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	·	7.51 µs (2.7×)	2.76 µs
D38	8.68 µs (1.7×)	8.68 µs (1.7×)	5.24 µs
D57	·	3.45 µs (2.6×)	1.31 µs
D76	6.14 µs (2.8×)	5.37 µs (2.4×)	2.22 µs
D115	·	11 µs (2.4×)	4.5 µs
D153	15.7 µs (2.4×)	14.5 µs (2.3×)	6.44 µs
D230	19.4 µs (2.5×)	18.8 µs (2.4×)	7.67 µs
D307	26.4 µs (2.4×)	25.9 µs (2.4×)	11 µs
D462	·	35.3 µs (2.3×)	15.2 µs
D616	·	46.7 µs (2.3×)	20.3 µs
D924	·	62.9 µs (1.8×)	34.4 µs
D1232	·	83.2 µs (1.6×)	53 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	·	4.7 µs (1×)	4.51 µs
D38	86.5 µs (14×)	5.97 µs (0.98×)	6.09 µs
D57	·	17.8 µs (3.5×)	5.11 µs
D76	29.3 µs (3.7×)	25.8 µs (3.3×)	7.82 µs
D115	·	65.4 µs (4×)	16.2 µs
D153	78.5 µs (3.9×)	70.6 µs (3.5×)	20.2 µs
D230	88.2 µs (4.5×)	82.3 µs (4.2×)	19.5 µs
D307	108 µs (4.6×)	98.3 µs (4.2×)	23.6 µs
D462	·	105 µs (3.9×)	26.8 µs
D616	·	138 µs (4.3×)	31.9 µs
D924	·	195 µs (4.3×)	44.9 µs
D1232	·	260 µs (4.4×)	58.7 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.

exp2

Width	0.3.3	0.4.4	0.5.0
D18	·	3.92 µs (15×)	264 ns
D38	82.6 µs (13×)	6.08 µs (0.99×)	6.16 µs
D57	·	200 µs (16×)	12.2 µs
D76	30 µs (1.9×)	279 µs (18×)	15.7 µs
D115	·	882 µs (20×)	43.9 µs
D153	79.9 µs (1.6×)	960 µs (19×)	50.6 µs
D230	91.1 µs (1.3×)	1.32 ms (18×)	72.1 µs
D307	112 µs (0.93×)	2.81 ms (23×)	121 µs
D462	·	2 ms (18×)	113 µs
D616	·	5.76 ms (18×)	327 µs
D924	·	6.49 ms (19×)	350 µs
D1232	·	6.3 ms (5.6×)	1.13 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	·	280 ns (1.1×)	256 ns
D38	4.34 µs (7.8×)	4.36 µs (7.8×)	556 ns
D57	·	2.98 µs (3.3×)	889 ns
D76	4.79 µs (3.4×)	4.94 µs (3.5×)	1.4 µs
D115	·	8.75 µs (3.2×)	2.77 µs
D153	12.4 µs (2.7×)	12.2 µs (2.7×)	4.56 µs
D230	13.9 µs (2×)	15.1 µs (2.2×)	7 µs
D307	13.8 µs (1.3×)	18.1 µs (1.7×)	10.7 µs
D462	·	27.7 µs (1.5×)	18.8 µs
D616	·	34.6 µs (1.3×)	27.1 µs
D924	·	49 µs (0.95×)	51.5 µs
D1232	·	61 µs (0.83×)	73.4 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.

