# fdars Performance Report

A single-threaded head-to-head of `fdars-core` against scikit-fda 0.10.1 and the
R FDA ecosystem (`fda`, `fda.usc`), before and after the v0.47.0 optimization
pass. Every number below is traceable to a committed CSV in
`benchmarks/results/` and the environment snapshot in `benchmarks/results/env.json`
— see [Methodology](#methodology) and [Reproduction](#reproduction) for the
exact commands that produced it.

## How to read this report

- **†** (dagger) — the fdars measurement failed the noise gate (RSD >= 5% or
  CI-width >= 5%). A daggered cell is never headlined as a confirmed win or
  loss, even when the raw ratio looks favorable.
- **Significant?** — "yes" means the two 95% confidence intervals are
  strictly non-overlapping (touching CIs count as "no"). Only a "yes" backs a
  speedup or regression claim; everything else is reported as a directional
  ratio with the caveat spelled out in prose.
- **Ratio semantics** — every `fdars vs X` ratio is `X time / fdars time`.
  A ratio at least 10% above 1.0 is "N× faster" (fdars wins); a ratio at
  least 10% below 1.0 is "N× slower" (fdars loses); anything within that
  +/-10% parity band is reported as "comparable", not as a win either way.
- **Single-threaded throughout** — every table in this report, and every
  reproduction command below, pins `OMP_NUM_THREADS`, `OPENBLAS_NUM_THREADS`,
  `MKL_NUM_THREADS`, `RAYON_NUM_THREADS`, `NUMEXPR_NUM_THREADS`, and
  `VECLIB_MAXIMUM_THREADS` to `1` on every side (fdars, scikit-fda, R). No
  table in this document reports a multi-threaded number; the `parallel`
  feature and rayon are discussed only qualitatively (see
  [Threading](#threading)).

## Summary

<!-- BEGIN GENERATED: key-findings -->
_Generated by `benchmarks/render_report.py` from comparison.csv, comparison_baseline.csv, ab/manifest.json, rerun_log.json — do not edit by hand._

| Finding | Value | Evidence |
|---|---|---|
| Headline A/B (phase116_face_covariance_n200_m30) | 1.19× faster | perf_face_covariance/n200_m30 |
| Elastic-alignment A/B (phase114_elastic_cross_banded_n500_m50) | -2.0% (not significant (CIs overlap)) | before noise: FAIL-NOISY |
| SVD re-bench | see phase115_svd_rebench | faer thin SVD re-benchmark (near-optimal verdict) |
| Largest-cell verdict vs scikit-fda | 6 faster / 0 comparable / 0 slower | headline cell N=500, M=200, noise-passing only |
| Largest-cell verdict vs R | 6 faster / 0 comparable / 0 slower | headline cell N=500, M=200, noise-passing only |
| Re-run coverage (missing rows) | id-not-produced: 9, inferred-timeout: 3, orphan: 20, timeout: 4 | classify_missing over baseline/after diff |
<!-- END GENERATED: key-findings -->

- **face_covariance (the one committed A/B win): headlined at 1.19× faster,
  pinned and noise-clean.** The controlled, single-threaded, thread-pinned
  re-measurement (`phase116_face_covariance_n200_m30`, this phase) is the
  only A/B entry that is `headline_eligible`: both sides pass the noise gate
  and the CIs are strictly disjoint. The larger `3.45×` figure from Phase 115
  is real evidence but was measured on the default (unpinned, multi-threaded)
  rayon pool with a BEFORE cell that failed the noise gate — it is shown in
  the table above for provenance but is not reproduced under single-threaded,
  noise-gated conditions and is never claimed as this report's headline.
- **Elastic alignment: numeric-identical, within noise, not a speedup.** The
  Phase 114 `dp_fill_grid` banded-iteration refactor is proven bit-identical
  by the golden-fixture suite; its A/B entry's CIs overlap and its BEFORE
  cell failed the noise gate. This report does not claim elastic alignment
  got faster — the hot path was already near-optimal going in (symmetry
  exploitation, one-time SRSF precompute, thread-local scratch reuse).
- **SVD: already near-optimal, no change made.** faer's thin SVD is already
  the production path under the `linalg` feature (`regression.rs`); Phase 115
  re-benchmarked it at tighter sample counts and found nothing worth
  changing. There is no before/after pair for SVD in this report — only the
  re-benchmark entry in the A/B table.
- **Head-to-head at the largest grid cell (N=500, M=200): fdars leads on
  every op that passed the noise gate**, per the "Largest-cell verdict" rows
  in the table above — every measured op that passed the gate favored fdars
  against both scikit-fda and R, with none comparable or slower.
- **The Phase 114–115 optimizations are not on any harness op's code path.**
  The harness `elastic` op times the unbanded pairwise alignment
  (`elastic_align_pair`), while Phase 114 changed only the banded DP arm
  (114-02-SUMMARY); `face_covariance` has no scikit-fda/R comparator at all.
  The cross-language cells in this report were therefore never expected to
  move because of Phase 114/115 — the "before/after vs the Phase 113
  baseline" tables below measure re-run drift and methodology changes
  (thread pinning, mixed-vintage baseline), not an optimization effect.
- **Re-run coverage:** 7 heavy single-threaded elastic/Karcher chunks did not
  complete inside the 540s per-chunk bound and are recorded as timed out or
  inferred-timed-out (never silently dropped); a further set of legacy audit
  groups are orphaned (removed from the bench files) or did not reproduce
  a specific criterion id. Every one of them is listed by name, with a
  reason, in [Before/after vs the Phase 113 baseline](#beforeafter-vs-the-phase-113-baseline).

## Headline — largest grid cell (N=500, M=200)

<!-- BEGIN GENERATED: headline -->
_Generated by `benchmarks/render_report.py` from comparison.csv — do not edit by hand._

| Op | N | M | fdars (ms) | scikit-fda (ms) | R (ms) | fdars vs scikit-fda | fdars vs R |
|----|---|---|------------|------------------|--------|----------------------|------------|
| fpca | 500 | 200 | 10.152 | 12.357 | 41.017 | 1.22× faster | 4.04× faster |
| basis_smoothing | 500 | 200 | 0.834 | 4.199 | 4.324 | 5.04× faster | 5.19× faster |
| depth | 500 | 200 | 3.511 | 15.591 | 8.855 | 4.44× faster | 2.52× faster |
| functional_boxplot | 500 | 200 | 3.617 | 16.616 | 21.627 | 4.59× faster | 5.98× faster |
| fpcr | 500 | 200 | 10.241 | 12.636 | 1049.904 | 1.23× faster | 102.52× faster |
| elastic | 500 | 200 | 27.470 | 33.542 | 32.517 | 1.22× faster | 1.18× faster |

† fdars measurement failed the noise gate (RSD >= 5% or CI-width >= 5%) — not headlined as significant.
<!-- END GENERATED: headline -->

N=500, M=200 is the largest cell on the locked grid (N in {100, 300, 500},
M in {50, 200}) — the point where asymptotic behavior is most visible and
where a real regression or win is least likely to be an artifact of
constant-factor noise.

## Head-to-head across the N×M grid

<!-- BEGIN GENERATED: head-to-head -->
_Generated by `benchmarks/render_report.py` from comparison.csv — do not edit by hand._

#### fpca

| N | M | fdars (ms) [95% CI] | scikit-fda (ms) | R SVD-matched (ms) | R native pca.fd (ms)¹ | fdars vs scikit-fda | fdars vs R |
|---|---|---|---|---|---|---|---|
| 100 | 50 | 0.424 [0.423, 0.426] | 1.554 | 1.006 | 7.019 | 3.66× faster | 2.37× faster |
| 100 | 200 | 1.985 [1.981, 1.992] | 3.755 | 5.189 | 7.460 | 1.89× faster | 2.61× faster |
| 300 | 50 | 0.683 [0.679, 0.688] | 1.501 | 1.915 | 9.172 | 2.20× faster | 2.80× faster |
| 300 | 200 | 7.209 [7.194, 7.228] | 8.759 | 25.561 | 9.048 | 1.22× faster | 3.55× faster |
| 500 | 50 | 0.913 [0.908, 0.921] | 1.270 | 2.873 | 10.860 | 1.39× faster | 3.15× faster |
| 500 | 200 | 10.152 [10.128, 10.183] | 12.357 | 41.017 | 9.449 | 1.22× faster | 4.04× faster |

¹ R native `fda::pca.fd` — ecosystem-realistic timing, not gated (B-spline coefficient space).

