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 | A | B | F | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
| size | 284 | 284 | 407 | 1951 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.43 | 6.87 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.694 | 14.131 | 4.430 | 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 | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 350 | 350 | 1315 | 3286 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 3.76 | 9.39 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.080 | 6.802 | 40.017 | 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 | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 433 | 433 | 1408 | 4606 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 3.25 | 10.64 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.501 | 6.843 | 10.129 | 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(-1) | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 670 | 670 | 1284 | 5534 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.92 | 8.26 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.426 | 7.643 | 13.978 | 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 | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 566 | 566 | 1227 | 4259 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 2.17 | 7.52 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.983 | 7.342 | 17.409 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 472 | 472 | 1198 | 3311 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 2.54 | 7.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.422 | 7.529 | 6.684 | 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 | F | F | F(-1) |
| verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
| size | 449 | 449 | 1196 | 2381 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 2.66 | 5.30 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.439 | 6.847 | 7.089 | 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 | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
| size | 418 | 418 | 1236 | 2468 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 2.96 | 5.90 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.149 | 6.823 | 7.188 | 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 | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 353 | 353 | 1314 | 3556 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 3.72 | 10.07 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.113 | 6.969 | 7.307 | 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 | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 433 | 433 | 1407 | 4605 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 3.25 | 10.64 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.576 | 6.982 | 7.447 | 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(-1) | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 779 | 779 | 1353 | 7110 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.74 | 9.13 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 3.524 | 7.869 | 10.207 | 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 | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 664 | 664 | 1287 | 5791 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.94 | 8.72 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.628 | 7.745 | 2.784 | 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 | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 563 | 563 | 1251 | 4802 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 2.22 | 8.53 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.039 | 8.266 | 2.797 | 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(-1) | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 547 | 547 | 1241 | 4453 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 2.27 | 8.14 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.944 | 6.960 | 2.666 | 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(-1) | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 536 | 536 | 1269 | 4719 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 