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 | C | F(-2) | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 627 | 627 | 1635 | 1792 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 2.61 | 2.86 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.680 | 26.491 | 6.205 | 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 | No | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 601 | 542 | 1958 | 1179 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.90 | 3.26 | 1.96 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.980 | 24.426 | 6.376 | 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 | No | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 528 | 494 | 1193 | 1253 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.94 | 2.26 | 2.37 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.674 | 21.640 | 6.729 | 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 | No | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 468 | 445 | 1184 | 1070 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.95 | 2.53 | 2.29 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.043 | 21.363 | 6.327 | 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 | No | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 432 | 413 | 1183 | 1217 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.96 | 2.74 | 2.82 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.857 | 20.412 | 6.532 | 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 | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 527 | 527 | 2136 | 652 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 4.05 | 1.24 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.761 | 25.690 | 1.004 | 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(-2) | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 651 | 651 | 2183 | 1662 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 3.35 | 2.55 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.762 | 28.965 | 8.317 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | F | C | B | F | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | N/A | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 926 | 0 | 1623 | 3600 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.00 | 1.75 | 3.89 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.000 | 48.700 | 12.879 | 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 | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 578 | 546 | 176 | 2591 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.94 | 0.30 | 4.48 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.112 | 18.426 | 3.024 | 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 | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 509 | 481 | 178 | 854 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.94 | 0.35 | 1.68 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.454 | 10.250 | 2.973 | 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 | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 208 | 185 | 371 | 482 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.89 | 1.78 | 2.32 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.650 | 13.318 | 1.811 | 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 | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 320 | 290 | 1619 | 1673 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.91 | 5.06 | 5.23 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.527 | 24.009 | 1.839 | 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 | 366 | 340 | 1645 | 2100 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.93 | 4.49 | 5.74 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.957 | 23.920 | 1.880 | 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 | 513 | 492 | 1726 | 2462 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.96 | 3.36 | 4.80 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 3.561 | 24.780 | 1.872 | 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 | 598 | 581 | 1768 | 3327 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.97 | 2.96 | 5.56 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 4.542 | 23.914 | 2.193 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | F | C | B | F | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | N/A | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 982 | 0 | 1898 | 3721 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.00 | 1.93 | 3.79 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.000 | 48.508 | 2.522 | 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 | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 611 | 643 | 601 | 2845 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.05 | 0.98 | 4.66 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.859 | 19.694 | 3.066 | 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 | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 577 | 605 | 178 | 1179 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.05 | 0.31 | 2.04 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.402 | 12.084 | 1.822 | 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 | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 321 | 353 | 1095 | 1784 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.10 | 3.41 | 5.56 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.603 | 18.549 | 1.597 | 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 | 435 | 460 | 1138 | 2397 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.06 | 2.62 | 5.51 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.724 | 21.751 | 1.804 | 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 | 525 | 558 | 1165 | 2340 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.06 | 2.22 | 4.46 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 3.387 | 20.976 | 1.960 | 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 | 688 | 714 | 1210 | 3333 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.04 | 1.76 | 4.84 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 4.952 | 21.746 | 2.169 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | F | C | B | F | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | N/A | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 936 | 0 | 1615 | 5708 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.00 | 1.73 | 6.10 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.000 | 26.929 | 5.003 | 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 | 572 | 552 | 1399 | 4109 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.97 | 2.45 | 7.18 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.298 | 25.366 | 3.039 | 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 | 616 | 597 | 1611 | 3156 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.97 | 2.62 | 5.12 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.836 | 25.753 | 3.365 | 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 | 359 | 346 | 1656 | 2837 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.96 | 4.61 | 7.90 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.884 | 24.747 | 1.940 | 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 | 519 | 495 | 1734 | 3621 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.95 | 3.34 | 6.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 3.404 | 23.597 | 2.081 | 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 | 612 | 593 | 1776 | 4018 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.97 | 2.90 | 6.57 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 4.363 | 22.895 | 2.270 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | F | C | B | F | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | N/A | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 822 | 0 | 1850 | 4945 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.00 | 2.25 | 6.