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 | C | A | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 217 | 214 | 336 | 261 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.99 | 1.55 | 1.20 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.278 | 2.987 | 4.193 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 261 | 263 | 370 | 303 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.01 | 1.42 | 1.16 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.344 | 4.585 | 4.461 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 324 | 338 | 443 | 371 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.04 | 1.37 | 1.15 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.466 | 8.108 | 4.551 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 60 | 60 | 341 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 5.68 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.183 | 10.340 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 59 | 59 | 232 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 3.93 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.182 | 10.216 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 59 | 59 | 393 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 6.66 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.185 | 10.296 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 62 | 62 | 386 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 6.23 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.185 | 10.534 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 62 | 62 | 550 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 8.87 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.185 | 10.976 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | B | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 541 | 505 | 1171 | 711 | 0 | 1555 | 0 | 0 | 0 |
| N.S. |
1 | 0.93 | 2.16 | 1.31 | 0.00 | 2.87 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.792 | 12.279 | 5.124 | 0.000 | 94.183 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | B | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 458 | 432 | 908 | 609 | 0 | 1246 | 0 | 0 | 0 |
| N.S. |
1 | 0.94 | 1.98 | 1.33 | 0.00 | 2.72 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.645 | 11.742 | 4.972 | 0.000 | 18.185 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | B | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 391 | 375 | 651 | 505 | 0 | 954 | 0 | 0 | 0 |
| N.S. |
1 | 0.96 | 1.66 | 1.29 | 0.00 | 2.44 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.496 | 11.002 | 4.803 | 0.000 | 1.954 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 217 | 222 | 344 | 259 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.02 | 1.59 | 1.19 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.282 | 3.845 | 4.321 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 267 | 251 | 366 | 297 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.94 | 1.37 | 1.11 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.308 | 4.298 | 4.320 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 307 | 294 | 407 | 307 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.96 | 1.33 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.356 | 6.353 | 4.374 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 377 | 369 | 428 | 426 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.98 | 1.14 | 1.13 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.464 | 13.679 | 4.462 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 463 | 466 | 337 | 475 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.01 | 0.73 | 1.03 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.632 | 15.745 | 4.687 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | F | F | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 60 | 60 | 285 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 4.75 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.183 | 10.467 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 59 | 59 | 407 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 6.90 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.183 | 10.624 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | F | F | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 59 | 59 | 418 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 7.08 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.185 | 10.679 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | F | F | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 62 | 62 | 531 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 8.56 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.187 | 10.918 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | F | F | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 62 | 62 | 515 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 8.31 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.184 | 11.481 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 155 | 161 | 90 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.04 | 0.58 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.250 | 5.738 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 155 | 161 | 90 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.04 | 0.58 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.251 | 5.460 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 