- FPCA fdars-vs-python subspace cos=0.9816 (hard-gated on fdars-vs-r=1.0; python DISCLOSED — scikit-fda trapezoidal vs fdars/R Simpson's quadrature tilts trailing PCs; Phase 116 finding)
- FPCA fdars-vs-python subspace cos=0.9986 (hard-gated on fdars-vs-r=1.0; python DISCLOSED — scikit-fda trapezoidal vs fdars/R Simpson's quadrature tilts trailing PCs; Phase 116 finding)
- FPCA fdars-vs-python subspace cos=0.9992 (hard-gated on fdars-vs-r=1.0; python DISCLOSED — scikit-fda trapezoidal vs fdars/R Simpson's quadrature tilts trailing PCs; Phase 116 finding)
- FPCA fdars-vs-python subspace cos=0.9994 (hard-gated on fdars-vs-r=1.0; python DISCLOSED — scikit-fda trapezoidal vs fdars/R Simpson's quadrature tilts trailing PCs; Phase 116 finding)
- FPCA fdars-vs-python subspace cos=0.9998 (hard-gated on fdars-vs-r=1.0; python DISCLOSED — scikit-fda trapezoidal vs fdars/R Simpson's quadrature tilts trailing PCs; Phase 116 finding)

#### basis_smoothing

| N | M | fdars (ms) [95% CI] | scikit-fda (ms) | R SVD-matched (ms) | fdars vs scikit-fda | fdars vs R |
|---|---|---|---|---|---|---|
| 100 | 50 | 0.053 [0.052, 0.055]† | 0.370 | 0.796 | 6.95× faster | 14.95× faster |
| 100 | 200 | 0.211 [0.203, 0.223]† | 1.461 | 1.707 | 6.92× faster | 8.09× faster |
| 300 | 50 | 0.137 [0.136, 0.137] | 0.453 | 1.643 | 3.32× faster | 12.03× faster |
| 300 | 200 | 0.514 [0.513, 0.517] | 2.829 | 3.132 | 5.50× faster | 6.09× faster |
| 500 | 50 | 0.216 [0.216, 0.217] | 0.525 | 2.507 | 2.43× faster | 11.60× faster |
| 500 | 200 | 0.834 [0.828, 0.842] | 4.199 | 4.324 | 5.04× faster | 5.19× faster |

#### depth

| N | M | fdars (ms) [95% CI] | scikit-fda (ms) | R SVD-matched (ms) | fdars vs scikit-fda | fdars vs R |
|---|---|---|---|---|---|---|
| 100 | 50 | 0.105 [0.104, 0.106] | 1.329 | 0.829 | 12.61× faster | 7.87× faster |
| 100 | 200 | 0.546 [0.518, 0.578]† | 3.720 | 2.748 | 6.81× faster | 5.03× faster |
| 300 | 50 | 0.506 [0.461, 0.561]† | 2.660 | 1.762 | 5.25× faster | 3.48× faster |
| 300 | 200 | 2.068 [2.035, 2.104] | 9.692 | 6.955 | 4.69× faster | 3.36× faster |
| 500 | 50 | 0.757 [0.748, 0.767] | 4.074 | 2.787 | 5.38× faster | 3.68× faster |
| 500 | 200 | 3.511 [3.454, 3.570] | 15.591 | 8.855 | 4.44× faster | 2.52× faster |

#### functional_boxplot

| N | M | fdars (ms) [95% CI] | scikit-fda (ms) | R SVD-matched (ms) | fdars vs scikit-fda | fdars vs R |
|---|---|---|---|---|---|---|
| 100 | 50 | 0.124 [0.119, 0.129]† | 1.794 | 2.070 | 14.48× faster | 16.70× faster |
| 100 | 200 | 0.617 [0.589, 0.653]† | 4.170 | 6.683 | 6.76× faster | 10.83× faster |
| 300 | 50 | 0.509 [0.498, 0.522]† | 3.183 | 4.233 | 6.25× faster | 8.32× faster |
| 300 | 200 | 2.158 [2.095, 2.225]† | 10.064 | 14.303 | 4.66× faster | 6.63× faster |
| 500 | 50 | 0.926 [0.909, 0.943]† | 4.712 | 7.058 | 5.09× faster | 7.62× faster |
| 500 | 200 | 3.617 [3.570, 3.671] | 16.616 | 21.627 | 4.59× faster | 5.98× faster |

#### fpcr

| N | M | fdars (ms) [95% CI] | scikit-fda (ms) | R SVD-matched (ms) | fdars vs scikit-fda | fdars vs R |
|---|---|---|---|---|---|---|
| 100 | 50 | 0.430 [0.428, 0.432] | 1.308 | 36.030 | 3.04× faster | 83.80× faster |
| 100 | 200 | 2.007 [2.000, 2.016] | 3.721 | 85.633 | 1.85× faster | 42.66× faster |
| 300 | 50 | 0.699 [0.697, 0.701] | 1.631 | 96.773 | 2.33× faster | 138.51× faster |
| 300 | 200 | 7.452 [7.374, 7.541] | 9.246 | 619.725 | 1.24× faster | 83.16× faster |
| 500 | 50 | 0.940 [0.937, 0.943] | 1.420 | 153.821 | 1.51× faster | 163.72× faster |
| 500 | 200 | 10.241 [10.154, 10.344] | 12.636 | 1049.904 | 1.23× faster | 102.52× faster |

- FPCR cross-library agreement corr=0.7944 @ n=500 (scikit-fda FPCA->OLS vs R fda.usc fregre.pc: related but not identical FPCR; NOT hard-gated — disclosed divergence for the Phase 116 report)
- FPCR cross-library agreement corr=0.8061 @ n=300 (scikit-fda FPCA->OLS vs R fda.usc fregre.pc: related but not identical FPCR; NOT hard-gated — disclosed divergence for the Phase 116 report)
- FPCR cross-library agreement corr=0.8585 @ n=500 (scikit-fda FPCA->OLS vs R fda.usc fregre.pc: related but not identical FPCR; NOT hard-gated — disclosed divergence for the Phase 116 report)
- FPCR cross-library agreement corr=0.9236 @ n=300 (scikit-fda FPCA->OLS vs R fda.usc fregre.pc: related but not identical FPCR; NOT hard-gated — disclosed divergence for the Phase 116 report)
- FPCR cross-library agreement corr=0.9495 @ n=100 (scikit-fda FPCA->OLS vs R fda.usc fregre.pc: related but not identical FPCR; NOT hard-gated — disclosed divergence for the Phase 116 report)
- FPCR cross-library agreement corr=0.9797 @ n=100 (scikit-fda FPCA->OLS vs R fda.usc fregre.pc: related but not identical FPCR; NOT hard-gated — disclosed divergence for the Phase 116 report)

#### elastic

| N | M | fdars (ms) [95% CI] | scikit-fda (ms) | R SVD-matched (ms) | fdars vs scikit-fda | fdars vs R |
|---|---|---|---|---|---|---|
| 100 | 50 | 1.839 [1.679, 2.008]† | 3.106 | 2.784 | 1.69× faster | 1.51× faster |
| 100 | 200 | 27.701 [27.401, 28.031] | 33.616 | 32.529 | 1.21× faster | 1.17× faster |
| 300 | 50 | 1.593 [1.516, 1.686]† | 2.877 | 1.921 | 1.81× faster | 1.21× faster |
| 300 | 200 | 28.597 [27.936, 29.292]† | 33.571 | 32.815 | 1.17× faster | 1.15× faster |
| 500 | 50 | 1.499 [1.475, 1.526] | 2.882 | 1.918 | 1.92× faster | 1.28× faster |
| 500 | 200 | 27.470 [27.237, 27.714] | 33.542 | 32.517 | 1.22× faster | 1.18× faster |

- Karcher-mean elastic excluded from grid baseline: noise-gated (RSD 29-46%); anchor uses pairwise elastic_align_pair
<!-- END GENERATED: head-to-head -->

- **FPCA has two R comparators.** `r_svd` is a hand-rolled, Simpson-weighted
  SVD port of fdars' own algorithm — it is the ecosystem-independent,
  hard-gated comparator (fdars-vs-R subspace cosine = 1.0 on every cell).
  `r_native_pca_fd` is R's own `fda::pca.fd`, which works in B-spline
  coefficient space rather than raw evaluation-point space; it is timed for
  ecosystem realism but is not gated (it was found in Phase 113 to diverge
  numerically from fdars at PC3–PC5 because of the coefficient-space
  smoothing, not because either implementation is wrong).
- **FPCR is a disclosed, not a gated, cross-library comparison.** scikit-fda's
  FPCR (FPCA scores → OLS) and R's `fda.usc::fregre.pc` are related but not
  identical algorithms; their correlation is reported per-cell in the table
  above for transparency, never used to pass/fail a run.
- **The FPCA quadrature convention differs by ecosystem.** scikit-fda
  integrates with the trapezoid rule; fdars and the R `r_svd` port both use
  Simpson's rule. This is disclosed (not hard-gated) for the fdars-vs-python
  FPCA comparison and is the reason that comparison's subspace cosine is
  below 1.0 while fdars-vs-R stays at 1.0 on every cell.
- **The `elastic` op is pairwise and N-independent by construction.** The
  harness always times a fixed 2-curve alignment regardless of the grid's N,
  so its row varies with M only — this is a property of what is being
  measured, not a claim about how `elastic_align_pair` scales with corpus
  size (see [N×M scaling](#nm-scaling) for the M-only exponent).

