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 | B | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 42 | 42 | 49 | 130 | 0 | 205 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.17 | 3.10 | 0.00 | 4.88 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.264 | 1.833 | 3.439 | 0.000 | 0.340 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | C | F | B | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 46 | 46 | 49 | 133 | 0 | 207 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.07 | 2.89 | 0.00 | 4.50 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.261 | 1.801 | 3.220 | 0.000 | 0.385 | 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 | 44 | 44 | 47 | 129 | 0 | 50 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.07 | 2.93 | 0.00 | 1.14 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.251 | 1.812 | 3.428 | 0.000 | 0.339 | 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 | 44 | 44 | 51 | 134 | 0 | 59 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.16 | 3.05 | 0.00 | 1.34 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.243 | 1.815 | 3.280 | 0.000 | 0.292 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | A | F | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 69 | 69 | 84 | 0 | 0 | 1240 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.22 | 0.00 | 0.00 | 17.97 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.347 | 7.404 | 0.000 | 0.000 | 1.068 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | B | F | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 71 | 71 | 84 | 0 | 0 | 1294 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.18 | 0.00 | 0.00 | 18.23 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.350 | 7.399 | 0.000 | 0.000 | 1.046 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | A | F | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 72 | 72 | 85 | 0 | 0 | 1245 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.18 | 0.00 | 0.00 | 17.29 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.339 | 7.339 | 0.000 | 0.000 | 1.056 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | B | F | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 72 | 72 | 87 | 0 | 0 | 1303 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.21 | 0.00 | 0.00 | 18.10 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.324 | 7.289 | 0.000 | 0.000 | 1.093 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | F | F | A | F | F(-2) | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 73 | 73 | 663 | 0 | 0 | 1273 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 9.08 | 0.00 | 0.00 | 17.44 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.352 | 10.974 | 0.000 | 0.000 | 0.720 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | F | F | B | F | F(-2) | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 75 | 75 | 648 | 0 | 0 | 1330 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 8.64 | 0.00 | 0.00 | 17.73 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.364 | 10.858 | 0.000 | 0.000 | 0.718 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | F | F | A | F | F(-2) | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 76 | 76 | 649 | 0 | 0 | 1278 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 8.54 | 0.00 | 0.00 | 16.82 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.355 | 10.903 | 0.000 | 0.000 | 0.680 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | F | F | B | F | F(-2) | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 76 | 76 | 666 | 0 | 0 | 1339 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 8.76 | 0.00 | 0.00 | 17.62 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.343 | 10.878 | 0.000 | 0.000 | 0.728 | 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 | 42 | 42 | 49 | 131 | 0 | 50 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.17 | 3.12 | 0.00 | 1.19 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.241 | 2.018 | 2.469 | 0.000 | 0.282 | 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 | 46 | 46 | 49 | 135 | 0 | 59 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.07 | 2.93 | 0.00 | 1.28 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.255 | 1.795 | 2.469 | 0.000 | 0.297 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | C | F | B | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 44 | 44 | 47 | 131 | 0 | 204 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.07 | 2.98 | 0.00 | 4.64 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.255 | 1.748 | 2.528 | 0.000 | 0.290 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | C | F | B | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 44 | 44 | 51 | 135 | 0 | 206 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.16 | 3.07 | 0.00 | 4.68 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.247 | 1.795 | 2.437 | 0.000 | 0.336 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | A | F | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 69 | 69 | 84 | 0 | 0 | 1236 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.22 | 0.00 | 0.00 | 17.91 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.332 | 7.316 | 0.000 | 0.000 | 1.045 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | B | F | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 71 | 71 | 84 | 0 | 0 | 1288 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.18 | 0.00 | 0.00 | 18.14 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.345 | 7.177 | 0.000 | 0.000 | 1.034 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | A | F | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 72 | 72 | 85 | 0 | 0 | 1239 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.18 | 0.00 | 0.00 | 17.21 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.343 | 7.238 | 0.000 | 0.000 | 1.039 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | B | F | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 72 | 72 | 87 | 0 | 0 | 1299 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.21 | 0.00 | 0.00 | 18.04 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.327 | 7.183 | 0.000 | 0.000 | 1.071 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | F | F | A | F | F(-2) | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 73 | 73 | 667 | 0 | 0 | 1270 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 9.14 | 0.00 | 0.00 | 17.40 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.334 | 10.755 | 0.000 | 0.000 | 0.738 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | F | F | B | F | F(-2) | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 75 | 75 | 649 | 0 | 0 | 1324 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 8.65 | 0.00 | 0.00 | 17.65 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.351 | 10.818 | 0.000 | 0.000 | 0.719 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | F | F | A | F | F(-2) | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 76 | 76 | 650 | 0 | 0 | 1273 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 8.55 | 0.00 | 0.00 | 16.75 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.340 | 10.845 | 0.000 | 0.000 | 0.731 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | F | F | B | F | F(-2) | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 76 | 76 | 670 | 0 | 0 | 1335 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 8.82 | 0.00 | 0.00 | 17.57 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.328 | 10.829 | 0.000 | 0.000 | 0.717 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | C | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 145 | 145 | 269 | 245 | 0 | 55 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.86 | 1.69 | 0.00 | 0.38 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.395 | 20.393 | 2.427 | 0.000 | 0.106 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | C | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 145 | 145 | 267 | 245 | 0 | 210 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.84 | 1.69 | 0.00 | 1.45 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.430 | 20.357 | 2.444 | 0.000 | 0.114 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | C | F | F(-2) | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 173 | 173 | 291 | 260 | 0 | 716 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.68 | 1.50 | 0.00 | 4.14 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.450 | 20.465 | 1.587 | 0.000 | 0.159 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | C | F | F(-2) | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 187 | 184 | 291 | 264 | 0 | 735 | 0 | 0 | 0 |
| N.S. |
1 | 0.98 | 1.56 | 1.41 | 0.00 | 3.93 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.490 | 20.519 | 1.472 | 0.000 | 0.183 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | C | F | F(-2) | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 190 | 187 | 289 | 262 | 0 | 723 | 0 | 0 | 0 |
