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 and IntegrateAlgebraic to I.A.
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | I.A. | |
| grade |
A | A | C | C | F | F(-1) | F(-1) | F(-1) | B | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD | Yes |
| size | 1668 | 1668 | 223 | 134 | 0 | 0 | 0 | 0 | 359169 | 0 |
| N.S. | 1 | 1.00 | 0.13 | 0.08 | 0.00 | 0.00 | 0.00 | 0.00 | 215.33 | 0.00 |
| time (sec) |
N/A | 4.008 | 1.681 | 0.017 | 0.000 | 0.000 | 0.000 | 0.000 | 40.553 | 0.001 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | I.A. | |
| grade |
A | A | F(-1) | F | F | A | F(-1) | F | F | A |
| verified |
N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD | N/A |
| size | 75 | 75 | 0 | 0 | 0 | 137 | 0 | 0 | -1 | 84 |
| N.S. | 1 | 1.00 | 0.00 | 0.00 | 0.00 | 1.83 | 0.00 | 0.00 | -0.01 | 1.12 |
| time (sec) |
N/A | 0.531 | 0.000 | 0.066 | 0.000 | 1.103 | 0.000 | 0.000 | 0.000 | 53.490 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | I.A. | |
| grade |
A | A | A | A | A | A | B | B | B | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD | Yes |
| size | 20 | 20 | 19 | 33 | 35 | 35 | 63 | 66 | 35 | 0 |
| N.S. | 1 | 1.00 | 0.95 | 1.65 | 1.75 | 1.75 | 3.15 | 3.30 | 1.75 | 0.00 |
| time (sec) |
N/A | 0.024 | 0.333 | 0.051 | 1.219 | 1.174 | 50.333 | 0.841 | 2.181 | 0.214 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | I.A. | |
| grade |
A | A | A | F | F | A | F(-1) | A | B | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD | Yes |
| size | 45 | 45 | 45 | 0 | 0 | 48 | 0 | 39 | 39 | 0 |
| N.S. | 1 | 1.00 | 1.00 | 0.00 | 0.00 | 1.07 | 0.00 | 0.87 | 0.87 | 0.00 |
| time (sec) |
N/A | 0.079 | 0.214 | 0.095 | 0.000 | 1.089 | 0.000 | 35.009 | 2.557 | 0.705 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | I.A. | |
| grade |
A | A | A | F | F | A | F(-1) | F | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD | Yes |
| size | 65 | 65 | 64 | 0 | 0 | 69 | 0 | 0 | -1 | 0 |
| N.S. | 1 | 1.00 | 0.98 | 0.00 | 0.00 | 1.06 | 0.00 | 0.00 | -0.02 | 0.00 |
| time (sec) |
N/A | 0.156 | 0.144 | 0.089 | 0.000 | 1.373 | 0.000 | 0.000 | 0.000 | 1.461 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | I.A. | |
| grade |
A | A | F(-1) | F | F | A | F(-1) | B | B | A |
| verified |
N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD | N/A |
| size | 75 | 75 | 0 | 0 | 0 | 109 | 0 | 187 | 80 | 84 |
| N.S. | 1 | 1.00 | 0.00 | 0.00 | 0.00 | 1.45 | 0.00 | 2.49 | 1.07 | 1.12 |
| time (sec) |
N/A | 0.108 | 0.000 | 0.029 | 0.000 | 1.171 | 0.000 | 4.721 | 2.454 | 53.643 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | I.A. | |
| grade |
A | A | F(-1) | F | F | A | F(-1) | F | F | F |
| verified |
N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD | N/A |
| size | 95 | 95 | 0 | 0 | 0 | 132 | 0 | 0 | -1 | 0 |
| N.S. | 1 | 1.00 | 0.00 | 0.00 | 0.00 | 1.39 | 0.00 | 0.00 | -0.01 | 0.00 |
| time (sec) |
N/A | 0.217 | 0.000 | 0.025 | 0.000 | 1.299 | 0.000 | 0.000 | 0.000 | 120.661 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | I.A. | |
| grade |
A | A | A | F | B | B | F(-1) | B | B | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD | Yes |
| size | 29 | 29 | 24 | 0 | 60 | 65 | 0 | 96 | 50 | 0 |
| N.S. | 1 | 1.00 | 0.83 | 0.00 | 2.07 | 2.24 | 0.00 | 3.31 | 1.72 | 0.00 |
| time (sec) |
N/A | 0.071 | 0.434 | 0.058 | 1.181 | 1.054 | 0.000 | 1.555 | 2.245 | 0.785 |