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.000 | 24.084 | 2.533 | 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 | 616 | 636 | 1318 | 3415 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.03 | 2.14 | 5.54 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.613 | 25.006 | 3.318 | 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 | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 508 | 530 | 518 | 885 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.04 | 1.02 | 1.74 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.541 | 11.804 | 1.891 | 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 | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 209 | 233 | 373 | 444 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.11 | 1.78 | 2.12 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.723 | 12.919 | 1.764 | 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 | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 273 | 298 | 652 | 523 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.09 | 2.39 | 1.92 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.296 | 14.554 | 1.624 | 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 | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 320 | 346 | 715 | 1135 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.08 | 2.23 | 3.55 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.720 | 14.248 | 1.718 | 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 | 424 | 457 | 1140 | 1623 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.08 | 2.69 | 3.83 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.903 | 21.754 | 2.152 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | F | C | B | F | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | N/A | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 1064 | 0 | 1290 | 2013 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.00 | 1.21 | 1.89 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.000 | 25.904 | 3.749 | 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 | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 379 | 358 | 1648 | 1185 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.94 | 4.35 | 3.13 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.941 | 23.740 | 2.276 | 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 | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 374 | 352 | 1274 | 1209 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.94 | 3.41 | 3.23 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.234 | 21.860 | 2.180 | 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 | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 380 | 350 | 1279 | 1204 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.92 | 3.37 | 3.17 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.163 | 22.131 | 2.313 | 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 | 568 | 495 | 1707 | 1487 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.87 | 3.01 | 2.62 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 3.880 | 25.279 | 2.457 | 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 | 673 | 590 | 1727 | 1842 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.88 | 2.57 | 2.74 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 4.808 | 24.130 | 2.627 | 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 | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 331 | 356 | 717 | 3173 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.08 | 2.17 | 9.59 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.642 | 16.271 | 2.427 | 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 | A | A | F | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 82 | 86 | 82 | 79 | 75 | 72 | 0 | 119 | 112 |
| N.S. |
1 | 1.05 | 1.00 | 0.96 | 0.91 | 0.88 | 0.00 | 1.45 | 1.37 |
| time (sec) |
N/A | 0.409 | 0.371 | 0.681 | 0.281 | 0.289 | 0.000 | 0.462 | 18.100 |
| 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 | 65 | 74 | 63 | 66 | 62 | 61 | 0 | 104 | 98 |
| N.S. |
1 | 1.14 | 0.97 | 1.02 | 0.95 | 0.94 | 0.00 | 1.60 | 1.51 |
| time (sec) |