2.37 | 8.80 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.966 | 6.955 | 2.773 | 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 | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 493 | 493 | 1319 | 4433 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 2.68 | 8.99 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.467 | 7.116 | 30.757 | 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 | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 434 | 434 | 1409 | 4874 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 3.25 | 11.23 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.533 | 7.207 | 41.164 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 522 | 522 | 1517 | 5955 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 2.91 | 11.41 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.147 | 7.437 | 48.852 | 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 | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 622 | 622 | 1640 | 7345 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 2.64 | 11.81 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 3.557 | 7.953 | 59.356 | 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 | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 571 | 571 | 1229 | 4001 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 2.15 | 7.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.899 | 7.407 | 22.664 | 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 | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 479 | 479 | 1175 | 2523 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 2.45 | 5.27 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.356 | 19.411 | 16.826 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 391 | 427 | 402 | 980 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.09 | 1.03 | 2.51 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.338 | 10.484 | 12.451 | 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 | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 228 | 228 | 144 | 181 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.63 | 0.79 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.425 | 3.404 | 11.536 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
| size | 230 | 230 | 299 | 771 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.30 | 3.35 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.484 | 13.469 | 15.847 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
| size | 290 | 290 | 416 | 1844 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.43 | 6.36 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.712 | 15.796 | 22.720 | 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 | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 363 | 363 | 1319 | 3292 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 3.63 | 9.07 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.063 | 6.857 | 31.543 | 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 | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 620 | 620 | 1297 | 5442 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 2.09 | 8.78 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.160 | 7.561 | 22.184 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 500 | 500 | 1234 | 3562 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 2.47 | 7.12 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.529 | 7.281 | 17.381 | 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 | F | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 416 | 416 | 1012 | 1819 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 2.43 | 4.37 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.823 | 18.236 | 9.092 | 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 | F | F | F(-1) |
| verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
| size | 284 | 284 | 1223 | 1533 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 4.31 | 5.40 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.747 | 6.889 | 11.012 | 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 | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
