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 | C | C | F | C | F | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 408 | 408 | 253 | 136 | 0 | 491 | 0 | 0 | -1 |
| N.S. | 1 | 1.00 | 0.62 | 0.33 | 0.00 | 1.20 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.433 | 0.277 | 0.155 | 0.000 | 0.408 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | C | C | F | C | F(-1) | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 714 | 714 | 383 | 1184 | 0 | 670 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 0.54 | 1.66 | 0.00 | 0.94 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.662 | 0.153 | 0.434 | 0.000 | 0.401 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | C | C | F | C | F(-1) | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 371 | 371 | 214 | 823 | 0 | 482 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 0.58 | 2.22 | 0.00 | 1.30 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.374 | 0.126 | 0.095 | 0.000 | 0.406 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | C | C | F | C | F(-1) | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 691 | 691 | 408 | 508 | 0 | 655 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 0.59 | 0.74 | 0.00 | 0.95 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.856 | 0.155 | 0.073 | 0.000 | 0.411 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | C | C | F | C | F(-1) | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 735 | 735 | 406 | 248 | 0 | 669 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 0.55 | 0.34 | 0.00 | 0.91 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.822 | 0.160 | 0.059 | 0.000 | 0.399 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | C | C | F | C | F | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 693 | 693 | 446 | 233 | 0 | 588 | 0 | 0 | -1 |
| N.S. | 1 | 1.00 | 0.64 | 0.34 | 0.00 | 0.85 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.953 | 0.370 | 0.178 | 0.000 | 0.423 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | C | C | F | C | F(-1) | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 712 | 712 | 445 | 284 | 0 | 726 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 0.62 | 0.40 | 0.00 | 1.02 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.996 | 0.488 | 0.253 | 0.000 | 0.413 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | C | C | F | C | F(-1) | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 800 | 800 | 470 | 388 | 0 | 908 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 0.59 | 0.48 | 0.00 | 1.14 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 1.149 | 0.600 | 0.332 | 0.000 | 0.437 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | C | C | F | C | F(-1) | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 772 | 772 | 457 | 2035 | 0 | 890 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 0.59 | 2.64 | 0.00 | 1.15 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 1.719 | 0.435 | 1.343 | 0.000 | 0.425 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | C | C | F | C | F(-1) | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 777 | 777 | 449 | 1396 | 0 | 935 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 0.58 | 1.80 | 0.00 | 1.20 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.927 | 0.310 | 0.188 | 0.000 | 0.415 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | C | C | F | C | F(-1) | F | F |
| verified |
N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 1141 | 1141 | 698 | 847 | 0 | 1319 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 0.61 | 0.74 | 0.00 | 1.16 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 1.969 | 0.408 | 0.136 | 0.000 | 0.464 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | C | C | F | C | F(-1) | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 1161 | 1161 | 675 | 392 | 0 | 1223 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 0.58 | 0.34 | 0.00 | 1.05 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 2.084 | 0.320 | 0.106 | 0.000 | 0.435 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | C | C | F | C | F | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 1163 | 1163 | 2109 | 363 | 0 | 1125 | 0 | 0 | -1 |
| N.S. | 1 | 1.00 | 1.81 | 0.31 | 0.00 | 0.97 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 2.426 | 0.510 | 0.540 | 0.000 | 0.473 | 0.000 | 0.000 | 0.000 |