N/A | 0.403 | 0.227 | 0.671 | 0.279 | 0.270 | 0.000 | 0.404 | 15.886 |
| 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 | 38 | 38 | 47 | 54 | 39 | 47 | 0 | 58 | 55 |
| N.S. |
1 | 1.00 | 1.24 | 1.42 | 1.03 | 1.24 | 0.00 | 1.53 | 1.45 |
| time (sec) |
N/A | 0.248 | 0.009 | 0.476 | 0.283 | 0.261 | 0.000 | 0.391 | 11.876 |
| 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 | 27 | 28 | 36 | 32 | 32 | 36 | 0 | 43 | 41 |
| N.S. |
1 | 1.04 | 1.33 | 1.19 | 1.19 | 1.33 | 0.00 | 1.59 | 1.52 |
| time (sec) |
N/A | 0.293 | 0.013 | 0.298 | 0.297 | 0.276 | 0.000 | 0.386 | 10.894 |
| 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 | 36 | 33 | 56 | 41 | 48 | 65 | 0 | 48 | 52 |
| N.S. |
1 | 0.92 | 1.56 | 1.14 | 1.33 | 1.81 | 0.00 | 1.33 | 1.44 |
| time (sec) |
N/A | 0.334 | 0.017 | 0.624 | 0.201 | 0.267 | 0.000 | 0.387 | 11.011 |
| 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 | 48 | 42 | 68 | 61 | 59 | 96 | 0 | 103 | 92 |
| N.S. |
1 | 0.88 | 1.42 | 1.27 | 1.23 | 2.00 | 0.00 | 2.15 | 1.92 |
| time (sec) |
N/A | 0.386 | 0.104 | 0.677 | 0.276 | 0.267 | 0.000 | 0.420 | 10.958 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | A | A | A | F(-1) | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 75 | 73 | 172 | 83 | 84 | 128 | 0 | 116 | 127 |
| N.S. |
1 | 0.97 | 2.29 | 1.11 | 1.12 | 1.71 | 0.00 | 1.55 | 1.69 |
| time (sec) |
N/A | 0.417 | 0.288 | 0.651 | 0.210 | 0.279 | 0.000 | 0.438 | 11.375 |
| 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 | 94 | 106 | 104 | 107 | 97 | 91 | 0 | 172 | 149 |
| N.S. |
1 | 1.13 | 1.11 | 1.14 | 1.03 | 0.97 | 0.00 | 1.83 | 1.59 |
| time (sec) |
N/A | 0.520 | 0.631 | 0.834 | 0.290 | 0.268 | 0.000 | 0.413 | 18.282 |
| 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 | 94 | 94 | 77 | 89 | 83 | 81 | 0 | 137 | 145 |
| N.S. |
1 | 1.00 | 0.82 | 0.95 | 0.88 | 0.86 | 0.00 | 1.46 | 1.54 |
| time (sec) |
N/A | 0.336 | 0.237 | 0.662 | 0.275 | 0.277 | 0.000 | 0.402 | 17.044 |
| 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 | 42 | 42 | 66 | 72 | 56 | 59 | 0 | 82 | 81 |
| N.S. |
1 | 1.00 | 1.57 | 1.71 | 1.33 | 1.40 | 0.00 | 1.95 | 1.93 |
| time (sec) |
N/A | 0.261 | 0.479 | 0.539 | 0.273 | 0.291 | 0.000 | 0.404 | 11.741 |
| 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 | 46 | 87 | 58 | 57 | 64 | 77 | 0 | 57 | 62 |
| N.S. |
1 | 1.89 | 1.26 | 1.24 | 1.39 | 1.67 | 0.00 | 1.24 | 1.35 |
| time (sec) |
N/A | 0.474 | 0.766 | 0.589 | 0.193 | 0.280 | 0.000 | 0.407 | 11.339 |
| 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 | 59 | 54 | 102 | 75 | 71 | 113 | 0 | 128 | 108 |
| N.S. |
1 | 0.92 | 1.73 | 1.27 | 1.20 | 1.92 | 0.00 | 2.17 | 1.83 |
| time (sec) |
N/A | 0.575 | 0.924 | 0.773 | 0.203 | 0.261 | 0.000 | 0.608 | 11.458 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | A | A | A | F(-1) | A | B |
| verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 100 | 129 | 238 | 116 | 123 | 186 | 0 | 157 | 148 |
| N.S. |
1 | 1.29 | 2.38 | 1.16 | 1.23 | 1.86 | 0.00 | 1.57 | 1.48 |
| time (sec) |
N/A | 0.582 | 1.037 | 0.723 | 0.216 | 0.271 | 0.000 | 0.503 | 11.129 |
| 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 | 104 | 106 | 196 | 136 | 123 | 192 | 0 | 204 | 194 |
| N.S. |
1 | 1.02 | 1.88 | 1.31 | 1.18 | 1.85 | 0.00 | 1.96 | 1.87 |
| time (sec) |
N/A | 0.564 | 1.433 | 0.765 | 0.256 | 0.277 | 0.000 | 0.438 | 11.277 |
| 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 | 197 | 197 | 147 | 152 | 164 | 135 | 0 | 336 | 323 |
| N.S. |
1 | 1.00 | 0.75 | 0.77 | 0.83 | 0.69 | 0.00 | 1.71 | 1.64 |
| time (sec) |
N/A | 0.502 | 0.920 | 1.029 | 0.306 | 0.272 | 0.000 | 0.455 | 15.328 |
| 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 | 146 | 146 | 113 | 130 | 119 | 116 | 0 | 207 | 249 |
| N.S. |
1 | 1.00 | 0.77 | 0.89 | 0.82 | 0.79 | 0.00 | 1.42 | 1.71 |
| time (sec) |
N/A | 0.415 | 0.472 | 0.877 | 0.382 | 0.276 | 0.000 | 0.463 | 16.217 |
| 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 | 75 | 76 | 91 | 107 | 99 | 90 | 0 | 148 | 219 |