| size | 305 | 305 | 1281 | 1978 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 4.20 | 6.49 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.832 | 6.976 | 19.581 | 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 | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 393 | 393 | 1357 | 3846 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 3.45 | 9.79 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.208 | 7.115 | 28.214 | 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(-1) | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 674 | 674 | 1396 | 10417 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 2.07 | 15.46 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.474 | 7.776 | 23.269 | 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(-1) | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 545 | 545 | 1342 | 6574 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 2.46 | 12.06 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.652 | 7.552 | 16.230 | 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 | F | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 391 | 391 | 1335 | 4743 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 3.41 | 12.13 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.118 | 7.239 | 11.416 | 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 | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 429 | 429 | 1384 | 5455 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 3.23 | 12.72 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.213 | 7.033 | 15.094 | 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 | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 456 | 456 | 1431 | 6516 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 3.14 | 14.29 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.470 | 7.200 | 25.253 | 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 | A | A | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 156 | 156 | 117 | 121 | 166 | 121 | 428 | 129 | 259 |
| N.S. |
1 | 1.00 | 0.75 | 0.78 | 1.06 | 0.78 | 2.74 | 0.83 | 1.66 |
| time (sec) |
N/A | 0.248 | 0.497 | 0.391 | 0.348 | 0.280 | 0.282 | 0.310 | 5.726 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 128 | 128 | 118 | 94 | 132 | 97 | 320 | 102 | 150 |
| N.S. |
1 | 1.00 | 0.92 | 0.73 | 1.03 | 0.76 | 2.50 | 0.80 | 1.17 |
| time (sec) |
N/A | 0.154 | 0.305 | 0.249 | 0.364 | 0.311 | 0.188 | 0.307 | 2.460 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 80 | 113 | 85 | 75 | 98 | 70 | 189 | 76 | 100 |
| N.S. |
1 | 1.41 | 1.06 | 0.94 | 1.22 | 0.88 | 2.36 | 0.95 | 1.25 |
| time (sec) |
N/A | 0.111 | 0.176 | 0.183 | 0.598 | 0.276 | 0.127 | 0.307 | 2.324 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 69 | 69 | 68 | 82 | 82 | 73 | 0 | 159 | 156 |
| N.S. |
1 | 1.00 | 0.99 | 1.19 | 1.19 | 1.06 | 0.00 | 2.30 | 2.26 |
| time (sec) |
N/A | 0.150 | 0.115 | 0.270 | 0.226 | 0.308 | 0.000 | 0.317 | 2.443 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 52 | 52 | 71 | 67 | 92 | 101 | 0 | 132 | 159 |
| N.S. |
1 | 1.00 | 1.37 | 1.29 | 1.77 | 1.94 | 0.00 | 2.54 | 3.06 |
| time (sec) |
N/A | 0.155 | 0.015 | 0.284 | 0.212 | 0.279 | 0.000 | 0.319 | 2.467 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 69 | 69 | 92 | 92 | 130 | 118 | 0 | 168 | 164 |
| N.S. |
1 | 1.00 | 1.33 | 1.33 | 1.88 | 1.71 | 0.00 | 2.43 | 2.38 |
| time (sec) |
N/A | 0.184 | 0.019 | 0.340 | 0.208 | 0.305 | 0.000 | 0.337 | 2.900 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 101 | 101 | 73 | 106 | 162 | 128 | 0 | 261 | 190 |
| N.S. |
1 | 1.00 | 0.72 | 1.05 | 1.60 | 1.27 | 0.00 | 2.58 | 1.88 |
| time (sec) |
N/A | 0.233 | 0.477 | 0.431 | 0.211 | 0.295 | 0.000 | 0.323 | 5.393 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F(-1) | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 137 | 137 | 100 | 136 | 218 | 158 | 0 | 428 | 256 |
| N.S. |
1 | 1.00 | 0.73 | 0.99 | 1.59 | 1.15 | 0.00 | 3.12 | 1.87 |
| time (sec) |
