History — Roots and Exponents

How the root and exponential functions have moved release over release. See the History overview for the time units, the width reference map, and how these timings are measured.

cbrt

Width	0.3.3	0.4.4	0.5.0
D18	·	14.6 µs (2.7×)	5.36 µs
D38	17.3 µs (1.7×)	17.3 µs (1.7×)	10.1 µs
D57	·	4.29 µs (3.3×)	1.28 µs
D76	5.97 µs (2.9×)	5.27 µs (2.5×)	2.09 µs
D115	·	10.8 µs (2.3×)	4.6 µs
D153	15.8 µs (2.4×)	14.6 µs (2.2×)	6.47 µs
D230	19.9 µs (2.6×)	19.3 µs (2.5×)	7.71 µs
D307	25.2 µs (2.7×)	23.6 µs (2.5×)	9.43 µs
D462	·	36.6 µs (2.4×)	14.9 µs
D616	·	50 µs (2.4×)	21.1 µs
D924	·	40.9 µs (1.9×)	21.2 µs
D1232	·	86.1 µs (1.6×)	52.7 µs

Median time vs width (log scale), one line per release with a shaded min–max band; the multiplier is the slowdown relative to the latest.

exp

Width	0.3.3	0.4.4	0.5.0
D18	·	6.61 µs (1×)	6.58 µs
D38	172 µs (18×)	9.18 µs (0.98×)	9.32 µs
D57	·	28 µs (5.2×)	5.35 µs
D76	35.3 µs (4.7×)	30.1 µs (4×)	7.45 µs
D115	·	63.7 µs (3.9×)	16.4 µs
D153	73.8 µs (3.7×)	71.5 µs (3.6×)	20.1 µs
D230	95.7 µs (4.9×)	87.4 µs (4.5×)	19.4 µs
D307	116 µs (5.5×)	101 µs (4.8×)	21.2 µs
D462	·	104 µs (3.9×)	26.7 µs
D616	·	156 µs (4.7×)	33.2 µs
D924	·	123 µs (4.7×)	26.3 µs
D1232	·	262 µs (4.3×)	61.1 µs

Median time vs width (log scale), one line per release with a shaded min–max band; the multiplier is the slowdown relative to the latest.

exp2

Width	0.3.3	0.4.4	0.5.0
D18	·	5.91 µs (25×)	241 ns
D38	167 µs (18×)	9.29 µs (0.99×)	9.38 µs
D57	·	265 µs (21×)	12.7 µs
D76	35.7 µs (2.4×)	276 µs (19×)	14.7 µs
D115	·	880 µs (20×)	44.1 µs
D153	75.3 µs (1.5×)	924 µs (18×)	50.3 µs
D230	98.2 µs (1.4×)	1.25 ms (18×)	71.3 µs
D307	121 µs (1.1×)	2.13 ms (20×)	105 µs
D462	·	2.04 ms (18×)	111 µs
D616	·	6.22 ms (17×)	359 µs
D924	·	2.76 ms (13×)	221 µs
D1232	·	6.31 ms (5.2×)	1.2 ms

Median time vs width (log scale), one line per release with a shaded min–max band; the multiplier is the slowdown relative to the latest.

hypot

Width	0.3.3	0.4.4	0.5.0
D18	·	261 ns (1×)	261 ns
D38	6.01 µs (11×)	6.02 µs (11×)	541 ns
D57	·	4.05 µs (5×)	812 ns
D76	5.96 µs (4.3×)	5.04 µs (3.6×)	1.39 µs
D115	·	8.56 µs (3.1×)	2.73 µs
D153	12.7 µs (2.8×)	11.3 µs (2.5×)	4.52 µs
D230	13.9 µs (2×)	15.5 µs (2.2×)	6.94 µs
D307	15.1 µs (1.6×)	18 µs (1.9×)	9.62 µs
D462	·	28 µs (1.5×)	18.3 µs
D616	·	35.8 µs (1.3×)	27.7 µs
D924	·	32.4 µs (1.1×)	29.3 µs
D1232	·	65.5 µs (0.82×)	79.8 µs

Median time vs width (log scale), one line per release with a shaded min–max band; the multiplier is the slowdown relative to the latest.

ln

Width	0.3.3	0.4.4	0.5.0
D18	·	6.17 µs (0.97×)	6.39 µs
D38	188 µs (19×)	9.47 µs (0.96×)	9.89 µs
D57	·	25.8 µs (9.5×)	2.71 µs
D76	47.6 µs (14×)	29.9 µs (8.5×)	3.53 µs
D115	·	54.4 µs (9.7×)	5.63 µs
D153	97.4 µs (13×)	65.1 µs (8.4×)	7.74 µs
D230	116 µs (14×)	76.3 µs (8.9×)	8.57 µs
D307	132 µs (12×)	88.5 µs (8.2×)	10.8 µs
D462	·	87.8 µs (4.3×)	20.4 µs
D616	·	126 µs (5×)	25.2 µs
D924	·	101 µs (4.2×)	23.7 µs
D1232	·	217 µs (3.7×)	58.4 µs

