metal,0,0.010272707790136337,0.009604125283658504,0.010956583078950644,0.0029698750004172325,379646737.7125929,5,fp32,2962.440192 | |
| 56 | +realized_fused,1,390,390,cpu,1,1.4998950064182281e-06,1.416075974702835e-06,4.041939973831177e-06,0.0,260018200.16144055,5,fp64,2962.440192 | |
| 57 | +realized_fused,1,390,390,cpu,18,1.4998950064182281e-06,1.4579854905605316e-06,1.6670674085617065e-06,0.0,260018200.16144055,5,fp64,2962.440192 | |
| 58 | +realized_fused,1,390,390,metal,0,0.0002344171516597271,0.00019499985501170158,0.00025337468832731247,3.199989441782236e-05,1663700.7882687368,5,fp32,3432.742912 | |
| 59 | +realized_fused,1,3900,3900,cpu,1,1.1624768376350403e-05,1.1375173926353455e-05,1.2792181223630905e-05,0.0,335490555.4879026,5,fp64,2962.440192 | |
| 60 | +realized_fused,1,3900,3900,cpu,18,1.116609200835228e-05,1.1124648153781891e-05,1.2124888598918915e-05,0.0,349271705.5423496,5,fp64,3432.742912 | |
| 61 | +realized_fused,1,3900,3900,metal,0,0.0006333747878670692,0.0001420830376446247,0.000777125358581543,2.037500962615013e-05,6157491.7011356,5,fp32,2913.878016 | |
| 62 | +realized_fused,1,39000,39000,cpu,1,0.00018258299678564072,0.0001637078821659088,0.00037499982863664627,0.0,213601489.11230472,5,fp64,2962.440192 | |
| 63 | +realized_fused,1,39000,39000,cpu,18,0.0001671668142080307,0.00015920819714665413,0.00017870916053652763,0.0,233299893.79032168,5,fp64,2962.440192 | |
| 64 | +realized_fused,1,39000,39000,metal,0,0.000206624623388052,0.0001971670426428318,0.00024229194968938828,4.3874955736100674e-05,188748075.42543435,5,fp32,3355.901952 | |
| 65 | +realized_fused,1,390000,390000,cpu,1,0.002032375428825617,0.002019832842051983,0.002052249852567911,0.0,191893679.91196227,5,fp64,3222.339584 | |
| 66 | +realized_fused,1,390000,390000,cpu,18,0.0020858747884631157,0.002067000139504671,0.0027133747935295105,0.0,186971913.25053322,5,fp64,2962.440192 | |
| 67 | +realized_fused,1,390000,390000,metal,0,0.0009353337809443474,0.00017445813864469528,0.0009425836615264416,1.2583332136273384e-05,416963449.78178984,5,fp32,781.1072 | |
| 68 | +realized_fused,10,390,3900,cpu,1,1.1292286217212677e-05,1.1167023330926895e-05,1.2415926903486252e-05,0.0,345368504.214433,5,fp64,3432.742912 | |
| 69 | +realized_fused,10,390,3900,cpu,18,0.00014200014993548393,0.0001277080737054348,0.0001649591140449047,0.0,27464759.732802525,5,fp64,577.175552 | |
| 70 | +realized_fused,10,390,3900,metal,0,0.0002327919937670231,0.00019591627642512321,0.0002467092126607895,3.124994691461325e-05,16753153.477877328,5,fp32,3255.451648 | |
| 71 | +realized_fused,10,3900,39000,cpu,1,0.00018791621550917625,0.00017224997282028198,0.00020966678857803345,0.0,207539300.929012,5,fp64,3431.858176 | |
| 72 | +realized_fused,10,3900,39000,cpu,18,0.000135000329464674,0.00012287497520446777,0.0001421659253537655,0.0,288888183.86332357,5,fp64,3360.096256 | |
| 73 | +realized_fused,10,3900,39000,metal,0,0.00016404176130890846,0.00015954114496707916,0.0009339582175016403,1.6249949112534523e-05,237744338.32467064,5,fp32,3222.339584 | |
| 74 | +realized_fused,10,39000,390000,cpu,1,0.002572625409811735,0.0020360001362860203,0.0035845423117280006,0.0,151596108.2062624,5,fp64,2962.440192 | |