## Optimization results (controlled A/B)

<!-- BEGIN GENERATED: ab-evidence -->
_Generated by `benchmarks/render_report.py` from ab/manifest.json — do not edit by hand._

| Entry | Kind | Before (ms) | After (ms) | Speedup | Significant? | Noise before/after | Thread config | SHAs | Headline? |
|---|---|---|---|---|---|---|---|---|---|
| phase114_elastic_cross_banded_n500_m50 | ab | 7310.074 | 7163.866 | 1.02× | no | FAIL-NOISY/PASS | default rayon pool (not thread-pinned); identical configuration on both sides | 8c0b1d7d -> 30d2c9a2 |  |
| phase115_face_covariance_n200_m30 | ab | 268.166 | 77.786 | 3.45× | yes | FAIL-NOISY/PASS | default rayon pool (not thread-pinned); identical configuration on both sides | 328215e7 -> c0e84bd8 |  |
| phase115_svd_rebench | rebench | — | — | — | — | — | default rayon pool (not thread-pinned); identical configuration across cells | 74b9ab0d |  |
| phase116_face_covariance_n200_m30 | ab | 300.891 | 252.512 | 1.19× | yes | PASS/PASS | pinned: all six *_NUM_THREADS=1 (identical both sides) | 7cde79b24ea259318f358e4d57957bb2435f8995 -> e98b862dd3b39a2843fe1f33889e876aebc46921 | yes |
<!-- END GENERATED: ab-evidence -->

Every A/B entry above controls for confounds the same way: identical bench
invocation, identical criterion settings, and a `Cargo.lock` copied into both
scratch worktrees so dependency versions cannot drift between the before and
after measurement — the two sides differ only in the commit checked out. The
Phase 114 and Phase 115 entries were measured on the default (unpinned)
rayon thread pool, disclosed verbatim in each entry's `thread_config` column;
they are legitimate evidence for those phases' own verdicts but are not
apples-to-apples with a single-threaded head-to-head. Phase 116 re-measured
`face_covariance` a third time, this time thread-pinned and at raised
settings (`sample_size` 15, 30s measurement, 3s warm-up — round 0), because
Phase 115's BEFORE cell for that same criterion id failed the noise gate; a
single round sufficed and no further rounds were needed.

## Before/after vs the Phase 113 baseline

Read every table in this section as a **traceability record of what changed
between Phase 113 and Phase 116**, not as an optimization measurement (the
A/B tables above are the optimization measurement). Four things changed
between the two runs simultaneously, and this report does not attempt to
separate their individual contributions to any one row's delta:

- Phase 113 re-ran only `fregre_lm` and `functional_boxplot` live on the
  fdars side; every other fdars row in the Phase 113 baseline came from
  whatever criterion output already existed on disk at the time — of mixed
  vintage, spanning several earlier optimization phases.
- Those pre-existing baseline rows were measured under the default,
  multi-core rayon pool (no thread pinning). Several of the large deltas
  below on `elastic`/`karcher`-family groups are exactly this: losing
  rayon's parallelism between the baseline and a single-threaded re-run,
  not a regression in the underlying algorithm.
- Six benchmark groups present in the Phase 113 baseline no longer exist in
  the current bench files (`coclustering_co_cluster`, `face_covariance`,
  `fem_smooth`, `fpca_variants_fsvd`, `frechet_anova`,
  `fts_long_run_covariance`) — they are flagged `orphan` in the table below,
  not silently dropped.
- The Phase 116 after-run is thread-pinned end-to-end (all six
  `*_NUM_THREADS=1`), matching the cross-language harness's fairness
  contract.

### fdars rows for ops with a scikit-fda/R comparator

<!-- BEGIN GENERATED: before-after-crosslang-fdars -->
_Generated by `benchmarks/render_report.py` from comparison_baseline.csv, comparison.csv — do not edit by hand._

before = Phase 113 comparison_baseline.csv (fdars rows collected from on-disk criterion output, not thread-pinned, mixed vintage); after = Phase 116 thread-pinned re-run (rerun_log head_sha 242ab06722cfb68de28dd57203d3eb4757062a6f); delta is not an optimization measure — see A/B evidence.

**fdars-only before/after for ops that ALSO have a scikit-fda/R comparator elsewhere in this report (see “fdars vs Python/R” above) — rows below compare the SAME rust criterion id across two runs; they are not themselves validated against Python/R at this cell. Several rows (the audit_p3_elastic_*/audit_karcher/karcher_mean self- and cross-distance-matrix and payback sweeps) measure a different sub-operation than the grid-aligned comparator bench and have no direct Python/R equivalent.**

| Source | N | M | Before ms [CI] | After ms [CI] | delta % | Significant? | Noise before/after |
|---|---|---|---|---|---|---|---|
| audit_depth/n500_m200 | 500.0 | 200.0 | 0.469 [0.460, 0.478] | 3.365 [3.102, 3.637] | +617.7% | yes | FAIL-NOISY/FAIL-NOISY |
| audit_elastic/n100_m50_capped | 100.0 | 50.0 | 816.797 [809.964, 824.040] | 7139.152 [7108.057, 7173.160] | +774.0% | yes | PASS/PASS |
| audit_fpca/n500_m200 | 500.0 | 200.0 | 16.391 [16.325, 16.465] | 4.939 [4.875, 5.003] | -69.9% | yes | PASS/PASS |
| audit_karcher/n100_m50 | 100.0 | 50.0 | 162.283 [159.698, 165.016] | 1583.859 [1577.355, 1593.096] | +876.0% | yes | PASS/PASS |
| audit_p3_elastic_cross/n100_m50 | 100.0 | 50.0 | 1565.454 [1540.027, 1592.022] | 14355.925 [14322.811, 14393.542] | +817.0% | yes | PASS/PASS |
| audit_p3_elastic_cross_banded/n100_m50 | 100.0 | 50.0 | 324.137 [320.564, 328.018] | 3251.989 [3215.115, 3288.837] | +903.3% | yes | PASS/PASS |
| audit_p3_elastic_self/n100_m50 | 100.0 | 50.0 | 1479.460 [1308.937, 1666.878] | 7104.962 [7090.892, 7120.024] | +380.2% | yes | FAIL-NOISY/PASS |