122 | 122 | 89 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.73 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.219 | 5.698 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 122 | 122 | 89 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.73 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.211 | 3.783 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 87 | 87 | 86 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.99 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.185 | 3.504 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 87 | 87 | 86 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.99 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.184 | 5.619 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 87 | 87 | 89 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.182 | 3.489 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 121 | 121 | 89 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.74 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.211 | 5.541 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 121 | 121 | 89 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.74 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.216 | 5.681 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 153 | 160 | 90 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.05 | 0.59 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.256 | 5.698 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 153 | 160 | 90 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.05 | 0.59 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.255 | 5.720 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | F | F | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 79 | 79 | 172 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 2.18 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.223 | 0.300 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | C | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 167 | 175 | 106 | 0 | 0 | 0 | 121 | 0 | 0 |
| N.S. |
1 | 1.05 | 0.63 | 0.00 | 0.00 | 0.00 | 0.72 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.339 | 0.210 | 0.000 | 0.000 | 0.000 | 90.092 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | C | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 84 | 85 | 90 | 0 | 0 | 0 | 75 | 0 | 0 |
| N.S. |
1 | 1.01 | 1.07 | 0.00 | 0.00 | 0.00 | 0.89 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.221 | 0.143 | 0.000 | 0.000 | 0.000 | 34.200 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | F | F | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 57 | 57 | 162 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 2.84 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.193 | 0.350 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | F | F | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 57 | 57 | 162 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 2.84 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.188 | 0.442 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 298 | 288 | 137 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.97 | 0.46 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.537 | 8.446 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | C | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 176 | 175 | 106 | 0 | 0 | 0 | 121 | 0 | 0 |
| N.S. |
1 | 0.99 | 0.60 | 0.00 | 0.00 | 0.00 | 0.69 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.336 | 5.186 | 0.000 | 0.000 | 0.000 | 89.965 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | C | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 93 | 85 | 90 | 0 | 0 | 0 | 75 | 0 | 0 |
| N.S. |
1 | 0.91 | 0.97 | 0.00 | 0.00 | 0.00 | 0.81 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.220 | 0.140 | 0.000 | 0.000 | 0.000 | 33.081 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | F | F | F | C | F | B |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 44 | 44 | 203 | 0 | 0 | 0 | 34 | 0 | 41 |
| N.S. |
1 | 1.00 | 4.61 | 0.00 | 0.00 | 0.00 | 0.77 | 0.00 | 0.93 |
| time (sec) |
N/A | 0.170 | 0.179 | 0.000 | 0.000 | 0.000 | 5.070 | 0.000 | 5.426 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | F | F | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 57 | 57 | 162 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 2.84 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.183 | 0.342 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | F | F | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 57 | 57 | 162 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 2.84 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.180 | 0.405 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | F | F | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 57 | 57 | 162 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 2.84 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.181 | 0.547 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | A | F(-1) | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 53 | 53 | 52 | 71 | 0 | 91 | 0 | 0 | 131 |
| N.S. |
1 | 1.00 | 0.98 | 1.34 | 0.00 | 1.72 | 0.00 | 0.00 | 2.47 |
| time (sec) |
N/A | 0.178 | 0.562 | 7.138 | 0.000 | 0.303 | 0.000 | 0.000 | 5.925 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | A | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 94 | 94 | 94 | 95 | 96 | 96 | 107 | 98 | 88 |