| 75 | +realized_fused,10,39000,390000,cpu,18,0.00036349985748529434,0.00035787513479590416,0.00039070891216397285,0.0,1072902759.0217906,5,fp64,3369.04192 | |
| 76 | +realized_fused,10,39000,390000,metal,0,0.0007184999994933605,0.000268666073679924,0.0007987502031028271,5.52500132471323e-05,542797495.1635388,5,fp32,3355.901952 | |
| 77 | +realized_fused,10,390000,3900000,cpu,1,0.02089220890775323,0.020823125261813402,0.021495667286217213,0.0,186672458.48535842,5,fp64,3431.497728 | |
| 78 | +realized_fused,10,390000,3900000,cpu,18,0.0025267917662858963,0.0025061247870326042,0.0027628750540316105,0.0,1543459200.7289019,5,fp64,3431.858176 | |
| 79 | +realized_fused,10,390000,3900000,metal,0,0.0010219174437224865,0.001003749668598175,0.0010474580340087414,8.649996016174555e-05,3816355248.6134977,5,fp32,3222.339584 | |
| 80 | +realized_fused,100,390,39000,cpu,1,0.0001871250569820404,0.00016624992713332176,0.00021525006741285324,0.0,208416770.2016683,5,fp64,2962.440192 | |
| 81 | +realized_fused,100,390,39000,cpu,18,0.0005520828999578953,0.0004998329095542431,0.0005905842408537865,0.0,70641564.88631389,5,fp64,3431.530496 | |
| 82 | +realized_fused,100,390,39000,metal,0,0.00022633420303463936,0.00017816666513681412,0.00027566729113459587,3.15000070258975e-05,172311561.73966,5,fp32,3368.943616 | |
| 83 | +realized_fused,100,3900,390000,cpu,1,0.002043417189270258,0.0020072502084076405,0.0020909998565912247,0.0,190856767.7945766,5,fp64,3432.742912 | |
| 84 | +realized_fused,100,3900,390000,cpu,18,0.0006015831604599953,0.0005330839194357395,0.0006621670909225941,0.0,648289423.0313727,5,fp64,3355.8528 | |
| 85 | +realized_fused,100,3900,390000,metal,0,0.0006413329392671585,0.000292791984975338,0.0008833748288452625,5.287490785121918e-05,608108481.7593294,5,fp32,490.962944 | |
| 86 | +realized_fused,100,39000,3900000,cpu,1,0.020590624772012234,0.020551583264023066,0.020679709035903215,0.0,189406588.83265492,5,fp64,3222.339584 | |
| 87 | +realized_fused,100,39000,3900000,cpu,18,0.0021904585883021355,0.001996333710849285,0.002361500170081854,0.0,1780449089.8971806,5,fp64,2962.440192 | |
| 88 | +realized_fused,100,39000,3900000,metal,0,0.0011692089028656483,0.0008370000869035721,0.0011960407719016075,0.000259208376519382,3335588696.289753,5,fp32,3360.096256 | |
| 89 | +realized_fused,100,390000,39000000,cpu,1,0.2325868341140449,0.2128961249254644,0.24819900002330542,0.0,167679310.60481706,5,fp64,2962.440192 | |
| 90 | +realized_fused,100,390000,39000000,cpu,18,0.01879258267581463,0.016645667143166065,0.02031658310443163,0.0,2075286865.7159925,5,fp64,2962.440192 | |
| 91 | +realized_fused,100,390000,39000000,metal,0,0.008720249868929386,0.007397250272333622,0.008947291877120733,0.0021910000359639525,4472348910.43187,5,fp32,486.178816 | |
| 92 | +realized_fused,1000,390,390000,cpu,1,0.002235791180282831,0.0021259579807519913,0.003065959084779024,0.0,174434895.10083154,5,fp64,2962.440192 | |
| 93 | +realized_fused,1000,390,390000,cpu,18,0.0008399169892072678,0.0007132496684789658,0.0009002499282360077,0.0,464331600.6360231,5,fp64,3355.8528 | |
| 94 | +realized_fused,1000,390,390000,metal,0,0.00033845799043774605,0.00033012498170137405,0.00035137496888637543,0.00013987498823553324,1152284806.4410944,5,fp32,3431.87456 | |
