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 | A | F(-2) | B | F | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 272 | 272 | 438 | 330 | 0 | 1343 | 0 | 384 | 6677 |
| N.S. |
1 | 1.00 | 1.61 | 1.21 | 0.00 | 4.94 | 0.00 | 1.41 | 24.55 |
| time (sec) |
N/A | 0.996 | 6.972 | 0.756 | 0.000 | 11.636 | 0.000 | 0.342 | 28.305 |
| 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 | 164 | 164 | 240 | 245 | 0 | 1114 | 0 | 404 | 5436 |
| N.S. |
1 | 1.00 | 1.46 | 1.49 | 0.00 | 6.79 | 0.00 | 2.46 | 33.15 |
| time (sec) |
N/A | 0.683 | 4.088 | 0.553 | 0.000 | 7.358 | 0.000 | 0.327 | 26.216 |
| 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 | 131 | 131 | 191 | 185 | 0 | 694 | 0 | 229 | 3751 |
| N.S. |
1 | 1.00 | 1.46 | 1.41 | 0.00 | 5.30 | 0.00 | 1.75 | 28.63 |
| time (sec) |
N/A | 0.394 | 0.860 | 0.398 | 0.000 | 2.256 | 0.000 | 0.324 | 24.720 |
| 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 | 100 | 100 | 97 | 132 | 0 | 389 | 0 | 174 | 106 |
| N.S. |
1 | 1.00 | 0.97 | 1.32 | 0.00 | 3.89 | 0.00 | 1.74 | 1.06 |
| time (sec) |
N/A | 0.159 | 0.381 | 0.236 | 0.000 | 0.279 | 0.000 | 0.300 | 17.306 |
| 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 | 124 | 124 | 119 | 168 | 0 | 561 | 0 | 201 | 3763 |
| N.S. |
1 | 1.00 | 0.96 | 1.35 | 0.00 | 4.52 | 0.00 | 1.62 | 30.35 |
| time (sec) |
N/A | 0.325 | 0.789 | 0.298 | 0.000 | 0.307 | 0.000 | 0.319 | 25.186 |
| 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 | 180 | 180 | 147 | 213 | 0 | 788 | 0 | 1107 | 3264 |
| N.S. |
1 | 1.00 | 0.82 | 1.18 | 0.00 | 4.38 | 0.00 | 6.15 | 18.13 |
| time (sec) |
N/A | 0.751 | 1.192 | 0.463 | 0.000 | 0.310 | 0.000 | 0.427 | 22.248 |
| 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 | 261 | 261 | 184 | 270 | 0 | 970 | 0 | 340 | 6730 |
| N.S. |
1 | 1.00 | 0.70 | 1.03 | 0.00 | 3.72 | 0.00 | 1.30 | 25.79 |
| time (sec) |
N/A | 1.075 | 1.529 | 0.601 | 0.000 | 0.328 | 0.000 | 0.330 | 26.792 |
| 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 | 289 | 289 | 418 | 380 | 0 | 2111 | 0 | 581 | 9286 |
| N.S. |
1 | 1.00 | 1.45 | 1.31 | 0.00 | 7.30 | 0.00 | 2.01 | 32.13 |
| time (sec) |
N/A | 1.612 | 7.026 | 1.062 | 0.000 | 27.361 | 0.000 | 0.409 | 30.300 |
| 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 | 220 | 220 | 270 | 305 | 0 | 1419 | 0 | 486 | 6899 |
| N.S. |
1 | 1.00 | 1.23 | 1.39 | 0.00 | 6.45 | 0.00 | 2.21 | 31.36 |
| time (sec) |
N/A | 0.858 | 1.556 | 0.693 | 0.000 | 10.231 | 0.000 | 0.379 | 27.137 |
| 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 | 180 | 180 | 157 | 238 | 0 | 750 | 0 | 400 | 251 |
| N.S. |
1 | 1.00 | 0.87 | 1.32 | 0.00 | 4.17 | 0.00 | 2.22 | 1.39 |
| time (sec) |
N/A | 0.449 | 0.635 | 0.394 | 0.000 | 0.330 | 0.000 | 0.361 | 20.645 |
| 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 | 164 | 164 | 172 | 236 | 0 | 752 | 0 | 399 | 251 |
| N.S. |
1 | 1.00 | 1.05 | 1.44 | 0.00 | 4.59 | 0.00 | 2.43 | 1.53 |
| time (sec) |
N/A | 0.322 | 1.087 | 0.361 | 0.000 | 0.319 | 0.000 | 0.352 | 20.765 |
| 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 | 205 | 205 | 203 | 287 | 0 | 1152 | 0 | 457 | 6911 |
| N.S. |
1 | 1.00 | 0.99 | 1.40 | 0.00 | 5.62 | 0.00 | 2.23 | 33.71 |
| time (sec) |
N/A | 0.664 | 1.667 | 0.445 | 0.000 | 0.353 | 0.000 | 0.374 | 27.333 |
| 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 | 290 | 290 | 232 | 347 | 0 | 1568 | 0 | 546 | 5530 |
| N.S. |
1 | 1.00 | 0.80 | 1.20 | 0.00 | 5.41 | 0.00 | 1.88 | 19.07 |
| time (sec) |
N/A | 1.701 | 2.370 | 0.804 | 0.000 | 0.365 | 0.000 | 0.379 | 25.082 |
