1-D Array 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_1d.py --repeats 15 --warmups 3

Times are median microseconds per call over 15 samples after 3 warmups; the lowest and highest samples are discarded. Short inputs batch repeated calls using max(1, min(100000, 1000000 // length)) calls per sample. 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 validate=False. Weights are uniform on [0.5, 1.5). var uses ddof=0, std uses ddof=1. Percentile requests [16, 50, 84]; quantile requests [0.16, 0.50, 0.84]. NaN-aware inputs contain sparse NaNs. For NumPy nanaverage, the validity mask is prepared before timing; selecting values and weights is timed.

Plain, float64

function	np (µs)	bn (µs)	rd (µs)	np/rd	bn/rd
`mean`	1.18	-	0.13	9.39x	-
`average`	2.74	-	0.28	9.63x	-
`median`	4.54	0.12	0.25	18.18x	0.50x
`sum`	0.82	-	0.18	4.63x	-
`min`	0.82	-	0.13	6.26x	-
`max`	0.83	-	0.14	6.10x	-
`minmax`	1.65	-	0.15	11.05x	-
`var`	3.49	-	0.17	19.93x	-
`std`	3.81	-	0.25	15.52x	-
`percentile`	14.25	-	3.51	4.06x	-
`quantile`	13.86	-	3.91	3.54x	-

function	np (µs)	bn (µs)	rd (µs)	np/rd	bn/rd
`mean`	1.16	-	0.14	8.53x	-
`average`	2.76	-	0.31	8.98x	-
`median`	4.92	0.19	0.52	9.42x	0.37x
`sum`	0.84	-	0.18	4.61x	-
`min`	0.86	-	0.16	5.56x	-
`max`	0.85	-	0.15	5.62x	-
`minmax`	1.73	-	0.18	9.70x	-
`var`	3.68	-	0.21	17.53x	-
`std`	3.95	-	0.28	14.13x	-
`percentile`	14.88	-	4.17	3.57x	-
`quantile`	13.82	-	4.31	3.21x	-

function	np (µs)	bn (µs)	rd (µs)	np/rd	bn/rd
`mean`	2.44	-	1.53	1.60x	-
`average`	7.79	-	2.31	3.37x	-
`median`	28.88	18.49	28.63	1.01x	0.65x
`sum`	1.97	-	1.80	1.09x	-
`min`	1.34	-	2.35	0.57x	-
`max`	1.39	-	2.19	0.63x	-
`minmax`	2.74	-	3.10	0.88x	-
`var`	9.38	-	3.76	2.49x	-
`std`	9.61	-	3.89	2.47x	-
`percentile`	51.95	-	47.41	1.10x	-
`quantile`	50.17	-	47.38	1.06x	-

function	np (µs)	bn (µs)	rd (µs)	np/rd	bn/rd
`mean`	1198.33	-	1353.00	0.89x	-
`average`	4569.13	-	1872.87	2.44x	-
`median`	70134.54	67513.58	28021.33	2.50x	2.41x
`sum`	1229.21	-	1368.46	0.90x	-
`min`	897.17	-	508.63	1.76x	-
`max`	939.21	-	504.37	1.86x	-
`minmax`	1864.04	-	551.83	3.38x	-
`var`	5038.17	-	3585.33	1.41x	-
`std`	5194.33	-	3643.00	1.43x	-
`percentile`	114479.79	-	45393.58	2.52x	-
`quantile`	114218.25	-	45280.83	2.52x	-

Plain, float32

function	np (µs)	bn (µs)	rd (µs)	np/rd	bn/rd
`mean`	1.90	-	0.14	13.32x	-
`average`	2.68	-	0.33	8.11x	-
`median`	5.46	0.12	0.27	20.45x	0.44x
`sum`	0.82	-	0.19	4.20x	-
`min`	0.80	-	0.15	5.44x	-
`max`	0.81	-	0.15	5.47x	-
`minmax`	1.65	-	0.16	10.17x	-
`var`	4.51	-	0.20	23.02x	-
`std`	4.96	-	0.26	18.96x	-
`percentile`	14.45	-	3.54	4.08x	-
`quantile`	14.00	-	3.89	3.60x	-

