Stack Axis Benchmarks

Recorded 2026-09-08, reducers 0.4.0 + overflow fix (eb27fc0). Environment and setup · Complete output · Excluded baselines

uv run --no-sync python benchmarks/benchmark_axis.py --repeats 15 --warmups 3

Times are median milliseconds per call over 15 samples after 3 warmups; the lowest and highest samples are discarded. Ratios above 1 favor reducers; bold means a ratio above 0.95 (within 5%). - means unavailable; n/a means the baseline failed the accuracy check. Ratios use unrounded times.

Inputs are prebuilt contiguous arrays; reducers uses its default validation. var uses ddof=0, std uses ddof=1. Averages use one weight per reduced-axis position, uniform on [0.5, 1.5). NumPy nanaverage uses a masked array prepared before timing. Percentile requests [16, 50, 84]; quantile requests [0.16, 0.50, 0.84]. NaN-aware inputs have a NaN every 97 elements. Axis nanpercentile/nanquantile are outside this matrix; no speed claim is made for them. Cheap calls can be sensitive to scheduling noise.

Plain, float64

function	np (ms)	bn (ms)	rd (ms)	np/rd	bn/rd
`mean`	0.16	-	0.10	1.57x	-
`average`	0.28	-	0.38	0.74x	-
`median`	8.68	7.77	0.66	13.24x	11.84x
`var`	0.61	-	0.17	3.53x	-
`std`	0.61	-	0.17	3.66x	-
`min`	0.17	-	0.11	1.53x	-
`max`	0.17	-	0.13	1.30x	-
`minmax`	0.34	-	0.14	2.51x	-
`sum`	0.15	-	0.10	1.56x	-
`percentile`	14.30	-	1.70	8.43x	-
`quantile`	14.21	-	1.64	8.65x	-

function	np (ms)	bn (ms)	rd (ms)	np/rd	bn/rd
`mean`	0.18	-	0.07	2.49x	-
`average`	0.48	-	0.15	3.24x	-
`median`	8.36	7.43	0.62	13.49x	11.99x
`var`	0.69	-	0.19	3.55x	-
`std`	0.70	-	0.20	3.55x	-
`min`	0.12	-	0.15	0.81x	-
`max`	0.12	-	0.15	0.80x	-
`minmax`	0.26	-	0.19	1.36x	-
`sum`	0.17	-	0.07	2.41x	-
`percentile`	13.65	-	1.55	8.79x	-
`quantile`	13.83	-	1.57	8.80x	-

function	np (ms)	bn (ms)	rd (ms)	np/rd	bn/rd
`mean`	0.02	-	0.02	0.91x	-
`average`	0.04	-	0.06	0.78x	-
`median`	0.84	0.64	0.23	3.69x	2.82x
`var`	0.07	-	0.07	0.99x	-
`std`	0.08	-	0.08	1.00x	-
`min`	0.02	-	0.03	0.77x	-
`max`	0.02	-	0.03	0.77x	-
`minmax`	0.04	-	0.04	1.00x	-
`sum`	0.02	-	0.03	0.84x	-
`percentile`	1.26	-	0.61	2.05x	-
`quantile`	1.23	-	0.63	1.97x	-

function	np (ms)	bn (ms)	rd (ms)	np/rd	bn/rd
`mean`	0.06	-	0.06	0.99x	-
`average`	0.10	-	0.14	0.77x	-
`median`	2.99	2.42	0.31	9.50x	7.69x
`var`	0.19	-	0.17	1.11x	-
`std`	0.20	-	0.17	1.13x	-
`min`	0.05	-	0.06	0.84x	-
`max`	0.05	-	0.06	0.84x	-
`minmax`	0.11	-	0.10	1.08x	-
`sum`	0.05	-	0.06	0.82x	-
`percentile`	4.99	-	0.83	6.03x	-
`quantile`	4.96	-	0.83	5.95x	-

function	np (ms)	bn (ms)	rd (ms)	np/rd	bn/rd
`mean`	0.52	-	0.24	2.20x	-
`average`	0.89	-	0.90	0.99x	-
`median`	29.77	23.44	3.29	9.06x	7.13x
`var`	1.97	-	0.44	4.44x	-
`std`	1.97	-	0.45	4.37x	-
`min`	0.51	-	0.21	2.42x	-
`max`	0.49	-	0.24	2.06x	-
`minmax`	0.99	-	0.34	2.91x	-
`sum`	0.54	-	0.23	2.38x	-
`percentile`	35.83	-	10.26	3.49x	-
`quantile`	35.90	-	10.12	3.55x	-