| 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 | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 485 | 485 | 3734 | 5582 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 7.70 | 11.51 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.676 | 25.138 | 37.074 | 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 | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 397 | 397 | 3330 | 4327 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 8.39 | 10.90 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.200 | 22.564 | 26.612 | 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 | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 314 | 314 | 434 | 3107 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.38 | 9.89 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.681 | 16.532 | 17.964 | 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 | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 256 | 256 | 358 | 2194 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.40 | 8.57 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.357 | 12.659 | 12.297 | 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 | 320 | 320 | 663 | 1840 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 2.07 | 5.75 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.445 | 18.280 | 4.602 | 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 | 344 | 344 | 843 | 1856 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 2.45 | 5.40 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.555 | 14.200 | 5.408 | 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 | 429 | 429 | 1149 | 2768 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 2.68 | 6.45 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.938 | 18.247 | 4.146 | 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(-1) | F | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 573 | 573 | 4220 | 6882 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 7.36 | 12.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.313 | 30.220 | 44.842 | 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 | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 475 | 475 | 654 | 5584 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.38 | 11.76 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.374 | 22.235 | 39.269 | 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 | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 387 | 387 | 547 | 4326 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.41 | 11.18 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.060 | 17.485 | 24.451 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | F | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 312 | 312 | 456 | 3366 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.46 | 10.79 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.545 | 17.749 | 20.711 | 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 | 380 | 380 | 6017 | 2988 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 15.83 | 7.86 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.619 | 24.239 | 6.365 | 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 | 361 | 361 | 971 | 2955 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 2.69 | 8.19 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.709 | 18.786 | 6.536 | 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 | 428 | 428 | 1179 | 3286 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 2.75 | 7.68 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.025 | 20.265 | 5.328 | 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 | 520 | 520 | 1516 | 4264 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 2.92 | 8.20 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.542 | 20.012 | 6.300 | 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(-1) | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 565 | 565 | 4227 | 6884 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 7.48 | 12.18 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.022 | 26.987 | 110.835 | 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(-1) | F | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 469 | 469 | 3781 | 5584 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 8.06 | 11.91 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.430 | 24.767 | 60.366 | 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 | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 384 | 384 | 555 | 4582 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.45 | 11.93 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.796 | 19.212 | 38.802 | 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 | 442 | 442 | 7094 | 4180 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 16.05 | 9.46 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.851 | 27.272 | 10.507 | 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 | 433 | 433 | 7745 | 4119 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 17.89 | 9.51 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.897 | 28.774 | 19.829 | 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 | 450 | 450 | 1326 | 4409 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 2.95 | 9.80 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.088 | 20.235 | 53.966 | 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 | 518 | 518 | 1530 | 4781 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 2.95 | 9.23 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.560 | 20.357 | 169.179 | 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 | 617 | 617 | 5172 | 5805 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 8.38 | 9.41 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.027 | 22.635 | 506.523 | 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 | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 411 | 411 | 3426 | 4328 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 8.34 | 10.53 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.241 | 23.933 | 33.594 | 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 | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 329 | 329 | 453 | 3111 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.38 | 9.46 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.786 | 17.848 | 22.515 | 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 | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 261 | 261 | 335 | 1945 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.28 | 7.45 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.494 | 13.338 | 12.728 | 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 | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 210 | 210 | 312 | 931 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.49 | 4.43 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.199 | 13.040 | 10.119 | 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 | 208 | 208 | 145 | 182 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.70 | 0.88 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.239 | 3.778 | 3.891 | 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 | 348 | 348 | 418 | 1351 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.20 | 3.88 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.593 | 13.279 | 5.104 | 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(-1) | F | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 471 | 471 | 3953 | 5461 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 8.39 | 11.59 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.517 | 23.511 | 22.523 | 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(-1) | F | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 329 | 329 | 527 | 4221 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.60 | 12.83 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.988 | 20.798 | 20.083 | 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(-1) | F | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 