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 | Reduce | Mupad | |
| grade |
N/A | A | A | B | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 509 | 482 | 927 | 1245 | 0 | 0 | 0 | 0 | 108 | 0 |
| N.S. |
1 | 0.95 | 1.82 | 2.45 | 0.00 | 0.00 | 0.00 | 0.00 | 0.21 | 0.00 |
| time (sec) |
N/A | 2.385 | 17.647 | 14.680 | 0.000 | 0.000 | 0.000 | 0.000 | 0.287 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | B | B | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 532 | 496 | 1134 | 1389 | 0 | 0 | 0 | 0 | 90 | 0 |
| N.S. |
1 | 0.93 | 2.13 | 2.61 | 0.00 | 0.00 | 0.00 | 0.00 | 0.17 | 0.00 |
| time (sec) |
N/A | 2.456 | 19.174 | 12.402 | 0.000 | 0.000 | 0.000 | 0.000 | 0.236 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | B | B | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 626 | 589 | 1489 | 1739 | 0 | 0 | 0 | 0 | 114 | 0 |
| N.S. |
1 | 0.94 | 2.38 | 2.78 | 0.00 | 0.00 | 0.00 | 0.00 | 0.18 | 0.00 |
| time (sec) |
N/A | 3.175 | 20.981 | 11.607 | 0.000 | 0.000 | 0.000 | 0.000 | 0.191 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | B | B | F | F(-1) | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 730 | 696 | 1888 | 2280 | 0 | 0 | 0 | 0 | 114 | 0 |
| N.S. |
1 | 0.95 | 2.59 | 3.12 | 0.00 | 0.00 | 0.00 | 0.00 | 0.16 | 0.00 |
| time (sec) |
N/A | 3.728 | 22.340 | 13.075 | 0.000 | 0.000 | 0.000 | 0.000 | 0.212 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | B | F(-1) | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 662 | 659 | 4198 | 0 | 0 | 0 | 0 | 0 | 159 | 0 |
| N.S. |
1 | 1.00 | 6.34 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.24 | 0.00 |
| time (sec) |
N/A | 3.685 | 30.005 | 180.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.353 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | B | F(-1) | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 562 | 554 | 3755 | 0 | 0 | 0 | 0 | 0 | 159 | 0 |
| N.S. |
1 | 0.99 | 6.68 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.28 | 0.00 |
| time (sec) |
N/A | 2.941 | 28.412 | 180.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.350 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | B | F(-1) | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 474 | 466 | 3348 | 0 | 0 | 0 | 0 | 0 | 159 | 0 |
| N.S. |
1 | 0.98 | 7.06 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.34 | 0.00 |
| time (sec) |
N/A | 2.287 | 26.752 | 180.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.368 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | B | F(-1) | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 553 | 520 | 7032 | 0 | 0 | 0 | 0 | 0 | 159 | 0 |
| N.S. |
1 | 0.94 | 12.72 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.29 | 0.00 |
| time (sec) |
N/A | 2.482 | 27.647 | 180.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.354 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | B | F(-1) | F | F(-1) | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 596 | 568 | 7700 | 0 | 0 | 0 | 0 | 0 | 159 | 0 |
| N.S. |
1 | 0.95 | 12.92 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.27 | 0.00 |
| time (sec) |
N/A | 3.077 | 28.062 | 180.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.351 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | B | B | F | F(-1) | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 607 | 576 | 1278 | 1854 | 0 | 0 | 0 | 0 | 151 | 0 |
| N.S. |
1 | 0.95 | 2.11 | 3.05 | 0.00 | 0.00 | 0.00 | 0.00 | 0.25 | 0.00 |
| time (sec) |