| N.S. |
1 | 1.00 | 1.00 | 1.01 | 1.02 | 1.02 | 1.14 | 1.04 | 0.94 |
| time (sec) |
N/A | 0.254 | 0.024 | 3.955 | 0.204 | 0.266 | 0.033 | 0.305 | 5.409 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | A | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 70 | 70 | 70 | 72 | 70 | 70 | 76 | 74 | 66 |
| N.S. |
1 | 1.00 | 1.00 | 1.03 | 1.00 | 1.00 | 1.09 | 1.06 | 0.94 |
| time (sec) |
N/A | 0.237 | 0.017 | 3.905 | 0.212 | 0.246 | 0.025 | 0.293 | 5.394 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | A | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 50 | 50 | 50 | 49 | 48 | 48 | 53 | 50 | 48 |
| N.S. |
1 | 1.00 | 1.00 | 0.98 | 0.96 | 0.96 | 1.06 | 1.00 | 0.96 |
| time (sec) |
N/A | 0.199 | 0.013 | 4.159 | 0.204 | 0.257 | 0.022 | 0.293 | 0.050 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | A | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 28 | 28 | 28 | 25 | 24 | 24 | 26 | 26 | 25 |
| N.S. |
1 | 1.00 | 1.00 | 0.89 | 0.86 | 0.86 | 0.93 | 0.93 | 0.89 |
| time (sec) |
N/A | 0.174 | 0.008 | 0.178 | 0.207 | 0.282 | 0.024 | 0.315 | 0.038 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | C | A | C | A | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 223 | 220 | 196 | 42 | 212 | 560 | 87 | 245 | 720 |
| N.S. |
1 | 0.99 | 0.88 | 0.19 | 0.95 | 2.51 | 0.39 | 1.10 | 3.23 |
| time (sec) |
N/A | 0.411 | 0.133 | 4.324 | 0.294 | 0.283 | 0.284 | 0.281 | 0.235 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | C | A | C | A | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 245 | 247 | 212 | 65 | 236 | 648 | 112 | 266 | 740 |
| N.S. |
1 | 1.01 | 0.87 | 0.27 | 0.96 | 2.64 | 0.46 | 1.09 | 3.02 |
| time (sec) |
N/A | 0.424 | 0.168 | 4.087 | 0.288 | 0.280 | 0.399 | 0.275 | 5.688 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | C | A | C | A | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 273 | 272 | 243 | 84 | 271 | 739 | 151 | 286 | 762 |
| N.S. |
1 | 1.00 | 0.89 | 0.31 | 0.99 | 2.71 | 0.55 | 1.05 | 2.79 |
| time (sec) |
N/A | 0.454 | 0.208 | 3.934 | 0.288 | 0.301 | 0.522 | 0.291 | 5.934 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | A | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 154 | 154 | 154 | 160 | 158 | 158 | 185 | 173 | 146 |
| N.S. |
1 | 1.00 | 1.00 | 1.04 | 1.03 | 1.03 | 1.20 | 1.12 | 0.95 |
| time (sec) |
N/A | 0.322 | 0.034 | 3.949 | 0.203 | 0.275 | 0.031 | 0.271 | 5.647 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | A | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 122 | 122 | 122 | 123 | 124 | 124 | 139 | 132 | 116 |
| N.S. |
1 | 1.00 | 1.00 | 1.01 | 1.02 | 1.02 | 1.14 | 1.08 | 0.95 |
| time (sec) |
N/A | 0.295 | 0.024 | 3.876 | 0.276 | 0.260 | 0.036 | 0.289 | 5.590 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | A | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 82 | 82 | 82 | 86 | 82 | 82 | 97 | 91 | 75 |
| N.S. |
1 | 1.00 | 1.00 | 1.05 | 1.00 | 1.00 | 1.18 | 1.11 | 0.91 |
| time (sec) |
N/A | 0.236 | 0.019 | 4.004 | 0.256 | 0.350 | 0.028 | 0.298 | 0.046 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | A | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 50 | 50 | 50 | 49 | 48 | 48 | 53 | 50 | 48 |
| N.S. |
1 | 1.00 | 1.00 | 0.98 | 0.96 | 0.96 | 1.06 | 1.00 | 0.96 |
| time (sec) |
N/A | 0.198 | 0.010 | 3.949 | 0.216 | 0.270 | 0.026 | 0.286 | 0.044 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | C | A | C | A | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 253 | 253 | 231 | 78 | 286 | 1092 | 187 | 353 | 1081 |
| N.S. |
1 | 1.00 | 0.91 | 0.31 | 1.13 | 4.32 | 0.74 | 1.40 | 4.27 |
| time (sec) |
N/A | 0.386 | 0.106 | 3.986 | 0.309 | 0.307 | 0.584 | 0.295 | 5.840 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | C | A | C | A | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 291 | 291 | 298 | 101 | 319 | 1210 | 219 | 376 | 1254 |
| N.S. |
1 | 1.00 | 1.02 | 0.35 | 1.10 | 4.16 | 0.75 | 1.29 | 4.31 |
| time (sec) |
N/A | 0.521 | 0.175 | 3.965 | 0.324 | 0.283 | 2.016 | 0.296 | 5.950 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | C | A | C | A | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 349 | 311 | 319 | 131 | 361 | 1294 | 264 | 407 | 1401 |
| N.S. |
1 | 0.89 | 0.91 | 0.38 | 1.03 | 3.71 | 0.76 | 1.17 | 4.01 |
| time (sec) |
N/A | 0.533 | 0.212 | 4.014 | 0.308 | 0.306 | 85.141 | 0.294 | 6.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | C | A | C | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 332 | 332 | 322 | 201 | 489 | 2190 | 435 | 617 | 1822 |
| N.S. |
1 | 1.00 | 0.97 | 0.61 | 1.47 | 6.60 | 1.31 | 1.86 | 5.49 |
| time (sec) |
N/A | 0.494 | 0.210 | 4.205 | 0.282 | 0.295 | 22.351 | 0.290 | 5.745 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | C | A | C | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 288 | 288 | 271 | 131 | 385 | 1642 | 303 | 481 | 1433 |
| N.S. |
1 | 1.00 | 0.94 | 0.45 | 1.34 | 5.70 | 1.05 | 1.67 | 4.98 |
| time (sec) |
N/A | 0.407 | 0.163 | 3.980 | 0.285 | 0.299 | 1.296 | 0.293 | 0.236 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | C | A | C | A | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 253 | 253 | 231 | 78 | 287 | 1093 | 187 | 353 | 1081 |
| N.S. |
1 | 1.00 | 0.91 | 0.31 | 1.13 | 4.32 | 0.74 | 1.40 | 4.27 |
| time (sec) |
