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
0.5.1
D18
·
15.3 µs (2.8×)
5.35 µs (0.99×)
5.42 µs
D38
17.3 µs (1.7×)
17.3 µs (1.7×)
10.3 µs (1×)
10.1 µs
D57
·
4.34 µs (3.3×)
1.68 µs (1.3×)
1.33 µs
D76
5.94 µs (2.9×)
5.25 µs (2.6×)
2.48 µs (1.2×)
2.01 µs
D115
·
10.7 µs (2.3×)
5.86 µs (1.3×)
4.62 µs
D153
14.6 µs (2.4×)
13.9 µs (2.3×)
6.78 µs (1.1×)
6.02 µs
D230
20 µs (2.5×)
19.4 µs (2.4×)
9.2 µs (1.1×)
8.04 µs
D307
23.3 µs (2.4×)
23.6 µs (2.5×)
10.4 µs (1.1×)
9.54 µs
D462
·
33.7 µs (2.2×)
16.2 µs (1.1×)
15 µs
D616
·
45.8 µs (2.3×)
20.7 µs (1×)
20.2 µs
D924
·
48.4 µs (1.9×)
25.4 µs (1×)
25 µs
D1232
·
88.7 µs (1.7×)
50.2 µs (0.97×)
51.6 µs
1 µs 10 µs 100 µs 1 ms 10 ms 100 ms 18 38 57 76 115 153 230 307 462 616 924 1232 0.3.3 0.4.4 0.5.0 0.5.1 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
0.5.1
D18
·
6.58 µs (1×)
6.56 µs (1×)
6.57 µs
D38
172 µs (19×)
9.14 µs (0.98×)
9.47 µs (1×)
9.31 µs
D57
·
27.4 µs (4.8×)
5.58 µs (0.97×)
5.73 µs
D76
35.3 µs (4.5×)
28.8 µs (3.7×)
7.6 µs (0.98×)
7.79 µs
D115
·
59.2 µs (3.4×)
17 µs (0.99×)
17.2 µs
D153
66 µs (3.1×)
61.1 µs (2.9×)
20.7 µs (0.98×)
21.1 µs
D230
89.9 µs (4.4×)
87.5 µs (4.2×)
20.3 µs (0.98×)
20.6 µs
D307
102 µs (4.6×)
94.3 µs (4.3×)
21.8 µs (0.98×)
22.2 µs
D462
·
104 µs (3.8×)
27 µs (0.99×)
27.2 µs
D616
·
139 µs (4.4×)
31.5 µs (1×)
31.7 µs
D924
·
150 µs (4.5×)
32.7 µs (0.99×)
33.1 µs
D1232
·
266 µs (4.4×)
55.7 µs (0.92×)
60.4 µs
100 ns 1 µs 10 µs 100 µs 1 ms 10 ms 100 ms 18 38 57 76 115 153 230 307 462 616 924 1232 0.3.3 0.4.4 0.5.0 0.5.1 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
0.5.1
D18
·
5.87 µs (23×)
250 ns (0.96×)
260 ns
D38
167 µs (18×)
9.23 µs (0.98×)
9.53 µs (1×)
9.39 µs
D57
·
257 µs (19×)
13.2 µs (0.98×)
13.5 µs
D76
35.9 µs (2.4×)
283 µs (19×)
14.9 µs (0.98×)
15.2 µs
D115
·
967 µs (21×)
45.2 µs (1×)
45.3 µs
D153
66.9 µs (1.3×)
1.03 ms (19×)
52.7 µs (0.99×)
53.1 µs
D230
93.7 µs (1.3×)
1.48 ms (20×)
73.1 µs (0.99×)
74.1 µs
D307
103 µs (0.91×)
4.29 ms (38×)
112 µs (0.98×)
113 µs
D462
·
3.64 ms (32×)
113 µs (0.99×)
114 µs
D616
·
6.37 ms (20×)
322 µs (1×)
323 µs
D924
·
4.88 ms (18×)
260 µs (0.97×)
269 µs
D1232
·
6.33 ms (5.5×)
1.13 ms (0.98×)
1.14 ms
100 ns 1 µs 10 µs 100 µs 1 ms 10 ms 100 ms 1 s 18 38 57 76 115 153 230 307 462 616 924 1232 0.3.3 0.4.4 0.5.0 0.5.1 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.