function	np (µs)	bn (µs)	rd (µs)	np/rd	bn/rd
`mean`	2.00	-	0.16	12.81x	-
`average`	2.72	-	0.36	7.66x	-
`median`	5.59	0.23	0.51	11.04x	0.45x
`sum`	0.82	-	0.20	4.15x	-
`min`	0.83	-	0.17	5.03x	-
`max`	0.85	-	0.15	5.62x	-
`minmax`	1.66	-	0.18	9.48x	-
`var`	4.59	-	0.24	19.29x	-
`std`	4.99	-	0.31	16.09x	-
`percentile`	14.78	-	4.12	3.59x	-
`quantile`	14.45	-	4.36	3.31x	-

function	np (µs)	bn (µs)	rd (µs)	np/rd	bn/rd
`mean`	3.11	-	1.85	1.68x	-
`average`	6.55	-	3.49	1.88x	-
`median`	28.41	18.32	27.63	1.03x	0.66x
`sum`	1.92	-	1.89	1.02x	-
`min`	1.04	-	1.29	0.81x	-
`max`	1.02	-	1.26	0.82x	-
`minmax`	2.08	-	1.60	1.29x	-
`var`	8.39	-	3.99	2.10x	-
`std`	8.83	-	4.09	2.16x	-
`percentile`	51.55	-	45.04	1.14x	-
`quantile`	50.34	-	45.17	1.11x	-

function	np (µs)	bn (µs)	rd (µs)	np/rd	bn/rd
`mean`	1143.50	-	1698.96	0.67x	-
`average`	3310.12	-	3091.21	1.07x	-
`median`	78067.21	61903.75	27209.46	2.87x	2.28x
`sum`	1154.08	-	1697.42	0.68x	-
`min`	429.87	-	299.58	1.43x	-
`max`	464.17	-	321.33	1.44x	-
`minmax`	906.62	-	362.21	2.50x	-
`var`	3538.71	-	3862.71	0.92x	-
`std`	3581.17	-	3875.25	0.92x	-
`percentile`	117098.29	-	43294.92	2.70x	-
`quantile`	117619.17	-	43184.33	2.72x	-

NaN-aware, float64

function	np (µs)	bn (µs)	rd (µs)	np/rd	bn/rd
`nanmean`	4.27	0.07	0.14	30.61x	0.50x
`nanaverage`	3.10	-	0.30	10.19x	-
`nanmedian`	6.58	0.11	0.24	27.51x	0.44x
`nansum`	1.75	0.07	0.19	9.39x	0.38x
`nanmin`	1.55	0.06	0.14	10.79x	0.40x
`nanmax`	1.58	0.06	0.15	10.84x	0.39x
`nanminmax`	3.18	0.11	0.16	19.58x	0.68x
`nanvar`	9.43	0.12	0.20	48.20x	0.60x
`nanstd`	9.86	0.16	0.26	37.95x	0.61x
`nanpercentile`	16.50	-	3.51	4.70x	-
`nanquantile`	15.92	-	3.81	4.18x	-

function	np (µs)	bn (µs)	rd (µs)	np/rd	bn/rd
`nanmean`	4.27	0.16	0.16	26.41x	0.98x
`nanaverage`	3.15	-	0.32	9.75x	-
`nanmedian`	6.81	0.21	0.35	19.40x	0.60x
`nansum`	1.74	0.15	0.20	8.83x	0.78x
`nanmin`	1.64	0.09	0.16	10.52x	0.57x
`nanmax`	1.63	0.09	0.16	10.53x	0.57x
`nanminmax`	3.29	0.17	0.19	17.52x	0.89x
`nanvar`	9.48	0.29	0.24	39.56x	1.20x
`nanstd`	9.95	0.33	0.31	32.06x	1.08x
`nanpercentile`	16.86	-	4.02	4.20x	-
`nanquantile`	16.15	-	4.31	3.75x	-

function	np (µs)	bn (µs)	rd (µs)	np/rd	bn/rd
`nanmean`	12.44	12.32	3.16	3.94x	3.90x
`nanaverage`	16.73	-	3.05	5.48x	-
`nanmedian`	30.57	20.31	30.88	0.99x	0.66x
`nansum`	7.54	11.14	3.15	2.39x	3.53x
`nanmin`	2.27	4.83	1.72	1.32x	2.81x
`nanmax`	2.25	4.94	1.74	1.30x	2.84x
`nanminmax`	4.62	9.47	2.27	2.03x	4.17x
`nanvar`	28.29	24.71	6.28	4.51x	3.94x
`nanstd`	28.76	24.53	6.36	4.52x	3.86x
`nanpercentile`	58.11	-	48.18	1.21x	-
`nanquantile`	54.89	-	49.47	1.11x	-

