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 | A | C | A | A | C | F | B |
| verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
| size | 92 | 95 | 92 | 113 | 124 | 87 | 60 | 0 | 100 |
| N.S. |
1 | 1.03 | 1.00 | 1.23 | 1.35 | 0.95 | 0.65 | 0.00 | 1.09 |
| time (sec) |
N/A | 0.074 | 0.469 | 0.939 | 0.231 | 0.383 | 1.394 | 0.000 | 0.458 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | C | A | A | C | F | F(-1) |
| verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
| size | 95 | 95 | 86 | 99 | 124 | 88 | 65 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.91 | 1.04 | 1.31 | 0.93 | 0.68 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.083 | 1.152 | 0.669 | 0.240 | 0.397 | 1.100 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | C | A | C | F | A | F | F | F(-1) |
| verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
| size | 107 | 196 | 107 | 164 | 0 | 109 | 0 | 0 | 0 |
| N.S. |
1 | 1.83 | 1.00 | 1.53 | 0.00 | 1.02 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.184 | 1.662 | 0.794 | 0.000 | 0.396 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | C | F | A | F | F | F(-1) |
| verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
| size | 111 | 118 | 111 | 125 | 0 | 119 | 0 | 0 | 0 |
| N.S. |
1 | 1.06 | 1.00 | 1.13 | 0.00 | 1.07 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.239 | 0.592 | 0.939 | 0.000 | 0.351 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | C | C | C | F | B | F | F | F(-1) |
| verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
| size | 147 | 239 | 123 | 133 | 0 | 125 | 0 | 0 | 0 |
| N.S. |
1 | 1.63 | 0.84 | 0.90 | 0.00 | 0.85 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.245 | 10.156 | 0.664 | 0.000 | 0.359 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | C | A | C | F | A | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 90 | 261 | 90 | 290 | 0 | 104 | 0 | 0 | 0 |
| N.S. |
1 | 2.90 | 1.00 | 3.22 | 0.00 | 1.16 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.351 | 0.194 | 0.466 | 0.000 | 1.358 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | C | A | C | F | A | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 85 | 134 | 85 | 292 | 0 | 78 | 0 | 0 | 0 |
| N.S. |
1 | 1.58 | 1.00 | 3.44 | 0.00 | 0.92 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.399 | 1.460 | 0.526 | 0.000 | 1.156 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | C | A | C | F | A | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 110 | 103 | 110 | 600 | 0 | 133 | 0 | 0 | 0 |
| N.S. |
1 | 0.94 | 1.00 | 5.45 | 0.00 | 1.21 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.372 | 1.049 | 5.344 | 0.000 | 1.499 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | F | A | C | F | F(-2) | F(-1) | F | F(-1) |
| verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 119 | 0 | 119 | 1329 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.00 | 1.00 | 11.17 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.000 | 5.407 | 6.459 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | F | A | C | F | A | F | F | F(-1) |
| verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 102 | 0 | 102 | 607 | 0 | 106 | 0 | 0 | 0 |
| N.S. |
1 | 0.00 | 1.00 | 5.95 | 0.00 | 1.04 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.000 | 15.220 | 0.812 | 0.000 | 0.647 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | F | F | C | F | A | F | F | F(-1) |
| verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 125 | 0 | 0 | 606 | 0 | 107 | 0 | 0 | 0 |
| N.S. |
1 | 0.00 | 0.00 | 4.85 | 0.00 | 0.86 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.000 | 0.000 | 0.604 | 0.000 | 0.498 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | F | F | C | F | A | F | F | F(-1) |
| verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 166 | 0 | 0 | 461 | 0 | 137 | 0 | 0 | 0 |
| N.S. |
1 | 0.00 | 0.00 | 2.78 | 0.00 | 0.83 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.000 | 0.000 | 0.697 | 0.000 | 0.651 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | F | A | C | F | A | F | F | F(-1) |
| verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 113 | 0 | 113 | 458 | 0 | 130 | 0 | 0 | 0 |
| N.S. |
1 | 0.00 | 1.00 | 4.05 | 0.00 | 1.15 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.000 | 31.584 | 1.348 | 0.000 | 0.515 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | F | F | C | F | A | F | F | F(-1) |
| verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 166 | 0 | 0 | 682 | 0 | 146 | 0 | 0 | 0 |
| N.S. |
1 | 0.00 | 0.00 | 4.11 | 0.00 | 0.88 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.000 | 0.000 | 0.635 | 0.000 | 0.654 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | F | F | C | F | A | F | F | F(-1) |
| verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 194 | 0 | 0 | 845 | 0 | 174 | 0 | 0 | 0 |
| N.S. |
1 | 0.00 | 0.00 | 4.36 | 0.00 | 0.90 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.000 | 0.000 | 1.282 | 0.000 | 3.209 | 0.000 | 0.000 | 0.000 |