| N.S. |
1 | 0.98 | 1.52 | 1.38 | 0.00 | 3.81 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.467 | 20.511 | 1.416 | 0.000 | 0.175 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | C | F | F(-2) | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 183 | 183 | 293 | 258 | 0 | 724 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.60 | 1.41 | 0.00 | 3.96 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.475 | 20.456 | 1.519 | 0.000 | 0.166 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | F | F | C | F | F(-1) | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 332 | 332 | 456 | 0 | 0 | 7008 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.37 | 0.00 | 0.00 | 21.11 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.745 | 11.493 | 0.000 | 0.000 | 27.024 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | F | F | C | F | F(-1) | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 336 | 336 | 466 | 0 | 0 | 7063 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.39 | 0.00 | 0.00 | 21.02 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.776 | 11.257 | 0.000 | 0.000 | 26.954 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | F | F | C | F | F(-1) | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 345 | 345 | 467 | 0 | 0 | 7009 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.35 | 0.00 | 0.00 | 20.32 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.775 | 11.322 | 0.000 | 0.000 | 26.477 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | F | F | C | F | F(-1) | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 345 | 345 | 459 | 0 | 0 | 7078 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.33 | 0.00 | 0.00 | 20.52 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.727 | 11.444 | 0.000 | 0.000 | 26.451 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 136 | 177 | 209 | 255 | 0 | 58 | 0 | 0 | 0 |
| N.S. |
1 | 1.30 | 1.54 | 1.88 | 0.00 | 0.43 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.444 | 10.393 | 2.446 | 0.000 | 0.112 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | C | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 152 | 193 | 232 | 257 | 0 | 69 | 0 | 0 | 0 |
| N.S. |
1 | 1.27 | 1.53 | 1.69 | 0.00 | 0.45 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.486 | 10.536 | 2.317 | 0.000 | 0.110 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | C | F | F(-2) | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 164 | 187 | 230 | 255 | 0 | 213 | 0 | 0 | 0 |
| N.S. |
1 | 1.14 | 1.40 | 1.55 | 0.00 | 1.30 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.477 | 11.528 | 2.401 | 0.000 | 0.123 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | C | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 156 | 179 | 211 | 253 | 0 | 217 | 0 | 0 | 0 |
| N.S. |
1 | 1.15 | 1.35 | 1.62 | 0.00 | 1.39 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.455 | 10.379 | 2.373 | 0.000 | 0.109 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | C | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 147 | 164 | 225 | 253 | 0 | 214 | 0 | 0 | 0 |
| N.S. |
1 | 1.12 | 1.53 | 1.72 | 0.00 | 1.46 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.465 | 10.493 | 2.451 | 0.000 | 0.107 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | F | F | C | F | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 278 | 295 | 445 | 0 | 0 | 1288 | 0 | 0 | 0 |
| N.S. |
1 | 1.06 | 1.60 | 0.00 | 0.00 | 4.63 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.695 | 11.284 | 0.000 | 0.000 | 0.889 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | F | F | C | F | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 286 | 303 | 454 | 0 | 0 | 1354 | 0 | 0 | 0 |
| N.S. |
1 | 1.06 | 1.59 | 0.00 | 0.00 | 4.73 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.705 | 11.082 | 0.000 | 0.000 | 0.819 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | F | F | C | F | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 282 | 319 | 455 | 0 | 0 | 1295 | 0 | 0 | 0 |
| N.S. |
1 | 1.13 | 1.61 | 0.00 | 0.00 | 4.59 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.700 | 11.019 | 0.000 | 0.000 | 0.902 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | F | F | C | F | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 278 | 315 | 448 | 0 | 0 | 1348 | 0 | 0 | 0 |
| N.S. |
1 | 1.13 | 1.61 | 0.00 | 0.00 | 4.85 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.713 | 11.239 | 0.000 | 0.000 | 0.895 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | F | F | F | F(-1) |
| verified |
N/A | No | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 317 | 297 | 214 | 275 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.94 | 0.68 | 0.87 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.147 | 10.492 | 1.380 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | F(-1) | F | F | F(-1) |
| verified |
N/A | No | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 329 | 302 | 235 | 264 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.92 | 0.71 | 0.80 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.129 | 10.567 | 1.397 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | F(-1) | F | F | F(-1) |
| verified |
N/A | No | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 325 | 300 | 233 | 273 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.92 | 0.72 | 0.84 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.049 | 10.540 | 1.309 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | F(-2) | F | F | F(-1) |
| verified |
N/A | No | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 321 | 299 | 233 | 266 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.93 | 0.73 | 0.83 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.091 | 10.544 | 1.288 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | F | F | F | F(-1) |
| verified |
N/A | No | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 358 | 309 | 213 | 275 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.86 | 0.59 | 0.77 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.067 | 10.517 | 1.233 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | F(-1) | F | F | F(-1) |
| verified |
N/A | No | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 346 | 301 | 235 | 268 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.87 | 0.68 | 0.77 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.038 | 10.565 | 1.281 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | F(-1) | F | F | F(-1) |
| verified |
N/A | No | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 342 | 299 | 233 | 277 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.87 | 0.68 | 0.81 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.971 | 10.536 | 1.092 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | F(-2) | F | F | F(-1) |
| verified |
N/A | No | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 362 | 311 | 233 | 266 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.86 | 0.64 | 0.73 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.038 | 10.570 | 1.212 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | C | F | C | A | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 125 | 125 | 39 | 90 | 0 | 33 | 56 | 0 | 334 |
| N.S. |
1 | 1.00 | 0.31 | 0.72 | 0.00 | 0.26 | 0.45 | 0.00 | 2.67 |
| time (sec) |
N/A | 0.283 | 10.036 | 1.445 | 0.000 | 0.121 | 2.268 | 0.000 | 17.624 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | C | F | C | A | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 139 | 139 | 40 | 101 | 0 | 36 | 99 | 0 | 373 |
| N.S. |
1 | 1.00 | 0.29 | 0.73 | 0.00 | 0.26 | 0.71 | 0.00 | 2.68 |
| time (sec) |
N/A | 0.278 | 10.040 | 1.352 | 0.000 | 0.116 | 3.743 | 0.000 | 18.953 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | C | A | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 142 | 142 | 58 | 132 | 0 | 52 | 94 | 0 | 334 |
| N.S. |
1 | 1.00 | 0.41 | 0.93 | 0.00 | 0.37 | 0.66 | 0.00 | 2.35 |
| time (sec) |
N/A | 0.283 | 10.035 | 1.840 | 0.000 | 0.113 | 3.808 | 0.000 | 18.892 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | C | F | C | A | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 136 | 136 | 61 | 94 | 0 | 61 | 61 | 0 | 376 |
| N.S. |
1 | 1.00 | 0.45 | 0.69 | 0.00 | 0.45 | 0.45 | 0.00 | 2.76 |
| time (sec) |
N/A | 0.295 | 10.036 | 1.830 | 0.000 | 0.106 | 2.434 | 0.000 | 21.455 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | C | F | C | A | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 127 | 127 | 41 | 90 | 0 | 33 | 56 | 0 | 334 |
| N.S. |
1 | 1.00 | 0.32 | 0.71 | 0.00 | 0.26 | 0.44 | 0.00 | 2.63 |
| time (sec) |
N/A | 0.273 | 10.030 | 1.067 | 0.000 | 0.092 | 2.268 | 0.000 | 19.813 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | C | F | C | A | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 141 | 141 | 42 | 101 | 0 | 36 | 99 | 0 | 373 |