275 | 275 | 466 | 3042 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.69 | 11.06 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.611 | 15.558 | 11.832 | 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 | 254 | 254 | 324 | 2190 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.28 | 8.62 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.357 | 16.936 | 8.612 | 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 | 376 | 376 | 1092 | 2987 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 2.90 | 7.94 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.599 | 13.735 | 4.382 | 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 | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 427 | 427 | 1597 | 3865 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 3.74 | 9.05 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.939 | 17.237 | 6.036 | 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(-1) | F | F | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 509 | 509 | 4342 | 9479 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 8.53 | 18.62 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.795 | 25.293 | 20.989 | 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(-1) | F | F | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 417 | 417 | 3920 | 7755 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 9.40 | 18.60 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.179 | 25.891 | 19.506 | 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(-1) | F | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 387 | 387 | 3514 | 6307 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 9.08 | 16.30 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.836 | 22.995 | 12.109 | 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(-1) | F | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 353 | 353 | 559 | 5262 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.58 | 14.91 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.651 | 18.434 | 11.622 | 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 | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 495 | 495 | 1545 | 7241 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 3.12 | 14.63 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.027 | 18.818 | 5.337 | 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(-1) | F | F | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 446 | 446 | 723 | 9224 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.62 | 20.68 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.950 | 22.174 | 17.391 | 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(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 101 | 101 | 76 | 217 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.75 | 2.15 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.331 | 2.440 | 1.578 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | C | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 138 | 138 | 91 | 253 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.66 | 1.83 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.593 | 0.908 | 6.779 | 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 | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 229 | 229 | 21744 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 94.95 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.332 | 30.155 | 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 | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 229 | 229 | 21684 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 94.69 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.300 | 26.975 | 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 | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 226 | 226 | 12792 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 56.60 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.298 | 55.944 | 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 | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 226 | 226 | 7106 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 31.44 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.273 | 50.984 | 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 | A | A | A | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 165 | 165 | 124 | 159 | 266 | 182 | 0 | 473 | 301 |