expm1
Width
0.3.3
0.4.4
0.5.0
0.5.1
D18
·
·
·
9.71 µs
D38
·
·
·
11.9 µs
D57
·
·
·
12.9 µs
D76
·
·
·
14.6 µs
D115
·
·
·
38.1 µs
D153
·
·
·
46.2 µs
D230
·
·
·
59.4 µs
D307
·
·
·
87.5 µs
D462
·
·
·
87.7 µs
D616
·
·
·
147 µs
D924
·
·
·
138 µs
D1232
·
·
·
337 µs
1 µs 10 µs 100 µs 1 ms 10 ms 100 ms 18 38 57 76 115 153 230 307 462 616 924 1232 0.3.3 0.4.4 0.5.0 0.5.1 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
0.5.1
D18
·
276 ns (1×)
266 ns (0.99×)
270 ns
D38
6.04 µs (11×)
6.04 µs (11×)
711 ns (1.3×)
531 ns
D57
·
4.16 µs (5×)
981 ns (1.2×)
831 ns
D76
5.97 µs (4.1×)
5.03 µs (3.4×)
1.86 µs (1.3×)
1.46 µs
D115
·
8.57 µs (3.1×)
3.01 µs (1.1×)
2.8 µs
D153
9.94 µs (2.3×)
11.3 µs (2.6×)
4.77 µs (1.1×)
4.28 µs
D230
14 µs (1.9×)
13.7 µs (1.9×)
7.96 µs (1.1×)
7.19 µs
D307
12.9 µs (1.3×)
18.1 µs (1.8×)
10 µs (1×)
10 µs
D462
·
25.5 µs (1.4×)
18.8 µs (1×)
18.3 µs
D616
·
33.1 µs (1.2×)
28.5 µs (1.1×)
26.9 µs
D924
·
37.1 µs (1.1×)
34 µs (0.99×)
34.4 µs
D1232
·
64.4 µs (0.86×)
73.7 µs (0.98×)
75 µs
100 ns 1 µs 10 µs 100 µs 1 ms 10 ms 100 ms 18 38 57 76 115 153 230 307 462 616 924 1232 0.3.3 0.4.4 0.5.0 0.5.1 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
0.5.1
D18
·
6.17 µs (0.97×)
6.4 µs (1×)
6.39 µs
D38
192 µs (19×)
9.53 µs (0.96×)
10.2 µs (1×)
9.94 µs
D57
·
26 µs (8.7×)
3.04 µs (1×)
2.98 µs
D76
46.5 µs (13×)
29.8 µs (8.1×)
3.8 µs (1×)
3.69 µs
D115
·
52.3 µs (8.7×)
5.92 µs (0.99×)
6.01 µs
D153
82.6 µs (11×)
54.7 µs (7.2×)
7.58 µs (1×)
7.59 µs
D230
111 µs (12×)
78.1 µs (8.6×)
9.18 µs (1×)
9.08 µs
D307
118 µs (11×)
78.1 µs (7.2×)
10.9 µs (1×)
10.9 µs
D462
·
90.2 µs (4.4×)
20.6 µs (1×)
20.5 µs
D616
·
117 µs (4.7×)
24.9 µs (1×)
24.8 µs
D924
·
120 µs (4.2×)
27.8 µs (0.96×)
28.9 µs
