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 | C | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
| size | 234 | 262 | 157 | 1731 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.12 | 0.67 | 7.40 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.780 | 0.308 | 77.723 | 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 | 374 | 532 | 243 | 531 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.42 | 0.65 | 1.42 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 4.177 | 0.551 | 96.556 | 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 | F | F | F(-1) |
| verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
| size | 332 | 580 | 195 | 4175 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.75 | 0.59 | 12.58 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 6.077 | 1.511 | 233.768 | 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 | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 212 | 261 | 105 | 123 | 289 | 117 | 0 | 0 | 205 |
| N.S. |
1 | 1.23 | 0.50 | 0.58 | 1.36 | 0.55 | 0.00 | 0.00 | 0.97 |
| time (sec) |
N/A | 0.721 | 0.205 | 1.392 | 0.319 | 0.234 | 0.000 | 0.000 | 0.657 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 237 | 410 | 111 | 145 | 334 | 130 | 0 | 0 | 188 |
| N.S. |
1 | 1.73 | 0.47 | 0.61 | 1.41 | 0.55 | 0.00 | 0.00 | 0.79 |
| time (sec) |
N/A | 1.487 | 0.077 | 1.299 | 0.353 | 0.248 | 0.000 | 0.000 | 0.600 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 208 | 237 | 103 | 123 | 272 | 117 | 0 | 0 | 189 |
| N.S. |
1 | 1.14 | 0.50 | 0.59 | 1.31 | 0.56 | 0.00 | 0.00 | 0.91 |
| time (sec) |
N/A | 0.617 | 0.078 | 1.347 | 0.332 | 0.251 | 0.000 | 0.000 | 0.611 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 225 | 284 | 114 | 153 | 335 | 132 | 0 | 0 | 199 |
| N.S. |
1 | 1.26 | 0.51 | 0.68 | 1.49 | 0.59 | 0.00 | 0.00 | 0.88 |
| time (sec) |
N/A | 0.934 | 0.115 | 1.397 | 0.347 | 0.255 | 0.000 | 0.000 | 0.596 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | C | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
| size | 332 | 515 | 208 | 1841 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.55 | 0.63 | 5.55 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 3.195 | 0.238 | 93.257 | 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 | F | F | F(-1) |
| verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
| size | 332 | 539 | 232 | 1799 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.62 | 0.70 | 5.42 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 4.123 | 0.430 | 82.408 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | F | A | A | F | F | F | F | F(-1) |
| verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 478 | 0 | 295 | 579 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.00 | 0.62 | 1.21 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.000 | 0.811 | 95.914 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | F | A | C | F(-1) | F | F | F | F(-1) |
| verified |
N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD |
| size | 432 | 0 | 302 | 2062 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.00 | 0.70 | 4.77 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.000 | 1.155 | 136.483 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | F | A | A | F | F | F | F(-2) | F(-1) |
| verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 523 | 0 | 262 | 417 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.00 | 0.50 | 0.80 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.000 | 1.015 | 4.347 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | A | F | F | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 747 | 1306 | 1844 | 460 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.75 | 2.47 | 0.62 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 9.631 | 12.232 | 4.585 | 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(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 373 | 264 | 206 | 370 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.71 | 0.55 | 0.99 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.038 | 0.612 | 3.947 | 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(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 626 | 400 | 258 | 422 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.64 | 0.41 | 0.67 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.362 | 0.636 | 4.336 | 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(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 600 | 357 | 366 | 454 