| audit_p3_elastic_self_banded/n100_m200 | 100.0 | 200.0 | 3423.428 [3297.206, 3565.520] | 28353.333 [28272.721, 28448.654] | +728.2% | yes | FAIL-NOISY/PASS |
| audit_p3_elastic_self_banded/n100_m50 | 100.0 | 50.0 | 406.670 [311.848, 507.154] | 1469.353 [1460.451, 1480.550] | +261.3% | yes | FAIL-NOISY/PASS |
| audit_p3_elastic_self_banded/n500_m50 | 500.0 | 50.0 | 4223.193 [4051.851, 4416.070] | 36890.583 [36856.435, 36919.544] | +773.5% | yes | FAIL-NOISY/PASS |
| audit_p3_karcher/n100_m200 | 100.0 | 200.0 | 6483.449 [5407.426, 7711.390] | 30478.628 [30368.935, 30626.327] | +370.1% | yes | FAIL-NOISY/PASS |
| audit_p3_karcher/n100_m50 | 100.0 | 50.0 | 644.766 [541.582, 757.205] | 3055.021 [3019.727, 3108.543] | +373.8% | yes | FAIL-NOISY/PASS |
| audit_p3_karcher/n500_m50 | 500.0 | 50.0 | 3979.197 [3210.227, 4769.585] | 15076.405 [15023.533, 15138.689] | +278.9% | yes | FAIL-NOISY/PASS |
| audit_p3_karcher_banded/n100_m200 | 100.0 | 200.0 | 754.891 [740.368, 775.895] | 6704.583 [6677.103, 6738.090] | +788.2% | yes | PASS/PASS |
| audit_p3_karcher_banded/n100_m50 | 100.0 | 50.0 | 75.449 [67.359, 88.607] | 626.955 [622.427, 631.788] | +731.0% | yes | FAIL-NOISY/PASS |
| audit_p3_karcher_banded/n500_m200 | 500.0 | 200.0 | 4872.579 [4204.307, 5831.564] | 33445.998 [33389.439, 33513.317] | +586.4% | yes | FAIL-NOISY/PASS |
| audit_p3_karcher_banded/n500_m50 | 500.0 | 50.0 | 421.493 [371.738, 489.380] | 3129.779 [3116.317, 3144.433] | +642.5% | yes | FAIL-NOISY/PASS |
| audit_p4_elastic_fpca/joint_fpca_n100_m50 | 100.0 | 50.0 | 1.885 [1.884, 1.885] | 1.966 [1.940, 1.993] | +4.3% | yes | PASS/PASS |
| audit_p4_elastic_fpca/vert_fpca_n100_m50 | 100.0 | 50.0 | 0.301 [0.301, 0.301] | 0.352 [0.339, 0.366] | +17.0% | yes | PASS/FAIL-NOISY |
| audit_p4_fpca/n1000_m200 | 1000.0 | 200.0 | 38.901 [38.858, 38.942] | 9.660 [9.177, 10.343] | -75.2% | yes | PASS/FAIL-NOISY |
| audit_p4_fpca/n1000_m50 | 1000.0 | 50.0 | 3.182 [3.180, 3.183] | 0.826 [0.710, 0.978] | -74.0% | yes | PASS/FAIL-NOISY |
| audit_p4_fpca/n100_m200 | 100.0 | 200.0 | 1.709 [1.707, 1.714] | 0.709 [0.708, 0.710] | -58.5% | yes | PASS/PASS |
| audit_p4_fpca/n100_m50 | 100.0 | 50.0 | 0.213 [0.213, 0.213] | 0.198 [0.174, 0.236] | -6.9% | no | PASS/FAIL-NOISY |
| audit_p4_fpca/n500_m200 | 500.0 | 200.0 | 15.978 [15.973, 15.985] | 5.833 [5.553, 6.148] | -63.5% | yes | PASS/FAIL-NOISY |
| audit_p4_fpca/n500_m50 | 500.0 | 50.0 | 1.233 [1.232, 1.235] | 0.368 [0.360, 0.377] | -70.2% | yes | PASS/FAIL-NOISY |
| audit_p5_karcher_paybackN/n100_m50 | 100.0 | 50.0 | 343.770 [341.044, 346.629] | 1591.791 [1574.794, 1618.384] | +363.0% | yes | PASS/PASS |
| audit_p5_karcher_paybackN/n10_m50 | 10.0 | 50.0 | 55.668 [51.836, 61.519] | 160.653 [159.679, 162.044] | +188.6% | yes | FAIL-NOISY/PASS |
| audit_p5_karcher_paybackN/n25_m50 | 25.0 | 50.0 | 124.956 [118.686, 133.253] | 404.555 [395.937, 414.756] | +223.8% | yes | FAIL-NOISY/PASS |
| audit_p5_karcher_paybackN/n50_m50 | 50.0 | 50.0 | 196.100 [193.017, 200.833] | 785.839 [784.227, 788.138] | +300.7% | yes | PASS/PASS |
| audit_streaming_depth/n500_m200 | 500.0 | 200.0 | 0.526 [0.503, 0.552] | 2.537 [2.480, 2.600] | +382.6% | yes | FAIL-NOISY/FAIL-NOISY |
| elastic_align_pair/m/100 | — | — | 12.377 [12.091, 12.681] | 7.364 [7.134, 7.619] | -40.5% | yes | FAIL-NOISY/FAIL-NOISY |
| elastic_align_pair/m/200 | — | — | 51.742 [51.574, 51.910] | 40.924 [39.234, 42.592] | -20.9% | yes | PASS/FAIL-NOISY |
| elastic_align_pair/m/50 | — | — | 2.802 [2.780, 2.821] | 1.708 [1.655, 1.766] | -39.0% | yes | PASS/FAIL-NOISY |
| elastic_align_pair/m100_lambda0.1 | — | 100.0 | 13.008 [12.913, 13.111] | 7.427 [7.171, 7.707] | -42.9% | yes | PASS/FAIL-NOISY |
| elastic_align_pair/m_band0.1/100 | — | — | 2.656 [2.649, 2.663] | 1.616 [1.562, 1.673] | -39.1% | yes | PASS/FAIL-NOISY |
| elastic_align_pair/m_band0.1/200 | — | — | 11.252 [11.158, 11.316] | 6.853 [6.641, 7.082] | -39.1% | yes | PASS/FAIL-NOISY |
| elastic_align_pair/m_band0.1/50 | — | — | 0.573 [0.572, 0.574] | 0.475 [0.456, 0.494] | -17.1% | yes | PASS/FAIL-NOISY |
| fregre_lm/ncomp/10 | — | — | 0.280 [0.262, 0.301] | 0.243 [0.222, 0.266] | -13.4% | no | FAIL-NOISY/FAIL-NOISY |
| fregre_lm/ncomp/3 | — | — | 0.630 [0.627, 0.633] | 0.213 [0.202, 0.228] | -66.1% | yes | PASS/FAIL-NOISY |
| fregre_lm/ncomp/5 | — | — | 0.626 [0.621, 0.632] | 0.264 [0.240, 0.290] | -57.9% | yes | PASS/FAIL-NOISY |
| fregre_lm/scale/n200_nc5 | 200.0 | — | 0.504 [0.445, 0.566] | 0.300 [0.284, 0.319] | -40.5% | yes | FAIL-NOISY/FAIL-NOISY |
| fregre_lm/scale/n50_nc5 | 50.0 | — | 0.369 [0.368, 0.371] | 0.210 [0.196, 0.224] | -43.2% | yes | PASS/FAIL-NOISY |
| functional_boxplot/N/1000 | — | — | 12.713 [11.887, 13.539] | 10.560 [9.976, 11.192] | -16.9% | yes | FAIL-NOISY/FAIL-NOISY |
| functional_boxplot/N/200 | — | — | 1.621 [1.526, 1.718] | 1.043 [0.999, 1.094] | -35.6% | yes | FAIL-NOISY/FAIL-NOISY |
| functional_boxplot/N/2300 | — | — | 44.705 [42.571, 46.710] | 26.741 [25.368, 28.236] | -40.2% | yes | FAIL-NOISY/FAIL-NOISY |
| functional_boxplot/N/50 | — | — | 0.316 [0.299, 0.334] | 0.235 [0.223, 0.247] | -25.6% | yes | FAIL-NOISY/FAIL-NOISY |
| functional_boxplot/N/500 | — | — | 6.048 [5.676, 6.408] | 3.901 [3.643, 4.181] | -35.5% | yes | FAIL-NOISY/FAIL-NOISY |
| karcher_mean/n10_m50 | 10.0 | 50.0 | 210.487 [203.862, 216.958] | 247.301 [242.701, 252.367] | +17.5% | yes | FAIL-NOISY/FAIL-NOISY |
| karcher_mean/n20_m50 | 20.0 | 50.0 | 317.509 [299.522, 335.291] | 475.092 [471.541, 478.855] | +49.6% | yes | FAIL-NOISY/PASS |
<!-- END GENERATED: before-after-crosslang-fdars -->