Plain, float32

function	np (ms)	bn (ms)	rd (ms)	np/rd	bn/rd
`mean`	0.07	-	0.08	0.87x	-
`average`	0.13	-	0.34	0.39x	-
`median`	8.79	7.88	0.67	13.20x	11.82x
`var`	0.25	-	0.15	1.66x	-
`std`	0.26	-	0.15	1.74x	-
`min`	0.07	-	0.09	0.73x	-
`max`	0.06	-	0.09	0.71x	-
`minmax`	0.13	-	0.11	1.21x	-
`sum`	0.06	-	0.10	0.60x	-
`percentile`	14.54	-	1.77	8.21x	-
`quantile`	15.01	-	1.72	8.73x	-

function	np (ms)	bn (ms)	rd (ms)	np/rd	bn/rd
`mean`	0.17	-	0.10	1.66x	-
`average`	0.31	-	0.20	1.60x	-
`median`	8.25	7.67	0.65	12.76x	11.86x
`var`	0.52	-	0.23	2.23x	-
`std`	0.52	-	0.25	2.09x	-
`min`	0.10	-	0.10	1.01x	-
`max`	0.11	-	0.10	1.04x	-
`minmax`	0.20	-	0.12	1.67x	-
`sum`	0.17	-	0.11	1.54x	-
`percentile`	13.97	-	1.60	8.75x	-
`quantile`	13.77	-	1.64	8.37x	-

function	np (ms)	bn (ms)	rd (ms)	np/rd	bn/rd
`mean`	0.01	-	0.02	0.79x	-
`average`	0.02	-	0.05	0.46x	-
`median`	0.89	0.72	0.19	4.74x	3.79x
`var`	0.04	-	0.06	0.67x	-
`std`	0.04	-	0.07	0.65x	-
`min`	0.01	-	0.01	0.64x	-
`max`	0.01	-	0.01	0.63x	-
`minmax`	0.02	-	0.02	0.89x	-
`sum`	0.01	-	0.02	0.57x	-
`percentile`	1.25	-	0.59	2.12x	-
`quantile`	1.25	-	0.60	2.06x	-

function	np (ms)	bn (ms)	rd (ms)	np/rd	bn/rd
`mean`	0.03	-	0.04	0.72x	-
`average`	0.05	-	0.13	0.40x	-
`median`	3.02	2.59	0.28	10.94x	9.41x
`var`	0.09	-	0.15	0.60x	-
`std`	0.09	-	0.18	0.53x	-
`min`	0.02	-	0.03	0.80x	-
`max`	0.02	-	0.03	0.65x	-
`minmax`	0.04	-	0.05	0.92x	-
`sum`	0.02	-	0.04	0.60x	-
`percentile`	5.15	-	0.74	6.93x	-
`quantile`	5.08	-	0.74	6.84x	-

function	np (ms)	bn (ms)	rd (ms)	np/rd	bn/rd
`mean`	0.37	-	0.20	1.85x	-
`average`	0.44	-	0.87	0.50x	-
`median`	29.52	23.52	2.30	12.85x	10.24x
`var`	1.17	-	0.37	3.12x	-
`std`	1.15	-	0.39	2.92x	-
`min`	0.25	-	0.15	1.65x	-
`max`	0.25	-	0.14	1.70x	-
`minmax`	0.48	-	0.20	2.37x	-
`sum`	0.27	-	0.17	1.62x	-
`percentile`	36.05	-	13.33	2.70x	-
`quantile`	35.99	-	13.45	2.68x	-

NaN-aware, float64

function	np (ms)	bn (ms)	rd (ms)	np/rd	bn/rd
`nanmean`	0.94	0.73	0.17	5.37x	4.18x
`nanaverage`	3.70	-	0.45	8.31x	-
`nanmedian`	28.10	7.50	0.47	59.39x	15.85x
`nanvar`	2.10	1.66	0.27	7.74x	6.12x
`nanstd`	2.10	1.69	0.28	7.54x	6.05x
`nanmin`	0.17	0.65	0.09	1.88x	7.12x
`nanmax`	0.17	0.66	0.09	1.84x	6.99x
`nanminmax`	0.35	1.33	0.13	2.61x	9.98x
`nansum`	0.49	0.64	0.19	2.63x	3.40x

function	np (ms)	bn (ms)	rd (ms)	np/rd	bn/rd
`nanmean`	0.71	0.66	0.15	4.70x	4.39x
`nanaverage`	3.95	-	0.16	25.07x	-
`nanmedian`	25.48	8.04	0.96	26.48x	8.35x
`nanvar`	1.96	1.62	0.32	6.12x	5.06x
`nanstd`	1.95	1.65	0.32	6.02x	5.08x
`nanmin`	0.12	0.64	0.12	1.06x	5.50x
`nanmax`	0.13	0.64	0.12	1.05x	5.27x
`nanminmax`	0.25	1.32	0.17	1.50x	7.87x
`nansum`	0.50	0.63	0.15	3.38x	4.26x

function	np (ms)	bn (ms)	rd (ms)	np/rd	bn/rd
`nanmean`	0.12	0.03	0.05	2.11x	0.62x
`nanaverage`	0.49	-	0.08	6.30x	-
`nanmedian`	1.80	0.71	0.20	8.99x	3.55x
`nanvar`	0.25	0.09	0.10	2.46x	0.92x
`nanstd`	0.26	0.10	0.10	2.50x	0.98x
`nanmin`	0.02	0.04	0.02	1.05x	2.08x
`nanmax`	0.02	0.04	0.02	1.04x	2.07x
`nanminmax`	0.04	0.08	0.03	1.24x	2.45x
`nansum`	0.06	0.04	0.05	1.09x	0.72x