N/A | 0.374 | 0.103 | 4.109 | 0.281 | 0.287 | 0.530 | 0.279 | 5.706 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | C | A | C | A | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 223 | 219 | 196 | 42 | 212 | 560 | 87 | 245 | 720 |
| N.S. |
1 | 0.98 | 0.88 | 0.19 | 0.95 | 2.51 | 0.39 | 1.10 | 3.23 |
| time (sec) |
N/A | 0.399 | 0.115 | 3.941 | 0.280 | 0.290 | 0.309 | 0.281 | 0.223 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | C | F(-1) | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 449 | 426 | 340 | 226 | 365 | 1171 | 0 | 437 | 6153 |
| N.S. |
1 | 0.95 | 0.76 | 0.50 | 0.81 | 2.61 | 0.00 | 0.97 | 13.70 |
| time (sec) |
N/A | 0.601 | 0.126 | 4.086 | 0.373 | 0.392 | 0.000 | 0.300 | 7.296 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | C | F(-1) | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 513 | 485 | 498 | 262 | 481 | 2955 | 0 | 667 | 21975 |
| N.S. |
1 | 0.95 | 0.97 | 0.51 | 0.94 | 5.76 | 0.00 | 1.30 | 42.84 |
| time (sec) |
N/A | 0.714 | 0.307 | 4.097 | 0.302 | 12.016 | 0.000 | 0.296 | 8.177 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | C | A | C | F(-1) | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 407 | 407 | 391 | 304 | 644 | 2884 | 0 | 798 | 2490 |
| N.S. |
1 | 1.00 | 0.96 | 0.75 | 1.58 | 7.09 | 0.00 | 1.96 | 6.12 |
| time (sec) |
N/A | 0.600 | 0.366 | 4.025 | 0.293 | 0.401 | 0.000 | 0.290 | 5.856 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | C | A | C | F(-1) | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 357 | 357 | 341 | 219 | 521 | 2315 | 0 | 642 | 2043 |
| N.S. |
1 | 1.00 | 0.96 | 0.61 | 1.46 | 6.48 | 0.00 | 1.80 | 5.72 |
| time (sec) |
N/A | 0.540 | 0.306 | 3.987 | 0.283 | 0.331 | 0.000 | 0.287 | 0.318 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | C | A | C | A | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 317 | 317 | 301 | 151 | 405 | 1741 | 337 | 496 | 1616 |
| N.S. |
1 | 1.00 | 0.95 | 0.48 | 1.28 | 5.49 | 1.06 | 1.56 | 5.10 |
| time (sec) |
N/A | 0.489 | 0.243 | 4.011 | 0.294 | 0.323 | 86.251 | 0.274 | 5.719 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | C | A | C | A | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 291 | 291 | 297 | 101 | 319 | 1210 | 219 | 376 | 1254 |
| N.S. |
1 | 1.00 | 1.02 | 0.35 | 1.10 | 4.16 | 0.75 | 1.29 | 4.31 |
| time (sec) |
N/A | 0.519 | 0.178 | 4.264 | 0.285 | 0.319 | 1.147 | 0.283 | 0.304 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | C | A | C | A | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 245 | 247 | 212 | 65 | 236 | 648 | 112 | 266 | 740 |
| N.S. |
1 | 1.01 | 0.87 | 0.27 | 0.96 | 2.64 | 0.46 | 1.09 | 3.02 |
| time (sec) |
N/A | 0.430 | 0.167 | 4.001 | 0.287 | 0.293 | 0.457 | 0.298 | 5.701 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | C | F(-1) | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 513 | 484 | 499 | 263 | 470 | 2955 | 0 | 667 | 21975 |
| N.S. |
1 | 0.94 | 0.97 | 0.51 | 0.92 | 5.76 | 0.00 | 1.30 | 42.84 |
| time (sec) |
N/A | 0.723 | 0.309 | 4.121 | 0.303 | 12.457 | 0.000 | 0.302 | 7.956 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | C | F(-1) | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 596 | 551 | 561 | 298 | 670 | 5234 | 0 | 967 | 37266 |
| N.S. |
1 | 0.92 | 0.94 | 0.50 | 1.12 | 8.78 | 0.00 | 1.62 | 62.53 |
| time (sec) |
N/A | 0.862 | 0.945 | 4.195 | 0.292 | 165.512 | 0.000 | 0.449 | 9.949 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | C | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 321 | 324 | 290 | 350 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.01 | 0.90 | 1.09 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.626 | 10.698 | 6.409 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | C | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 277 | 272 | 341 | 306 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.98 | 1.23 | 1.10 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.486 | 10.352 | 6.264 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | C | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 240 | 232 | 155 | 259 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.97 | 0.65 | 1.08 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.390 | 10.183 | 4.139 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | C | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 162 | 162 | 156 | 183 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.96 | 1.13 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.294 | 10.224 | 4.233 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | C | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 281 | 269 | 381 | 301 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.96 | 1.36 | 1.07 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.468 | 10.263 | 4.152 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | C | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 334 | 340 | 422 | 361 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.02 | 1.26 | 1.08 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.628 | 10.716 | 4.184 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | C | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 926 | 1004 | 346 | 319 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.08 | 0.37 | 0.34 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.563 | 10.473 | 6.444 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | C | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 881 | 965 | 161 | 273 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.10 | 0.18 | 0.31 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.372 | 10.186 | 4.142 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | C | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 742 | 860 | 161 | 191 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.16 | 0.22 | 0.26 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.217 | 10.057 | 4.165 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | C | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 913 | 1001 | 331 | 313 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.10 | 0.36 | 0.34 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.433 | 10.278 | 4.184 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | C | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 976 | 1071 | 429 | 371 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.10 | 0.44 | 0.38 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.644 | 10.818 | 4.164 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | C | F | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 426 | 422 | 477 | 539 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.99 | 1.12 | 1.27 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.821 | 10.818 | 7.936 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | C | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 365 | 356 | 396 | 411 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.98 | 1.08 | 1.13 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.648 | 10.584 | 7.161 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | C | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 309 | 299 | 342 | 328 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.97 | 1.11 | 1.06 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.518 | 10.332 | 4.033 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | C | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 276 | 270 | 233 | 293 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.98 | 0.84 | 1.06 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.464 | 10.166 | 4.351 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | C | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 310 | 286 | 386 | 321 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.92 | 1.25 | 1.04 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.492 | 10.281 | 4.477 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | C | F | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 362 | 347 | 374 | 374 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.96 | 1.03 | 1.03 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.663 | 10.520 | 4.751 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | C | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 439 | 439 | 382 | 484 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.87 | 1.10 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.873 | 10.879 | 4.427 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 103 | 101 | 81 | 89 | 0 | 437 | 0 | 0 | 0 |
| N.S. |
1 | 0.98 | 0.79 | 0.86 | 0.00 | 4.24 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.211 | 0.553 | 5.254 | 0.000 | 0.578 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 116 | 116 | 88 | 141 | 0 | 482 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.76 | 1.22 | 0.00 | 4.16 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.199 | 0.519 | 6.369 | 0.000 | 0.576 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 211 | 220 | 288 | 401 | 0 | 1962 | 0 | 0 | 0 |
| N.S. |
1 | 1.04 | 1.36 | 1.90 | 0.00 | 9.30 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.417 | 1.796 | 8.934 | 0.000 | 1.706 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 173 | 181 | 255 | 338 | 0 | 733 | 0 | 0 | 0 |
| N.S. |
1 | 1.05 | 1.47 | 1.95 | 0.00 | 4.24 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.317 | 1.199 | 5.585 | 0.000 | 0.405 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 105 | 105 | 178 | 244 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.70 | 2.32 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.220 | 0.879 | 4.252 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 134 | 146 | 229 | 325 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.09 | 1.71 | 2.43 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.263 | 1.788 | 4.146 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 180 | 206 | 621 | 329 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.14 | 3.45 | 1.83 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.363 | 12.117 | 4.390 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 233 | 279 | 1172 | 381 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.20 | 5.03 | 1.64 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.491 | 14.498 | 4.440 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 316 | 287 | 294 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.91 | 0.93 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.625 | 10.647 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 274 | 239 | 346 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.87 | 1.26 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.443 | 10.339 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |