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 | C | C | F(-1) | F(-1) | F(-1) | F | F | F(-1) |
| verified |
N/A | No | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 685 | 664 | 1014 | 4347 | 0 | 0 | 0 | 0 | 93 | 0 |
| N.S. |
1 | 0.97 | 1.48 | 6.35 | 0.00 | 0.00 | 0.00 | 0.00 | 0.14 | 0.00 |
| time (sec) |
N/A | 3.630 | 6.949 | 14.586 | 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 | C | B | F(-1) | F(-1) | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | No | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 671 | 633 | 2102 | 4829 | 0 | 0 | 0 | 0 | 84 | 0 |
| N.S. |
1 | 0.94 | 3.13 | 7.20 | 0.00 | 0.00 | 0.00 | 0.00 | 0.13 | 0.00 |
| time (sec) |
N/A | 3.162 | 26.328 | 608.562 | 0.000 | 0.000 | 0.000 | 0.000 | 0.232 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | C | F(-1) | F(-1) | F(-1) | F | F | F(-1) |
| verified |
N/A | No | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 557 | 526 | 937 | 5023 | 0 | 0 | 0 | 0 | 84 | 0 |
| N.S. |
1 | 0.94 | 1.68 | 9.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.15 | 0.00 |
| time (sec) |
N/A | 2.534 | 26.092 | 578.915 | 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 | C | B | F | F(-2) | F(-1) | F | F | F(-1) |
| verified |
N/A | No | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 571 | 545 | 2020 | 4572 | 0 | 0 | 0 | 0 | 84 | 0 |
| N.S. |
1 | 0.95 | 3.54 | 8.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.15 | 0.00 |
| time (sec) |
N/A | 2.575 | 25.989 | 344.110 | 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 | C | C | F | F(-1) | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | No | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 591 | 532 | 900 | 5002 | 0 | 0 | 0 | 0 | 84 | 0 |
| N.S. |
1 | 0.90 | 1.52 | 8.46 | 0.00 | 0.00 | 0.00 | 0.00 | 0.14 | 0.00 |
| time (sec) |
N/A | 2.526 | 25.997 | 340.462 | 0.000 | 0.000 | 0.000 | 0.000 | 0.187 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | No | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 597 | 549 | 1263 | 4367 | 0 | 0 | 0 | 0 | 741 | 0 |
| N.S. |
1 | 0.92 | 2.12 | 7.31 | 0.00 | 0.00 | 0.00 | 0.00 | 1.24 | 0.00 |
| time (sec) |
N/A | 2.650 | 23.629 | 343.845 | 0.000 | 0.000 | 0.000 | 0.000 | 0.214 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | C | F | F(-1) | F(-1) | F | F | F(-1) |
| verified |
N/A | No | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 574 | 528 | 892 | 4585 | 0 | 0 | 0 | 0 | 84 | 0 |
| N.S. |
1 | 0.92 | 1.55 | 7.99 | 0.00 | 0.00 | 0.00 | 0.00 | 0.15 | 0.00 |
| time (sec) |
N/A | 2.504 | 25.975 | 340.007 | 0.000 | 0.000 | 0.000 | 0.000 | 0.203 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | No | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 592 | 551 | 1263 | 3936 | 0 | 0 | 0 | 0 | 1315 | 0 |
| N.S. |
1 | 0.93 | 2.13 | 6.65 | 0.00 | 0.00 | 0.00 | 0.00 | 2.22 | 0.00 |
| time (sec) |
N/A | 2.574 | 22.776 | 10.444 | 0.000 | 0.000 | 0.000 | 0.000 | 0.224 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | C | F | F(-1) | F(-1) | F | F | F(-1) |
| verified |
N/A | No | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 579 | 544 | 900 | 3713 | 0 | 0 | 0 | 0 | 73 | 0 |
| N.S. |
1 | 0.94 | 1.55 | 6.41 | 0.00 | 0.00 | 0.00 | 0.00 | 0.13 | 0.00 |
| time (sec) |
N/A | 2.637 | 6.624 | 8.162 | 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 | C | B | F(-1) | F(-1) | F(-1) | F | F | F(-1) |
| verified |
N/A | No | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 593 | 565 | 1276 | 3113 | 0 | 0 | 0 | 0 | 107 | 0 |
| N.S. |
1 | 0.95 | 2.15 | 5.25 | 0.00 | 0.00 | 0.00 | 0.00 | 0.18 | 0.00 |
| time (sec) |
N/A | 2.785 | 23.530 | 9.135 | 0.000 | 0.000 | 0.000 | 0.000 | 0.238 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | C | F(-1) | F(-1) | F(-1) | F | F | F(-1) |
| verified |
N/A | No | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 674 | 648 | 996 | 5211 | 0 | 0 | 0 | 0 | 117 | 0 |
| N.S. |
1 | 0.96 | 1.48 | 7.73 | 0.00 | 0.00 | 0.00 | 0.00 | 0.17 | 0.00 |
| time (sec) |
N/A | 3.483 | 7.015 | 12.710 | 0.000 | 0.000 | 0.000 | 0.000 | 0.197 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | B | C | B | F | F | F | F | F | F(-1) |
| verified |
N/A | No | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 183 | 393 | 117 | 652 | 0 | 0 | 0 | 0 | 52 | 0 |
| N.S. |
1 | 2.15 | 0.64 | 3.56 | 0.00 | 0.00 | 0.00 | 0.00 | 0.28 | 0.00 |
| time (sec) |
N/A | 0.452 | 0.404 | 8.343 | 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 | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 229 | 226 | 273 | 0 | 0 | 0 | 0 | 0 | 166 | 0 |
| N.S. |
1 | 0.99 | 1.19 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.72 | 0.00 |
| time (sec) |
N/A | 0.817 | 15.855 | 0.000 | 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 | C | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 157 | 154 | 7484 | 0 | 0 | 0 | 0 | 0 | 111 | 0 |
| N.S. |
1 | 0.98 | 47.67 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.71 | 0.00 |
| time (sec) |
N/A | 0.498 | 27.069 | 0.000 | 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 | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 97 | 97 | 75 | 0 | 0 | 0 | 0 | 0 | 57 | 0 |