N/A | 0.286 | 0.646 | 0.539 | 0.209 | 0.287 | 0.000 | 0.326 | 5.929 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F(-1) | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 165 | 165 | 123 | 159 | 266 | 182 | 0 | 473 | 302 |
| N.S. |
1 | 1.00 | 0.75 | 0.96 | 1.61 | 1.10 | 0.00 | 2.87 | 1.83 |
| time (sec) |
N/A | 0.313 | 1.211 | 0.573 | 0.214 | 0.296 | 0.000 | 0.333 | 5.532 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 224 | 224 | 169 | 167 | 233 | 171 | 570 | 184 | 256 |
| N.S. |
1 | 1.00 | 0.75 | 0.75 | 1.04 | 0.76 | 2.54 | 0.82 | 1.14 |
| time (sec) |
N/A | 0.400 | 2.277 | 0.342 | 0.211 | 0.277 | 0.290 | 0.324 | 3.418 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 191 | 191 | 137 | 131 | 187 | 134 | 420 | 146 | 214 |
| N.S. |
1 | 1.00 | 0.72 | 0.69 | 0.98 | 0.70 | 2.20 | 0.76 | 1.12 |
| time (sec) |
N/A | 0.272 | 2.659 | 0.263 | 0.210 | 0.277 | 0.198 | 0.306 | 2.363 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 134 | 134 | 158 | 132 | 150 | 127 | 0 | 346 | 263 |
| N.S. |
1 | 1.00 | 1.18 | 0.99 | 1.12 | 0.95 | 0.00 | 2.58 | 1.96 |
| time (sec) |
N/A | 0.389 | 2.415 | 0.308 | 0.216 | 0.283 | 0.000 | 0.342 | 2.600 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 126 | 126 | 155 | 121 | 148 | 147 | 0 | 229 | 274 |
| N.S. |
1 | 1.00 | 1.23 | 0.96 | 1.17 | 1.17 | 0.00 | 1.82 | 2.17 |
| time (sec) |
N/A | 0.365 | 3.967 | 0.383 | 0.213 | 0.286 | 0.000 | 0.327 | 2.586 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | A | A | A | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 118 | 118 | 277 | 130 | 189 | 165 | 0 | 239 | 257 |
| N.S. |
1 | 1.00 | 2.35 | 1.10 | 1.60 | 1.40 | 0.00 | 2.03 | 2.18 |
| time (sec) |
N/A | 0.391 | 3.912 | 0.485 | 0.222 | 0.298 | 0.000 | 0.334 | 3.852 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F(-1) | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 141 | 141 | 104 | 143 | 221 | 179 | 0 | 364 | 512 |
| N.S. |
1 | 1.00 | 0.74 | 1.01 | 1.57 | 1.27 | 0.00 | 2.58 | 3.63 |
| time (sec) |
N/A | 0.404 | 0.674 | 0.529 | 0.234 | 0.297 | 0.000 | 0.355 | 3.593 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F(-1) | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 184 | 184 | 137 | 182 | 313 | 209 | 0 | 630 | 389 |
| N.S. |
1 | 1.00 | 0.74 | 0.99 | 1.70 | 1.14 | 0.00 | 3.42 | 2.11 |
| time (sec) |
N/A | 0.501 | 1.055 | 0.635 | 0.222 | 0.299 | 0.000 | 0.362 | 5.952 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F(-1) | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 232 | 232 | 167 | 197 | 357 | 243 | 0 | 766 | 455 |
| N.S. |
1 | 1.00 | 0.72 | 0.85 | 1.54 | 1.05 | 0.00 | 3.30 | 1.96 |
| time (sec) |
N/A | 0.567 | 2.557 | 0.682 | 0.218 | 0.318 | 0.000 | 0.349 | 6.099 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 327 | 327 | 368 | 245 | 360 | 256 | 966 | 283 | 471 |
| N.S. |
1 | 1.00 | 1.13 | 0.75 | 1.10 | 0.78 | 2.95 | 0.87 | 1.44 |
| time (sec) |
N/A | 0.723 | 2.646 | 0.486 | 0.242 | 0.293 | 0.439 | 0.354 | 4.355 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 277 | 277 | 288 | 199 | 288 | 207 | 685 | 227 | 359 |
| N.S. |
1 | 1.00 | 1.04 | 0.72 | 1.04 | 0.75 | 2.47 | 0.82 | 1.30 |
| time (sec) |
N/A | 0.492 | 3.226 | 0.408 | 0.235 | 0.276 | 0.326 | 0.318 | 2.853 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 207 | 207 | 218 | 190 | 239 | 189 | 0 | 723 | 3250 |
| N.S. |
1 | 1.00 | 1.05 | 0.92 | 1.15 | 0.91 | 0.00 | 3.49 | 15.70 |
| time (sec) |
N/A | 0.636 | 2.998 | 0.500 | 0.237 | 0.280 | 0.000 | 0.345 | 4.704 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 192 | 192 | 266 | 170 | 216 | 201 | 0 | 418 | 2470 |
| N.S. |
1 | 1.00 | 1.39 | 0.89 | 1.12 | 1.05 | 0.00 | 2.18 | 12.86 |
| time (sec) |
N/A | 0.651 | 3.804 | 0.543 | 0.373 | 0.283 | 0.000 | 0.360 | 4.439 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F(-1) | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 204 | 204 | 318 | 184 | 243 | 208 | 0 | 538 | 3879 |
| N.S. |
1 | 1.00 | 1.56 | 0.90 | 1.19 | 1.02 | 0.00 | 2.64 | 19.01 |
| time (sec) |