N/A | 3.105 | 20.927 | 20.537 | 0.000 | 0.000 | 0.000 | 0.000 | 0.322 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | B | B | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 624 | 593 | 1504 | 2004 | 0 | 0 | 0 | 0 | 127 | 0 |
| N.S. |
1 | 0.95 | 2.41 | 3.21 | 0.00 | 0.00 | 0.00 | 0.00 | 0.20 | 0.00 |
| time (sec) |
N/A | 3.242 | 22.725 | 12.481 | 0.000 | 0.000 | 0.000 | 0.000 | 0.294 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | B | B | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 724 | 693 | 1857 | 2353 | 0 | 0 | 0 | 0 | 159 | 0 |
| N.S. |
1 | 0.96 | 2.56 | 3.25 | 0.00 | 0.00 | 0.00 | 0.00 | 0.22 | 0.00 |
| time (sec) |
N/A | 3.884 | 21.841 | 11.881 | 0.000 | 0.000 | 0.000 | 0.000 | 0.188 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F | F(-1) | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 839 | 807 | 703 | 2924 | 0 | 0 | 0 | 0 | 159 | 0 |
| N.S. |
1 | 0.96 | 0.84 | 3.49 | 0.00 | 0.00 | 0.00 | 0.00 | 0.19 | 0.00 |
| time (sec) |
N/A | 4.533 | 18.084 | 15.783 | 0.000 | 0.000 | 0.000 | 0.000 | 0.201 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | B | B | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 403 | 396 | 2987 | 1517 | 0 | 0 | 0 | 0 | 29 | 0 |
| N.S. |
1 | 0.98 | 7.41 | 3.76 | 0.00 | 0.00 | 0.00 | 0.00 | 0.07 | 0.00 |
| time (sec) |
N/A | 1.676 | 23.587 | 32.020 | 0.000 | 0.000 | 0.000 | 0.000 | 0.177 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 330 | 315 | 355 | 940 | 0 | 0 | 0 | 0 | 29 | 0 |
| N.S. |
1 | 0.95 | 1.08 | 2.85 | 0.00 | 0.00 | 0.00 | 0.00 | 0.09 | 0.00 |
| time (sec) |
N/A | 1.209 | 17.172 | 15.308 | 0.000 | 0.000 | 0.000 | 0.000 | 0.171 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 270 | 251 | 302 | 486 | 0 | 0 | 0 | 0 | 27 | 0 |
| N.S. |
1 | 0.93 | 1.12 | 1.80 | 0.00 | 0.00 | 0.00 | 0.00 | 0.10 | 0.00 |
| time (sec) |
N/A | 0.877 | 16.223 | 10.220 | 0.000 | 0.000 | 0.000 | 0.000 | 0.175 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 268 | 249 | 157 | 179 | 0 | 0 | 0 | 0 | 21 | 0 |
| N.S. |
1 | 0.93 | 0.59 | 0.67 | 0.00 | 0.00 | 0.00 | 0.00 | 0.08 | 0.00 |
| time (sec) |
N/A | 0.813 | 4.857 | 7.375 | 0.000 | 0.000 | 0.000 | 0.000 | 0.185 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 487 | 457 | 814 | 507 | 0 | 0 | 0 | 0 | 29 | 0 |
| N.S. |
1 | 0.94 | 1.67 | 1.04 | 0.00 | 0.00 | 0.00 | 0.00 | 0.06 | 0.00 |
| time (sec) |
N/A | 2.043 | 20.712 | 9.119 | 0.000 | 0.000 | 0.000 | 0.000 | 0.174 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | B | B | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 539 | 501 | 1157 | 1054 | 0 | 0 | 0 | 0 | 29 | 0 |
| N.S. |
1 | 0.93 | 2.15 | 1.96 | 0.00 | 0.00 | 0.00 | 0.00 | 0.05 | 0.00 |
| time (sec) |
N/A | 2.276 | 20.963 | 11.359 | 0.000 | 0.000 | 0.000 | 0.000 | 0.164 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | B | B | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 433 | 433 | 3433 | 1938 | 0 | 0 | 0 | 0 | 41 | 0 |
| N.S. |
1 | 1.00 | 7.93 | 4.48 | 0.00 | 0.00 | 0.00 | 0.00 | 0.09 | 0.00 |
| time (sec) |
N/A | 1.933 | 26.313 | 30.927 | 0.000 | 0.000 | 0.000 | 0.000 | 0.177 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | B | B | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 345 | 352 | 2988 | 1300 | 0 | 0 | 0 | 0 | 39 | 0 |
| N.S. |
1 | 1.02 | 8.66 | 3.77 | 0.00 | 0.00 | 0.00 | 0.00 | 0.11 | 0.00 |
| time (sec) |
N/A | 1.344 | 22.964 | 12.939 | 0.000 | 0.000 | 0.000 | 0.000 | 0.166 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 324 | 328 | 305 | 916 | 0 | 0 | 0 | 0 | 33 | 0 |
| N.S. |
1 | 1.01 | 0.94 | 2.83 | 0.00 | 0.00 | 0.00 | 0.00 | 0.10 | 0.00 |