function	np (ms)	bn (ms)	rd (ms)	np/rd	bn/rd
`nanmean`	0.29	0.14	0.14	2.14x	0.99x
`nanaverage`	1.18	-	0.20	5.88x	-
`nanmedian`	6.48	2.56	0.31	20.56x	8.14x
`nanvar`	0.66	0.37	0.25	2.62x	1.45x
`nanstd`	0.67	0.38	0.25	2.63x	1.48x
`nanmin`	0.06	0.13	0.05	1.03x	2.43x
`nanmax`	0.06	0.13	0.05	1.02x	2.43x
`nanminmax`	0.11	0.26	0.09	1.22x	2.91x
`nansum`	0.16	0.13	0.13	1.16x	0.98x

function	np (ms)	bn (ms)	rd (ms)	np/rd	bn/rd
`nanmean`	2.92	1.45	0.39	7.49x	3.72x
`nanaverage`	11.75	-	1.09	10.77x	-
`nanmedian`	57.99	24.46	2.93	19.78x	8.34x
`nanvar`	6.45	5.43	0.59	10.96x	9.23x
`nanstd`	6.78	5.13	0.64	10.61x	8.03x
`nanmin`	0.51	1.37	0.18	2.78x	7.52x
`nanmax`	0.52	1.39	0.20	2.55x	6.78x
`nanminmax`	0.98	2.76	0.67	1.47x	4.14x
`nansum`	1.53	1.34	0.38	4.09x	3.57x

NaN-aware, float32

function	np (ms)	bn (ms)	rd (ms)	np/rd	bn/rd
`nanmean`	0.74	0.69	0.19	3.86x	3.63x
`nanaverage`	3.11	-	0.48	6.47x	-
`nanmedian`	26.48	7.41	0.47	56.54x	15.81x
`nanvar`	1.61	1.62	0.30	5.38x	5.39x
`nanstd`	1.63	1.64	0.30	5.38x	5.39x
`nanmin`	0.06	0.63	0.07	0.93x	9.08x
`nanmax`	0.07	0.61	0.07	0.92x	8.43x
`nanminmax`	0.13	1.26	0.09	1.48x	14.05x
`nansum`	0.30	0.63	0.19	1.60x	3.32x

function	np (ms)	bn (ms)	rd (ms)	np/rd	bn/rd
`nanmean`	0.65	0.66	0.16	4.06x	4.14x
`nanaverage`	3.46	-	0.22	15.80x	-
`nanmedian`	25.28	7.47	0.48	52.40x	15.49x
`nanvar`	1.65	1.61	0.26	6.26x	6.11x
`nanstd`	1.65	1.63	0.28	5.86x	5.78x
`nanmin`	0.10	0.66	0.09	1.15x	7.37x
`nanmax`	0.10	0.61	0.09	1.12x	6.63x
`nanminmax`	0.21	1.26	0.10	1.98x	12.11x
`nansum`	0.41	0.66	0.15	2.64x	4.27x

function	np (ms)	bn (ms)	rd (ms)	np/rd	bn/rd
`nanmean`	0.10	0.04	0.06	1.66x	0.69x
`nanaverage`	0.43	-	0.08	5.63x	-
`nanmedian`	1.77	0.77	0.15	11.84x	5.13x
`nanvar`	0.21	0.09	0.10	1.99x	0.91x
`nanstd`	0.21	0.10	0.11	1.95x	0.92x
`nanmin`	0.01	0.04	0.01	1.18x	4.99x
`nanmax`	0.01	0.04	0.01	1.17x	4.98x
`nanminmax`	0.02	0.08	0.02	1.29x	5.48x
`nansum`	0.04	0.04	0.06	0.67x	0.69x

function	np (ms)	bn (ms)	rd (ms)	np/rd	bn/rd
`nanmean`	0.24	0.13	0.15	1.63x	0.88x
`nanaverage`	1.06	-	0.20	5.29x	-
`nanmedian`	6.43	2.55	0.32	19.96x	7.92x
`nanvar`	0.52	0.36	0.27	1.94x	1.33x
`nanstd`	0.52	0.35	0.27	1.92x	1.27x
`nanmin`	0.02	0.13	0.02	1.09x	6.18x
`nanmax`	0.02	0.13	0.02	1.09x	6.21x
`nanminmax`	0.05	0.26	0.04	1.20x	6.87x
`nansum`	0.10	0.13	0.15	0.67x	0.88x

function	np (ms)	bn (ms)	rd (ms)	np/rd	bn/rd
`nanmean`	2.38	1.42	0.38	6.26x	3.73x
`nanaverage`	10.28	-	1.08	9.48x	-
`nanmedian`	52.74	24.55	3.00	17.61x	8.19x
`nanvar`	5.13	5.38	0.60	8.61x	9.02x
`nanstd`	5.26	5.47	0.60	8.69x	9.05x
`nanmin`	0.27	1.38	0.12	2.34x	11.79x
`nanmax`	0.27	1.38	0.11	2.34x	12.01x
`nanminmax`	0.52	2.75	0.19	2.73x	14.39x
`nansum`	0.95	1.34	0.41	2.34x	3.30x