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 | C | F | F | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 1 | 103 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 103.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.304 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.194 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 264 | 225 | 208 | 0 | 0 | 0 | 1096 | 0 | 337 | 0 |
| N.S. |
1 | 0.85 | 0.79 | 0.00 | 0.00 | 0.00 | 4.15 | 0.00 | 1.28 | 0.00 |
| time (sec) |
N/A | 0.862 | 2.066 | 0.000 | 0.000 | 0.000 | 9.270 | 0.000 | 0.167 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 144 | 144 | 129 | 0 | 0 | 0 | 692 | 0 | 115 | 0 |
| N.S. |
1 | 1.00 | 0.90 | 0.00 | 0.00 | 0.00 | 4.81 | 0.00 | 0.80 | 0.00 |
| time (sec) |
N/A | 0.559 | 0.942 | 0.000 | 0.000 | 0.000 | 5.656 | 0.000 | 0.162 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 99 | 99 | 99 | 0 | 0 | 0 | 289 | 0 | 56 | 0 |
| N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 2.92 | 0.00 | 0.57 | 0.00 |
| time (sec) |
N/A | 0.363 | 0.299 | 0.000 | 0.000 | 0.000 | 2.706 | 0.000 | 0.150 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | F(-2) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 188 | 188 | 160 | 0 | 0 | 0 | 0 | 0 | 107 | 0 |
| N.S. |
1 | 1.00 | 0.85 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.57 | 0.00 |
| time (sec) |
N/A | 0.664 | 0.677 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.177 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | F(-2) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 325 | 289 | 257 | 0 | 0 | 0 | 0 | 0 | 191 | 0 |
| N.S. |
1 | 0.89 | 0.79 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.59 | 0.00 |
| time (sec) |
N/A | 0.923 | 1.608 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.172 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | B | F | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 139 | 139 | 617 | 0 | 0 | 0 | 0 | 0 | 60 | 0 |
| N.S. |
1 | 1.00 | 4.44 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.43 | 0.00 |
| time (sec) |
N/A | 0.389 | 1.342 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 200.028 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | A | F | F | F | F(-2) | F | B | F(-1) |
| verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 936 | 0 | 684 | 0 | 0 | 0 | 0 | 0 | 66 | 0 |
| N.S. |
1 | 0.00 | 0.73 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.07 | 0.00 |
| time (sec) |
N/A | 0.000 | 7.037 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.150 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | A | F | F | F | F(-1) | F | B | F(-1) |
| verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 355 | 0 | 347 | 0 | 0 | 0 | 0 | 0 | 17 | 0 |
| N.S. |
1 | 0.00 | 0.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.05 | 0.00 |
| time (sec) |
N/A | 0.000 | 2.787 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.155 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | A | F | F | F | F | F | B | F(-1) |
| verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 204 | 0 | 195 | 0 | 0 | 0 | 0 | 0 | 1 | 0 |
| N.S. |
1 | 0.00 | 0.96 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.000 | 0.186 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.174 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | F(-2) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 345 | 345 | 306 | 0 | 0 | 0 | 0 | 0 | 11 | 0 |
| N.S. |
1 | 1.00 | 0.89 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.03 | 0.00 |
| time (sec) |
N/A | 1.246 | 1.982 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.184 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | F(-2) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 609 | 552 | 509 | 0 | 0 | 0 | 0 | 0 | 24 | 0 |
| N.S. |
1 | 0.91 | 0.84 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.04 | 0.00 |
| time (sec) |
N/A | 1.927 | 3.933 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.154 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | C | A | F | F | F(-1) | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 119 | 565 | 109 | 0 | 0 | 0 | 0 | 0 | 98 | 0 |
| N.S. |
1 | 4.75 | 0.92 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.82 | 0.00 |
| time (sec) |
N/A | 1.079 | 0.450 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.220 | 0.000 |