| time (sec) |
N/A | 1.263 | 15.447 | 5.618 | 0.000 | 0.000 | 0.000 | 0.000 | 0.155 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | B | B | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 476 | 441 | 1050 | 1098 | 0 | 0 | 0 | 0 | 46 | 0 |
| N.S. |
1 | 0.93 | 2.21 | 2.31 | 0.00 | 0.00 | 0.00 | 0.00 | 0.10 | 0.00 |
| time (sec) |
N/A | 1.720 | 14.527 | 8.880 | 0.000 | 0.000 | 0.000 | 0.000 | 0.167 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | B | B | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 560 | 548 | 1551 | 1597 | 0 | 0 | 0 | 0 | 50 | 0 |
| N.S. |
1 | 0.98 | 2.77 | 2.85 | 0.00 | 0.00 | 0.00 | 0.00 | 0.09 | 0.00 |
| time (sec) |
N/A | 2.651 | 20.591 | 11.391 | 0.000 | 0.000 | 0.000 | 0.000 | 0.165 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | B | B | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 607 | 602 | 4316 | 3734 | 0 | 0 | 0 | 0 | 57 | 0 |
| N.S. |
1 | 0.99 | 7.11 | 6.15 | 0.00 | 0.00 | 0.00 | 0.00 | 0.09 | 0.00 |
| time (sec) |
N/A | 2.955 | 29.596 | 34.253 | 0.000 | 0.000 | 0.000 | 0.000 | 0.162 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | B | B | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 496 | 498 | 3891 | 2960 | 0 | 0 | 0 | 0 | 55 | 0 |
| N.S. |
1 | 1.00 | 7.84 | 5.97 | 0.00 | 0.00 | 0.00 | 0.00 | 0.11 | 0.00 |
| time (sec) |
N/A | 2.188 | 27.543 | 15.615 | 0.000 | 0.000 | 0.000 | 0.000 | 0.189 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | B | B | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 469 | 465 | 3493 | 2439 | 0 | 0 | 0 | 0 | 49 | 0 |
| N.S. |
1 | 0.99 | 7.45 | 5.20 | 0.00 | 0.00 | 0.00 | 0.00 | 0.10 | 0.00 |
| time (sec) |
N/A | 1.963 | 26.049 | 11.176 | 0.000 | 0.000 | 0.000 | 0.000 | 0.183 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | B | B | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 431 | 431 | 3155 | 1970 | 0 | 0 | 0 | 0 | 68 | 0 |
| N.S. |
1 | 1.00 | 7.32 | 4.57 | 0.00 | 0.00 | 0.00 | 0.00 | 0.16 | 0.00 |
| time (sec) |
N/A | 1.771 | 23.661 | 7.430 | 0.000 | 0.000 | 0.000 | 0.000 | 0.174 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | B | B | F | F(-1) | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 602 | 590 | 1496 | 2667 | 0 | 0 | 0 | 0 | 74 | 0 |
| N.S. |
1 | 0.98 | 2.49 | 4.43 | 0.00 | 0.00 | 0.00 | 0.00 | 0.12 | 0.00 |
| time (sec) |
N/A | 2.722 | 16.653 | 11.912 | 0.000 | 0.000 | 0.000 | 0.000 | 0.182 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | B | B | F | F(-1) | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 733 | 719 | 2318 | 4167 | 0 | 0 | 0 | 0 | 74 | 0 |
| N.S. |
1 | 0.98 | 3.16 | 5.68 | 0.00 | 0.00 | 0.00 | 0.00 | 0.10 | 0.00 |
| time (sec) |
N/A | 3.645 | 23.352 | 17.741 | 0.000 | 0.000 | 0.000 | 0.000 | 0.206 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 266 | 246 | 298 | 382 | 0 | 0 | 0 | 0 | 41 | 0 |
| N.S. |
1 | 0.92 | 1.12 | 1.44 | 0.00 | 0.00 | 0.00 | 0.00 | 0.15 | 0.00 |
| time (sec) |
N/A | 0.807 | 6.073 | 28.578 | 0.000 | 0.000 | 0.000 | 0.000 | 0.282 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 130 | 130 | 104 | 110 | 0 | 0 | 0 | 0 | 35 | 0 |
| N.S. |
1 | 1.00 | 0.80 | 0.85 | 0.00 | 0.00 | 0.00 | 0.00 | 0.27 | 0.00 |
| time (sec) |
N/A | 0.432 | 0.117 | 13.697 | 0.000 | 0.000 | 0.000 | 0.000 | 0.257 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 137 | 137 | 147 | 140 | 0 | 0 | 0 | 0 | 48 | 0 |
| N.S. |
1 | 1.00 | 1.07 | 1.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.35 | 0.00 |
| time (sec) |