### fdars internal before/after (no scikit-fda/R comparator)

<!-- BEGIN GENERATED: before-after-internal -->
_Generated by `benchmarks/render_report.py` from comparison_baseline.csv, comparison.csv — do not edit by hand._

before = Phase 113 comparison_baseline.csv (fdars rows collected from on-disk criterion output, not thread-pinned, mixed vintage); after = Phase 116 thread-pinned re-run (rerun_log head_sha 242ab06722cfb68de28dd57203d3eb4757062a6f); delta is not an optimization measure — see A/B evidence.

**fdars-internal before/after (no scikit-fda/R comparator)**

| Source | N | M | Before ms [CI] | After ms [CI] | delta % | Significant? | Noise before/after |
|---|---|---|---|---|---|---|---|
| audit_cv/n100_m50_capped | 100.0 | 50.0 | 0.951 [0.949, 0.953] | 0.901 [0.885, 0.918] | -5.3% | yes | PASS/PASS |
| audit_p5_streaming_paybackN/n10_m200 | 10.0 | 200.0 | 0.038 [0.038, 0.038] | 0.033 [0.032, 0.034] | -12.5% | yes | PASS/FAIL-NOISY |
| audit_p5_streaming_paybackN/n1_m200 | 1.0 | 200.0 | 0.021 [0.021, 0.021] | 0.017 [0.017, 0.018] | -16.6% | yes | PASS/FAIL-NOISY |
| audit_p5_streaming_paybackN/n200_m200 | 200.0 | 200.0 | 0.207 [0.207, 0.208] | 0.834 [0.821, 0.851] | +302.7% | yes | PASS/FAIL-NOISY |
| audit_p5_streaming_paybackN/n500_m200 | 500.0 | 200.0 | 0.554 [0.553, 0.555] | 2.434 [2.400, 2.471] | +339.6% | yes | PASS/PASS |
| audit_p5_streaming_paybackN/n50_m200 | 50.0 | 200.0 | 0.068 [0.068, 0.068] | 0.154 [0.150, 0.159] | +126.4% | yes | PASS/FAIL-NOISY |
| audit_p6_svd_conversion/n1000_m200 | 1000.0 | 200.0 | 0.000 [0.000, 0.000] | 0.000 [0.000, 0.000] | -55.0% | yes | FAIL-NOISY/FAIL-NOISY |
| audit_p6_svd_conversion/n1000_m50 | 1000.0 | 50.0 | 0.000 [0.000, 0.000] | 0.000 [0.000, 0.000] | -48.6% | yes | FAIL-NOISY/PASS |
| audit_p6_svd_conversion/n100_m200 | 100.0 | 200.0 | 0.000 [0.000, 0.000] | 0.000 [0.000, 0.000] | -66.6% | yes | FAIL-NOISY/PASS |
| audit_p6_svd_conversion/n100_m50 | 100.0 | 50.0 | 0.000 [0.000, 0.000] | 0.000 [0.000, 0.000] | -59.3% | yes | FAIL-NOISY/PASS |
| audit_p6_svd_conversion/n500_m200 | 500.0 | 200.0 | 0.000 [0.000, 0.000] | 0.000 [0.000, 0.000] | -62.6% | yes | FAIL-NOISY/FAIL-NOISY |
| audit_p6_svd_conversion/n500_m50 | 500.0 | 50.0 | 0.000 [0.000, 0.000] | 0.000 [0.000, 0.000] | -51.4% | yes | FAIL-NOISY/PASS |
| audit_p6_svd_conversion/n500_m500 | 500.0 | 500.0 | 0.000 [0.000, 0.000] | 0.000 [0.000, 0.000] | -54.9% | yes | FAIL-NOISY/PASS |
| audit_p6_svd_faer_seq/n1000_m200 | 1000.0 | 200.0 | 24.923 [19.334, 30.466] | 9.547 [8.579, 10.525] | -61.7% | yes | FAIL-NOISY/FAIL-NOISY |
| audit_p6_svd_faer_seq/n1000_m50 | 1000.0 | 50.0 | 1.380 [1.078, 1.837] | 0.735 [0.637, 0.868] | -46.7% | yes | FAIL-NOISY/FAIL-NOISY |
| audit_p6_svd_faer_seq/n100_m200 | 100.0 | 200.0 | 2.124 [1.799, 2.477] | 1.040 [0.946, 1.148] | -51.0% | yes | FAIL-NOISY/FAIL-NOISY |
| audit_p6_svd_faer_seq/n100_m50 | 100.0 | 50.0 | 0.500 [0.431, 0.575] | 0.209 [0.196, 0.223] | -58.2% | yes | FAIL-NOISY/FAIL-NOISY |
| audit_p6_svd_faer_seq/n500_m200 | 500.0 | 200.0 | 17.498 [15.023, 19.987] | 6.761 [6.282, 7.251] | -61.4% | yes | FAIL-NOISY/FAIL-NOISY |
| audit_p6_svd_faer_seq/n500_m50 | 500.0 | 50.0 | 1.157 [0.858, 1.503] | 0.387 [0.355, 0.428] | -66.6% | yes | FAIL-NOISY/FAIL-NOISY |
| audit_p6_svd_faer_seq/n500_m500 | 500.0 | 500.0 | 108.362 [101.742, 118.468] | 47.119 [46.454, 47.794] | -56.5% | yes | FAIL-NOISY/PASS |
| audit_p6_svd_nalgebra/n1000_m200 | 1000.0 | 200.0 | 89.877 [86.593, 93.323] | 46.265 [41.997, 51.420] | -48.5% | yes | FAIL-NOISY/FAIL-NOISY |
| audit_p6_svd_nalgebra/n1000_m50 | 1000.0 | 50.0 | 6.787 [6.559, 7.084] | 3.240 [3.044, 3.448] | -52.3% | yes | FAIL-NOISY/FAIL-NOISY |
| audit_p6_svd_nalgebra/n100_m200 | 100.0 | 200.0 | 4.192 [3.968, 4.483] | 1.705 [1.645, 1.776] | -59.3% | yes | FAIL-NOISY/FAIL-NOISY |
| audit_p6_svd_nalgebra/n100_m50 | 100.0 | 50.0 | 0.520 [0.498, 0.546] | 0.208 [0.201, 0.217] | -60.0% | yes | FAIL-NOISY/FAIL-NOISY |
| audit_p6_svd_nalgebra/n500_m200 | 500.0 | 200.0 | 37.537 [34.975, 40.691] | 16.751 [15.808, 17.757] | -55.4% | yes | FAIL-NOISY/FAIL-NOISY |
| audit_p6_svd_nalgebra/n500_m50 | 500.0 | 50.0 | 2.834 [2.766, 2.910] | 1.302 [1.227, 1.385] | -54.1% | yes | FAIL-NOISY/FAIL-NOISY |
| audit_p6_svd_nalgebra/n500_m500 | 500.0 | 500.0 | 311.339 [298.175, 323.231] | 176.147 [165.663, 186.610] | -43.4% | yes | FAIL-NOISY/FAIL-NOISY |
| audit_smooth/n500_m200 | 500.0 | 200.0 | 0.110 [0.105, 0.116] | 0.605 [0.588, 0.623] | +447.8% | yes | FAIL-NOISY/FAIL-NOISY |
| boosting_boost_fosr/n100_m50_p2_mstop100 | 100.0 | 50.0 | 28.229 [28.156, 28.303] | 11.835 [11.799, 11.869] | -58.1% | yes | PASS/PASS |
| boosting_boost_fosr/n100_m50_p2_mstop50 | 100.0 | 50.0 | 14.563 [14.419, 14.707] | 5.966 [5.944, 5.992] | -59.0% | yes | PASS/PASS |
| coclustering_co_cluster_select/n120_m40_grid2x2 | 120.0 | 40.0 | 229.332 [224.421, 234.243] | 96.976 [95.913, 98.082] | -57.7% | yes | PASS/PASS |
| density_lqd_fpca/n100_m81_ncomp3 | 100.0 | 81.0 | 3.013 [2.966, 3.060] | 1.436 [1.434, 1.438] | -52.3% | yes | PASS/PASS |
| density_wasserstein_barycenter/n100_m81 | 100.0 | 81.0 | 0.390 [0.389, 0.391] | 0.132 [0.131, 0.134] | -66.1% | yes | PASS/PASS |
| elastic_self_distance_matrix/n/10 | — | — | 48.865 [46.469, 51.442] | 65.243 [64.849, 65.902] | +33.5% | yes | FAIL-NOISY/PASS |
| elastic_self_distance_matrix/n/30 | — | — | 356.063 [340.982, 371.940] | 627.510 [625.744, 629.745] | +76.2% | yes | FAIL-NOISY/PASS |
| elastic_self_distance_matrix/n/50 | — | — | 757.224 [726.249, 793.015] | 1765.080 [1762.009, 1768.566] | +133.1% | yes | FAIL-NOISY/PASS |
| elastic_self_distance_matrix/n_band0.1/10 | — | — | 14.835 [14.078, 15.648] | 13.636 [13.548, 13.742] | -8.1% | yes | FAIL-NOISY/PASS |
| elastic_self_distance_matrix/n_band0.1/30 | — | — | 87.870 [84.262, 91.648] | 129.941 [129.452, 130.552] | +47.9% | yes | FAIL-NOISY/PASS |
| elastic_self_distance_matrix/n_band0.1/50 | — | — | 186.782 [175.080, 199.842] | 366.789 [365.471, 368.265] | +96.4% | yes | FAIL-NOISY/PASS |
| fem_smooth_gcv/nodes256_ngrid5 | — | — | 305.012 [303.683, 306.341] | 194.273 [193.991, 194.587] | -36.3% | yes | PASS/PASS |
| fpca_der/n200_m50_ncomp5_nderiv1 | 200.0 | 50.0 | 10.272 [9.421, 11.124] | 0.228 [0.228, 0.229] | -97.8% | yes | FAIL-NOISY/PASS |
| fpca_fsvd/n200_m50_ncomp5 | 200.0 | 50.0 | 1.254 [1.218, 1.289] | 0.555 [0.544, 0.567] | -55.7% | yes | FAIL-NOISY/PASS |
| frechet_global_reg/n24_m81_xout5 | 24.0 | 81.0 | 0.260 [0.255, 0.266] | 0.146 [0.145, 0.146] | -44.1% | yes | PASS/PASS |
| fts_ftsm/n200_m50_ncomp3 | 200.0 | 50.0 | 11.649 [9.960, 13.337] | 0.272 [0.271, 0.273] | -97.7% | yes | FAIL-NOISY/PASS |
| inference_t_perm_test/na30_nb30_m50_nperm999 | — | 50.0 | 2.200 [2.194, 2.206] | 1.883 [1.876, 1.893] | -14.4% | yes | PASS/PASS |
| mface_covariance/vars2_n100_m30 | 100.0 | 30.0 | 1251.421 [1219.669, 1283.172] | 752.167 [747.990, 756.847] | -39.9% | yes | FAIL-NOISY/PASS |
| perf_dpca/n200_m50 | 200.0 | 50.0 | 68.212 [62.715, 73.055] | 35.607 [35.373, 35.890] | -47.8% | yes | FAIL-NOISY/PASS |
| perf_face_covariance/n200_m30 | 200.0 | 30.0 | 207.489 [186.049, 229.894] | 287.022 [275.992, 298.998] | +38.3% | yes | FAIL-NOISY/FAIL-NOISY |
<!-- END GENERATED: before-after-internal -->

### scikit-fda and R control (unchanged libraries)

Neither scikit-fda nor R changed between the two runs — any drift here is
run-to-run measurement noise (machine load, cold-cache effects), not a code
change, and is reported only as a summary statistic rather than per-cell.

<!-- BEGIN GENERATED: before-after-control -->
_Generated by `benchmarks/render_report.py` from comparison_baseline.csv, comparison.csv — do not edit by hand._

Python and R rows carry no confidence interval (a single measurement per cell); drift is reported as a median/max absolute percent change only, never as a significance test.

| Library | Median \|delta %\| | Max \|delta %\| | Paired cells |
|---|---|---|---|
| python | 1.4% | 16.7% | 36 |
| r_svd | 0.9% | 44.5% | 36 |
| r_native_pca_fd | 1.0% | 2.4% | 6 |
<!-- END GENERATED: before-after-control -->

### Baseline rows not re-measured

<!-- BEGIN GENERATED: not-rerun -->
_Generated by `benchmarks/render_report.py` from comparison_baseline.csv, comparison.csv, rerun_log.json — do not edit by hand._

