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 | F | F | B | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 53 | 53 | 94 | 0 | 0 | 1365 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.77 | 0.00 | 0.00 | 25.75 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.344 | 0.083 | 0.000 | 0.000 | 0.314 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | B | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 90 | 110 | 159 | 0 | 0 | 6475 | 0 | 0 | 0 |
| N.S. |
1 | 1.22 | 1.77 | 0.00 | 0.00 | 71.94 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.328 | 0.819 | 0.000 | 0.000 | 0.459 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | B | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 68 | 73 | 129 | 0 | 0 | 3360 | 0 | 0 | 0 |
| N.S. |
1 | 1.07 | 1.90 | 0.00 | 0.00 | 49.41 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.334 | 0.635 | 0.000 | 0.000 | 0.408 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | B | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 86 | 96 | 169 | 0 | 0 | 5170 | 0 | 0 | 0 |
| N.S. |
1 | 1.12 | 1.97 | 0.00 | 0.00 | 60.12 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.418 | 0.336 | 0.000 | 0.000 | 0.424 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | B | F | B | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 49 | 54 | 49 | 0 | 0 | 2194 | 0 | 93 | 0 |
| N.S. |
1 | 1.10 | 1.00 | 0.00 | 0.00 | 44.78 | 0.00 | 1.90 | 0.00 |
| time (sec) |
N/A | 0.280 | 0.274 | 0.000 | 0.000 | 0.322 | 0.000 | 0.356 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | F | F | B | F | A | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 51 | 51 | 128 | 0 | 0 | 1733 | 0 | 86 | 0 |
| N.S. |
1 | 1.00 | 2.51 | 0.00 | 0.00 | 33.98 | 0.00 | 1.69 | 0.00 |
| time (sec) |
N/A | 0.358 | 0.551 | 0.000 | 0.000 | 0.311 | 0.000 | 0.362 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | A | F | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 43 | 48 | 98 | 46 | 0 | 2034 | 61 | 85 | 35 |
| N.S. |
1 | 1.12 | 2.28 | 1.07 | 0.00 | 47.30 | 1.42 | 1.98 | 0.81 |
| time (sec) |
N/A | 0.249 | 0.483 | 0.155 | 0.000 | 0.324 | 2.828 | 0.342 | 2.592 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | B | F | A | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 57 | 57 | 107 | 0 | 0 | 2095 | 0 | 72 | 0 |
| N.S. |
1 | 1.00 | 1.88 | 0.00 | 0.00 | 36.75 | 0.00 | 1.26 | 0.00 |
| time (sec) |
N/A | 0.243 | 0.612 | 0.000 | 0.000 | 0.328 | 0.000 | 0.351 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | B | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 79 | 99 | 155 | 0 | 0 | 6939 | 0 | 0 | 0 |
| N.S. |
1 | 1.25 | 1.96 | 0.00 | 0.00 | 87.84 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.331 | 0.674 | 0.000 | 0.000 | 0.470 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | B | F | B | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 88 | 98 | 120 | 0 | 0 | 3941 | 0 | 254 | 0 |
| N.S. |
1 | 1.11 | 1.36 | 0.00 | 0.00 | 44.78 | 0.00 | 2.89 | 0.00 |
| time (sec) |
N/A | 0.435 | 0.384 | 0.000 | 0.000 | 0.432 | 0.000 | 0.442 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | B | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 118 | 146 | 178 | 0 | 0 | 11939 | 0 | 0 | 0 |
| N.S. |
1 | 1.24 | 1.51 | 0.00 | 0.00 | 101.18 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.490 | 0.576 | 0.000 | 0.000 | 0.708 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | B | F | B | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 76 | 81 | 126 | 0 | 0 | 5184 | 0 | 297 | 0 |
| N.S. |
1 | 1.07 | 1.66 | 0.00 | 0.00 | 68.21 | 0.00 | 3.91 | 0.00 |
| time (sec) |
N/A | 0.355 | 0.628 | 0.000 | 0.000 | 0.501 | 0.000 | 0.396 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | F | F | B | F | B | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 90 | 97 | 290 | 0 | 0 | 3559 | 0 | 242 | 0 |
| N.S. |
1 | 1.08 | 3.22 | 0.00 | 0.00 | 39.54 | 0.00 | 2.69 | 0.00 |
| time (sec) |
N/A | 0.402 | 1.462 | 0.000 | 0.000 | 0.473 | 0.000 | 0.406 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | B | F | B | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 68 | 79 | 124 | 0 | 0 | 4644 | 0 | 285 | 0 |
| N.S. |
1 | 1.16 | 1.82 | 0.00 | 0.00 | 68.29 | 0.00 | 4.19 | 0.00 |
| time (sec) |
N/A | 0.284 | 1.042 | 0.000 | 0.000 | 0.477 | 0.000 | 0.395 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | F | F | B | F | B | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 88 | 95 | 290 | 0 | 0 | 4989 | 0 | 264 | 0 |
| N.S. |
1 | 1.08 | 3.30 | 0.00 | 0.00 | 56.69 | 0.00 | 3.00 | 0.00 |
| time (sec) |
N/A | 0.393 | 0.437 | 0.000 | 0.000 | 0.506 | 0.000 | 0.398 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 62 | 73 | 112 | 61 | 0 | 3994 | 82 | 257 | 50 |
| N.S. |
1 | 1.18 | 1.81 | 0.98 | 0.00 | 64.42 | 1.32 | 4.15 | 0.81 |
| time (sec) |
N/A | 0.270 | 0.338 | 0.118 | 0.000 | 0.463 | 5.987 | 0.409 | 4.028 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | B | F | B | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 95 | 110 | 130 | 0 | 0 | 6299 | 0 | 232 | 0 |
| N.S. |
1 | 1.16 | 1.37 | 0.00 | 0.00 | 66.31 | 0.00 | 2.44 | 0.00 |
| time (sec) |
N/A | 0.283 | 0.340 | 0.000 | 0.000 | 0.518 | 0.000 | 0.407 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | F | F | B | F(-1) | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 109 | 143 | 242 | 0 | 0 | 18563 | 0 | 0 | 0 |
| N.S. |
1 | 1.31 | 2.22 | 0.00 | 0.00 | 170.30 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.372 | 0.960 | 0.000 | 0.000 | 0.915 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | B | F(-1) | B | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 133 | 155 | 155 | 0 | 0 | 11205 | 0 | 854 | 0 |
| N.S. |
1 | 1.17 | 1.17 | 0.00 | 0.00 | 84.25 | 0.00 | 6.42 | 0.00 |
| time (sec) |
N/A | 0.542 | 0.648 | 0.000 | 0.000 | 0.978 | 0.000 | 0.580 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | B | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 183 | 205 | 221 | 0 | 0 | 18565 | 0 | 0 | 0 |
| N.S. |
1 | 1.12 | 1.21 | 0.00 | 0.00 | 101.45 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.375 | 1.860 | 0.000 | 0.000 | 1.826 | 0.000 | 0.000 | 0.000 |