| N.S. |
1 | 1.00 | 0.30 | 0.72 | 0.00 | 0.26 | 0.70 | 0.00 | 2.65 |
| time (sec) |
N/A | 0.292 | 10.026 | 1.105 | 0.000 | 0.102 | 3.738 | 0.000 | 20.839 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | C | A | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 144 | 144 | 60 | 132 | 0 | 51 | 94 | 0 | 334 |
| N.S. |
1 | 1.00 | 0.42 | 0.92 | 0.00 | 0.35 | 0.65 | 0.00 | 2.32 |
| time (sec) |
N/A | 0.287 | 10.032 | 1.102 | 0.000 | 0.099 | 3.825 | 0.000 | 20.251 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | C | F | C | A | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 138 | 138 | 63 | 94 | 0 | 60 | 61 | 0 | 376 |
| N.S. |
1 | 1.00 | 0.46 | 0.68 | 0.00 | 0.43 | 0.44 | 0.00 | 2.72 |
| time (sec) |
N/A | 0.286 | 10.030 | 1.080 | 0.000 | 0.106 | 2.406 | 0.000 | 21.677 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | F | F | F | B |
| verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 332 | 328 | 194 | 240 | 0 | 0 | 0 | 0 | 207 |
| N.S. |
1 | 0.99 | 0.58 | 0.72 | 0.00 | 0.00 | 0.00 | 0.00 | 0.62 |
| time (sec) |
N/A | 0.936 | 10.228 | 0.958 | 0.000 | 0.000 | 0.000 | 0.000 | 0.269 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | F | F | F | B |
| verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 377 | 378 | 195 | 240 | 0 | 0 | 0 | 0 | 224 |
| N.S. |
1 | 1.00 | 0.52 | 0.64 | 0.00 | 0.00 | 0.00 | 0.00 | 0.59 |
| time (sec) |
N/A | 0.991 | 10.217 | 0.924 | 0.000 | 0.000 | 0.000 | 0.000 | 0.206 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | F | F | F | B |
| verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 373 | 381 | 193 | 240 | 0 | 0 | 0 | 0 | 208 |
| N.S. |
1 | 1.02 | 0.52 | 0.64 | 0.00 | 0.00 | 0.00 | 0.00 | 0.56 |
| time (sec) |
N/A | 1.024 | 10.202 | 0.984 | 0.000 | 0.000 | 0.000 | 0.000 | 19.663 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | F | F | F | B |
| verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 341 | 328 | 196 | 240 | 0 | 0 | 0 | 0 | 223 |
| N.S. |
1 | 0.96 | 0.57 | 0.70 | 0.00 | 0.00 | 0.00 | 0.00 | 0.65 |
| time (sec) |
N/A | 0.954 | 10.221 | 0.979 | 0.000 | 0.000 | 0.000 | 0.000 | 0.094 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | F(-1) | F | F | B |
| verified |
N/A | No | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 450 | 449 | 211 | 274 | 0 | 0 | 0 | 0 | 356 |
| N.S. |
1 | 1.00 | 0.47 | 0.61 | 0.00 | 0.00 | 0.00 | 0.00 | 0.79 |
| time (sec) |
N/A | 1.399 | 10.446 | 1.024 | 0.000 | 0.000 | 0.000 | 0.000 | 0.147 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | F(-1) | F | F | B |
| verified |
N/A | No | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 474 | 460 | 233 | 265 | 0 | 0 | 0 | 0 | 387 |
| N.S. |
1 | 0.97 | 0.49 | 0.56 | 0.00 | 0.00 | 0.00 | 0.00 | 0.82 |
| time (sec) |
N/A | 1.385 | 10.582 | 1.023 | 0.000 | 0.000 | 0.000 | 0.000 | 20.107 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | F(-1) | F | F | B |
| verified |
N/A | No | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 475 | 463 | 231 | 274 | 0 | 0 | 0 | 0 | 355 |
| N.S. |
1 | 0.97 | 0.49 | 0.58 | 0.00 | 0.00 | 0.00 | 0.00 | 0.75 |
| time (sec) |
N/A | 1.207 | 10.527 | 1.099 | 0.000 | 0.000 | 0.000 | 0.000 | 0.108 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | F(-1) | F | F | B |
| verified |
N/A | No | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 463 | 460 | 213 | 265 | 0 | 0 | 0 | 0 | 388 |
| N.S. |
1 | 0.99 | 0.46 | 0.57 | 0.00 | 0.00 | 0.00 | 0.00 | 0.84 |
| time (sec) |
N/A | 1.275 | 10.443 | 0.944 | 0.000 | 0.000 | 0.000 | 0.000 | 0.112 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | C | F | C | A | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 120 | 120 | 34 | 53 | 0 | 30 | 42 | 0 | 207 |
| N.S. |
1 | 1.00 | 0.28 | 0.44 | 0.00 | 0.25 | 0.35 | 0.00 | 1.72 |
| time (sec) |
N/A | 0.259 | 10.039 | 0.984 | 0.000 | 0.109 | 1.265 | 0.000 | 20.504 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | C | F | C | A | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 134 | 134 | 34 | 57 | 0 | 33 | 65 | 0 | 223 |
| N.S. |
1 | 1.00 | 0.25 | 0.43 | 0.00 | 0.25 | 0.49 | 0.00 | 1.66 |
| time (sec) |
N/A | 0.266 | 10.445 | 0.930 | 0.000 | 0.095 | 1.412 | 0.000 | 20.350 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | C | F | C | A | F | B |
| verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
| size | 137 | 137 | 52 | 93 | 0 | 26 | 60 | 0 | 207 |
| N.S. |