| 95 | +realized_fused,1000,3900,3900000,cpu,1,0.021244540810585022,0.021230708342045546,0.021389917004853487,0.0,183576573.14282066,5,fp64,3431.530496 | |
| 96 | +realized_fused,1000,3900,3900000,cpu,18,0.0017422502860426903,0.0017107920721173286,0.0017863749526441097,0.0,2238484350.522551,5,fp64,3431.46496 | |
| 97 | +realized_fused,1000,3900,3900000,metal,0,0.0008750832639634609,0.0008294158615171909,0.0015468327328562737,0.0002547500189393759,4456718761.065055,5,fp32,3432.742912 | |
| 98 | +realized_fused,1000,39000,39000000,cpu,1,0.23877166723832488,0.21975037455558777,0.2514020833186805,0.0,163335962.13939813,5,fp64,2962.440192 | |
| 99 | +realized_fused,1000,39000,39000000,cpu,18,0.02024729223921895,0.019154875073581934,0.029473000206053257,0.0,1926183488.5979028,5,fp64,2962.440192 | |
| 100 | +realized_fused,1000,39000,39000000,metal,0,0.005891874898225069,0.005617166869342327,0.00844891695305705,0.0009469999931752682,6619285146.693929,5,fp32,3369.04192 | |
| 101 | +realized_fused,10000,390,3900000,cpu,1,0.021238334011286497,0.020878124982118607,0.021370540838688612,0.0,183630222.49897087,5,fp64,3431.858176 | |
| 102 | +realized_fused,10000,390,3900000,cpu,18,0.002125917002558708,0.0019880831241607666,0.002400666009634733,0.0,1834502473.6647966,5,fp64,2962.440192 | |
| 103 | +realized_fused,10000,390,3900000,metal,0,0.0022132499143481255,0.0018930002115666866,0.0032122922129929066,0.001203041640110314,1762114605.6380522,5,fp32,3431.87456 | |
| 104 | +realized_fused,10000,3900,39000000,cpu,1,0.2336724577471614,0.22654250031337142,0.24493679078295827,0.0,166900285.87878695,5,fp64,2962.440192 | |
| 105 | +realized_fused,10000,3900,39000000,cpu,18,0.01569391693919897,0.015392750035971403,0.01590104214847088,0.0,2485039276.7524476,5,fp64,3432.742912 | |
| 106 | +realized_fused,10000,3900,39000000,metal,0,0.0078027499839663506,0.006132957991212606,0.008690916933119297,0.0019207500154152513,4998237811.046104,5,fp32,577.1264 | |
| 107 | +regression_stats,1,390,390,cpu,1,3.1669624149799347e-06,3.125052899122238e-06,3.2088719308376312e-06,0.0,123146393.57741508,5,fp64,2962.440192 | |
| 108 | +regression_stats,1,390,390,cpu,18,3.2088719308376312e-06,3.2079406082630157e-06,3.3332034945487976e-06,0.0,121538038.41532433,5,fp64,2962.440192 | |
| 109 | +regression_stats,1,390,390,metal,0,0.000894167460501194,0.00017508305609226227,0.000988542102277279,7.087492849677801e-05,436159.91100973333,5,fp32,3368.910848 | |
| 110 | +regression_stats,1,3900,3900,cpu,1,2.9958784580230713e-05,2.950010821223259e-05,3.0708033591508865e-05,0.0,130178845.859239,5,fp64,3368.894464 | |
| 111 | +regression_stats,1,3900,3900,cpu,18,3.0207913368940353e-05,3.008265048265457e-05,3.0375085771083832e-05,0.0,129105243.13175379,5,fp64,2962.440192 | |
| 112 | +regression_stats,1,3900,3900,metal,0,0.0003482499159872532,0.0003069578669965267,0.0003833337686955929,0.00019212497863918543,11198854.101497471,5,fp32,2962.440192 | |
| 113 | +regression_stats,1,39000,39000,cpu,1,0.00030233291909098625,0.00030054105445742607,0.0003049168735742569,0.0,128996869.13770398,5,fp64,2962.440192 | |