N/A | 0.689 | 6.455 | 0.628 | 0.420 | 0.283 | 0.000 | 0.384 | 5.157 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | A | A | A | F(-1) | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 196 | 196 | 429 | 181 | 280 | 225 | 0 | 438 | 2437 |
| N.S. |
1 | 1.00 | 2.19 | 0.92 | 1.43 | 1.15 | 0.00 | 2.23 | 12.43 |
| time (sec) |
N/A | 0.672 | 8.404 | 0.690 | 0.241 | 0.297 | 0.000 | 0.364 | 4.358 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F(-1) | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 223 | 223 | 165 | 219 | 372 | 257 | 0 | 759 | 3210 |
| N.S. |
1 | 1.00 | 0.74 | 0.98 | 1.67 | 1.15 | 0.00 | 3.40 | 14.39 |
| time (sec) |
N/A | 0.716 | 1.317 | 0.625 | 0.253 | 0.306 | 0.000 | 0.378 | 4.956 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F(-1) | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 278 | 278 | 204 | 243 | 452 | 292 | 0 | 989 | 601 |
| N.S. |
1 | 1.00 | 0.73 | 0.87 | 1.63 | 1.05 | 0.00 | 3.56 | 2.16 |
| time (sec) |
N/A | 0.867 | 4.839 | 0.703 | 0.213 | 0.302 | 0.000 | 0.376 | 4.494 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F(-1) | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 336 | 336 | 252 | 283 | 565 | 342 | 0 | 1370 | 766 |
| N.S. |
1 | 1.00 | 0.75 | 0.84 | 1.68 | 1.02 | 0.00 | 4.08 | 2.28 |
| time (sec) |
N/A | 1.012 | 2.949 | 0.892 | 0.233 | 0.324 | 0.000 | 0.407 | 4.134 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 445 | 445 | 528 | 317 | 498 | 354 | 1334 | 390 | 675 |
| N.S. |
1 | 1.00 | 1.19 | 0.71 | 1.12 | 0.80 | 3.00 | 0.88 | 1.52 |
| time (sec) |
N/A | 1.111 | 3.141 | 0.642 | 0.216 | 0.309 | 0.606 | 0.363 | 7.107 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 375 | 375 | 432 | 278 | 415 | 292 | 1066 | 326 | 534 |
| N.S. |
1 | 1.00 | 1.15 | 0.74 | 1.11 | 0.78 | 2.84 | 0.87 | 1.42 |
| time (sec) |
N/A | 0.752 | 4.555 | 0.498 | 0.229 | 0.300 | 0.455 | 0.348 | 5.018 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 290 | 290 | 382 | 255 | 340 | 262 | 0 | 1094 | 4118 |
| N.S. |
1 | 1.00 | 1.32 | 0.88 | 1.17 | 0.90 | 0.00 | 3.77 | 14.20 |
| time (sec) |
N/A | 0.961 | 3.823 | 0.667 | 0.220 | 0.295 | 0.000 | 0.366 | 5.597 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F(-1) | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 273 | 273 | 383 | 235 | 305 | 263 | 0 | 802 | 4781 |
| N.S. |
1 | 1.00 | 1.40 | 0.86 | 1.12 | 0.96 | 0.00 | 2.94 | 17.51 |
| time (sec) |
N/A | 1.008 | 6.588 | 0.724 | 0.221 | 0.284 | 0.000 | 0.374 | 6.341 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F(-1) | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 274 | 274 | 367 | 233 | 311 | 262 | 0 | 541 | 4837 |
| N.S. |
1 | 1.00 | 1.34 | 0.85 | 1.14 | 0.96 | 0.00 | 1.97 | 17.65 |
| time (sec) |
N/A | 1.071 | 9.251 | 0.816 | 0.227 | 0.293 | 0.000 | 0.392 | 6.724 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F(-1) | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 303 | 303 | 351 | 235 | 335 | 269 | 0 | 550 | 4849 |
| N.S. |
1 | 1.00 | 1.16 | 0.78 | 1.11 | 0.89 | 0.00 | 1.82 | 16.00 |
| time (sec) |
N/A | 1.188 | 9.186 | 0.809 | 0.230 | 0.339 | 0.000 | 0.406 | 5.942 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F(-1) | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 293 | 293 | 462 | 257 | 431 | 302 | 0 | 840 | 4710 |
| N.S. |
1 | 1.00 | 1.58 | 0.88 | 1.47 | 1.03 | 0.00 | 2.87 | 16.08 |
| time (sec) |
N/A | 1.085 | 6.525 | 0.847 | 0.232 | 0.330 | 0.000 | 0.412 | 6.373 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F(-1) | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 314 | 314 | 230 | 280 | 511 | 340 | 0 | 1140 | 4068 |
| N.S. |
1 | 1.00 | 0.73 | 0.89 | 1.63 | 1.08 | 0.00 | 3.63 | 12.96 |
| time (sec) |
N/A | 1.143 | 2.138 | 0.746 | 0.236 | 0.314 | 0.000 | 0.413 | 6.016 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F(-1) | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 381 | 381 | 406 | 329 | 660 | 391 | 0 | 1658 | 942 |
| N.S. |
1 | 1.00 | 1.07 | 0.86 | 1.73 | 1.03 | 0.00 | 4.35 | 2.47 |
| time (sec) |
N/A | 1.354 | 6.331 | 1.003 | 0.225 | 0.320 | 0.000 | 0.422 | 4.202 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F(-1) | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 454 | 454 | 341 | 354 | 746 | 450 | 0 | 1888 | 1044 |
