Detailed conclusion table per each integral is given by 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 just an F.
In this table,the column N.S. in the table below, which stands for normalized size is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To help make the table fit, Mathematica was abbreviated to MMA.
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | F | F | B | F | F(-2) | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 53 | 53 | 94 | 0 | 0 | 1365 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 1.77 | 0.00 | 0.00 | 25.75 | 0.00 | 0.00 | -0.02 |
| time (sec) |
N/A | 0.129 | 0.078 | 1.802 | 0.000 | 0.452 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | F | F | B | F | F(-2) | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 90 | 90 | 159 | 0 | 0 | 6475 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 1.77 | 0.00 | 0.00 | 71.94 | 0.00 | 0.00 | -0.01 |
| time (sec) |
N/A | 0.118 | 0.514 | 1.827 | 0.000 | 0.619 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | F | F | B | F | F(-2) | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 68 | 68 | 129 | 0 | 0 | 3360 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 1.90 | 0.00 | 0.00 | 49.41 | 0.00 | 0.00 | -0.01 |
| time (sec) |
N/A | 0.099 | 0.320 | 1.677 | 0.000 | 0.540 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | F | F | B | F | F(-2) | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 86 | 86 | 169 | 0 | 0 | 5170 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 1.97 | 0.00 | 0.00 | 60.12 | 0.00 | 0.00 | -0.01 |
| time (sec) |
N/A | 0.164 | 0.256 | 1.555 | 0.000 | 0.602 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | B | F | F | B | F | F(-2) | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 49 | 49 | 103 | 0 | 0 | 2194 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 2.10 | 0.00 | 0.00 | 44.78 | 0.00 | 0.00 | -0.02 |
| time (sec) |
N/A | 0.077 | 0.147 | 1.300 | 0.000 | 0.445 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | B | F | F | B | F | F(-2) | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 51 | 51 | 128 | 0 | 0 | 1733 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 2.51 | 0.00 | 0.00 | 33.98 | 0.00 | 0.00 | -0.02 |
| time (sec) |
N/A | 0.140 | 0.505 | 1.304 | 0.000 | 0.426 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | B | A | F | B | A | F(-2) | B |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 43 | 43 | 98 | 46 | 0 | 2034 | 44 | 0 | 35 |
| N.S. |
1 | 1.00 | 2.28 | 1.07 | 0.00 | 47.30 | 1.02 | 0.00 | 0.81 |
| time (sec) |
N/A | 0.052 | 0.235 | 0.507 | 0.000 | 0.465 | 3.371 | 0.000 | 1.741 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | F | F | B | F | F(-2) | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 57 | 57 | 107 | 0 | 0 | 2095 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 1.88 | 0.00 | 0.00 | 36.75 | 0.00 | 0.00 | -0.02 |
| time (sec) |
N/A | 0.032 | 0.558 | 1.181 | 0.000 | 0.507 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | F | F | B | F | F(-2) | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 79 | 79 | 155 | 0 | 0 | 6939 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 1.96 | 0.00 | 0.00 | 87.84 | 0.00 | 0.00 | -0.01 |
| time (sec) |
N/A | 0.097 | 0.422 | 1.540 | 0.000 | 0.572 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | F | F | B | F | F(-2) | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 88 | 88 | 120 | 0 | 0 | 3941 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 1.36 | 0.00 | 0.00 | 44.78 | 0.00 | 0.00 | -0.01 |
| time (sec) |
N/A | 0.182 | 0.299 | 1.624 | 0.000 | 0.517 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | F | F | B | F | F(-2) | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 118 | 118 | 178 | 0 | 0 | 11939 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 1.51 | 0.00 | 0.00 | 101.18 | 0.00 | 0.00 | -0.01 |
| time (sec) |
N/A | 0.229 | 0.486 | 1.573 | 0.000 | 0.868 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | F | F | B | F | F(-2) | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 76 | 76 | 126 | 0 | 0 | 5184 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 1.66 | 0.00 | 0.00 | 68.21 | 0.00 | 0.00 | -0.01 |
| time (sec) |
N/A | 0.106 | 0.371 | 1.534 | 0.000 | 0.627 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | B | F | F | B | F | F(-2) | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 90 | 90 | 290 | 0 | 0 | 3559 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 3.22 | 0.00 | 0.00 | 39.54 | 0.00 | 0.00 | -0.01 |
| time (sec) |
N/A | 0.172 | 1.377 | 1.552 | 0.000 | 0.634 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | F | F | B | F | F(-2) | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 68 | 68 | 124 | 0 | 0 | 4644 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 1.82 | 0.00 | 0.00 | 68.29 | 0.00 | 0.00 | -0.01 |
| time (sec) |
N/A | 0.090 | 0.620 | 1.329 | 0.000 | 0.597 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | B | F | F | B | F | F(-2) | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 88 | 88 | 290 | 0 | 0 | 4989 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 3.30 | 0.00 | 0.00 | 56.69 | 0.00 | 0.00 | -0.01 |
| time (sec) |
N/A | 0.169 | 0.767 | 1.303 | 0.000 | 0.618 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | A | F | B | A | F(-2) | B |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 62 | 62 | 112 | 67 | 0 | 3994 | 65 | 0 | 50 |
| N.S. |
1 | 1.00 | 1.81 | 1.08 | 0.00 | 64.42 | 1.05 | 0.00 | 0.81 |
| time (sec) |
N/A | 0.060 | 0.466 | 0.523 | 0.000 | 0.606 | 7.702 | 0.000 | 3.069 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | F | F | B | F | F(-2) | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 95 | 95 | 130 | 0 | 0 | 6299 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 1.37 | 0.00 | 0.00 | 66.31 | 0.00 | 0.00 | -0.01 |
| time (sec) |
N/A | 0.062 | 0.301 | 1.161 | 0.000 | 0.583 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | B | F | F | B | F(-1) | F(-2) | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 109 | 109 | 242 | 0 | 0 | 18563 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 2.22 | 0.00 | 0.00 | 170.30 | 0.00 | 0.00 | -0.01 |
| time (sec) |
N/A | 0.144 | 0.730 | 1.643 | 0.000 | 0.954 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | F | F | B | F(-1) | F(-2) | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 133 | 133 | 155 | 0 | 0 | 11205 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 1.17 | 0.00 | 0.00 | 84.25 | 0.00 | 0.00 | -0.01 |
| time (sec) |
N/A | 0.247 | 0.540 | 1.682 | 0.000 | 0.986 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | F | F | B | F | F(-2) | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 183 | 183 | 330 | 0 | 0 | 18565 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 1.80 | 0.00 | 0.00 | 101.45 | 0.00 | 0.00 | -0.01 |
| time (sec) |
N/A | 0.138 | 4.949 | 2.991 | 0.000 | 1.658 | 0.000 | 0.000 | 0.000 |