| Source | Op | Library | N | M | Status | Detail |
|---|---|---|---|---|---|---|
| audit_p3_elastic_cross/n100_m200 | elastic | rust | 100.0 | 200.0 | timeout | timeout at 540 s (single-threaded) |
| audit_p3_elastic_cross/n500_m50 | elastic | rust | 500.0 | 50.0 | inferred-timeout | cheaper sibling in the same group (filter '^audit_p3_elastic_cross/n500_m50$') timed out |
| audit_p3_elastic_cross_banded/n100_m200 | elastic | rust | 100.0 | 200.0 | timeout | timeout at 540 s (single-threaded) |
| audit_p3_elastic_cross_banded/n500_m50 | elastic | rust | 500.0 | 50.0 | inferred-timeout | cheaper sibling in the same group (filter '^audit_p3_elastic_cross_banded/n500_m50$') timed out |
| audit_p3_elastic_self/n100_m200 | elastic | rust | 100.0 | 200.0 | timeout | timeout at 540 s (single-threaded) |
| audit_p3_elastic_self/n500_m50 | elastic | rust | 500.0 | 50.0 | inferred-timeout | cheaper sibling in the same group (filter '^audit_p3_elastic_self/n500_m50$') timed out |
| audit_p3_karcher/n500_m200 | elastic | rust | 500.0 | 200.0 | timeout | timeout at 540 s (single-threaded) |
| boosting_boost_fosr/n100_m50 | boosting_boost_fosr | rust | 100.0 | 50.0 | id-not-produced | chunk completed ok but this id was not produced |
| boosting_boost_fosr/n50_m100 | boosting_boost_fosr | rust | 50.0 | 100.0 | id-not-produced | chunk completed ok but this id was not produced |
| boosting_boost_fosr/n50_m50 | boosting_boost_fosr | rust | 50.0 | 50.0 | id-not-produced | chunk completed ok but this id was not produced |
| coclustering_co_cluster/n100_m50 | coclustering_co_cluster | rust | 100.0 | 50.0 | orphan | group 'coclustering_co_cluster' no longer defined in any fdars-core bench file |
| coclustering_co_cluster/n50_m100 | coclustering_co_cluster | rust | 50.0 | 100.0 | orphan | group 'coclustering_co_cluster' no longer defined in any fdars-core bench file |
| coclustering_co_cluster/n50_m50 | coclustering_co_cluster | rust | 50.0 | 50.0 | orphan | group 'coclustering_co_cluster' no longer defined in any fdars-core bench file |
| density_wasserstein_barycenter/n200_m101 | density_wasserstein_barycenter | rust | 200.0 | 101.0 | id-not-produced | chunk completed ok but this id was not produced |
| density_wasserstein_barycenter/n50_m101 | density_wasserstein_barycenter | rust | 50.0 | 101.0 | id-not-produced | chunk completed ok but this id was not produced |
| density_wasserstein_barycenter/n50_m201 | density_wasserstein_barycenter | rust | 50.0 | 201.0 | id-not-produced | chunk completed ok but this id was not produced |
| face_covariance/n200_m30 | face_covariance | rust | 200.0 | 30.0 | orphan | group 'face_covariance' no longer defined in any fdars-core bench file |
| face_covariance/n50_m30 | face_covariance | rust | 50.0 | 30.0 | orphan | group 'face_covariance' no longer defined in any fdars-core bench file |
| face_covariance/n50_m60 | face_covariance | rust | 50.0 | 60.0 | orphan | group 'face_covariance' no longer defined in any fdars-core bench file |
| fem_smooth/nodes256_tris450 | fem_smooth | rust | — | — | orphan | group 'fem_smooth' no longer defined in any fdars-core bench file |
| fem_smooth/nodes576_tris1058 | fem_smooth | rust | — | — | orphan | group 'fem_smooth' no longer defined in any fdars-core bench file |
| fem_smooth/nodes64_tris98 | fem_smooth | rust | — | — | orphan | group 'fem_smooth' no longer defined in any fdars-core bench file |
| fpca_variants_fsvd/n1000_m50 | fpca_variants_fsvd | rust | 1000.0 | 50.0 | orphan | group 'fpca_variants_fsvd' no longer defined in any fdars-core bench file |
| fpca_variants_fsvd/n200_m50 | fpca_variants_fsvd | rust | 200.0 | 50.0 | orphan | group 'fpca_variants_fsvd' no longer defined in any fdars-core bench file |
| fpca_variants_fsvd/n50_m200 | fpca_variants_fsvd | rust | 50.0 | 200.0 | orphan | group 'fpca_variants_fsvd' no longer defined in any fdars-core bench file |
| fpca_variants_fsvd/n50_m50 | fpca_variants_fsvd | rust | 50.0 | 50.0 | orphan | group 'fpca_variants_fsvd' no longer defined in any fdars-core bench file |
| frechet_anova/n200_m50 | frechet_anova | rust | 200.0 | 50.0 | orphan | group 'frechet_anova' no longer defined in any fdars-core bench file |
| frechet_anova/n50_m200 | frechet_anova | rust | 50.0 | 200.0 | orphan | group 'frechet_anova' no longer defined in any fdars-core bench file |
| frechet_anova/n50_m50 | frechet_anova | rust | 50.0 | 50.0 | orphan | group 'frechet_anova' no longer defined in any fdars-core bench file |
| fts_long_run_covariance/n1000_m50 | fts_long_run_covariance | rust | 1000.0 | 50.0 | orphan | group 'fts_long_run_covariance' no longer defined in any fdars-core bench file |
| fts_long_run_covariance/n200_m50 | fts_long_run_covariance | rust | 200.0 | 50.0 | orphan | group 'fts_long_run_covariance' no longer defined in any fdars-core bench file |
| fts_long_run_covariance/n50_m200 | fts_long_run_covariance | rust | 50.0 | 200.0 | orphan | group 'fts_long_run_covariance' no longer defined in any fdars-core bench file |
| fts_long_run_covariance/n50_m50 | fts_long_run_covariance | rust | 50.0 | 50.0 | orphan | group 'fts_long_run_covariance' no longer defined in any fdars-core bench file |
| inference_t_perm_test/n200_m50 | inference_t_perm_test | rust | 200.0 | 50.0 | id-not-produced | chunk completed ok but this id was not produced |
| inference_t_perm_test/n50_m200 | inference_t_perm_test | rust | 50.0 | 200.0 | id-not-produced | chunk completed ok but this id was not produced |
| inference_t_perm_test/n50_m50 | inference_t_perm_test | rust | 50.0 | 50.0 | id-not-produced | chunk completed ok but this id was not produced |

**Excluded by design (thread-scaling benches, D-12):**

- `audit_p5_karcher_threads` — multi-thread scaling bench, excluded from the single-threaded head-to-head
- `audit_p5_streaming_threads` — multi-thread scaling bench, excluded from the single-threaded head-to-head
- `perf_parallelism_co_cluster` — multi-thread scaling bench, excluded from the single-threaded head-to-head
- `perf_parallelism_frechet_anova` — multi-thread scaling bench, excluded from the single-threaded head-to-head
<!-- END GENERATED: not-rerun -->

## N×M scaling

<!-- BEGIN GENERATED: scaling -->
_Generated by `benchmarks/render_report.py` from comparison.csv — do not edit by hand._

#### fpca scaling

**rust**

| N \ M | 50 | 200 |
|---|---|---|
| 100 | 0.424 | 1.985 |
| 300 | 0.683 | 7.209 |
| 500 | 0.913 | 10.152 |

**python**

| N \ M | 50 | 200 |
|---|---|---|
| 100 | 1.554 | 3.755 |
| 300 | 1.501 | 8.759 |
| 500 | 1.270 | 12.357 |

**r_svd**

| N \ M | 50 | 200 |
|---|---|---|
| 100 | 1.006 | 5.189 |
| 300 | 1.915 | 25.561 |
| 500 | 2.873 | 41.017 |

| Library | N@M=50 | N@M=200 | M@N=100 | M@N=300 | M@N=500 | Theory | Source |
|---|---|---|---|---|---|---|---|
| rust | 0.47 | 1.04 | 1.11 | 1.70 | 1.74 | O(N*M*min(N,M)) thin SVD of the weighted, centered N x M data matrix | fdars-core/src/regression.rs::fdata_to_pc |

_M-slopes are 2-point log-log estimates (only two M values in the grid)._

#### basis_smoothing scaling

**rust**

| N \ M | 50 | 200 |
|---|---|---|
| 100 | 0.053† | 0.211† |
| 300 | 0.137 | 0.514 |
| 500 | 0.216 | 0.834 |

**python**

| N \ M | 50 | 200 |
|---|---|---|
| 100 | 0.370 | 1.461 |
| 300 | 0.453 | 2.829 |
| 500 | 0.525 | 4.199 |

**r_svd**

| N \ M | 50 | 200 |
|---|---|---|
| 100 | 0.796 | 1.707 |
| 300 | 1.643 | 3.132 |
| 500 | 2.507 | 4.324 |

| Library | N@M=50 | N@M=200 | M@N=100 | M@N=300 | M@N=500 | Theory | Source |
|---|---|---|---|---|---|---|---|
| rust | 0.87† | 0.85† | 0.99† | 0.96† | 0.97† | O(N*M*K) per-curve basis projection (K=nbasis=10 fixed) plus a one-time O(M^2*K) hat-matrix build independent of N; regime-dependent (N>>M: linear in N and M; M>>N: quadratic in M, independent of N) | fdars-core/src/smooth_basis.rs::smooth_basis |

_M-slopes are 2-point log-log estimates (only two M values in the grid)._

#### depth scaling

**rust**

| N \ M | 50 | 200 |
|---|---|---|
| 100 | 0.105 | 0.546† |
| 300 | 0.506† | 2.068 |
| 500 | 0.757 | 3.511 |

**python**

| N \ M | 50 | 200 |
|---|---|---|
| 100 | 1.329 | 3.720 |
| 300 | 2.660 | 9.692 |
| 500 | 4.074 | 15.591 |

**r_svd**

| N \ M | 50 | 200 |
|---|---|---|
| 100 | 0.829 | 2.748 |
| 300 | 1.762 | 6.955 |
| 500 | 2.787 | 8.855 |

| Library | N@M=50 | N@M=200 | M@N=100 | M@N=300 | M@N=500 | Theory | Source |
|---|---|---|---|---|---|---|---|
| rust | 1.26† | 1.17† | 1.19† | 1.01† | 1.11† | O(N*M*log N) rank-based Modified Band Depth (sorted-reference presort, then an O(log N) rank query per curve/evaluation point) | fdars-core/src/streaming_depth/mbd.rs::depth_batch |