| N.S. |
1 | 1.01 | 1.21 | 1.43 | 1.32 | 1.20 | 0.00 | 1.97 | 2.92 |
| time (sec) |
N/A | 0.311 | 0.801 | 0.686 | 0.283 | 0.282 | 0.000 | 0.419 | 15.395 |
| 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 | 78 | 78 | 83 | 79 | 86 | 99 | 0 | 86 | 154 |
| N.S. |
1 | 1.00 | 1.06 | 1.01 | 1.10 | 1.27 | 0.00 | 1.10 | 1.97 |
| time (sec) |
N/A | 0.343 | 0.922 | 0.628 | 0.295 | 0.290 | 0.000 | 0.492 | 11.248 |
| 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 | 87 | 87 | 114 | 91 | 90 | 131 | 0 | 148 | 120 |
| N.S. |
1 | 1.00 | 1.31 | 1.05 | 1.03 | 1.51 | 0.00 | 1.70 | 1.38 |
| time (sec) |
N/A | 0.399 | 1.163 | 0.905 | 0.218 | 0.277 | 0.000 | 0.469 | 11.121 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | A | A | A | F(-1) | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 132 | 132 | 267 | 130 | 137 | 196 | 0 | 179 | 166 |
| N.S. |
1 | 1.00 | 2.02 | 0.98 | 1.04 | 1.48 | 0.00 | 1.36 | 1.26 |
| time (sec) |
N/A | 0.444 | 1.139 | 0.909 | 0.199 | 0.282 | 0.000 | 0.523 | 11.169 |
| 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 | 164 | 164 | 287 | 169 | 162 | 252 | 0 | 245 | 218 |
| N.S. |
1 | 1.00 | 1.75 | 1.03 | 0.99 | 1.54 | 0.00 | 1.49 | 1.33 |
| time (sec) |
N/A | 0.479 | 1.708 | 0.847 | 0.203 | 0.284 | 0.000 | 0.523 | 11.135 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | F | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 222 | 222 | 236 | 184 | 0 | 724 | 0 | 264 | 4797 |
| N.S. |
1 | 1.00 | 1.06 | 0.83 | 0.00 | 3.26 | 0.00 | 1.19 | 21.61 |
| time (sec) |
N/A | 0.636 | 1.669 | 0.920 | 0.000 | 0.311 | 0.000 | 0.587 | 19.207 |
| 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 | 212 | 212 | 162 | 155 | 0 | 534 | 0 | 222 | 276 |
| N.S. |
1 | 1.00 | 0.76 | 0.73 | 0.00 | 2.52 | 0.00 | 1.05 | 1.30 |
| time (sec) |
N/A | 0.544 | 0.885 | 0.728 | 0.000 | 0.290 | 0.000 | 0.435 | 14.566 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | F | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 200 | 200 | 169 | 162 | 0 | 569 | 0 | 251 | 313 |
| N.S. |
1 | 1.00 | 0.84 | 0.81 | 0.00 | 2.84 | 0.00 | 1.26 | 1.56 |
| time (sec) |
N/A | 0.558 | 0.607 | 0.821 | 0.000 | 0.313 | 0.000 | 0.340 | 15.690 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | F | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 133 | 154 | 169 | 164 | 0 | 557 | 0 | 243 | 310 |
| N.S. |
1 | 1.16 | 1.27 | 1.23 | 0.00 | 4.19 | 0.00 | 1.83 | 2.33 |
| time (sec) |
N/A | 0.612 | 0.776 | 0.831 | 0.000 | 0.289 | 0.000 | 0.343 | 16.172 |
| 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 | 229 | 229 | 203 | 185 | 0 | 957 | 0 | 314 | 2076 |
| N.S. |
1 | 1.00 | 0.89 | 0.81 | 0.00 | 4.18 | 0.00 | 1.37 | 9.07 |
| time (sec) |
N/A | 0.583 | 2.163 | 1.145 | 0.000 | 0.792 | 0.000 | 0.353 | 14.782 |
| 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 | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 248 | 248 | 254 | 215 | 0 | 1355 | 0 | 523 | 2151 |
| N.S. |
1 | 1.00 | 1.02 | 0.87 | 0.00 | 5.46 | 0.00 | 2.11 | 8.67 |
| time (sec) |
N/A | 0.661 | 2.446 | 1.342 | 0.000 | 0.790 | 0.000 | 0.368 | 13.380 |
| 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 | 295 | 295 | 356 | 261 | 0 | 1844 | 0 | 423 | 2302 |
| N.S. |
1 | 1.00 | 1.21 | 0.88 | 0.00 | 6.25 | 0.00 | 1.43 | 7.80 |
| time (sec) |
N/A | 0.695 | 6.901 | 1.541 | 0.000 | 1.356 | 0.000 | 0.389 | 13.945 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | F | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 388 | 388 | 195 | 222 | 0 | 906 | 0 | 351 | 585 |
| N.S. |
1 | 1.00 | 0.50 | 0.57 | 0.00 | 2.34 | 0.00 | 0.90 | 1.51 |
| time (sec) |
N/A | 0.895 | 2.551 | 2.348 | 0.000 | 0.344 | 0.000 | 0.432 | 18.390 |
| 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 | 366 | 366 | 204 | 243 | 0 | 917 | 0 | 377 | 583 |
| N.S. |
1 | 1.00 | 0.56 | 0.66 | 0.00 | 2.51 | 0.00 | 1.03 | 1.59 |
| time (sec) |