N/A | 0.436 | 0.156 | 11.740 | 0.000 | 0.000 | 0.000 | 0.000 | 0.222 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 479 | 446 | 236 | 373 | 0 | 0 | 0 | 0 | 52 | 0 |
| N.S. |
1 | 0.93 | 0.49 | 0.78 | 0.00 | 0.00 | 0.00 | 0.00 | 0.11 | 0.00 |
| time (sec) |
N/A | 1.845 | 1.653 | 14.588 | 0.000 | 0.000 | 0.000 | 0.000 | 0.181 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A | N/A |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 33 | 33 | 35 | 33 | 35 | 35 | 0 | 35 | 61 | 37 |
| N.S. |
1 | 1.00 | 1.06 | 1.00 | 1.06 | 1.06 | 0.00 | 1.06 | 1.85 | 1.12 |
| time (sec) |
N/A | 0.435 | 31.282 | 0.217 | 4.080 | 0.131 | 0.000 | 0.644 | 0.218 | 42.359 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 644 | 617 | 317 | 0 | 0 | 0 | 0 | 0 | 144 | 0 |
| N.S. |
1 | 0.96 | 0.49 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.22 | 0.00 |
| time (sec) |
N/A | 4.317 | 4.631 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.207 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 455 | 450 | 259 | 0 | 0 | 0 | 0 | 0 | 117 | 0 |
| N.S. |
1 | 0.99 | 0.57 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.26 | 0.00 |
| time (sec) |
N/A | 2.832 | 2.292 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.210 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 327 | 315 | 205 | 0 | 0 | 0 | 0 | 0 | 90 | 0 |
| N.S. |
1 | 0.96 | 0.63 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.28 | 0.00 |
| time (sec) |
N/A | 1.818 | 1.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.219 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 217 | 220 | 163 | 0 | 0 | 0 | 0 | 0 | 63 | 0 |
| N.S. |
1 | 1.01 | 0.75 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.29 | 0.00 |
| time (sec) |
N/A | 0.947 | 0.417 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.208 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | B | F | F | F | F | F(-2) | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 299 | 305 | 10630 | 0 | 0 | 0 | 0 | 0 | 14 | 0 |
| N.S. |
1 | 1.02 | 35.55 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.05 | 0.00 |
| time (sec) |
N/A | 1.397 | 36.705 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.170 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | N/A | F(-1) | N/A | N/A | N/A | F(-1) | N/A | N/A | N/A |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 35 | 35 | 0 | 33 | 35 | 54 | 0 | 35 | 97 | 37 |
| N.S. |
1 | 1.00 | 0.00 | 0.94 | 1.00 | 1.54 | 0.00 | 1.00 | 2.77 | 1.06 |
| time (sec) |
N/A | 1.100 | 0.000 | 0.232 | 2.093 | 0.141 | 0.000 | 1.119 | 0.267 | 45.437 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | 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 | TBD |
| size | 35 | 35 | 37 | 33 | 35 | 35 | 34 | 35 | 59 | 37 |
| N.S. |
1 | 1.00 | 1.06 | 0.94 | 1.00 | 1.00 | 0.97 | 1.00 | 1.69 | 1.06 |
| time (sec) |
N/A | 0.479 | 72.609 | 0.230 | 2.678 | 0.097 | 8.419 | 0.705 | 0.215 | 42.785 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | 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 | TBD |
| size | 35 | 35 | 37 | 33 | 35 | 35 | 34 | 35 | 26 | 37 |
| N.S. |
1 | 1.00 | 1.06 | 0.94 | 1.00 | 1.00 | 0.97 | 1.00 | 0.74 | 1.06 |
| time (sec) |
N/A | 0.513 | 53.186 | 0.238 | 2.887 | 0.109 | 3.112 | 0.673 | 0.184 | 44.113 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | 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 | TBD |
| size | 35 | 35 | 37 | 33 | 35 | 63 | 34 | 35 | 38 | 37 |
| N.S. |
1 | 1.00 | 1.06 | 0.94 | 1.00 | 1.80 | 0.97 | 1.00 | 1.09 | 1.06 |
| time (sec) |
N/A | 1.111 | 39.688 | 0.244 | 1.783 | 0.107 | 11.129 | 1.205 | 0.179 | 48.341 |