Median time vs width (log scale), one line per release with a shaded min–max band; the multiplier is the slowdown relative to the latest.

log

Width	0.3.3	0.4.4	0.5.0
D18	·	16.2 µs (0.99×)	16.4 µs
D38	381 µs (15×)	24.5 µs (0.98×)	24.9 µs
D57	·	95 µs (6.2×)	15.4 µs
D76	90.4 µs (5.1×)	112 µs (6.4×)	17.6 µs
D115	·	205 µs (4.4×)	46.3 µs
D153	185 µs (3.5×)	241 µs (4.6×)	53 µs
D230	225 µs (3.6×)	284 µs (4.6×)	62.3 µs
D307	257 µs (2.7×)	328 µs (3.4×)	96.3 µs
D462	·	326 µs (3×)	107 µs
D616	·	461 µs (2.7×)	171 µs
D924	·	361 µs (2.4×)	148 µs
D1232	·	794 µs (2.3×)	345 µs

Median time vs width (log scale), one line per release with a shaded min–max band; the multiplier is the slowdown relative to the latest.

log10

Width	0.3.3	0.4.4	0.5.0
D18	·	9.93 µs (1×)	9.97 µs
D38	194 µs (12×)	15.4 µs (0.99×)	15.6 µs
D57	·	50.5 µs (5.9×)	8.52 µs
D76	48.5 µs (5.1×)	59.1 µs (6.2×)	9.59 µs
D115	·	107 µs (4.2×)	25.7 µs
D153	100 µs (3.4×)	130 µs (4.4×)	29.4 µs
D230	122 µs (3.5×)	154 µs (4.4×)	35 µs
D307	139 µs (2.6×)	177 µs (3.3×)	53.7 µs
D462	·	176 µs (2.9×)	60.4 µs
D616	·	248 µs (2.6×)	96.3 µs
D924	·	197 µs (2.4×)	83.5 µs
D1232	·	433 µs (2.2×)	193 µs

Median time vs width (log scale), one line per release with a shaded min–max band; the multiplier is the slowdown relative to the latest.

log2

Width	0.3.3	0.4.4	0.5.0
D18	·	12 µs (1.2×)	10.2 µs
D38	208 µs (13×)	15.9 µs (0.99×)	16.1 µs
D57	·	52.5 µs (6×)	8.69 µs
D76	48.5 µs (4.9×)	61 µs (6.2×)	9.86 µs
D115	·	111 µs (4.2×)	26.4 µs
D153	100 µs (3.4×)	135 µs (4.5×)	29.9 µs
D230	122 µs (3.5×)	158 µs (4.5×)	35.4 µs
D307	141 µs (2.6×)	181 µs (3.3×)	54.1 µs
D462	·	180 µs (2.9×)	61.1 µs
D616	·	256 µs (2.6×)	96.8 µs
D924	·	198 µs (2.3×)	84.1 µs
D1232	·	436 µs (2.2×)	195 µs

Median time vs width (log scale), one line per release with a shaded min–max band; the multiplier is the slowdown relative to the latest.

powf

Width	0.3.3	0.4.4	0.5.0
D18	·	241 ns (0.75×)	320 ns
D38	354 µs (19×)	18.1 µs (0.97×)	18.6 µs
D57	·	76.6 µs (5.1×)	15 µs
D76	79.5 µs (4.8×)	87.2 µs (5.3×)	16.6 µs
D115	·	163 µs (3.5×)	46.5 µs
D153	165 µs (3.1×)	192 µs (3.6×)	53.9 µs
D230	208 µs (3.1×)	233 µs (3.5×)	67.4 µs
D307	244 µs (2.5×)	271 µs (2.7×)	99.2 µs
D462	·	267 µs (2.3×)	116 µs
D616	·	384 µs (1.8×)	217 µs
D924	·	301 µs (1.5×)	207 µs
D1232	·	662 µs (1.2×)	565 µs

Median time vs width (log scale), one line per release with a shaded min–max band; the multiplier is the slowdown relative to the latest.

sqrt

Width	0.3.3	0.4.4	0.5.0
D18	·	200 ns (0.83×)	241 ns
D38	5.09 µs (2.6×)	5.09 µs (2.6×)	1.92 µs
D57	·	3.26 µs (3×)	1.07 µs
D76	4.72 µs (3.6×)	4.05 µs (3.1×)	1.29 µs
D115	·	6.5 µs (2.3×)	2.85 µs
D153	9.69 µs (2.2×)	9.07 µs (2×)	4.43 µs
D230	11.2 µs (2×)	11 µs (2×)	5.54 µs
D307	12.2 µs (1.8×)	12.6 µs (1.8×)	6.93 µs
D462	·	19 µs (1.5×)	12.3 µs
D616	·	24 µs (1.4×)	17.4 µs
D924	·	21.8 µs (1.2×)	18.1 µs
D1232	·	43.8 µs (0.97×)	45 µs

Median time vs width (log scale), one line per release with a shaded min–max band; the multiplier is the slowdown relative to the latest.