1 | 1.00 | 0.38 | 0.68 | 0.00 | 0.19 | 0.44 | 0.00 | 1.51 |
| time (sec) |
N/A | 0.265 | 10.032 | 0.973 | 0.000 | 0.128 | 1.355 | 0.000 | 0.059 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | C | F | C | A | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 131 | 131 | 56 | 56 | 0 | 35 | 46 | 0 | 223 |
| N.S. |
1 | 1.00 | 0.43 | 0.43 | 0.00 | 0.27 | 0.35 | 0.00 | 1.70 |
| time (sec) |
N/A | 0.269 | 10.037 | 0.979 | 0.000 | 0.096 | 1.400 | 0.000 | 19.569 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F(-2) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 95 | 95 | 159 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.67 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.292 | 1.494 | 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 | F | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 234 | 227 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.97 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.452 | 0.000 | 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 | B | A | B | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 160 | 160 | 133 | 415 | 253 | 490 | 6397 | 835 | 495 |
| N.S. |
1 | 1.00 | 0.83 | 2.59 | 1.58 | 3.06 | 39.98 | 5.22 | 3.09 |
| time (sec) |
N/A | 0.336 | 0.156 | 0.903 | 0.200 | 0.288 | 2.031 | 0.314 | 19.818 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | A | B | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 126 | 126 | 104 | 283 | 184 | 348 | 3704 | 577 | 363 |
| N.S. |
1 | 1.00 | 0.83 | 2.25 | 1.46 | 2.76 | 29.40 | 4.58 | 2.88 |
| time (sec) |
N/A | 0.298 | 0.096 | 0.890 | 0.202 | 0.336 | 1.304 | 0.402 | 19.170 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | B | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 94 | 94 | 94 | 167 | 122 | 222 | 1906 | 361 | 247 |
| N.S. |
1 | 1.00 | 1.00 | 1.78 | 1.30 | 2.36 | 20.28 | 3.84 | 2.63 |
| time (sec) |
N/A | 0.248 | 0.094 | 0.878 | 0.187 | 0.277 | 0.814 | 0.428 | 19.414 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | B | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 99 | 99 | 94 | 0 | 0 | 0 | 675 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.95 | 0.00 | 0.00 | 0.00 | 6.82 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.258 | 0.087 | 0.000 | 0.000 | 0.000 | 2.560 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | B | B | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 294 | 294 | 252 | 1565 | 601 | 1565 | 26746 | 2660 | 1410 |
| N.S. |
1 | 1.00 | 0.86 | 5.32 | 2.04 | 5.32 | 90.97 | 9.05 | 4.80 |
| time (sec) |
N/A | 0.514 | 0.252 | 1.029 | 0.214 | 0.285 | 8.952 | 0.332 | 19.988 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | A | B | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 248 | 248 | 211 | 893 | 474 | 1216 | 18328 | 2034 | 1136 |
| N.S. |
1 | 1.00 | 0.85 | 3.60 | 1.91 | 4.90 | 73.90 | 8.20 | 4.58 |
| time (sec) |
N/A | 0.435 | 0.194 | 1.000 | 0.209 | 0.303 | 5.693 | 0.331 | 20.362 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | A | B | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 203 | 203 | 172 | 700 | 359 | 893 | 11851 | 1477 | 878 |
| N.S. |
1 | 1.00 | 0.85 | 3.45 | 1.77 | 4.40 | 58.38 | 7.28 | 4.33 |
| time (sec) |
N/A | 0.374 | 0.162 | 0.954 | 0.210 | 0.277 | 3.529 | 0.366 | 20.460 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | B | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 209 | 209 | 188 | 0 | 0 | 0 | 4690 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.90 | 0.00 | 0.00 | 0.00 | 22.44 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.398 | 0.168 | 0.000 | 0.000 | 0.000 | 4.222 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | B | B | B | F(-2) | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 459 | 459 | 402 | 3780 | 1153 | 3564 | 75191 | 0 | 2896 |
| N.S. |
1 | 1.00 | 0.88 | 8.24 | 2.51 | 7.76 | 163.81 | 0.00 | 6.31 |
| time (sec) |
N/A | 0.728 | 0.380 | 1.348 | 0.222 | 0.327 | 83.592 | 0.000 | 24.923 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | B | B | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 396 | 396 | 345 | 2972 | 953 | 2919 | 56151 | 4934 | 2436 |
| N.S. |
1 | 1.00 | 0.87 | 7.51 | 2.41 | 7.37 | 141.80 | 12.46 | 6.15 |
| time (sec) |
N/A | 0.634 | 0.308 | 1.162 | 0.234 | 0.324 | 34.118 | 0.372 | 22.664 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | B | B | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 337 | 337 | 290 | 2280 | 770 | 2313 | 40536 | 3874 | 2001 |