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.60 | 0.61 | 0.76 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.712 | 0.556 | 5.573 | 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(-2) | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 622 | 360 | 768 | 466 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.58 | 1.23 | 0.75 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.544 | 2.666 | 5.532 | 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(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 602 | 560 | 345 | 404 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.93 | 0.57 | 0.67 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 3.458 | 4.155 | 4.326 | 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(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 361 | 387 | 341 | 315 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.07 | 0.94 | 0.87 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 3.167 | 2.933 | 3.849 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | F | A | A | F | F | F | F(-2) | F(-1) |
| verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 652 | 0 | 538 | 469 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.00 | 0.83 | 0.72 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.000 | 2.780 | 4.035 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | F | B | A | F | F | F | F | F(-1) |
| verified |
N/A | N/A | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 882 | 0 | 4015 | 514 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.00 | 4.55 | 0.58 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.000 | 18.474 | 4.096 | 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(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 477 | 382 | 441 | 421 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.80 | 0.92 | 0.88 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.444 | 2.702 | 3.632 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | A | F | F | F | F(-2) | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 760 | 652 | 2105 | 466 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.86 | 2.77 | 0.61 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.304 | 12.727 | 3.747 | 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(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 726 | 629 | 555 | 511 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.87 | 0.76 | 0.70 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 5.837 | 1.215 | 4.733 | 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(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 901 | 768 | 1387 | 602 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.85 | 1.54 | 0.67 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 5.792 | 5.128 | 5.080 | 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(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 919 | 925 | 691 | 592 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.01 | 0.75 | 0.64 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 8.374 | 6.825 | 5.247 | 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(-2) | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 788 | 755 | 1508 | 557 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.96 | 1.91 | 0.71 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 7.700 | 9.605 | 4.726 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | F | A | A | F | F | F | F(-2) | F(-1) |
| verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 798 | 0 | 850 | 525 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.00 | 1.07 | 0.66 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.000 | 5.372 | 19.268 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | F | B | A | F | F | F | F | F(-1) |
| verified |
N/A | N/A | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 1019 | 0 | 6517 | 566 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.00 | 6.40 | 0.56 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.000 | 24.694 | 12.628 | 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(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 561 | 523 | 718 | 477 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.93 | 1.28 | 0.85 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.954 | 4.535 | 8.267 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | A | F | F | F | F(-2) | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 870 | 954 | 4281 | 518 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.10 | 4.92 | 0.60 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 3.642 | 18.945 | 6.195 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | F | A | A | F | F | F | F(-2) | F(-1) |
| verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 845 | 0 | 723 | 562 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.00 | 0.86 | 0.67 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.000 | 5.863 | 7.490 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | F | B | A | F | F | F | F(-2) | F(-1) |
| verified |
N/A | N/A | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 1027 | 0 | 3267 | 655 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.00 | 3.18 | 0.64 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.000 | 15.009 | 7.823 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | F | A | A | F | F | F | F(-2) | F(-1) |
| verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 1043 | 0 | 934 | 660 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.00 | 0.90 | 0.63 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.000 | 9.018 | 7.424 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | F | A | A | F | F | F | F(-2) | F(-1) |
| verified |
N/A | N/A | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 1061 | 0 | 1771 | 694 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.00 | 1.67 | 0.65 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.000 | 10.259 | 7.499 | 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(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 408 | 460 | 220 | 382 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.13 | 0.54 | 0.94 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 3.207 | 0.785 | 3.972 | 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 | 625 | 415 | 812 | 428 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.66 | 1.30 | 0.68 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.904 | 5.657 | 3.890 | 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 | 283 | 172 | 168 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.61 | 0.59 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.728 | 0.312 | 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 | 368 | 201 | 190 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.55 | 0.52 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.696 | 0.135 | 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 | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 327 | 178 | 208 | 261 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.54 | 0.64 | 0.80 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.773 | 0.279 | 4.419 | 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 | 260 | 157 | 174 | 230 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.60 | 0.67 | 0.88 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.847 | 0.414 | 4.268 | 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 | 597 | 375 | 345 | 410 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.63 | 0.58 | 0.69 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.866 | 3.111 | 4.351 | 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 | 396 | 418 | 343 | 324 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.06 | 0.87 | 0.82 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 3.399 | 4.919 | 4.206 | 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(-2) | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 403 | 291 | 308 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.72 | 0.76 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.554 | 0.764 | 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 | 495 | 311 | 639 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.63 | 1.29 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.450 | 1.204 | 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 | C | A | A | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 107 | 106 | 61 | 134 | 98 | 62 | 0 | 0 | 0 |
| N.S. |
1 | 0.99 | 0.57 | 1.25 | 0.92 | 0.58 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.361 | 0.115 | 2.627 | 0.604 | 0.249 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | C | A | A | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 100 | 101 | 56 | 132 | 99 | 58 | 0 | 0 | 0 |
| N.S. |