_M-slopes are 2-point log-log estimates (only two M values in the grid)._

#### functional_boxplot scaling

**rust**

| N \ M | 50 | 200 |
|---|---|---|
| 100 | 0.124† | 0.617† |
| 300 | 0.509† | 2.158† |
| 500 | 0.926† | 3.617 |

**python**

| N \ M | 50 | 200 |
|---|---|---|
| 100 | 1.794 | 4.170 |
| 300 | 3.183 | 10.064 |
| 500 | 4.712 | 16.616 |

**r_svd**

| N \ M | 50 | 200 |
|---|---|---|
| 100 | 2.070 | 6.683 |
| 300 | 4.233 | 14.303 |
| 500 | 7.058 | 21.627 |

| Library | N@M=50 | N@M=200 | M@N=100 | M@N=300 | M@N=500 | Theory | Source |
|---|---|---|---|---|---|---|---|
| rust | 1.26† | 1.11† | 1.16† | 1.04† | 0.98† | dominated by the underlying depth computation, O(N*M*log N), plus an additive O(N*M) central-region/fence pass | fdars-core/src/depth/dispatch.rs::functional_boxplot |

_M-slopes are 2-point log-log estimates (only two M values in the grid)._

#### fpcr scaling

**rust**

| N \ M | 50 | 200 |
|---|---|---|
| 100 | 0.430 | 2.007 |
| 300 | 0.699 | 7.452 |
| 500 | 0.940 | 10.241 |

**python**

| N \ M | 50 | 200 |
|---|---|---|
| 100 | 1.308 | 3.721 |
| 300 | 1.631 | 9.246 |
| 500 | 1.420 | 12.636 |

**r_svd**

| N \ M | 50 | 200 |
|---|---|---|
| 100 | 36.030 | 85.633 |
| 300 | 96.773 | 619.725 |
| 500 | 153.821 | 1049.904 |

| Library | N@M=50 | N@M=200 | M@N=100 | M@N=300 | M@N=500 | Theory | Source |
|---|---|---|---|---|---|---|---|
| rust | 0.48 | 1.04 | 1.11 | 1.71 | 1.72 | O(N*M*min(N,M)) FPCA (fdata_to_pc) followed by an O(N*ncomp^2) OLS solve on a fixed 5-component design (ncomp constant, so the FPCA term dominates) | fdars-core/src/scalar_on_function/fregre_lm.rs::fregre_lm |

_M-slopes are 2-point log-log estimates (only two M values in the grid)._

#### elastic scaling

**rust**

| N \ M | 50 | 200 |
|---|---|---|
| 100 | 1.839† | 27.701 |
| 300 | 1.593† | 28.597† |
| 500 | 1.499 | 27.470 |

**python**

| N \ M | 50 | 200 |
|---|---|---|
| 100 | 3.106 | 33.616 |
| 300 | 2.877 | 33.571 |
| 500 | 2.882 | 33.542 |

**r_svd**

| N \ M | 50 | 200 |
|---|---|---|
| 100 | 2.784 | 32.529 |
| 300 | 1.921 | 32.815 |
| 500 | 1.918 | 32.517 |

| Library | N@M=50 | N@M=200 | M@N=100 | M@N=300 | M@N=500 | Theory | Source |
|---|---|---|---|---|---|---|---|
| rust | -0.13† | 0.00† | 1.96† | 2.08† | 2.10† | O(M^2) dynamic-programming grid fill per pair (coprime neighbourhood), independent of N -- the crosslang_elastic bench always times a fixed 2-curve pair | fdars-core/src/alignment/pairwise.rs::elastic_align_pair |

_M-slopes are 2-point log-log estimates (only two M values in the grid)._
<!-- END GENERATED: scaling -->

The empirical N- and M-exponents above are log-log slopes fit across the
locked grid and are compared to the theory column, which is grounded in the
actual fdars-core source (not the module docstring's prose description —
see each row's `Source` column). For `elastic`, the theoretical O(M²) figure
is not a single measured slope: it is (pair count ∝ N², exact by
construction — the harness always times exactly one pair) × (per-pair DP
cost ∝ M², which IS what the pairwise M-slope above measures). The empirical
N-exponent near zero and M-exponent near two are both consistent with that
decomposition. Every M-slope in this table is a two-point log-log estimate
(the grid has only M ∈ {50, 200}) and should be read as directional, not as
a precise exponent.

## Methodology

### Environment

<!-- BEGIN GENERATED: environment -->
_Generated by `benchmarks/render_report.py` from env.json, env_baseline.json — do not edit by hand._

| Item | Phase 113 baseline | Phase 116 re-run | Changed? |
|---|---|---|---|
| cpu.cores_logical | 20 | 20 | no |
| cpu.model | 13th Gen Intel(R) Core(TM) i9-13900H | 13th Gen Intel(R) Core(TM) i9-13900H | no |
| criterion_version | 0.5 | 0.5 | no |
| python.numpy_blas | "name": "scipy-openblas", | "name": "scipy-openblas", | no |
| python.numpy_version | 2.5.3 | 2.5.3 | no |
| python.version | 3.14.7 | 3.14.7 | no |
| r.blas | /usr/lib/libblas.so.3.12.0 | /usr/lib/libblas.so.3.12.0 | no |
| r.lapack_version | /usr/lib/liblapack.so.3.12.0 | /usr/lib/liblapack.so.3.12.0 | no |
| r.version | 4.6.1 | 4.6.1 | no |
| r_packages.bench | 1.1.4 | 1.1.4 | no |
| r_packages.fda | 6.3.0 | 6.3.0 | no |
| r_packages.fda.usc | 2.2.0 | 2.2.0 | no |
| r_packages.fdapace | 0.6.0 | 0.6.0 | no |
| r_packages.fdasrvf | 2.5.0 | 2.5.0 | no |
| r_packages.jsonlite | 2.0.0 | 2.0.0 | no |
| r_packages.refund | 0.1.40 | 0.1.40 | no |
| r_packages.roahd | 1.4.3 | 1.4.3 | no |
| rust.features | linalg,parallel | linalg,parallel | no |
| rust.version | rustc 1.97.0 (2d8144b78 2026-07-07) | rustc 1.97.0 (2d8144b78 2026-07-07) | no |
| scikit_fda.version | 0.10.1 | 0.10.1 | no |
| thread_env.MKL_NUM_THREADS | 1 | 1 | no |
| thread_env.NUMEXPR_NUM_THREADS | 1 | 1 | no |
| thread_env.OMP_NUM_THREADS | 1 | 1 | no |
| thread_env.OPENBLAS_NUM_THREADS | 1 | 1 | no |
| thread_env.RAYON_NUM_THREADS | 1 | 1 | no |
| thread_env.VECLIB_MAXIMUM_THREADS | 1 | 1 | no |
| timestamp | 2026-09-23T08:10:19Z | 2026-09-25T00:15:39Z | yes |
<!-- END GENERATED: environment -->

**Background load disclosure.** A quiet-machine check (load average < 2) was
run and passed before the Phase 116 fdars re-run started, but unrelated
desktop workloads (an editor's language server, a search indexer, a browser)
returned partway through the ~2.9-hour run: the 1-minute load average at the
start of individual `--rust-next` scheduler calls ranged from 2.8 to 15.0 on
this 20-logical-core machine, not uniformly quiet throughout. All
measurements remain single-threaded, and every headline cell reported in
this document passes the 5% noise gate regardless — but this is disclosed
because background CPU contention inflates the wall-clock time of whatever
is being measured at that moment. The scikit-fda and R grid ran afterwards,
in separate processes, at a lower load (1-minute load average roughly
2.5–3), so the heavier contention window overlapped the fdars measurements.
Any bias this introduces therefore most likely runs against fdars, not in
its favor.

### Numeric agreement gate

<!-- BEGIN GENERATED: gate-tolerances -->
_Generated by `benchmarks/render_report.py` from gate.py — do not edit by hand._

| Op | Metric | Threshold | Status |
|---|---|---|---|
| fpca | subspace cos(largest principal angle) | >= 0.99 | hard-gated |
| basis_smoothing | max |diff| | < 0.001 | hard-gated |
| depth | Pearson |corr| | >= 0.99 | hard-gated |
| functional_boxplot | Pearson |corr| | >= 0.99 | hard-gated |
| fpcr | Pearson |corr| (disclosure only) | >= 0.95 | disclosed-only |
| elastic | L-infinity on warping values | < 0.01 | hard-gated |

fdars output itself is agreement-checked for FPCA only (`fpca_dump`, fdars-vs-R hard gate); for the other hard-gated ops (basis_smoothing, depth, functional_boxplot, elastic) the gate checks that scikit-fda and R agree with EACH OTHER, not that fdars agrees with either (`run_all.py` step 6b).
<!-- END GENERATED: gate-tolerances -->

The gate is fail-closed and runs BEFORE any timing is recorded for a cell —
if the gate fails, nothing downstream of it is measured for that cell. It is
unchanged in this phase (D-11): the same thresholds, computed the same way,
as the Phase 112/113 baseline runs. fdars' own output is agreement-checked
against another ecosystem only for FPCA (via the standalone `fpca_dump`
binary, checked against R); for the other hard-gated ops the gate checks
that scikit-fda and R agree with each other, which is a weaker but still
meaningful signal that the op is being compared fairly.