| 114 | +regression_stats,1,39000,39000,cpu,18,0.0003838753327727318,0.0003343336284160614,0.0006159590557217598,0.0,101595483.4042161,5,fp64,578.486272 | |
| 115 | +regression_stats,1,39000,39000,metal,0,0.0004085828550159931,0.0003508748486638069,0.00041229184716939926,0.00018866662867367268,95451875.96888623,5,fp32,3359.932416 | |
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| 119 | +regression_stats,10,390,3900,cpu,1,3.1250063329935074e-05,3.095809370279312e-05,4.149973392486572e-05,0.0,124799747.08608383,5,fp64,2920.185856 | |
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| 122 | +regression_stats,10,3900,39000,cpu,1,0.0002997498959302902,0.0002982090227305889,0.000300500076264143,0.0,130108468.85855077,5,fp64,2962.440192 | |
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| 131 | +regression_stats,100,390,39000,cpu,1,0.00036137504503130913,0.00033475039526820183,0.00036225002259016037,0.0,107921121.10735561,5,fp64,2962.440192 | |
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| 134 | +regression_stats,100,3900,390000,cpu,1,0.0029982919804751873,0.0029679168947041035,0.003063875250518322,0.0,130074056.34263493,5,fp64,3432.742912 | |
| 135 | +regression_stats,100,3900,390000,cpu,18,0.0004399162717163563,0.00042741699144244194,0.00046166684478521347,0.0,886532335.9792868,5,fp64,781.484032 | |
| 136 | +regression_stats,100,3900,390000,metal,0,0.0005946666933596134,0.0005814996547996998,0.0005976245738565922,0.00023925001733005047,655829566.9741753,5,fp32,2962.440192 | |
| 137 | +regression_stats,100,39000,3900000,cpu,1,0.03219050029292703,0.03135691722854972,0.03299033408984542,0.0,121153755.44060485,5,fp64,3355.901952 | |
| 138 | +regression_stats,100,39000,3900000,cpu,18,0.0031737093813717365,0.003017541952431202,0.0036639999598264694,0.0,1228845975.2777827,5,fp64,3355.901952 | |
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| 140 | +regression_stats,100,390000,39000000,cpu,1,0.3013692502863705,0.2989709582179785,0.3020119168795645,0.0,129409354.01651289,5,fp64,3431.87456 | |
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| 143 | +regression_stats,1000,390,390000,cpu,1,0.0031211250461637974,0.0030487077310681343,0.0040359580889344215,0.0,124954942.28254408,5,fp64,3432.742912 | |
| 144 | +regression_stats,1000,390,390000,cpu,18,0.0006971252150833607,0.0005761669017374516,0.0007857088930904865,0.0,559440386.8369108,5,fp64,2962.440192 | |
| 145 | +regression_stats,1000,390,390000,metal,0,0.0005814996547996998,0.0005787923000752926,0.0009665000252425671,0.00020362494979053736,670679675.870723,5,fp32,3431.858176 | |
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| 147 | +regression_stats,1000,3900,3900000,cpu,18,0.003421790897846222,0.0031987917609512806,0.003632874693721533,0.0,1139754040.0422413,5,fp64,3431.514112 | |
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| 149 | +regression_stats,1000,39000,39000000,cpu,1,0.3240363751538098,0.3117389581166208,0.326583041343838,0.0,120356858.02709013,5,fp64,3431.46496 | |
| 150 | +regression_stats,1000,39000,39000000,cpu,18,0.031240916810929775,0.029546833131462336,0.03264595801010728,0.0,1248362851.7059293,5,fp64,3431.87456 | |
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