N/A | 0.797 | 2.318 | 2.050 | 0.000 | 0.331 | 0.000 | 0.432 | 17.411 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | F | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 350 | 350 | 212 | 258 | 0 | 934 | 0 | 384 | 627 |
| N.S. |
1 | 1.00 | 0.61 | 0.74 | 0.00 | 2.67 | 0.00 | 1.10 | 1.79 |
| time (sec) |
N/A | 0.854 | 2.245 | 2.116 | 0.000 | 0.319 | 0.000 | 0.408 | 17.799 |
| 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 | 204 | 234 | 206 | 242 | 0 | 895 | 0 | 365 | 624 |
| N.S. |
1 | 1.15 | 1.01 | 1.19 | 0.00 | 4.39 | 0.00 | 1.79 | 3.06 |
| time (sec) |
N/A | 0.939 | 2.230 | 2.184 | 0.000 | 0.314 | 0.000 | 0.410 | 17.566 |
| 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 | 402 | 402 | 278 | 278 | 0 | 1623 | 0 | 411 | 2999 |
| N.S. |
1 | 1.00 | 0.69 | 0.69 | 0.00 | 4.04 | 0.00 | 1.02 | 7.46 |
| time (sec) |
N/A | 0.850 | 5.850 | 2.593 | 0.000 | 1.801 | 0.000 | 0.396 | 17.187 |
| 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 | 424 | 424 | 379 | 311 | 0 | 2140 | 0 | 633 | 3122 |
| N.S. |
1 | 1.00 | 0.89 | 0.73 | 0.00 | 5.05 | 0.00 | 1.49 | 7.36 |
| time (sec) |
N/A | 0.927 | 6.430 | 2.826 | 0.000 | 1.575 | 0.000 | 0.417 | 15.576 |
| 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 | 470 | 470 | 432 | 355 | 0 | 2672 | 0 | 900 | 3266 |
| N.S. |
1 | 1.00 | 0.92 | 0.76 | 0.00 | 5.69 | 0.00 | 1.91 | 6.95 |
| time (sec) |
N/A | 0.956 | 7.033 | 3.234 | 0.000 | 2.743 | 0.000 | 0.439 | 16.724 |
| 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 | 158 | 158 | 198 | 950 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.25 | 6.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.568 | 4.445 | 2.594 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | F | B | B | F | F | F(-1) | F | F(-1) |
| verified |
N/A | N/A | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 312 | 0 | 4593 | 1912 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.00 | 14.72 | 6.13 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.000 | 28.393 | 2.290 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | F | B | B | F | F | F(-1) | F | F(-1) |
| verified |
N/A | N/A | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 366 | 0 | 4665 | 1988 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.00 | 12.75 | 5.43 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.000 | 28.716 | 3.805 | 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 | F(-1) | A | B |
| verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 155 | 146 | 174 | 177 | 132 | 149 | 0 | 135 | 346 |
| N.S. |
1 | 0.94 | 1.12 | 1.14 | 0.85 | 0.96 | 0.00 | 0.87 | 2.23 |
| time (sec) |
N/A | 0.496 | 0.434 | 1.098 | 0.213 | 0.294 | 0.000 | 0.373 | 12.617 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F(-1) | A | B |
| verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 135 | 134 | 146 | 167 | 121 | 138 | 0 | 124 | 304 |
| N.S. |
1 | 0.99 | 1.08 | 1.24 | 0.90 | 1.02 | 0.00 | 0.92 | 2.25 |
| time (sec) |
N/A | 0.449 | 0.266 | 0.828 | 0.199 | 0.294 | 0.000 | 0.360 | 12.349 |
| 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 | 116 | 143 | 136 | 121 | 108 | 114 | 0 | 108 | 261 |
| N.S. |
1 | 1.23 | 1.17 | 1.04 | 0.93 | 0.98 | 0.00 | 0.93 | 2.25 |
| time (sec) |
N/A | 0.429 | 0.228 | 0.743 | 0.190 | 0.329 | 0.000 | 0.355 | 12.389 |
| 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 | 103 | 108 | 115 | 111 | 100 | 104 | 0 | 100 | 221 |
| N.S. |
1 | 1.05 | 1.12 | 1.08 | 0.97 | 1.01 | 0.00 | 0.97 | 2.15 |
| time (sec) |
N/A | 0.735 | 0.235 | 0.593 | 0.202 | 0.293 | 0.000 | 0.348 | 12.118 |
| 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 | 74 | 79 | 93 | 98 | 89 | 93 | 0 | 81 | 144 |
| N.S. |
1 | 1.07 | 1.26 | 1.32 | 1.20 | 1.26 | 0.00 | 1.09 | 1.95 |
| time (sec) |
N/A | 0.547 | 0.022 | 0.568 | 0.193 | 0.281 | 0.000 | 0.366 | 17.747 |
| 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 | 74 | 79 | 74 | 88 | 86 | 91 | 0 | 78 | 144 |
| N.S. |
1 | 1.07 | 1.00 | 1.19 | 1.16 | 1.23 | 0.00 | 1.05 | 1.95 |
| time (sec) |
N/A | 0.556 | 0.007 | 0.516 | 0.204 | 0.268 | 0.000 | 0.355 | 17.837 |