### Timing statistics and noise gate

Each ecosystem reports a different timing statistic, by design of its own
idiomatic benchmarking tool: fdars uses criterion 0.5's mean with a 95%
bootstrap confidence interval; scikit-fda uses Python's `timeit` mean over a
fixed repeat count per op (50 repeats for `fpca`/`basis_smoothing`/
`depth`/`functional_boxplot`/`fpcr`; 10 repeats for the pairwise `elastic`
op, since it is heavier per call); R uses `bench::mark()`'s median over a
fixed iteration count per op (10 iterations for the same five ops; 5
iterations for pairwise `elastic`). Python and R therefore carry no
confidence interval — they report one point estimate per cell, which is why
the before/after control table above reports drift as median/max percent
change rather than a significance test. The noise gate (shared with
`hotspot_ranking.md`, never redeclared) fails a criterion row when its
relative standard deviation is >= 5% or its CI width is >= 5%; it is the
only gate applied to fdars rows and has no equivalent for the single-sample
Python/R rows. Significance for any comparison is always the strict
non-overlapping-CI test; the ratio-label parity band is +/-10%.

### Criterion settings

<!-- BEGIN GENERATED: criterion-settings -->
_Generated by `benchmarks/render_report.py` from fdars-core/benches/*.rs — do not edit by hand._

| Group | Sample size | Measurement time (s) | Warm-up (s) |
|---|---|---|---|
| crosslang_basis_smoothing | 30 | 10 | 3 |
| crosslang_depth | 30 | 10 | 3 |
| crosslang_elastic | 30 | 30 | 5 |
| crosslang_fpca | 30 | 10 | 3 |
| crosslang_fpcr | 60 | 20 | 3 |
| crosslang_functional_boxplot | 30 | 10 | 3 |
| functional_boxplot | 50 | 20 | 5 |
| perf_face_covariance | 15 | 30 | 3 |
<!-- END GENERATED: criterion-settings -->

### Data parity

The grid-aligned fdars bench (`fdars-core/benches/crosslang_grid.rs`) reads
the exact same seeded CSVs the Python and R runners read, and hard-fails
(`FDARS_CROSSLANG_REQUIRE_CSV=1`) rather than silently falling back to a
different random draw when the harness invokes it. A standalone
`cargo bench` run (no harness) instead falls back to a deterministic
`StdRng(42)` generator, so the bench is still runnable in isolation but never
silently mismatched against the cross-language CSVs when it matters. Legacy,
non-grid-aligned criterion ids (the `audit_*`/`perf_*` benches used in the
before/after tables above) use their own in-bench generators and were never
intended to share data with the cross-language harness.

### Threading

All six `*_NUM_THREADS` environment variables are pinned to `1` for every
ecosystem in every table in this report. With the default `parallel`
feature enabled, fdars uses rayon for multi-core execution outside of this
report's fairness-first, single-threaded measurements — that capability is
real and shipped, but deliberately not tabulated here (D-12), because a
multi-threaded fdars number next to single-threaded Python/R numbers would
not be a fair comparison. The four `audit_p5_*_threads`/
`perf_parallelism_*` benchmark groups exist specifically to explore
thread-scaling and are excluded from every table above.

## Reproduction

The full re-run this report is based on can be reproduced end-to-end from a
clean clone:

1. Clone the repository:

   ```bash
   git clone https://github.com/sipemu/fdars.git
   cd fdars
   ```

2. Install a Rust toolchain matching the [Environment](#environment) table
   above (the `linalg` feature needs Rust 1.84+; the `crosslang_grid` bench
   itself only needs the workspace MSRV):

   ```bash
   rustup toolchain install 1.97.0
   rustup default 1.97.0
   ```

3. Create the Python virtual environment and install the pinned harness
   dependencies:

   ```bash
   python3 -m venv benchmarks/.venv
   benchmarks/.venv/bin/pip install -r benchmarks/requirements.lock
   ```

4. **Python 3.14 only:** apply the `multimethod` metaclass patch (see
   `benchmarks/README.md`'s "Python 3.14 multimethod patch" section for why
   this is needed):

   ```bash
   patch -p1 -d benchmarks/.venv/lib/python3.14/site-packages \
       < benchmarks/patches/multimethod-2.1-py314.patch
   ```

5. Restore the R packages from `benchmarks/renv.lock`, then verify them
   (see `benchmarks/README.md` for the exact `renv::restore()` invocation
   and why `.Rprofile`/`renv/` are gitignored and not auto-activated on a
   clean clone):

   ```bash
   Rscript -e "renv::restore()"
   Rscript benchmarks/r_deps_check.R
   ```

6. Run the single end-to-end reproduction command:

   ```bash
   benchmarks/.venv/bin/python benchmarks/run_all.py --full
   ```

   The default 540s per-chunk / per-cell bound matches the published run
   exactly (7 heavy single-threaded elastic/Karcher chunks are expected to
   time out under it — see
   [Before/after vs the Phase 113 baseline](#beforeafter-vs-the-phase-113-baseline)).
   Pass `--timeout-s 0` to remove fdars' per-chunk bound entirely and
   measure the cells the published run recorded as timeouts (this will take
   substantially longer — budget accordingly).

7. Render the report and verify it against the committed inputs:

   ```bash
   benchmarks/.venv/bin/python benchmarks/render_report.py
   benchmarks/.venv/bin/python benchmarks/render_report.py --check
   benchmarks/.venv/bin/python benchmarks/render_report.py --check-prose
   ```

### Measured runtime and disk footprint

<!-- BEGIN GENERATED: runtime -->
_Generated by `benchmarks/render_report.py` from rerun_log.json — do not edit by hand._

head_sha: `242ab06722cfb68de28dd57203d3eb4757062a6f`  
started_utc: `2026-09-24T21:05:14Z`

| Kind | Status | Count | Wall-clock (s) |
|---|---|---|---|
| footprint | ok | 1 | 0.0 |
| grid_cell | ok | 6 | 0.0 |
| prebuild | ok | 1 | 20.2 |
| remediation | ok | 1 | 206.4 |
| rust_chunk | interrupted | 9 | 1778.0 |
| rust_chunk | ok | 60 | 6370.7 |
| rust_chunk | skipped-inferred-timeout | 3 | 0.0 |
| rust_chunk | timeout | 4 | 2160.0 |

Total measured wall-clock: 2.93 hours
Disk footprint (target/): 57.83 GiB
<!-- END GENERATED: runtime -->

The published run above was not driven with a single blocking `--full` call
end to end — it used the same underlying steps but invoked as a resumable
sequence (`--rust-next --budget-s 540` repeated until
`RUST_CHUNKS_REMAINING=0`, then `--grid --cell <NxM>` once per grid cell)
so that a single interrupted call could resume without losing prior
progress; `--full` (step 6 above) wraps that exact sequence into one command
for a fresh reproduction run.

## Known limitations and disclosures

- **Background desktop load was present during part of the fdars re-run**
  (1-minute load average 2.8–15.0 at scheduler-call starts, despite a
  passing quiet-machine check before the run started) — see
  [Environment](#environment) for the full disclosure. The heavier load
  overlapped the fdars measurements, so any bias most likely runs against
  fdars (slower), not in its favor.
- **Timeouts and orphans are disclosed, not hidden.** 7 heavy
  single-threaded elastic/Karcher chunks did not complete inside the 540s
  bound (4 direct timeouts, 3 inferred from a cheaper sibling in the same
  group timing out) and are listed by criterion id in the
  "Baseline rows not re-measured" table above; 6 legacy benchmark groups no
  longer exist in the bench files and are flagged `orphan` in the same
  table, not silently dropped from the report.
- **The Phase 113 baseline is of mixed vintage and mostly not thread-pinned**
  — only `fregre_lm` and `functional_boxplot` were re-measured live in
  Phase 113; every other baseline row is on-disk criterion output from
  whatever optimization phase last touched that bench, measured on the
  default multi-core rayon pool. The before/after tables above are a
  traceability record against that baseline, not an optimization
  measurement.
- **fdars' own output is agreement-checked against another ecosystem for
  FPCA only.** For the other hard-gated ops the gate checks scikit-fda
  against R, not fdars against either — see
  [Numeric agreement gate](#numeric-agreement-gate).
- **FPCR is a disclosed, not gated, cross-library comparison** — scikit-fda's
  FPCA→OLS and R's `fda.usc::fregre.pc` are related but not numerically
  identical algorithms.
- **The R FPCA timing shown as the hard-gated comparator is a hand-rolled
  Simpson-weighted SVD port**, chosen because it agrees with fdars at
  subspace cosine 1.0; R's own native `fda::pca.fd` (B-spline coefficient
  space) is timed separately and shown alongside it, never conflated with
  it.
- **The Python 3.14 harness venv needs an in-place metaclass patch** to
  `multimethod/__init__.py` before scikit-fda will import; the patch file
  is committed at `benchmarks/patches/multimethod-2.1-py314.patch` and its
  provenance (pristine wheel hash matches the venv's own `dist-info/RECORD`
  entry) is documented in `benchmarks/README.md`.
- **Single machine, single run.** Every number in this report comes from one
  run on one machine (see [Environment](#environment)); it is not a
  statistical claim across hardware or repeated runs, though the noise gate
  and confidence intervals bound the uncertainty of any one criterion cell.
- **scikit-fda is this milestone's functionality yardstick, not its
  performance yardstick's peer in scope.** This report covers performance
  only — a separate audit (Phase-numbered elsewhere in this milestone's
  history) covers functionality-gap analysis against scikit-fda; the two
  should not be conflated.