| N.S. |
1 | 1.00 | 0.75 | 0.96 | 1.61 | 1.10 | 0.00 | 2.87 | 1.82 |
| time (sec) |
N/A | 0.261 | 0.929 | 1.166 | 0.238 | 0.285 | 0.000 | 0.326 | 20.283 |
| 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 | 137 | 137 | 100 | 136 | 218 | 158 | 0 | 428 | 260 |
| N.S. |
1 | 1.00 | 0.73 | 0.99 | 1.59 | 1.15 | 0.00 | 3.12 | 1.90 |
| time (sec) |
N/A | 0.254 | 0.481 | 1.142 | 0.243 | 0.281 | 0.000 | 0.314 | 20.031 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 101 | 101 | 75 | 106 | 155 | 128 | 0 | 261 | 190 |
| N.S. |
1 | 1.00 | 0.74 | 1.05 | 1.53 | 1.27 | 0.00 | 2.58 | 1.88 |
| time (sec) |
N/A | 0.154 | 0.283 | 0.842 | 0.237 | 0.269 | 0.000 | 0.325 | 19.826 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 69 | 69 | 92 | 85 | 116 | 118 | 0 | 170 | 164 |
| N.S. |
1 | 1.00 | 1.33 | 1.23 | 1.68 | 1.71 | 0.00 | 2.46 | 2.38 |
| time (sec) |
N/A | 0.086 | 0.013 | 0.650 | 0.235 | 0.268 | 0.000 | 0.315 | 17.242 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 52 | 52 | 71 | 74 | 92 | 101 | 0 | 134 | 153 |
| N.S. |
1 | 1.00 | 1.37 | 1.42 | 1.77 | 1.94 | 0.00 | 2.58 | 2.94 |
| time (sec) |
N/A | 0.134 | 0.012 | 0.471 | 0.224 | 0.290 | 0.000 | 0.296 | 16.588 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 69 | 69 | 68 | 82 | 89 | 73 | 0 | 159 | 156 |
| N.S. |
1 | 1.00 | 0.99 | 1.19 | 1.29 | 1.06 | 0.00 | 2.30 | 2.26 |
| time (sec) |
N/A | 0.177 | 0.098 | 0.260 | 0.235 | 0.265 | 0.000 | 0.303 | 16.410 |
| 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 | 92 | 92 | 85 | 74 | 98 | 70 | 0 | 227 | 100 |
| N.S. |
1 | 1.00 | 0.92 | 0.80 | 1.07 | 0.76 | 0.00 | 2.47 | 1.09 |
| time (sec) |
N/A | 0.206 | 0.126 | 0.419 | 0.229 | 0.259 | 0.000 | 0.296 | 16.643 |
| 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 | 116 | 116 | 117 | 93 | 132 | 97 | 0 | 392 | 150 |
| N.S. |
1 | 1.00 | 1.01 | 0.80 | 1.14 | 0.84 | 0.00 | 3.38 | 1.29 |
| time (sec) |
N/A | 0.255 | 0.215 | 0.583 | 0.217 | 0.268 | 0.000 | 0.300 | 16.388 |
| 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 | 156 | 156 | 117 | 120 | 166 | 121 | 0 | 437 | 258 |
| N.S. |
1 | 1.00 | 0.75 | 0.77 | 1.06 | 0.78 | 0.00 | 2.80 | 1.65 |
| time (sec) |
N/A | 0.263 | 0.356 | 0.786 | 0.238 | 0.267 | 0.000 | 0.308 | 20.393 |
| 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 | 233 | 281 | 178 | 197 | 357 | 243 | 0 | 766 | 455 |
| N.S. |
1 | 1.21 | 0.76 | 0.85 | 1.53 | 1.04 | 0.00 | 3.29 | 1.95 |
| time (sec) |
N/A | 0.660 | 3.641 | 1.382 | 0.246 | 0.276 | 0.000 | 0.340 | 19.834 |
| 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 | 200 | 200 | 138 | 182 | 306 | 209 | 0 | 630 | 389 |
| N.S. |
1 | 1.00 | 0.69 | 0.91 | 1.53 | 1.04 | 0.00 | 3.15 | 1.94 |
| time (sec) |
N/A | 0.403 | 2.049 | 1.230 | 0.223 | 0.282 | 0.000 | 0.328 | 20.043 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 134 | 134 | 108 | 136 | 207 | 179 | 0 | 364 | 512 |
| N.S. |
1 | 1.00 | 0.81 | 1.01 | 1.54 | 1.34 | 0.00 | 2.72 | 3.82 |
| time (sec) |
N/A | 0.205 | 1.738 | 0.922 | 0.228 | 0.281 | 0.000 | 0.333 | 18.161 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | A | A | A | F | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 126 | 126 | 453 | 152 | 189 | 165 | 0 | 241 | 257 |
| N.S. |
1 | 1.00 | 3.60 | 1.21 | 1.50 | 1.31 | 0.00 | 1.91 | 2.04 |
| time (sec) |
N/A | 0.237 | 4.666 | 0.761 | 0.217 | 0.291 | 0.000 | 0.317 | 18.025 |