| N.S. |
1 | 1.00 | 0.77 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.59 | 0.00 |
| time (sec) |
N/A | 0.297 | 0.155 | 0.000 | 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 | A | B | F | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 158 | 158 | 3815 | 0 | 0 | 0 | 0 | 0 | 27 | 0 |
| N.S. |
1 | 1.00 | 24.15 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.17 | 0.00 |
| time (sec) |
N/A | 0.318 | 21.554 | 0.000 | 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 | F | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 170 | 170 | 4727 | 0 | 0 | 0 | 0 | 0 | 43 | 0 |
| N.S. |
1 | 1.00 | 27.81 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.25 | 0.00 |
| time (sec) |
N/A | 0.304 | 27.084 | 0.000 | 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 | F | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 170 | 170 | 7781 | 0 | 0 | 0 | 0 | 0 | 59 | 0 |
| N.S. |
1 | 1.00 | 45.77 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.35 | 0.00 |
| time (sec) |
N/A | 0.302 | 31.703 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.197 | 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 | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 156 | 156 | 187 | 0 | 0 | 0 | 0 | 0 | 59 | 0 |
| N.S. |
1 | 1.00 | 1.20 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.38 | 0.00 |
| time (sec) |
N/A | 0.377 | 4.212 | 0.000 | 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 | A | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 156 | 156 | 187 | 0 | 0 | 0 | 0 | 0 | 26 | 0 |
| N.S. |
1 | 1.00 | 1.20 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.17 | 0.00 |
| time (sec) |
N/A | 0.324 | 4.559 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.184 | 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 | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 154 | 154 | 185 | 0 | 0 | 0 | 0 | 0 | 38 | 0 |
| N.S. |
1 | 1.00 | 1.20 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.25 | 0.00 |
| time (sec) |
N/A | 0.322 | 4.561 | 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 | A | A | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 154 | 154 | 185 | 0 | 0 | 0 | 0 | 0 | 54 | 0 |
| N.S. |
1 | 1.00 | 1.20 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.35 | 0.00 |
| time (sec) |
N/A | 0.324 | 6.411 | 0.000 | 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 | A | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 156 | 156 | 187 | 0 | 0 | 0 | 0 | 0 | 70 | 0 |
| N.S. |
1 | 1.00 | 1.20 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.45 | 0.00 |
| time (sec) |
N/A | 0.324 | 6.799 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.184 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | B | B | F(-1) | B | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 254 | 219 | 459 | 500 | 558 | 814 | 0 | 3579 | 23 | 1196 |
| N.S. |
1 | 0.86 | 1.81 | 1.97 | 2.20 | 3.20 | 0.00 | 14.09 | 0.09 | 4.71 |
| time (sec) |
N/A | 0.377 | 6.136 | 18.765 | 0.050 | 0.212 | 0.000 | 0.171 | 200.020 | 27.147 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | B | F(-1) | B | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 167 | 144 | 169 | 272 | 286 | 381 | 0 | 1410 | 23 | 641 |
| N.S. |
1 | 0.86 | 1.01 | 1.63 | 1.71 | 2.28 | 0.00 | 8.44 | 0.14 | 3.84 |
| time (sec) |
N/A | 0.310 | 1.300 | 6.101 | 0.041 | 0.131 | 0.000 | 0.136 | 0.356 | 20.889 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | B | B | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 92 | 81 | 74 | 122 | 117 | 142 | 2837 | 373 | 23 | 197 |
| N.S. |
1 | 0.88 | 0.80 | 1.33 | 1.27 | 1.54 | 30.84 | 4.05 | 0.25 | 2.14 |
| time (sec) |
N/A | 0.263 | 0.263 | 1.671 | 0.035 | 0.101 | 125.687 | 0.129 | 0.163 | 18.098 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 26 | 26 | 26 | 27 | 26 | 33 | 99 | 26 | 34 | 26 |
| N.S. |
1 | 1.00 | 1.00 | 1.04 | 1.00 | 1.27 | 3.81 | 1.00 | 1.31 | 1.00 |
| time (sec) |
N/A | 0.197 | 0.035 | 0.420 | 0.026 | 0.085 | 0.604 | 0.125 | 0.159 | 17.257 |
| 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 | 115 | 120 | 99 | 0 | 0 | 0 | 0 | 0 | 21 | 0 |
| N.S. |
1 | 1.04 | 0.86 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.18 | 0.00 |
| time (sec) |
N/A | 0.298 | 0.134 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.205 | 0.000 |
| 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 | 183 | 231 | 157 | 0 | 0 | 0 | 0 | 0 | 23 | 0 |
| N.S. |
1 | 1.26 | 0.86 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.13 | 0.00 |
| time (sec) |
N/A | 0.414 | 0.616 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.196 | 0.000 |
| 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 | 305 | 390 | 260 | 0 | 0 | 0 | 0 | 0 | 23 | 0 |
| N.S. |
1 | 1.28 | 0.85 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.08 | 0.00 |
| time (sec) |
N/A | 0.626 | 4.117 | 0.000 | 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 | F | F | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | No | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 118 | 129 | 0 | 0 | 0 | 0 | 0 | 0 | 23 | 0 |
| N.S. |
