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 | 509 | 482 | 927 | 2386 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.95 | 1.82 | 4.69 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.377 | 14.770 | 19.430 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | B | F | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 532 | 496 | 1134 | 3310 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.93 | 2.13 | 6.22 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.407 | 15.120 | 18.057 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | B | F | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 626 | 589 | 1489 | 4189 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.94 | 2.38 | 6.69 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 3.053 | 15.363 | 17.608 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | B | F | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 730 | 696 | 1888 | 5425 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.95 | 2.59 | 7.43 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 3.663 | 19.454 | 21.102 | 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(-1) | F | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 662 | 659 | 4198 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 6.34 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 3.674 | 24.740 | 180.000 | 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(-1) | F | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 562 | 554 | 629 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.99 | 1.12 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.869 | 19.362 | 180.000 | 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(-1) | F | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 474 | 466 | 524 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.98 | 1.11 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.303 | 17.200 | 180.000 | 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(-1) | F | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 553 | 520 | 7032 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.94 | 12.72 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.476 | 24.853 | 180.000 | 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(-1) | F | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 596 | 568 | 7700 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.95 | 12.92 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 3.079 | 23.262 | 180.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | B | F | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 607 | 576 | 1278 | 4459 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.95 | 2.11 | 7.35 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 3.048 | 16.118 | 21.309 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | B | F | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 624 | 593 | 1504 | 4802 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.95 | 2.41 | 7.70 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 3.085 | 16.972 | 20.147 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | B | F | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 724 | 693 | 1857 | 5695 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.96 | 2.56 | 7.87 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 3.765 | 16.903 | 21.539 | 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(-1) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 839 | 807 | 703 | 6970 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.96 | 0.84 | 8.31 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 4.584 | 13.174 | 23.115 | 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 | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 403 | 396 | 385 | 3320 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.98 | 0.96 | 8.24 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.673 | 13.679 | 25.691 | 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 | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 330 | 315 | 324 | 1864 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.95 | 0.98 | 5.65 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.175 | 11.153 | 21.358 | 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 | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 270 | 251 | 279 | 778 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.93 | 1.03 | 2.88 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.871 | 9.699 | 18.685 | 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 | 268 | 249 | 157 | 181 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.93 | 0.59 | 0.68 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.795 | 3.021 | 16.179 | 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 | 487 | 457 | 610 | 958 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.94 | 1.25 | 1.97 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.962 | 9.363 | 16.820 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | B | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 539 | 501 | 1157 | 2480 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.93 | 2.15 | 4.60 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.254 | 15.453 | 17.493 | 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 | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 433 | 433 | 498 | 3850 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.15 | 8.89 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.930 | 16.322 | 25.286 | 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 | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 345 | 352 | 375 | 1811 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.02 | 1.09 | 5.25 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.378 | 13.777 | 22.102 | 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 | 324 | 328 | 305 | 1316 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.01 | 0.94 | 4.06 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.236 | 9.266 | 18.912 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | B | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
| size | 476 | 441 | 1050 | 1602 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.93 | 2.21 | 3.37 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.745 | 12.798 | 17.634 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | B | F | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 560 | 548 | 1551 | 3270 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.98 | 2.77 | 5.84 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.604 | 15.813 | 18.009 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | B | F | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 607 | 602 | 4316 | 9528 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.99 | 7.11 | 15.70 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.896 | 24.300 | 25.711 | 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 | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 496 | 498 | 610 | 6408 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.23 | 12.92 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.165 | 18.731 | 22.023 | 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 | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 469 | 465 | 557 | 5287 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.99 | 1.19 | 11.27 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.960 | 17.147 | 18.875 | 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 | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 431 | 431 | 528 | 4567 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.23 | 10.60 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.792 | 14.532 | 17.006 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | B | F | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
| size | 602 | 590 | 1496 | 6418 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.98 | 2.49 | 10.66 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.707 | 14.197 | 19.327 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | B | F | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 733 | 719 | 2318 | 10353 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.98 | 3.16 | 14.12 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 3.653 | 20.137 | 21.290 | 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 | 266 | 246 | 298 | 659 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.92 | 1.12 | 2.48 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.807 | 6.055 | 20.427 | 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 | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 130 | 130 | 104 | 112 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.80 | 0.86 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.420 | 0.076 | 15.870 | 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 | 137 | 137 | 147 | 138 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.07 | 1.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.429 | 0.099 | 15.263 | 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(-1) | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 479 | 446 | 236 | 820 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.93 | 0.49 | 1.71 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.858 | 0.976 | 16.896 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 33 | 33 | 35 | 33 | 35 | 35 | 32 | 35 | 37 |
| N.S. |
1 | 1.00 | 1.06 | 1.00 | 1.06 | 1.06 | 0.97 | 1.06 | 1.12 |
| time (sec) |
N/A | 0.436 | 20.031 | 1.883 | 5.085 | 0.286 | 165.508 | 0.658 | 2.848 |
| 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 | 644 | 617 | 317 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.96 | 0.49 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 4.275 | 2.661 | 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 | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 455 | 450 | 259 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.99 | 0.57 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.826 | 1.425 | 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 | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 327 | 315 | 205 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.96 | 0.63 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.797 | 0.621 | 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 | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 217 | 220 | 163 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.01 | 0.75 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.912 | 0.250 | 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 | F(-2) | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 299 | 305 | 10630 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.02 | 35.55 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.372 | 32.020 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | N/A | F(-1) | N/A | N/A | N/A | F(-1) | N/A | N/A |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 35 | 35 | 0 | 33 | 35 | 54 | 0 | 35 | 37 |
| N.S. |
1 | 1.00 | 0.00 | 0.94 | 1.00 | 1.54 | 0.00 | 1.00 | 1.06 |
| time (sec) |
N/A | 1.062 | 0.000 | 2.019 | 2.686 | 0.312 | 0.000 | 1.159 | 5.760 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 35 | 35 | 37 | 33 | 35 | 35 | 34 | 35 | 37 |
| N.S. |
1 | 1.00 | 1.06 | 0.94 | 1.00 | 1.00 | 0.97 | 1.00 | 1.06 |
| time (sec) |
N/A | 0.477 | 33.021 | 1.774 | 2.710 | 0.281 | 8.463 | 0.694 | 3.271 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 35 | 35 | 37 | 33 | 35 | 35 | 34 | 35 | 37 |
| N.S. |
1 | 1.00 | 1.06 | 0.94 | 1.00 | 1.00 | 0.97 | 1.00 | 1.06 |
| time (sec) |
N/A | 0.501 | 39.765 | 1.580 | 2.614 | 0.278 | 3.118 | 0.730 | 4.944 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 35 | 35 | 37 | 33 | 35 | 63 | 34 | 35 | 37 |
| N.S. |
1 | 1.00 | 1.06 | 0.94 | 1.00 | 1.80 | 0.97 | 1.00 | 1.06 |
| time (sec) |
N/A | 1.101 | 31.590 | 1.713 | 2.316 | 0.304 | 11.397 | 1.261 | 8.631 |