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 | Reduce | Mupad | |
| grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 505 | 498 | 661 | 620 | 0 | 574 | 0 | 0 | 1143 | 0 |
| N.S. |
1 | 0.99 | 1.31 | 1.23 | 0.00 | 1.14 | 0.00 | 0.00 | 2.26 | 0.00 |
| time (sec) |
N/A | 0.788 | 14.251 | 3.857 | 0.000 | 0.237 | 0.000 | 0.000 | 1.490 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 360 | 363 | 525 | 426 | 0 | 376 | 0 | 0 | 1512 | 0 |
| N.S. |
1 | 1.01 | 1.46 | 1.18 | 0.00 | 1.04 | 0.00 | 0.00 | 4.20 | 0.00 |
| time (sec) |
N/A | 0.558 | 11.522 | 2.832 | 0.000 | 0.179 | 0.000 | 0.000 | 0.663 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 447 | 433 | 513 | 565 | 0 | 723 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.97 | 1.15 | 1.26 | 0.00 | 1.62 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.695 | 11.964 | 1.664 | 0.000 | 0.091 | 0.000 | 0.000 | 0.297 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | F | B | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 680 | 650 | 598 | 829 | 0 | 1948 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.96 | 0.88 | 1.22 | 0.00 | 2.86 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.041 | 12.965 | 1.770 | 0.000 | 0.129 | 0.000 | 0.000 | 1.020 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | F | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 19 | 19 | 19 | 18 | 17 | 17 | 0 | 60 | 30 | 17 |
| N.S. |
1 | 1.00 | 1.00 | 0.95 | 0.89 | 0.89 | 0.00 | 3.16 | 1.58 | 0.89 |
| time (sec) |
N/A | 0.161 | 10.122 | 1.186 | 0.093 | 0.075 | 0.000 | 0.436 | 0.180 | 18.237 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | F | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 57 | 57 | 51 | 52 | 51 | 82 | 0 | 138 | 87 | 51 |
| N.S. |
1 | 1.00 | 0.89 | 0.91 | 0.89 | 1.44 | 0.00 | 2.42 | 1.53 | 0.89 |
| time (sec) |
N/A | 0.283 | 10.178 | 1.971 | 0.085 | 0.081 | 0.000 | 0.361 | 0.184 | 18.236 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | F | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 57 | 57 | 48 | 53 | 49 | 80 | 0 | 136 | 88 | 51 |
| N.S. |
1 | 1.00 | 0.84 | 0.93 | 0.86 | 1.40 | 0.00 | 2.39 | 1.54 | 0.89 |
| time (sec) |
N/A | 0.298 | 10.113 | 1.885 | 0.071 | 0.074 | 0.000 | 0.370 | 0.199 | 18.368 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | F | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 69 | 69 | 61 | 63 | 94 | 92 | 0 | 164 | 98 | 62 |
| N.S. |
1 | 1.00 | 0.88 | 0.91 | 1.36 | 1.33 | 0.00 | 2.38 | 1.42 | 0.90 |
| time (sec) |
N/A | 0.311 | 10.220 | 2.132 | 0.083 | 0.082 | 0.000 | 0.382 | 0.179 | 18.257 |