ln

Width	0.3.3	0.4.4	0.5.0
D18	·	4.79 µs (1×)	4.78 µs
D38	94.9 µs (13×)	6.84 µs (0.97×)	7.03 µs
D57	·	16.7 µs (6.2×)	2.7 µs
D76	38.4 µs (10×)	25.5 µs (6.8×)	3.76 µs
D115	·	54.3 µs (9.9×)	5.47 µs
D153	99.7 µs (13×)	64.5 µs (8.4×)	7.67 µs
D230	112 µs (13×)	74.9 µs (8.7×)	8.65 µs
D307	126 µs (10×)	84.2 µs (7×)	12 µs
D462	·	93.9 µs (4.6×)	20.6 µs
D616	·	115 µs (4.6×)	25 µs
D924	·	160 µs (4.1×)	39 µs
D1232	·	213 µs (3.7×)	57.9 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	·	10.6 µs (1×)	10.5 µs
D38	194 µs (12×)	16.1 µs (1×)	16.1 µs
D57	·	61.8 µs (4.2×)	14.7 µs
D76	73 µs (3.9×)	94.3 µs (5×)	18.7 µs
D115	·	217 µs (4.8×)	45.6 µs
D153	190 µs (3.5×)	239 µs (4.4×)	54 µs
D230	217 µs (3.5×)	285 µs (4.5×)	62.7 µs
D307	241 µs (2.4×)	312 µs (3.1×)	102 µs
D462	·	337 µs (3.2×)	106 µs
D616	·	413 µs (2.5×)	165 µs
D924	·	591 µs (2.3×)	255 µs
D1232	·	787 µs (2.2×)	360 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	·	6.36 µs (0.98×)	6.5 µs
D38	98 µs (10×)	9.59 µs (1×)	9.64 µs
D57	·	33 µs (4×)	8.28 µs
D76	39.5 µs (3.9×)	49.3 µs (4.8×)	10.2 µs
D115	·	112 µs (4.4×)	25.4 µs
D153	103 µs (3.4×)	126 µs (4.2×)	30 µs
D230	117 µs (3.3×)	152 µs (4.3×)	35.5 µs
D307	133 µs (2.3×)	168 µs (2.9×)	57.2 µs
D462	·	175 µs (2.9×)	59.7 µs
D616	·	229 µs (2.4×)	93.7 µs
D924	·	323 µs (2.2×)	144 µs
D1232	·	424 µs (2.1×)	200 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	·	6.56 µs (1×)	6.56 µs
D38	106 µs (11×)	9.95 µs (0.99×)	10 µs
D57	·	34 µs (4×)	8.43 µs
D76	39.4 µs (3.8×)	51 µs (4.9×)	10.5 µs
D115	·	116 µs (4.5×)	26 µs
D153	103 µs (3.4×)	132 µs (4.3×)	30.5 µs
D230	118 µs (3.3×)	158 µs (4.4×)	35.8 µs
D307	134 µs (2.3×)	173 µs (3×)	57.7 µs
D462	·	181 µs (3×)	60.2 µs
D616	·	230 µs (2.4×)	94.4 µs
D924	·	322 µs (2.2×)	145 µs
D1232	·	432 µs (2.2×)	200 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	·	251 ns (0.77×)	328 ns
D38	181 µs (14×)	12.3 µs (0.99×)	12.5 µs
D57	·	49.7 µs (3.5×)	14.3 µs
D76	65.3 µs (3.7×)	73.6 µs (4.2×)	17.4 µs
D115	·	174 µs (3.8×)	46 µs
D153	172 µs (3.2×)	188 µs (3.5×)	53.7 µs
D230	197 µs (2.9×)	231 µs (3.4×)	67.2 µs
D307	228 µs (2.2×)	256 µs (2.5×)	104 µs
D462	·	280 µs (2.4×)	116 µs
D616	·	344 µs (1.6×)	217 µs
D924	·	485 µs (1.3×)	375 µs
D1232	·	649 µs (1.1×)	568 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 (0.82×)	244 ns
D38	3.63 µs (2.4×)	3.64 µs (2.4×)	1.52 µs
D57	·	2.23 µs (2.1×)	1.08 µs
D76	3.74 µs (2.9×)	3.49 µs (2.7×)	1.3 µs
D115	·	6.61 µs (2.4×)	2.77 µs
D153	9.48 µs (2.2×)	8.95 µs (2×)	4.4 µs
D230	11 µs (2×)	11.1 µs (2×)	5.57 µs
D307	11.1 µs (1.3×)	13 µs (1.6×)	8.21 µs
D462	·	19.1 µs (1.5×)	12.3 µs
D616	·	23.6 µs (1.4×)	17.3 µs
D924	·	32.7 µs (1.1×)	29.4 µs
D1232	·	41.1 µs (0.95×)	43.4 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.