| Maple | Mathematica | Magma | SAGE | GMP MPF | MPFR | PARI | NTL | CLN | mpmath |
| commercial | commercial | commercial | free (GPL) | free (LGPL) | free (LGPL) | free (GPL) | free (GPL) | free (GPL) | free (New BSD) |
| 10.00 | 6.0.1 | 2.13-5 | 2.8.14 | 4.2.2 | 2.3.0 | 2.3.2 | 5.4.1 | 1.2.0 | 0.9 |
| interactive | interactive | interactive | interactive | library | library | library | library | library | library |
The following tables give the cpu time in milliseconds spent by several systems or libraries for different operations, at different precisions (in digits). Those timings were obtained on a 16-core AMD Opteron 865 at 1.8GHz (sage.math.washington.edu) with 100GB of swap and 64GB of RAM under Linux 2.6.12-10-amd64-k8-smp. The version of GCC is 4.1.2.
GMP has been built with Gaudry's AMD64 patch. MPFR was built with --with-gmp-build, and make tune. PARI and NTL have been built with native support. CLN has been built with GMP support. The mpmath timings were kindly given by Ondrej Certik, with the script provided by Fredrik Johansson, and were obtained with gmpy enabled (without psyco).
An entry "na" means a function not available in the corresponding software tool. The boldface entries are the fastest in each row.
| 100 digits | Maple | Mathematica | Magma | SAGE | MPF | MPFR | Pari | NTL | CLN | mpmath |
| mult | 0.0048 | 0.0015 | 0.0006 | 0.0012 | 0.00017 | 0.00018 | 0.00017 | 0.00073 | 0.00034 | 0.00843 |
| div | 0.0064 | 0.0029 | 0.0010 | 0.0015 | 0.00064 | 0.00051 | 0.00065 | 0.00121 | 0.00086 | 0.01050 |
| sqrt | 0.0732 | 0.0033 | 0.0015 | 0.00235 | 0.00095 | 0.00086 | 0.00171 | 0.00751 | 0.00106 | 0.01544 |
| exp | 0.164 | 0.029 | 0.012 | 0.014 | na | 0.011 | 0.018 | 0.124 | 0.035 | 0.054 |
| log | 0.228 | 0.045 | 0.0179 | 0.0220 | na | 0.0168 | 0.0287 | 0.692 | 0.0475 | 0.1428 |
| sin | 0.280 | 0.027 | 0.0159 | 0.0156 | na | 0.0121 | 0.0158 | 0.137 | 0.0420 | 0.0811 |
| cos | 0.260 | 0.028 | 0.0117 | 0.0120 | na | 0.0092 | 0.0135 | 0.149 | 0.0370 | 0.0815 |
| acos | 2.12 | 0.083 | 0.235 | 0.093 | na | 0.082 | 0.061 | na | 0.055 | 0.421 |
| atan | 0.588 | 0.075 | 0.201 | 0.084 | na | 0.073 | 0.059 | na | 0.047 | 0.516 |
| 1000 digits | Maple | Mathematica | Magma | SAGE | MPF | MPFR | Pari | NTL | CLN | mpmath |
| mult | 0.0600 | 0.0088 | 0.0043 | 0.0050 | 0.0046 | 0.0039 | 0.0076 | 0.0247 | 0.0072 | 0.0139 |
| div | 0.0640 | 0.0152 | 0.0087 | 0.0092 | 0.0084 | 0.0082 | 0.0106 | 0.0332 | 0.0119 | 0.0216 |
| sqrt | 0.408 | 0.0144 | 0.0076 | 0.0092 | 0.0074 | 0.0074 | 0.0150 | 0.311 | 0.0092 | 0.0237 |
| exp | 2.92 | 0.668 | 0.275 | 0.259 | na | 0.253 | 0.674 | 10.55 | 0.608 | 0.456 |
| log | 0.800 | 0.792 | 0.240 | 0.242 | na | 0.232 | 0.496 | 85.87 | 0.633 | 0.905 |
| sin | 5.28 | 0.428 | 0.271 | 0.275 | na | 0.269 | 0.621 | 11.84 | 0.526 | 0.793 |
| cos | 5.28 | 0.432 | 0.263 | 0.258 | na | 0.254 | 0.598 | 12.57 | 0.489 | 0.790 |
| acos | 7.38 | 0.96 | 2.83 | 1.10 | na | 1.06 | 1.70 | na | 0.80 | 2.23 |
| atan | 5.36 | 0.93 | 2.43 | 1.00 | na | 0.97 | 1.67 | na | 0.74 | 2.19 |
| 10000 digits | Maple | Mathematica | Magma | SAGE | MPF | MPFR | Pari | NTL | CLN | mpmath |
| mult | 1.92 | 0.232 | 0.145 | 0.141 | 0.167 | 0.139 | 0.452 | 0.974 | 0.307 | 0.240 |
| div | 1.96 | 0.504 | 0.339 | 0.342 | 0.342 | 0.337 | 0.647 | 2.763 | 0.743 | 0.488 |
| sqrt | 9.04 | 0.332 | 0.233 | 0.237 | 0.236 | 0.233 | 0.649 | 34.06 | 0.453 | 0.334 |
| exp | 147 | 20.1 | 18.8 | 14.5 | na | 14.3 | 45.3 | 2924 | 25.9 | 42.7 |
| log | 87.6 | 17.8 | 10.5 | 9.9 | na | 9.7 | 29.7 | 30226 | 30.3 | 77.2 |
| sin | 295 | 37.7 | 24.4 | 25.6 | na | 25.5 | 102 | 3120 | 45.7 | 77.6 |
| cos | 295 | 37.6 | 24.0 | 25.2 | na | 25.0 | 102 | 14297 | 43.9 | 76.7 |
| acos | 246 | 79.7 | 219 | 44.0 | na | 43.7 | 117 | na | 54.8 | 106.3 |
| atan | 251 | 76.5 | 187 | 40.3 | na | 39.9 | 116 | na | 52.8 | 105.2 |
The source file of these tests is available for Maple, Mathematica, Magma, SAGE, MPF, MPFR, Pari, NTL, CLN, and mpmath.
Thanks to the National Science Foundation (grant No. 0555776) and to the University of Washington, which provided the machine and software for this comparison.