1 | 1.01 | 0.56 | 1.32 | 0.99 | 0.58 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.307 | 0.076 | 2.665 | 0.509 | 0.261 | 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 | 443 | 293 | 295 | 388 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.66 | 0.67 | 0.88 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.661 | 0.422 | 3.828 | 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 | 377 | 268 | 301 | 356 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.71 | 0.80 | 0.94 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.623 | 1.302 | 3.633 | 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(-2) | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 534 | 609 | 367 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.14 | 0.69 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 4.189 | 1.929 | 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 | 622 | 563 | 691 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.91 | 1.11 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 3.657 | 2.253 | 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 | C | F | A | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 237 | 305 | 104 | 312 | 0 | 113 | 0 | 0 | 0 |
| N.S. |
1 | 1.29 | 0.44 | 1.32 | 0.00 | 0.48 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.114 | 0.151 | 5.302 | 0.000 | 0.274 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | C | F | A | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 199 | 239 | 95 | 308 | 0 | 106 | 0 | 0 | 0 |
| N.S. |
1 | 1.20 | 0.48 | 1.55 | 0.00 | 0.53 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.847 | 0.118 | 4.792 | 0.000 | 0.267 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | C | F | A | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 199 | 220 | 91 | 312 | 0 | 103 | 0 | 0 | 0 |
| N.S. |
1 | 1.11 | 0.46 | 1.57 | 0.00 | 0.52 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.528 | 0.100 | 2.458 | 0.000 | 0.252 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | C | F | A | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 215 | 274 | 104 | 308 | 0 | 111 | 0 | 0 | 0 |
| N.S. |
1 | 1.27 | 0.48 | 1.43 | 0.00 | 0.52 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.816 | 0.088 | 4.166 | 0.000 | 0.254 | 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 | 553 | 523 | 347 | 560 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.95 | 0.63 | 1.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 3.372 | 0.679 | 4.061 | 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 | 493 | 552 | 399 | 528 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.12 | 0.81 | 1.07 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 3.991 | 1.968 | 3.768 | 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 | 22 | 22 | 24 | 22 | 952 | 37 | 53 | 3 | 24 |
| N.S. |
1 | 1.00 | 1.09 | 1.00 | 43.27 | 1.68 | 2.41 | 0.14 | 1.09 |
| time (sec) |
N/A | 0.213 | 1.523 | 3.824 | 13.156 | 0.258 | 28.468 | 149.213 | 0.468 |
| 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 | 20 | 20 | 22 | 20 | 435 | 22 | 31 | 3 | 22 |
| N.S. |
1 | 1.00 | 1.10 | 1.00 | 21.75 | 1.10 | 1.55 | 0.15 | 1.10 |
| time (sec) |
N/A | 0.192 | 0.736 | 3.265 | 6.271 | 0.241 | 12.472 | 145.872 | 0.464 |
| 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 | 22 | 22 | 24 | 22 | 24 | 24 | 20 | 3 | 24 |
| N.S. |
1 | 1.00 | 1.09 | 1.00 | 1.09 | 1.09 | 0.91 | 0.14 | 1.09 |
| time (sec) |
N/A | 0.221 | 0.950 | 1.847 | 0.586 | 0.250 | 3.133 | 136.658 | 0.401 |
| 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 | 22 | 22 | 24 | 22 | 24 | 39 | 31 | 3 | 24 |
| N.S. |
1 | 1.00 | 1.09 | 1.00 | 1.09 | 1.77 | 1.41 | 0.14 | 1.09 |
| time (sec) |
N/A | 0.221 | 0.645 | 4.655 | 0.607 | 0.244 | 4.312 | 159.301 | 0.425 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | F(-2) | N/A |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 24 | 24 | 26 | 22 | 24 | 24 | 0 | 0 | 24 |
| N.S. |
1 | 1.00 | 1.08 | 0.92 | 1.00 | 1.00 | 0.00 | 0.00 | 1.00 |
| time (sec) |
N/A | 0.259 | 1.155 | 4.275 | 0.692 | 0.249 | 0.000 | 0.000 | 0.527 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | F(-2) | N/A |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 24 | 24 | 26 | 22 | 24 | 24 | 24 | 0 | 24 |
| N.S. |
1 | 1.00 | 1.08 | 0.92 | 1.00 | 1.00 | 1.00 | 0.00 | 1.00 |
| time (sec) |
N/A | 0.246 | 0.162 | 3.660 | 0.464 | 0.236 | 71.719 | 0.000 | 0.458 |
| 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 | 24 | 24 | 26 | 22 | 24 | 24 | 24 | 3 | 24 |
| N.S. |
1 | 1.00 | 1.08 | 0.92 | 1.00 | 1.00 | 1.00 | 0.12 | 1.00 |
| time (sec) |
N/A | 0.252 | 0.668 | 3.778 | 0.443 | 0.249 | 49.953 | 59.756 | 0.507 |
| 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 | 24 | 24 | 26 | 22 | 24 | 51 | 24 | 3 | 24 |
| N.S. |