| N.S. |
1 | 1.00 | 0.75 | 0.78 | 1.64 | 0.99 | 0.00 | 4.16 | 2.30 |
| time (sec) |
N/A | 1.617 | 3.441 | 1.138 | 0.225 | 0.337 | 0.000 | 0.427 | 5.578 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 256 | 256 | 287 | 210 | 263 | 212 | 619 | 227 | 325 |
| N.S. |
1 | 1.00 | 1.12 | 0.82 | 1.03 | 0.83 | 2.42 | 0.89 | 1.27 |
| time (sec) |
N/A | 0.570 | 2.414 | 0.408 | 0.209 | 0.281 | 0.322 | 0.322 | 2.604 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 176 | 176 | 134 | 138 | 162 | 133 | 357 | 144 | 187 |
| N.S. |
1 | 1.00 | 0.76 | 0.78 | 0.92 | 0.76 | 2.03 | 0.82 | 1.06 |
| time (sec) |
N/A | 0.395 | 1.811 | 0.274 | 0.204 | 0.276 | 0.196 | 0.318 | 2.191 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 120 | 120 | 102 | 103 | 125 | 100 | 241 | 107 | 132 |
| N.S. |
1 | 1.00 | 0.85 | 0.86 | 1.04 | 0.83 | 2.01 | 0.89 | 1.10 |
| time (sec) |
N/A | 0.254 | 1.601 | 0.205 | 0.302 | 0.269 | 0.135 | 0.304 | 2.101 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | F(-1) | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 279 | 279 | 238 | 456 | 0 | 777 | 0 | 801 | 9661 |
| N.S. |
1 | 1.00 | 0.85 | 1.63 | 0.00 | 2.78 | 0.00 | 2.87 | 34.63 |
| time (sec) |
N/A | 1.081 | 2.643 | 0.529 | 0.000 | 0.324 | 0.000 | 0.325 | 12.376 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | F(-1) | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 206 | 206 | 179 | 275 | 0 | 599 | 0 | 424 | 7119 |
| N.S. |
1 | 1.00 | 0.87 | 1.33 | 0.00 | 2.91 | 0.00 | 2.06 | 34.56 |
| time (sec) |
N/A | 0.681 | 1.957 | 0.381 | 0.000 | 0.310 | 0.000 | 0.324 | 11.130 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 144 | 142 | 133 | 180 | 0 | 457 | 0 | 239 | 5594 |
| N.S. |
1 | 0.99 | 0.92 | 1.25 | 0.00 | 3.17 | 0.00 | 1.66 | 38.85 |
| time (sec) |
N/A | 0.376 | 1.375 | 0.267 | 0.000 | 0.308 | 0.000 | 0.322 | 10.106 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 97 | 97 | 92 | 117 | 0 | 331 | 3966 | 147 | 4410 |
| N.S. |
1 | 1.00 | 0.95 | 1.21 | 0.00 | 3.41 | 40.89 | 1.52 | 45.46 |
| time (sec) |
N/A | 0.165 | 0.876 | 0.198 | 0.000 | 0.301 | 171.149 | 0.315 | 6.253 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F(-2) | A | F | A | B |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 94 | 94 | 256 | 120 | 0 | 363 | 0 | 148 | 18201 |
| N.S. |
1 | 1.00 | 2.72 | 1.28 | 0.00 | 3.86 | 0.00 | 1.57 | 193.63 |
| time (sec) |
N/A | 0.164 | 1.734 | 0.309 | 0.000 | 1.689 | 0.000 | 0.324 | 13.069 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F(-2) | B | F | A | B |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 107 | 107 | 339 | 151 | 0 | 470 | 0 | 180 | 3483 |
| N.S. |
1 | 1.00 | 3.17 | 1.41 | 0.00 | 4.39 | 0.00 | 1.68 | 32.55 |
| time (sec) |
N/A | 0.305 | 3.943 | 0.345 | 0.000 | 3.116 | 0.000 | 0.337 | 8.659 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | A | F(-2) | B | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 154 | 154 | 314 | 247 | 0 | 633 | 0 | 287 | 5502 |
| N.S. |
1 | 1.00 | 2.04 | 1.60 | 0.00 | 4.11 | 0.00 | 1.86 | 35.73 |
| time (sec) |
N/A | 0.599 | 3.142 | 0.464 | 0.000 | 7.245 | 0.000 | 0.341 | 9.780 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | A | F(-2) | A | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 214 | 214 | 466 | 369 | 0 | 795 | 0 | 483 | 7033 |
| N.S. |
1 | 1.00 | 2.18 | 1.72 | 0.00 | 3.71 | 0.00 | 2.26 | 32.86 |
| time (sec) |
N/A | 0.980 | 4.007 | 0.596 | 0.000 | 14.202 | 0.000 | 0.351 | 11.094 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F(-2) | A | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 285 | 285 | 406 | 566 | 0 | 993 | 0 | 878 | 9543 |
| N.S. |
1 | 1.00 | 1.42 | 1.99 | 0.00 | 3.48 | 0.00 | 3.08 | 33.48 |
| time (sec) |
N/A | 1.481 | 2.618 | 0.776 | 0.000 | 28.216 | 0.000 | 0.361 | 12.547 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 398 | 398 | 256 | 391 | 0 | 1357 | 0 | 563 | 11768 |
| N.S. |
1 | 1.00 | 0.64 | 0.98 | 0.00 | 3.41 | 0.00 | 1.41 | 29.57 |
| time (sec) |
