Detailed conclusion table per each integral is given by the table below. The elapsed time is in seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2) if the failure was due to an exception being raised, which could indicate a bug in the system. If the failure was due to integral not being evaluated within the time limit, then it is given as F.
In this table, the column N.S. means normalized size and is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To make the table fit the page, the name Mathematica was abbreviated to MMA
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | C | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 408 | 408 | 253 | 136 | 0 | 489 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.62 | 0.33 | 0.00 | 1.20 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.859 | 0.232 | 0.453 | 0.000 | 0.299 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | C | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 714 | 725 | 383 | 1184 | 0 | 670 | 0 | 0 | 0 |
| N.S. |
1 | 1.02 | 0.54 | 1.66 | 0.00 | 0.94 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.508 | 0.171 | 0.928 | 0.000 | 0.299 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | C | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 371 | 374 | 214 | 823 | 0 | 482 | 0 | 0 | 0 |
| N.S. |
1 | 1.01 | 0.58 | 2.22 | 0.00 | 1.30 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.809 | 0.127 | 0.745 | 0.000 | 0.315 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | C | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 691 | 723 | 408 | 508 | 0 | 655 | 0 | 0 | 0 |
| N.S. |
1 | 1.05 | 0.59 | 0.74 | 0.00 | 0.95 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.721 | 0.160 | 0.630 | 0.000 | 0.313 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | C | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 735 | 830 | 406 | 248 | 0 | 669 | 0 | 0 | 0 |
| N.S. |
1 | 1.13 | 0.55 | 0.34 | 0.00 | 0.91 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.841 | 0.162 | 0.534 | 0.000 | 0.301 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | C | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 693 | 842 | 446 | 233 | 0 | 576 | 0 | 0 | 0 |
| N.S. |
1 | 1.22 | 0.64 | 0.34 | 0.00 | 0.83 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.015 | 0.396 | 0.506 | 0.000 | 0.337 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | C | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 712 | 920 | 445 | 284 | 0 | 720 | 0 | 0 | 0 |
| N.S. |
1 | 1.29 | 0.62 | 0.40 | 0.00 | 1.01 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.142 | 0.538 | 0.777 | 0.000 | 0.362 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | C | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 800 | 1059 | 470 | 315 | 0 | 898 | 0 | 0 | 0 |
| N.S. |
1 | 1.32 | 0.59 | 0.39 | 0.00 | 1.12 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.258 | 0.624 | 0.928 | 0.000 | 0.353 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | B | C | C | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 772 | 1592 | 457 | 1337 | 0 | 890 | 0 | 0 | 0 |
| N.S. |
1 | 2.06 | 0.59 | 1.73 | 0.00 | 1.15 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 3.479 | 0.461 | 2.246 | 0.000 | 0.325 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | C | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 777 | 860 | 449 | 918 | 0 | 935 | 0 | 0 | 0 |
| N.S. |
1 | 1.11 | 0.58 | 1.18 | 0.00 | 1.20 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.946 | 0.313 | 1.738 | 0.000 | 0.343 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | C | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 1141 | 1802 | 698 | 610 | 0 | 1319 | 0 | 0 | 0 |
| N.S. |
1 | 1.58 | 0.61 | 0.53 | 0.00 | 1.16 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 3.981 | 0.407 | 1.385 | 0.000 | 0.373 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | C | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 1161 | 2020 | 675 | 340 | 0 | 1223 | 0 | 0 | 0 |
| N.S. |
1 | 1.74 | 0.58 | 0.29 | 0.00 | 1.05 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 4.163 | 0.317 | 1.049 | 0.000 | 0.325 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | C | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 1163 | 2229 | 2109 | 363 | 0 | 1113 | 0 | 0 | 0 |
| N.S. |
1 | 1.92 | 1.81 | 0.31 | 0.00 | 0.96 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 4.586 | 0.553 | 1.089 | 0.000 | 0.352 | 0.000 | 0.000 | 0.000 |