This report gives the result of running the computer algebra independent integration problems (Lite version) obtained from from https://rulebasedintegration.org.
The following versions of Mathematica were tested.
The command AboluteTiming[] was used in Mathematica to obtain the CPU time.
A time limit of 3 minutes is used for all integrals in each CAS. If the integration does not complete within this time limit then the integral is considered to have failed.
The table below gives additional break down of the grading of quality of the antiderivatives generated by each CAS. The grading is given using the letters A,B,C and F with A being the best quality. The grading is accomplished by comparing the antiderivative generated with the optimal antiderivatives included in the test suite. The following table describes the meaning of these grades.
| grade |
description |
| A |
Integral was solved and antiderivative is optimal in quality and leaf size. |
|
B |
Integral was solved and antiderivative is optimal in quality but leaf size is larger than twice the optimal antiderivatives leaf size. |
|
C |
Integral was solved and antiderivative is non-optimal in quality. This can be due to one or more of the following reasons
|
|
F |
Integral was not solved. Either the integral was returned unevaluated within the time limit, or it timed out, or CAS hanged or crashed or an exception was raised. |
Based on the above, the following tables summarizes the grading for each test suite for each version
This table shows the percentage and count of solved and non solved integrals for each version. There are a total of [ 14944 ] integrals in the test suite.
| Version | percentage solved | number solved | number failed |
| 14 | 98.675 | 14746 | 198 |
| 13.3 | 98.675 | 14746 | 198 |
| 12.3.1 | 98.588 | 14733 | 211 |
| 12.1 | 98.548 | 14727 | 217 |
| 12 | 98.555 | 14728 | 216 |
| 11.3 | 97.223 | 14529 | 415 |
| 11.2 | 97.511 | 14572 | 372 |
| 10.3 | 93.395 | 13957 | 987 |
| 9 | 92.867 | 13878 | 1066 |
| 8 | 91.783 | 13716 | 1228 |
| 7 | 91.823 | 13722 | 1222 |
| 6.0.1 | 90.645 | 13546 | 1398 |
| 5.2 | 88.477 | 13222 | 1722 |
This figure shows the percentage of passed integrals in each version.
This Plot shows the number of A graded result for each version.
This table shows the grading performance for each version.
| Version | %A | %B | %C | %F |
| 14 | 79.979 (11952) | 5.179 (774) | 13.517 (2020) | 1.325 (198) |
| 13.3 | 79.865 (11935) | 5.333 (797) | 13.477 (2014) | 1.325 (198) |
| 12.3.1 | 77.048 (11514) | 5.822 (870) | 15.719 (2349) | 1.412 (211) |
| 12.1 | 77.001 (11507) | 5.795 (866) | 15.752 (2354) | 1.445 (216) |
| 12 | 76.807 (11478) | 5.989 (895) | 15.759 (2355) | 1.445 (216) |
| 11.3 | 75.174 (11234) | 7.889 (1179) | 14.16 (2116) | 2.777 (415) |
| 11.2 | 75.147 (11230) | 7.314 (1093) | 15.05 (2249) | 2.489 (372) |
| 10.3 | 71.079 (10622) | 7.347 (1098) | 14.969 (2237) | 6.605 (987) |
| 9 | 72.022 (10763) | 7.02 (1049) | 13.825 (2066) | 7.133 (1066) |
| 8 | 70.865 (10763) | 6.939 (1037) | 13.979 (2089) | 8.217 (1228) |
| 7 | 71.112 (10627) | 7.515 (1123) | 13.196 (1972) | 8.177 (1222) |
| 6.0.1 | 70.323 (10509) | 7.194 (1075) | 13.129 (1962) | 9.355 (1398) |
| 5.2 | 68.389 (10220) | 7.254 (1084) | 12.835 (1918) | 11.523 (1722) |
This figure show the normalized mean leaf size for each version. This was normalized to the size of the optimal result.
This figure show the mean leaf size for each version.
This figure show the median leaf size for each version.
This figure show the mean CPU time (sec) for each version.