N/A | 1.696 | 4.024 | 0.737 | 0.000 | 0.403 | 0.000 | 0.352 | 14.759 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 303 | 303 | 208 | 293 | 0 | 1077 | 0 | 376 | 10024 |
| N.S. |
1 | 1.00 | 0.69 | 0.97 | 0.00 | 3.55 | 0.00 | 1.24 | 33.08 |
| time (sec) |
N/A | 1.241 | 3.235 | 0.505 | 0.000 | 0.351 | 0.000 | 0.331 | 14.177 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 168 | 168 | 159 | 221 | 0 | 830 | 0 | 1249 | 3816 |
| N.S. |
1 | 1.00 | 0.95 | 1.32 | 0.00 | 4.94 | 0.00 | 7.43 | 22.71 |
| time (sec) |
N/A | 0.545 | 2.079 | 0.383 | 0.000 | 0.353 | 0.000 | 0.449 | 7.515 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 139 | 139 | 131 | 176 | 0 | 586 | 0 | 220 | 4556 |
| N.S. |
1 | 1.00 | 0.94 | 1.27 | 0.00 | 4.22 | 0.00 | 1.58 | 32.78 |
| time (sec) |
N/A | 0.255 | 0.959 | 0.203 | 0.000 | 0.338 | 0.000 | 0.323 | 10.858 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F(-2) | B | F | A | B |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 147 | 147 | 319 | 195 | 0 | 718 | 0 | 244 | 4548 |
| N.S. |
1 | 1.00 | 2.17 | 1.33 | 0.00 | 4.88 | 0.00 | 1.66 | 30.94 |
| time (sec) |
N/A | 0.402 | 4.365 | 0.431 | 0.000 | 5.422 | 0.000 | 0.339 | 10.790 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | B | F | B | B |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 211 | 211 | 331 | 256 | 0 | 1126 | 0 | 442 | 6450 |
| N.S. |
1 | 1.00 | 1.57 | 1.21 | 0.00 | 5.34 | 0.00 | 2.09 | 30.57 |
| time (sec) |
N/A | 0.813 | 4.547 | 0.587 | 0.000 | 16.734 | 0.000 | 0.347 | 11.791 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | B | F | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 307 | 307 | 389 | 362 | 0 | 1515 | 0 | 423 | 9931 |
| N.S. |
1 | 1.00 | 1.27 | 1.18 | 0.00 | 4.93 | 0.00 | 1.38 | 32.35 |
| time (sec) |
N/A | 1.568 | 6.697 | 0.835 | 0.000 | 34.689 | 0.000 | 0.364 | 13.455 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 405 | 405 | 519 | 488 | 0 | 1795 | 0 | 619 | 11677 |
| N.S. |
1 | 1.00 | 1.28 | 1.20 | 0.00 | 4.43 | 0.00 | 1.53 | 28.83 |
| time (sec) |
N/A | 2.177 | 4.724 | 0.952 | 0.000 | 52.254 | 0.000 | 0.373 | 14.629 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 456 | 456 | 883 | 483 | 0 | 2107 | 0 | 3417 | 16028 |
| N.S. |
1 | 1.00 | 1.94 | 1.06 | 0.00 | 4.62 | 0.00 | 7.49 | 35.15 |
| time (sec) |
N/A | 4.820 | 8.084 | 0.931 | 0.000 | 0.472 | 0.000 | 0.701 | 19.138 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 314 | 314 | 573 | 391 | 0 | 1666 | 0 | 666 | 6721 |
| N.S. |
1 | 1.00 | 1.82 | 1.25 | 0.00 | 5.31 | 0.00 | 2.12 | 21.40 |
| time (sec) |
N/A | 2.941 | 5.004 | 0.776 | 0.000 | 0.403 | 0.000 | 0.373 | 9.352 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 233 | 233 | 225 | 341 | 0 | 1234 | 0 | 603 | 8146 |
| N.S. |
1 | 1.00 | 0.97 | 1.46 | 0.00 | 5.30 | 0.00 | 2.59 | 34.96 |
| time (sec) |
N/A | 0.874 | 2.939 | 0.380 | 0.000 | 0.362 | 0.000 | 0.357 | 12.816 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 202 | 202 | 192 | 264 | 0 | 838 | 0 | 500 | 281 |
| N.S. |
1 | 1.00 | 0.95 | 1.31 | 0.00 | 4.15 | 0.00 | 2.48 | 1.39 |
| time (sec) |
N/A | 0.411 | 1.488 | 0.332 | 0.000 | 0.329 | 0.000 | 0.364 | 5.850 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F(-2) | B | F | B | B |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 238 | 238 | 473 | 360 | 0 | 1485 | 0 | 624 | 8151 |
| N.S. |
1 | 1.00 | 1.99 | 1.51 | 0.00 | 6.24 | 0.00 | 2.62 | 34.25 |
| time (sec) |
N/A | 1.028 | 5.484 | 0.727 | 0.000 | 23.910 | 0.000 | 0.402 | 13.149 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | B | F | B | B |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 339 | 339 | 444 | 427 | 0 | 2213 | 0 | 699 | 11417 |
| N.S. |
1 | 1.00 | 1.31 | 1.26 | 0.00 | 6.53 | 0.00 | 2.06 | 33.68 |
| time (sec) |
N/A | 3.578 | 4.565 | 1.117 | 0.000 | 68.112 | 0.000 | 0.406 | 14.852 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 462 | 462 | 606 | 550 | 0 | 2858 | 0 | 1744 | 15951 |
| N.S. |
1 | 1.00 | 1.31 | 1.19 | 0.00 | 6.19 | 0.00 | 3.77 | 34.53 |
| time (sec) |
N/A | 5.563 | 5.529 | 1.477 | 0.000 | 110.983 | 0.000 | 0.430 | 19.166 |