| N.S. |
1 | 1.00 | 0.86 | 6.77 | 2.28 | 6.86 | 120.28 | 11.50 | 5.94 |
| time (sec) |
N/A | 0.534 | 0.292 | 1.140 | 0.222 | 0.331 | 66.278 | 0.403 | 21.092 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | B | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 358 | 358 | 332 | 0 | 0 | 0 | 17189 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.93 | 0.00 | 0.00 | 0.00 | 48.01 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.561 | 0.302 | 0.000 | 0.000 | 0.000 | 13.326 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 324 | 324 | 284 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.88 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.968 | 0.558 | 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(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 332 | 332 | 292 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.88 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.912 | 0.596 | 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(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 293 | 293 | 239 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.82 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.686 | 0.266 | 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(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 253 | 253 | 213 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.84 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.543 | 0.202 | 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(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 288 | 288 | 237 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.82 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.515 | 0.225 | 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(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 263 | 263 | 222 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.84 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.433 | 0.147 | 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 | 300 | 300 | 244 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.81 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.766 | 0.295 | 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(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 326 | 326 | 273 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.84 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.768 | 0.337 | 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(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 253 | 253 | 213 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.84 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.723 | 0.335 | 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 | F | F | F | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 211 | 211 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.624 | 0.000 | 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 | C | A | F | F | F | F | F(-1) |
| verified |
N/A | No | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 1480 | 1361 | 877 | 1126 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.92 | 0.59 | 0.76 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.813 | 6.600 | 2.473 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | F | F | F | F | F | B | F | F(-1) |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 135 | 0 | 0 | 0 | 0 | 0 | 631 | 0 | 0 |
| N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 4.67 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 25.939 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | C | F | A | F | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 16 | 16 | 23 | 46 | 0 | 19 | 0 | 0 | 273 |
| N.S. |
1 | 1.00 | 1.44 | 2.88 | 0.00 | 1.19 | 0.00 | 0.00 | 17.06 |
| time (sec) |
N/A | 0.211 | 1.121 | 1.616 | 0.000 | 0.282 | 0.000 | 0.000 | 0.239 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | C | F | A | F | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 20 | 20 | 23 | 49 | 0 | 28 | 0 | 0 | 292 |
| N.S. |
1 | 1.00 | 1.15 | 2.45 | 0.00 | 1.40 | 0.00 | 0.00 | 14.60 |
| time (sec) |
N/A | 0.212 | 1.113 | 1.564 | 0.000 | 0.269 | 0.000 | 0.000 | 19.534 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | A | F | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 18 | 18 | 21 | 26 | 0 | 25 | 0 | 0 | 276 |
| N.S. |
1 | 1.00 | 1.17 | 1.44 | 0.00 | 1.39 | 0.00 | 0.00 | 15.33 |
| time (sec) |
N/A | 0.197 | 1.091 | 1.389 | 0.000 | 0.278 | 0.000 | 0.000 | 0.117 |