1 | 1.00 | 1.08 | 0.92 | 1.00 | 2.12 | 1.00 | 0.12 | 1.00 |
| time (sec) |
N/A | 0.268 | 0.812 | 3.869 | 0.478 | 0.261 | 59.521 | 4.246 | 0.603 |
| 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 | 18 | 18 | 20 | 18 | 20 | 21 | 22 | 3 | 20 |
| N.S. |
1 | 1.00 | 1.11 | 1.00 | 1.11 | 1.17 | 1.22 | 0.17 | 1.11 |
| time (sec) |
N/A | 0.184 | 0.388 | 13.419 | 0.293 | 0.269 | 0.690 | 30.612 | 0.461 |
| 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 | 17 | 17 | 19 | 17 | 19 | 19 | 22 | 3 | 19 |
| N.S. |
1 | 1.00 | 1.12 | 1.00 | 1.12 | 1.12 | 1.29 | 0.18 | 1.12 |
| time (sec) |
N/A | 0.174 | 0.350 | 13.406 | 0.299 | 0.250 | 0.614 | 28.823 | 0.443 |
| 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 | 20 | 20 | 22 | 20 | 22 | 22 | 22 | 3 | 22 |
| N.S. |
1 | 1.00 | 1.10 | 1.00 | 1.10 | 1.10 | 1.10 | 0.15 | 1.10 |
| time (sec) |
N/A | 0.191 | 0.568 | 8.867 | 0.271 | 0.230 | 0.922 | 30.286 | 0.438 |
| 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 | 20 | 20 | 22 | 20 | 22 | 36 | 39 | 3 | 22 |
| N.S. |
1 | 1.00 | 1.10 | 1.00 | 1.10 | 1.80 | 1.95 | 0.15 | 1.10 |
| time (sec) |
N/A | 0.196 | 0.477 | 13.138 | 0.299 | 0.246 | 1.340 | 36.116 | 0.414 |
| 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 | 19 | 19 | 21 | 19 | 21 | 34 | 39 | 3 | 21 |
| N.S. |
1 | 1.00 | 1.11 | 1.00 | 1.11 | 1.79 | 2.05 | 0.16 | 1.11 |
| time (sec) |
N/A | 0.181 | 0.375 | 28.274 | 0.289 | 0.245 | 0.982 | 33.645 | 0.418 |
| 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 | 22 | 22 | 24 | 22 | 24 | 37 | 39 | 3 | 24 |
| N.S. |
1 | 1.00 | 1.09 | 1.00 | 1.09 | 1.68 | 1.77 | 0.14 | 1.09 |
| time (sec) |
N/A | 0.205 | 0.666 | 43.575 | 0.293 | 0.241 | 2.187 | 35.609 | 0.424 |
| 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 | 20 | 20 | 22 | 20 | 22 | 47 | 54 | 3 | 22 |
| N.S. |
1 | 1.00 | 1.10 | 1.00 | 1.10 | 2.35 | 2.70 | 0.15 | 1.10 |
| time (sec) |
N/A | 0.195 | 0.501 | 71.722 | 0.290 | 0.240 | 1.453 | 40.445 | 0.442 |
| 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 | 19 | 19 | 21 | 19 | 21 | 45 | 54 | 3 | 21 |
| N.S. |
1 | 1.00 | 1.11 | 1.00 | 1.11 | 2.37 | 2.84 | 0.16 | 1.11 |
| time (sec) |
N/A | 0.181 | 0.418 | 59.869 | 0.294 | 0.248 | 1.348 | 39.037 | 0.450 |
| 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 | 22 | 22 | 24 | 22 | 24 | 48 | 54 | 3 | 24 |
| N.S. |
1 | 1.00 | 1.09 | 1.00 | 1.09 | 2.18 | 2.45 | 0.14 | 1.09 |
| time (sec) |
N/A | 0.205 | 0.682 | 160.841 | 0.306 | 0.243 | 2.649 | 42.117 | 0.426 |
| 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 | 22 | 22 | 24 | 22 | 24 | 24 | 22 | 3 | 24 |
| N.S. |
1 | 1.00 | 1.09 | 1.00 | 1.09 | 1.09 | 1.00 | 0.14 | 1.09 |
| time (sec) |
N/A | 0.217 | 1.253 | 0.342 | 0.250 | 0.236 | 0.555 | 19.569 | 0.394 |
| 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 | 20 | 20 | 22 | 20 | 22 | 22 | 20 | 3 | 22 |
| N.S. |
1 | 1.00 | 1.10 | 1.00 | 1.10 | 1.10 | 1.00 | 0.15 | 1.10 |
| time (sec) |
N/A | 0.200 | 0.716 | 0.401 | 0.243 | 0.249 | 0.564 | 14.974 | 0.386 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | A | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 12 | 12 | 12 | 13 | 15 | 12 | 8 | 0 | 12 |
| N.S. |
1 | 1.00 | 1.00 | 1.08 | 1.25 | 1.00 | 0.67 | 0.00 | 1.00 |
| time (sec) |
N/A | 0.176 | 0.109 | 0.883 | 0.192 | 0.240 | 0.266 | 0.000 | 0.094 |
| 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 | 22 | 22 | 24 | 22 | 24 | 23 | 22 | 3 | 24 |
| N.S. |
1 | 1.00 | 1.09 | 1.00 | 1.09 | 1.05 | 1.00 | 0.14 | 1.09 |
| time (sec) |
N/A | 0.221 | 0.148 | 0.323 | 0.256 | 0.245 | 0.814 | 15.166 | 0.379 |
| 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 | 22 | 22 | 24 | 22 | 24 | 25 | 24 | 3 | 24 |
| N.S. |
1 | 1.00 | 1.09 | 1.00 | 1.09 | 1.14 | 1.09 | 0.14 | 1.09 |
| time (sec) |
N/A | 0.222 | 0.219 | 0.288 | 0.272 | 0.254 | 0.742 | 20.443 | 0.396 |
| 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 | 22 | 22 | 24 | 22 | 24 | 39 | 37 | 3 | 24 |
| N.S. |
1 | 1.00 | 1.09 | 1.00 | 1.09 | 1.77 | 1.68 | 0.14 | 1.09 |
| time (sec) |
N/A | 0.219 | 3.253 | 9.681 | 0.275 | 0.238 | 0.788 | 49.150 | 0.409 |
| 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 | 22 | 22 | 24 | 22 | 24 | 39 | 37 | 3 | 24 |
| N.S. |
1 | 1.00 | 1.09 | 1.00 | 1.09 | 1.77 | 1.68 | 0.14 | 1.09 |
| time (sec) |
N/A | 0.219 | 1.724 | 2.194 | 0.285 | 0.240 | 0.787 | 47.612 | 0.406 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 33 | 28 | 25 | 24 | 0 | 74 | 0 | 0 | 0 |
| N.S. |