D1232
·
219 µs (3.9×)
57.3 µs (1×)
56.6 µs
100 ns 1 µs 10 µs 100 µs 1 ms 10 ms 100 ms 18 38 57 76 115 153 230 307 462 616 924 1232 0.3.3 0.4.4 0.5.0 0.5.1 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
0.5.1
D18
·
16.2 µs (0.98×)
16.4 µs (1×)
16.4 µs
D38
381 µs (15×)
24.5 µs (0.98×)
25.1 µs (1×)
25 µs
D57
·
95.6 µs (6×)
16.1 µs (1×)
16 µs
D76
88.5 µs (4.8×)
112 µs (6×)
18.2 µs (0.98×)
18.5 µs
D115
·
196 µs (3.9×)
47.1 µs (0.94×)
50.1 µs
D153
157 µs (2.8×)
206 µs (3.7×)
53.8 µs (0.97×)
55.4 µs
D230
214 µs (3.1×)
283 µs (4.1×)
63.6 µs (0.93×)
68.3 µs
D307
226 µs (2.3×)
293 µs (3×)
96.3 µs (1×)
96.2 µs
D462
·
324 µs (3.1×)
106 µs (1×)
103 µs
D616
·
418 µs (2.4×)
170 µs (0.97×)
175 µs
D924
·
440 µs (2.4×)
178 µs (0.97×)
184 µs
D1232
·
816 µs (2.1×)
352 µs (0.93×)
380 µs
100 ns 1 µs 10 µs 100 µs 1 ms 10 ms 100 ms 18 38 57 76 115 153 230 307 462 616 924 1232 0.3.3 0.4.4 0.5.0 0.5.1 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
0.5.1
D18
·
9.89 µs (0.99×)
9.98 µs (1×)
9.99 µs
D38
194 µs (12×)
15.4 µs (0.98×)
15.8 µs (1×)
15.7 µs
D57
·
50.8 µs (5.6×)
9 µs (1×)
9.04 µs
D76
47.4 µs (4.6×)
57.6 µs (5.6×)
9.96 µs (0.97×)
10.2 µs
D115
·
106 µs (3.8×)
26.6 µs (0.94×)
28.3 µs
D153
84.7 µs (2.8×)
109 µs (3.6×)
29.5 µs (0.96×)
30.5 µs
D230
116 µs (3×)
154 µs (4×)
36 µs (0.93×)
38.8 µs
D307
122 µs (2.3×)
156 µs (2.9×)
53.7 µs (0.99×)
54.1 µs
D462
·
174 µs (3×)
59.3 µs (1×)
58.6 µs
D616
·
226 µs (2.3×)
94.8 µs (0.97×)
98.2 µs
D924
·
243 µs (2.3×)
100 µs (0.95×)
105 µs
D1232
·
437 µs (2.1×)
194 µs (0.92×)
211 µs
100 ns 1 µs 10 µs 100 µs 1 ms 10 ms 100 ms 18 38 57 76 115 153 230 307 462 616 924 1232 0.3.3 0.4.4 0.5.0 0.5.1 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.