| 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 | 74 | 79 | 74 | 80 | 75 | 80 | 0 | 67 | 158 |
| N.S. |
1 | 1.07 | 1.00 | 1.08 | 1.01 | 1.08 | 0.00 | 0.91 | 2.14 |
| time (sec) |
N/A | 0.530 | 0.017 | 0.460 | 0.199 | 0.284 | 0.000 | 0.322 | 18.132 |
| 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 | 99 | 103 | 115 | 82 | 109 | 125 | 0 | 113 | 116 |
| N.S. |
1 | 1.04 | 1.16 | 0.83 | 1.10 | 1.26 | 0.00 | 1.14 | 1.17 |
| time (sec) |
N/A | 0.564 | 0.021 | 0.802 | 0.198 | 0.293 | 0.000 | 0.365 | 0.136 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | A | A | F(-1) | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 115 | 125 | 86 | 101 | 126 | 159 | 0 | 134 | 130 |
| N.S. |
1 | 1.09 | 0.75 | 0.88 | 1.10 | 1.38 | 0.00 | 1.17 | 1.13 |
| time (sec) |
N/A | 0.443 | 0.022 | 0.941 | 0.196 | 0.304 | 0.000 | 0.369 | 0.106 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | A | A | F(-1) | A | B |
| verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 135 | 135 | 100 | 129 | 140 | 211 | 0 | 133 | 146 |
| N.S. |
1 | 1.00 | 0.74 | 0.96 | 1.04 | 1.56 | 0.00 | 0.99 | 1.08 |
| time (sec) |
N/A | 0.473 | 0.017 | 0.970 | 0.205 | 0.317 | 0.000 | 0.392 | 11.294 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | A | A | F(-1) | A | B |
| verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 155 | 147 | 104 | 147 | 151 | 248 | 0 | 160 | 157 |
| N.S. |
1 | 0.95 | 0.67 | 0.95 | 0.97 | 1.60 | 0.00 | 1.03 | 1.01 |
| time (sec) |
N/A | 0.501 | 0.028 | 1.068 | 0.196 | 0.318 | 0.000 | 0.421 | 0.133 |
| 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 | 189 | 216 | 186 | 266 | 180 | 198 | 0 | 198 | 433 |
| N.S. |
1 | 1.14 | 0.98 | 1.41 | 0.95 | 1.05 | 0.00 | 1.05 | 2.29 |
| time (sec) |
N/A | 0.617 | 1.203 | 1.010 | 0.206 | 0.299 | 0.000 | 0.499 | 11.046 |
| 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 | 162 | 178 | 164 | 205 | 157 | 178 | 0 | 175 | 377 |
| N.S. |
1 | 1.10 | 1.01 | 1.27 | 0.97 | 1.10 | 0.00 | 1.08 | 2.33 |
| time (sec) |
N/A | 0.502 | 1.595 | 0.951 | 0.323 | 0.285 | 0.000 | 0.501 | 8.184 |
| 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 | 150 | 174 | 151 | 200 | 148 | 151 | 0 | 157 | 332 |
| N.S. |
1 | 1.16 | 1.01 | 1.33 | 0.99 | 1.01 | 0.00 | 1.05 | 2.21 |
| time (sec) |
N/A | 0.528 | 0.732 | 0.829 | 0.196 | 0.284 | 0.000 | 0.505 | 12.404 |
| 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 | 116 | 144 | 140 | 136 | 123 | 127 | 0 | 130 | 247 |
| N.S. |
1 | 1.24 | 1.21 | 1.17 | 1.06 | 1.09 | 0.00 | 1.12 | 2.13 |
| time (sec) |
N/A | 0.426 | 0.266 | 0.642 | 0.206 | 0.290 | 0.000 | 0.424 | 12.314 |
| 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 | 93 | 135 | 85 | 166 | 120 | 124 | 0 | 124 | 191 |
| N.S. |
1 | 1.45 | 0.91 | 1.78 | 1.29 | 1.33 | 0.00 | 1.33 | 2.05 |
| time (sec) |
N/A | 0.419 | 0.559 | 0.571 | 0.204 | 0.269 | 0.000 | 0.498 | 17.179 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | A | A | A | F(-1) | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 72 | 102 | 215 | 105 | 97 | 104 | 0 | 89 | 183 |
| N.S. |
1 | 1.42 | 2.99 | 1.46 | 1.35 | 1.44 | 0.00 | 1.24 | 2.54 |
| time (sec) |
N/A | 0.292 | 1.950 | 0.566 | 0.193 | 0.270 | 0.000 | 0.403 | 19.541 |
| 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 | 126 | 173 | 137 | 99 | 130 | 144 | 0 | 134 | 131 |
| N.S. |
1 | 1.37 | 1.09 | 0.79 | 1.03 | 1.14 | 0.00 | 1.06 | 1.04 |
| time (sec) |
N/A | 0.417 | 0.623 | 0.923 | 0.214 | 0.283 | 0.000 | 0.346 | 0.147 |
| 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 | 168 | 215 | 162 | 153 | 163 | 202 | 0 | 186 | 169 |
| N.S. |
1 | 1.28 | 0.96 | 0.91 | 0.97 | 1.20 | 0.00 | 1.11 | 1.01 |
| time (sec) |
N/A | 0.649 | 1.815 | 1.124 | 0.233 | 0.290 | 0.000 | 0.365 | 11.741 |
| 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 | 185 | 244 | 182 | 165 | 183 | 285 | 0 | 190 | 194 |
| N.S. |
1 | 1.32 | 0.98 | 0.89 | 0.99 | 1.54 | 0.00 | 1.03 | 1.05 |
| time (sec) |
N/A | 0.695 | 3.685 | 1.184 | 0.212 | 0.283 | 0.000 | 0.398 | 12.445 |