1 | 0.85 | 0.76 | 0.73 | 0.00 | 2.24 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.297 | 0.088 | 2.992 | 0.000 | 0.249 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 17 | 17 | 17 | 16 | 0 | 67 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.00 | 0.94 | 0.00 | 3.94 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.291 | 0.055 | 2.696 | 0.000 | 0.240 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 33 | 28 | 23 | 22 | 0 | 70 | 0 | 0 | 0 |
| N.S. |
1 | 0.85 | 0.70 | 0.67 | 0.00 | 2.12 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.267 | 0.036 | 3.169 | 0.000 | 0.245 | 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 | 22 | 22 | 24 | 22 | 24 | 38 | 37 | 3 | 24 |
| N.S. |
1 | 1.00 | 1.09 | 1.00 | 1.09 | 1.73 | 1.68 | 0.14 | 1.09 |
| time (sec) |
N/A | 0.215 | 0.598 | 3.414 | 0.286 | 0.238 | 1.142 | 36.890 | 0.396 |
| 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 | 22 | 22 | 24 | 22 | 24 | 40 | 39 | 3 | 24 |
| N.S. |
1 | 1.00 | 1.09 | 1.00 | 1.09 | 1.82 | 1.77 | 0.14 | 1.09 |
| time (sec) |
N/A | 0.222 | 1.020 | 4.403 | 0.273 | 0.230 | 1.254 | 38.578 | 0.393 |
| 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 | 22 | 22 | 24 | 22 | 24 | 50 | 51 | 3 | 24 |
| N.S. |
1 | 1.00 | 1.09 | 1.00 | 1.09 | 2.27 | 2.32 | 0.14 | 1.09 |
| time (sec) |
N/A | 0.219 | 6.442 | 8.089 | 0.301 | 0.245 | 1.043 | 72.357 | 0.432 |
| 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 | 22 | 22 | 24 | 22 | 24 | 50 | 51 | 3 | 24 |
| N.S. |
1 | 1.00 | 1.09 | 1.00 | 1.09 | 2.27 | 2.32 | 0.14 | 1.09 |
| time (sec) |
N/A | 0.216 | 6.092 | 8.674 | 0.282 | 0.248 | 1.185 | 73.615 | 0.415 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 50 | 39 | 34 | 35 | 0 | 174 | 0 | 0 | 0 |
| N.S. |
1 | 0.78 | 0.68 | 0.70 | 0.00 | 3.48 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.321 | 0.107 | 3.513 | 0.000 | 0.252 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 35 | 30 | 27 | 26 | 0 | 171 | 0 | 0 | 0 |
| N.S. |
1 | 0.86 | 0.77 | 0.74 | 0.00 | 4.89 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.303 | 0.115 | 2.886 | 0.000 | 0.255 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 33 | 28 | 25 | 24 | 0 | 120 | 0 | 0 | 0 |
| N.S. |
1 | 0.85 | 0.76 | 0.73 | 0.00 | 3.64 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.304 | 0.073 | 3.217 | 0.000 | 0.250 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 35 | 30 | 27 | 26 | 0 | 171 | 0 | 0 | 0 |
| N.S. |
1 | 0.86 | 0.77 | 0.74 | 0.00 | 4.89 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.284 | 0.086 | 2.844 | 0.000 | 0.243 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 50 | 39 | 34 | 33 | 0 | 174 | 0 | 0 | 0 |
| N.S. |
1 | 0.78 | 0.68 | 0.66 | 0.00 | 3.48 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.285 | 0.034 | 3.376 | 0.000 | 0.261 | 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 | 22 | 22 | 24 | 22 | 24 | 49 | 51 | 3 | 24 |
| N.S. |
1 | 1.00 | 1.09 | 1.00 | 1.09 | 2.23 | 2.32 | 0.14 | 1.09 |
| time (sec) |
N/A | 0.214 | 0.746 | 4.447 | 0.254 | 0.259 | 1.624 | 49.839 | 0.403 |
| 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 | 22 | 22 | 24 | 22 | 24 | 51 | 53 | 3 | 24 |
| N.S. |
1 | 1.00 | 1.09 | 1.00 | 1.09 | 2.32 | 2.41 | 0.14 | 1.09 |
| time (sec) |
N/A | 0.223 | 1.125 | 4.130 | 0.256 | 0.234 | 1.733 | 53.322 | 0.419 |
| 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 | 22 | 22 | 24 | 20 | 22 | 22 | 20 | 3 | 22 |
| N.S. |
1 | 1.00 | 1.09 | 0.91 | 1.00 | 1.00 | 0.91 | 0.14 | 1.00 |
| time (sec) |
N/A | 0.222 | 1.957 | 5.965 | 0.322 | 0.242 | 0.734 | 33.371 | 0.358 |
| 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 | 21 | 21 | 23 | 19 | 21 | 21 | 19 | 3 | 21 |
| N.S. |
1 | 1.00 | 1.10 | 0.90 | 1.00 | 1.00 | 0.90 | 0.14 | 1.00 |
| time (sec) |
N/A | 0.193 | 0.220 | 5.789 | 0.339 | 0.241 | 0.546 | 32.143 | 0.341 |
| 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 | 24 | 24 | 26 | 22 | 24 | 24 | 20 | 3 | 24 |
| N.S. |
1 | 1.00 | 1.08 | 0.92 | 1.00 | 1.00 | 0.83 | 0.12 | 1.00 |
| time (sec) |
N/A | 0.254 | 1.290 | 14.348 | 0.349 | 0.243 | 0.899 | 34.765 | 0.353 |
| 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 | 22 | 22 | 24 | 20 | 22 | 33 | 20 | 3 | 22 |
| N.S. |
1 | 1.00 | 1.09 | 0.91 | 1.00 | 1.50 | 0.91 | 0.14 | 1.00 |
| time (sec) |
N/A | 0.233 | 2.084 | 19.100 | 0.345 | 0.236 | 4.740 | 47.165 | 0.411 |
| 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 | 21 | 21 | 23 | 19 | 21 | 21 | 19 | 3 | 21 |
| N.S. |
1 | 1.00 | 1.10 | 0.90 | 1.00 | 1.00 | 0.90 | 0.14 | 1.00 |
| time (sec) |
N/A | 0.198 | 0.277 | 18.430 | 0.345 | 0.240 | 2.966 | 43.796 | 0.410 |