log1p
Width
0.3.3
0.4.4
0.5.0
0.5.1
D18
·
·
·
5.09 µs
D38
·
·
·
4.54 µs
D57
·
·
·
3.25 µs
D76
·
·
·
3.83 µs
D115
·
·
·
11.2 µs
D153
·
·
·
11.9 µs
D230
·
·
·
16.7 µs
D307
·
·
·
23 µs
D462
·
·
·
27.2 µs
D616
·
·
·
40.9 µs
D924
·
·
·
40.2 µs
D1232
·
·
·
95.5 µs
1 µs 10 µs 100 µs 1 ms 10 ms 18 38 57 76 115 153 230 307 462 616 924 1232 0.3.3 0.4.4 0.5.0 0.5.1 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
0.5.1
D18
·
10.2 µs (0.99×)
10.2 µs (1×)
10.3 µs
D38
209 µs (13×)
15.8 µs (0.98×)
16.4 µs (1×)
16.1 µs
D57
·
52.6 µs (5.7×)
9.23 µs (1×)
9.19 µs
D76
47.4 µs (4.5×)
59.7 µs (5.7×)
10.3 µs (0.98×)
10.5 µs
D115
·
111 µs (3.8×)
27.1 µs (0.93×)
29 µs
D153
85.2 µs (2.7×)
112 µs (3.6×)
30 µs (0.97×)
31 µs
D230
117 µs (3×)
158 µs (4.1×)
36.3 µs (0.93×)
39.1 µs
D307
122 µs (2.2×)
161 µs (3×)
54.1 µs (0.99×)
54.5 µs
D462
·
180 µs (3×)
60.4 µs (1×)
59 µs
D616
·
230 µs (2.3×)
95.6 µs (0.97×)
98.6 µs
D924
·
246 µs (2.3×)
102 µs (0.96×)
106 µs
D1232
·
447 µs (2.1×)
195 µs (0.91×)
214 µs
100 ns 1 µs 10 µs 100 µs 1 ms 10 ms 100 ms 18 38 57 76 115 153 230 307 462 616 924 1232 0.3.3 0.4.4 0.5.0 0.5.1 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
0.5.1
D18
·
261 ns (0.81×)
321 ns (1×)
321 ns
D38
357 µs (19×)
18.1 µs (0.98×)
18.7 µs (1×)
18.5 µs
D57
·
76 µs (4.8×)
15.6 µs (0.99×)
15.7 µs
D76
78.8 µs (4.6×)
86.5 µs (5.1×)
16.8 µs (0.98×)
17.1 µs
D115
·
162 µs (3.3×)
47.6 µs (0.98×)
48.3 µs
D153
143 µs (2.7×)
165 µs (3.1×)
53.7 µs (1×)
53.7 µs
D230
197 µs (2.8×)
231 µs (3.2×)
68.8 µs (0.96×)
71.5 µs
D307
212 µs (2.1×)
241 µs (2.4×)
99.1 µs (0.98×)
101 µs
D462
·
266 µs (2.3×)
116 µs (0.99×)
117 µs
D616
·
349 µs (1.6×)
220 µs (0.99×)
223 µs
D924
·
363 µs (1.4×)
251 µs (0.99×)
252 µs
D1232
·
665 µs (1.2×)
544 µs (0.96×)
567 µs
100 ns 1 µs 10 µs 100 µs 1 ms 10 ms 100 ms 18 38 57 76 115 153 230 307 462 616 924 1232 0.3.3 0.4.4 0.5.0 0.5.1 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
0.5.1
D18
·
201 ns (0.8×)
250 ns (1×)
250 ns
D38
5.11 µs (2.7×)
5.09 µs (2.7×)
2.1 µs (1.1×)
1.91 µs
D57
·
3.27 µs (3×)
1.55 µs (1.4×)
1.1 µs
D76
4.68 µs (3.6×)
3.99 µs (3.1×)
1.74 µs (1.3×)
1.3 µs
D115
·
6.46 µs (2.3×)
3.37 µs (1.2×)
2.85 µs
D153
7.47 µs (1.8×)
8.1 µs (2×)
4.51 µs (1.1×)
4.12 µs
D230
11 µs (1.9×)
11.4 µs (2×)
6.48 µs (1.1×)
5.75 µs
D307
10.3 µs (1.4×)
12 µs (1.7×)
7.59 µs (1.1×)
7.13 µs
D462
·
17.4 µs (1.5×)
12.6 µs (1.1×)
11.9 µs
D616
·
23.5 µs (1.4×)
17.5 µs (1×)
17.4 µs
D924
·
24.9 µs (1.2×)
21 µs (0.99×)
21.3 µs
D1232
·
43.9 µs (1×)
42.1 µs (0.99×)
42.6 µs
100 ns 1 µs 10 µs 100 µs 1 ms 10 ms 100 ms 18 38 57 76 115 153 230 307 462 616 924 1232 0.3.3 0.4.4 0.5.0 0.5.1 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.