1 | 1.09 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.19 | 0.00 |
| time (sec) |
N/A | 0.297 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 2.141 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | F | F | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | No | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 116 | 127 | 0 | 0 | 0 | 0 | 0 | 0 | 23 | 0 |
| N.S. |
1 | 1.09 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.20 | 0.00 |
| time (sec) |
N/A | 0.308 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.172 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | F | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 115 | 129 | 0 | 0 | 0 | 0 | 0 | 0 | 23 | 0 |
| N.S. |
1 | 1.12 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.20 | 0.00 |
| time (sec) |
N/A | 0.321 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.173 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | F | F | F | F | F(-2) | F | F | F(-1) |
| verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 118 | 129 | 0 | 0 | 0 | 0 | 0 | 0 | 23 | 0 |
| N.S. |
1 | 1.09 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.19 | 0.00 |
| time (sec) |
N/A | 0.302 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.239 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | F | F | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | No | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 123 | 134 | 0 | 0 | 0 | 0 | 0 | 0 | 36 | 0 |
| N.S. |
1 | 1.09 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.29 | 0.00 |
| time (sec) |
N/A | 0.321 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.239 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | F | F | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | No | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 123 | 134 | 0 | 0 | 0 | 0 | 0 | 0 | 32 | 0 |
| N.S. |
1 | 1.09 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.26 | 0.00 |
| time (sec) |
N/A | 0.324 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.184 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | F | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 123 | 134 | 0 | 0 | 0 | 0 | 0 | 0 | 25 | 0 |
| N.S. |
1 | 1.09 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.20 | 0.00 |
| time (sec) |
N/A | 0.324 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.176 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | F | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 121 | 134 | 0 | 0 | 0 | 0 | 0 | 0 | 36 | 0 |
| N.S. |
1 | 1.11 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.30 | 0.00 |
| time (sec) |
N/A | 0.310 | 0.000 | 0.000 | 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 | F | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 120 | 134 | 0 | 0 | 0 | 0 | 0 | 0 | 36 | 0 |
| N.S. |
1 | 1.12 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.30 | 0.00 |
| time (sec) |
N/A | 0.326 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.199 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | F | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 158 | 158 | 0 | 0 | 0 | 0 | 0 | 0 | 27 | 0 |
| N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.17 | 0.00 |
| time (sec) |
N/A | 0.361 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.172 | 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 | No | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 276 | 480 | 319 | 0 | 0 | 0 | 0 | 0 | 42 | 0 |
| N.S. |
1 | 1.74 | 1.16 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.15 | 0.00 |
| time (sec) |
N/A | 1.033 | 5.523 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.220 | 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 | 201 | 256 | 168 | 0 | 0 | 0 | 0 | 0 | 42 | 0 |
| N.S. |
1 | 1.27 | 0.84 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.21 | 0.00 |
| time (sec) |
N/A | 0.607 | 1.081 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.198 | 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 | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 132 | 132 | 132 | 0 | 0 | 0 | 0 | 0 | 42 | 0 |
| N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.32 | 0.00 |
| time (sec) |
N/A | 0.282 | 0.479 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.176 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | F | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 152 | 152 | 0 | 0 | 0 | 0 | 0 | 0 | 31 | 0 |
| N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.20 | 0.00 |
| time (sec) |
N/A | 0.345 | 0.000 | 0.000 | 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 | F | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 142 | 142 | 0 | 0 | 0 | 0 | 0 | 0 | 38 | 0 |
| N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.27 | 0.00 |
| time (sec) |
N/A | 0.307 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.168 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | F | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 152 | 152 | 0 | 0 | 0 | 0 | 0 | 0 | 42 | 0 |
| N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.28 | 0.00 |
| time (sec) |
N/A | 0.355 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.179 | 0.000 |