function	np (µs)	bn (µs)	rd (µs)	np/rd	bn/rd
`nanmean`	6617.96	11152.88	3055.38	2.17x	3.65x
`nanaverage`	12381.00	-	2580.04	4.80x	-
`nanmedian`	54945.29	61287.92	29037.04	1.89x	2.11x
`nansum`	4817.33	11168.96	3027.50	1.59x	3.69x
`nanmin`	900.83	4726.58	450.54	2.00x	10.49x
`nanmax`	991.75	4835.75	477.96	2.07x	10.12x
`nanminmax`	1854.54	9593.12	486.46	3.81x	19.72x
`nanvar`	16862.54	24540.00	6188.21	2.72x	3.97x
`nanstd`	17262.54	24611.38	6573.13	2.63x	3.74x
`nanpercentile`	117531.96	-	45452.63	2.59x	-
`nanquantile`	118207.71	-	46424.12	2.55x	-

NaN-aware, float32

function	np (µs)	bn (µs)	rd (µs)	np/rd	bn/rd
`nanmean`	5.14	0.07	0.17	30.92x	0.43x
`nanaverage`	3.07	-	0.35	8.80x	-
`nanmedian`	7.46	0.11	0.26	28.45x	0.42x
`nansum`	1.72	0.07	0.21	8.28x	0.34x
`nanmin`	1.63	0.06	0.16	9.89x	0.34x
`nanmax`	1.65	0.06	0.17	9.83x	0.34x
`nanminmax`	3.29	0.11	0.18	17.94x	0.61x
`nanvar`	10.62	0.12	0.22	48.63x	0.54x
`nanstd`	11.12	0.16	0.29	38.29x	0.55x
`nanpercentile`	17.06	-	3.58	4.77x	-
`nanquantile`	16.55	-	3.86	4.29x	-

function	np (µs)	bn (µs)	rd (µs)	np/rd	bn/rd
`nanmean`	5.17	0.16	0.18	28.38x	0.88x
`nanaverage`	3.13	-	0.37	8.44x	-
`nanmedian`	7.61	0.20	0.35	21.59x	0.58x
`nansum`	1.74	0.15	0.24	7.39x	0.64x
`nanmin`	1.65	0.09	0.17	9.52x	0.52x
`nanmax`	1.66	0.09	0.17	9.90x	0.53x
`nanminmax`	3.33	0.17	0.19	17.66x	0.89x
`nanvar`	10.58	0.28	0.26	40.56x	1.09x
`nanstd`	11.15	0.34	0.34	33.04x	1.00x
`nanpercentile`	17.37	-	4.08	4.26x	-
`nanquantile`	16.90	-	4.39	3.85x	-

function	np (µs)	bn (µs)	rd (µs)	np/rd	bn/rd
`nanmean`	12.32	n/a	3.20	3.85x	n/a
`nanaverage`	14.88	-	4.03	3.69x	-
`nanmedian`	31.37	19.69	29.95	1.05x	0.66x
`nansum`	5.96	n/a	3.22	1.85x	n/a
`nanmin`	1.90	4.80	0.95	2.00x	5.07x
`nanmax`	1.88	4.81	0.95	1.97x	5.03x
`nanminmax`	3.82	9.29	1.23	3.12x	7.57x
`nanvar`	26.69	n/a	6.21	4.30x	n/a
`nanstd`	27.37	24.54	6.15	4.45x	3.99x
`nanpercentile`	58.30	-	47.59	1.22x	-
`nanquantile`	56.41	-	47.82	1.18x	-

function	np (µs)	bn (µs)	rd (µs)	np/rd	bn/rd
`nanmean`	5355.67	n/a	3017.50	1.77x	n/a
`nanaverage`	9895.13	-	3719.75	2.66x	-
`nanmedian`	74527.29	59038.58	28337.37	2.63x	2.08x
`nansum`	3592.13	n/a	3067.50	1.17x	n/a
`nanmin`	433.92	4771.42	232.46	1.87x	20.53x
`nanmax`	457.58	4974.58	274.50	1.67x	18.12x
`nanminmax`	910.58	9691.21	324.13	2.81x	29.90x
`nanvar`	14348.04	n/a	6113.63	2.35x	n/a
`nanstd`	14223.42	n/a	6073.83	2.34x	n/a
`nanpercentile`	113032.42	-	43584.29	2.59x	-
`nanquantile`	113344.96	-	43631.63	2.60x	-