| 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 | 118 | 118 | 153 | 134 | 148 | 147 | 0 | 229 | 274 |
| N.S. |
1 | 1.00 | 1.30 | 1.14 | 1.25 | 1.25 | 0.00 | 1.94 | 2.32 |
| time (sec) |
N/A | 0.362 | 3.070 | 0.648 | 0.220 | 0.289 | 0.000 | 0.326 | 17.340 |
| 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 | 141 | 141 | 157 | 133 | 157 | 127 | 0 | 346 | 263 |
| N.S. |
1 | 1.00 | 1.11 | 0.94 | 1.11 | 0.90 | 0.00 | 2.45 | 1.87 |
| time (sec) |
N/A | 0.432 | 1.915 | 0.517 | 0.222 | 0.305 | 0.000 | 0.314 | 16.903 |
| 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 | 175 | 175 | 134 | 132 | 187 | 134 | 0 | 577 | 214 |
| N.S. |
1 | 1.00 | 0.77 | 0.75 | 1.07 | 0.77 | 0.00 | 3.30 | 1.22 |
| time (sec) |
N/A | 0.529 | 2.286 | 0.625 | 0.239 | 0.291 | 0.000 | 0.314 | 16.570 |
| 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 | 215 | 215 | 169 | 167 | 233 | 171 | 0 | 720 | 256 |
| N.S. |
1 | 1.00 | 0.79 | 0.78 | 1.08 | 0.80 | 0.00 | 3.35 | 1.19 |
| time (sec) |
N/A | 0.574 | 1.811 | 0.849 | 0.250 | 0.279 | 0.000 | 0.333 | 17.076 |
| 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 | 381 | 381 | 328 | 283 | 565 | 342 | 0 | 1370 | 769 |
| N.S. |
1 | 1.00 | 0.86 | 0.74 | 1.48 | 0.90 | 0.00 | 3.60 | 2.02 |
| time (sec) |
N/A | 0.947 | 11.189 | 1.725 | 0.237 | 0.302 | 0.000 | 0.397 | 18.684 |
| 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 | 286 | 286 | 206 | 243 | 445 | 292 | 0 | 989 | 601 |
| N.S. |
1 | 1.00 | 0.72 | 0.85 | 1.56 | 1.02 | 0.00 | 3.46 | 2.10 |
| time (sec) |
N/A | 0.673 | 5.780 | 1.396 | 0.242 | 0.291 | 0.000 | 0.372 | 19.041 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 207 | 207 | 168 | 212 | 358 | 257 | 0 | 759 | 3210 |
| N.S. |
1 | 1.00 | 0.81 | 1.02 | 1.73 | 1.24 | 0.00 | 3.67 | 15.51 |
| time (sec) |
N/A | 0.363 | 2.957 | 1.367 | 0.244 | 0.301 | 0.000 | 0.383 | 19.993 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | A | A | A | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 192 | 192 | 509 | 235 | 280 | 225 | 0 | 438 | 2437 |
| N.S. |
1 | 1.00 | 2.65 | 1.22 | 1.46 | 1.17 | 0.00 | 2.28 | 12.69 |
| time (sec) |
N/A | 0.411 | 9.469 | 1.060 | 0.243 | 0.284 | 0.000 | 0.375 | 19.070 |
| 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 | 204 | 204 | 320 | 212 | 243 | 208 | 0 | 540 | 3879 |
| N.S. |
1 | 1.00 | 1.57 | 1.04 | 1.19 | 1.02 | 0.00 | 2.65 | 19.01 |
| time (sec) |
N/A | 0.496 | 5.273 | 0.875 | 0.232 | 0.285 | 0.000 | 0.349 | 19.403 |
| 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 | 196 | 196 | 263 | 206 | 216 | 201 | 0 | 418 | 2470 |
| N.S. |
1 | 1.00 | 1.34 | 1.05 | 1.10 | 1.03 | 0.00 | 2.13 | 12.60 |
| time (sec) |
N/A | 0.670 | 3.213 | 0.886 | 0.222 | 0.293 | 0.000 | 0.353 | 19.085 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F(-1) | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 223 | 223 | 215 | 189 | 246 | 189 | 0 | 723 | 3250 |
| N.S. |
1 | 1.00 | 0.96 | 0.85 | 1.10 | 0.85 | 0.00 | 3.24 | 14.57 |
| time (sec) |
N/A | 0.717 | 2.309 | 0.897 | 0.237 | 0.292 | 0.000 | 0.368 | 19.847 |
| 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 | 269 | 269 | 288 | 203 | 288 | 207 | 0 | 926 | 359 |
| N.S. |
1 | 1.00 | 1.07 | 0.75 | 1.07 | 0.77 | 0.00 | 3.44 | 1.33 |
| time (sec) |
N/A | 0.849 | 2.776 | 0.822 | 0.242 | 0.288 | 0.000 | 0.347 | 17.735 |
| 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 | 320 | 320 | 369 | 244 | 360 | 256 | 0 | 1307 | 471 |
| N.S. |
1 | 1.00 | 1.15 | 0.76 | 1.12 | 0.80 | 0.00 | 4.08 | 1.47 |
| time (sec) |
N/A | 0.989 | 1.994 | 0.988 | 0.255 | 0.303 | 0.000 | 0.368 | 18.720 |
| 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 | 491 | 491 | 458 | 354 | 746 | 450 | 0 | 1888 | 1044 |
| N.S. |
1 | 1.00 | 0.93 | 0.72 | 1.52 | 0.92 | 0.00 | 3.85 | 2.13 |
| time (sec) |
N/A | 1.400 | 11.303 | 2.194 | 0.262 | 0.323 | 0.000 | 0.415 | 20.338 |
| 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 | 384 | 384 | 406 | 329 | 653 | 391 | 0 | 1658 | 942 |
| N.S. |
1 | 1.00 | 1.06 | 0.86 | 1.70 | 1.02 | 0.00 | 4.32 | 2.45 |
| time (sec) |
N/A | 1.047 | 11.200 | 1.975 | 0.256 | 0.321 | 0.000 | 0.415 | 19.124 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 290 | 290 | 232 | 273 | 497 | 340 | 0 | 1140 | 4068 |
| N.S. |
1 | 1.00 | 0.80 | 0.94 | 1.71 | 1.17 | 0.00 | 3.93 | 14.03 |
| time (sec) |
N/A | 0.647 | 6.303 | 1.702 | 0.236 | 0.311 | 0.000 | 0.394 | 20.101 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | A | A | A | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 273 | 273 | 813 | 355 | 431 | 302 | 0 | 840 | 4710 |
| N.S. |
1 | 1.00 | 2.98 | 1.30 | 1.58 | 1.11 | 0.00 | 3.08 | 17.25 |
| time (sec) |
N/A | 0.660 | 15.336 | 1.498 | 0.239 | 0.331 | 0.000 | 0.383 | 21.145 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F(-1) | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 274 | 274 | 348 | 295 | 335 | 269 | 0 | 550 | 4849 |
| N.S. |
1 | 1.00 | 1.27 | 1.08 | 1.22 | 0.98 | 0.00 | 2.01 | 17.70 |
| time (sec) |
N/A | 0.765 | 7.504 | 1.301 | 0.237 | 0.295 | 0.000 | 0.393 | 21.251 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F(-1) | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 303 | 303 | 370 | 284 | 311 | 262 | 0 | 543 | 4839 |
| N.S. |
1 | 1.00 | 1.22 | 0.94 | 1.03 | 0.86 | 0.00 | 1.79 | 15.97 |
| time (sec) |
N/A | 0.942 | 8.263 | 1.181 | 0.228 | 0.300 | 0.000 | 0.385 | 20.949 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F(-1) | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 293 | 293 | 382 | 287 | 305 | 263 | 0 | 802 | 4781 |
| N.S. |
1 | 1.00 | 1.30 | 0.98 | 1.04 | 0.90 | 0.00 | 2.74 | 16.32 |
| time (sec) |
N/A | 1.072 | 6.852 | 1.055 | 0.229 | 0.308 | 0.000 | 0.388 | 21.338 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F(-1) | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 314 | 314 | 382 | 258 | 347 | 262 | 0 | 1094 | 4118 |
| N.S. |
1 | 1.00 | 1.22 | 0.82 | 1.11 | 0.83 | 0.00 | 3.48 | 13.11 |
| time (sec) |
N/A | 1.169 | 2.995 | 1.002 | 0.242 | 0.326 | 0.000 | 0.389 | 20.418 |
| 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 | 372 | 372 | 432 | 278 | 415 | 292 | 0 | 1578 | 534 |
| N.S. |
1 | 1.00 | 1.16 | 0.75 | 1.12 | 0.78 | 0.00 | 4.24 | 1.44 |
| time (sec) |
N/A | 1.366 | 3.862 | 1.022 | 0.234 | 0.281 | 0.000 | 0.375 | 20.375 |
| 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 | 438 | 438 | 528 | 335 | 498 | 354 | 0 | 1815 | 675 |
| N.S. |
1 | 1.00 | 1.21 | 0.76 | 1.14 | 0.81 | 0.00 | 4.14 | 1.54 |
| time (sec) |
N/A | 1.576 | 3.581 | 1.344 | 0.243 | 0.322 | 0.000 | 0.397 | 21.867 |
| 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 | 214 | 214 | 170 | 219 | 320 | 268 | 0 | 658 | 3157 |
| N.S. |
1 | 1.00 | 0.79 | 1.02 | 1.50 | 1.25 | 0.00 | 3.07 | 14.75 |
| time (sec) |
N/A | 0.550 | 1.710 | 1.365 | 0.229 | 0.291 | 0.000 | 0.364 | 20.509 |
| 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 | 149 | 149 | 114 | 141 | 204 | 199 | 0 | 301 | 576 |
| N.S. |
1 | 1.00 | 0.77 | 0.95 | 1.37 | 1.34 | 0.00 | 2.02 | 3.87 |
| time (sec) |
N/A | 0.349 | 1.345 | 0.926 | 0.234 | 0.285 | 0.000 | 0.330 | 19.613 |
| 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 | 97 | 97 | 77 | 109 | 142 | 154 | 0 | 213 | 221 |
| N.S. |
1 | 1.00 | 0.79 | 1.12 | 1.46 | 1.59 | 0.00 | 2.20 | 2.28 |
| time (sec) |
N/A | 0.195 | 0.678 | 0.682 | 0.227 | 0.267 | 0.000 | 0.300 | 18.779 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F(-2) | A | F | B | B |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 215 | 215 | 512 | 369 | 0 | 817 | 0 | 483 | 7016 |
| N.S. |
1 | 1.00 | 2.38 | 1.72 | 0.00 | 3.80 | 0.00 | 2.25 | 32.63 |
| time (sec) |
N/A | 0.853 | 4.236 | 0.575 | 0.000 | 12.791 | 0.000 | 0.345 | 26.263 |