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 | C | A | A | A | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 69 | 79 | 86 | 69 | 73 | 120 | 442 | 74 | 84 |
| N.S. |
1 | 1.14 | 1.25 | 1.00 | 1.06 | 1.74 | 6.41 | 1.07 | 1.22 |
| time (sec) |
N/A | 0.490 | 0.713 | 0.332 | 0.436 | 0.248 | 0.368 | 0.365 | 4.633 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | A | B | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 88 | 103 | 95 | 83 | 93 | 157 | 790 | 83 | 104 |
| N.S. |
1 | 1.17 | 1.08 | 0.94 | 1.06 | 1.78 | 8.98 | 0.94 | 1.18 |
| time (sec) |
N/A | 0.619 | 0.713 | 0.322 | 0.362 | 0.241 | 0.451 | 0.393 | 4.512 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | A | F | F(-1) | B |
| verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 456 | 519 | 167 | 556 | 0 | 416 | 0 | 0 | 371 |
| N.S. |
1 | 1.14 | 0.37 | 1.22 | 0.00 | 0.91 | 0.00 | 0.00 | 0.81 |
| time (sec) |
N/A | 1.230 | 21.544 | 1.753 | 0.000 | 0.254 | 0.000 | 0.000 | 21.515 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | B | F | F(-1) | B |
| verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 159 | 172 | 140 | 370 | 0 | 334 | 0 | 0 | 354 |
| N.S. |
1 | 1.08 | 0.88 | 2.33 | 0.00 | 2.10 | 0.00 | 0.00 | 2.23 |
| time (sec) |
N/A | 0.908 | 0.995 | 0.982 | 0.000 | 0.258 | 0.000 | 0.000 | 9.737 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | A | F | F(-1) | B |
| verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 382 | 427 | 115 | 494 | 0 | 349 | 0 | 0 | 231 |
| N.S. |
1 | 1.12 | 0.30 | 1.29 | 0.00 | 0.91 | 0.00 | 0.00 | 0.60 |
| time (sec) |
N/A | 0.720 | 0.266 | 1.296 | 0.000 | 0.260 | 0.000 | 0.000 | 7.252 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F(-2) | B | F | F(-1) | B |
| verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 106 | 105 | 100 | 325 | 0 | 284 | 0 | 0 | 290 |
| N.S. |
1 | 0.99 | 0.94 | 3.07 | 0.00 | 2.68 | 0.00 | 0.00 | 2.74 |
| time (sec) |
N/A | 0.547 | 0.124 | 1.395 | 0.000 | 0.239 | 0.000 | 0.000 | 5.910 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F(-2) | A | F | F(-2) | B |
| verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 358 | 402 | 87 | 650 | 0 | 319 | 0 | 0 | 213 |
| N.S. |
1 | 1.12 | 0.24 | 1.82 | 0.00 | 0.89 | 0.00 | 0.00 | 0.59 |
| time (sec) |
N/A | 0.607 | 0.038 | 3.641 | 0.000 | 0.250 | 0.000 | 0.000 | 5.073 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F(-1) | F | B | F | F(-2) | B |
| verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 116 | 117 | 111 | 0 | 0 | 614 | 0 | 0 | 682 |
| N.S. |
1 | 1.01 | 0.96 | 0.00 | 0.00 | 5.29 | 0.00 | 0.00 | 5.88 |
| time (sec) |
N/A | 0.880 | 0.121 | 180.000 | 0.000 | 0.266 | 0.000 | 0.000 | 4.809 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | A | F | F(-1) | B |
| verified |
N/A | No | Yes | No | TBD | TBD | TBD | TBD | TBD |
| size | 415 | 465 | 139 | 1278502 | 0 | 847 | 0 | 0 | 832 |
| N.S. |
1 | 1.12 | 0.33 | 3080.73 | 0.00 | 2.04 | 0.00 | 0.00 | 2.00 |
| time (sec) |
N/A | 1.290 | 0.811 | 34.818 | 0.000 | 0.285 | 0.000 | 0.000 | 4.901 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | B | F | F(-2) | B |
| verified |
N/A | No | Yes | No | TBD | TBD | TBD | TBD | TBD |
| size | 189 | 202 | 166 | 1957605 | 0 | 818 | 0 | 0 | 1910 |
| N.S. |
1 | 1.07 | 0.88 | 10357.70 | 0.00 | 4.33 | 0.00 | 0.00 | 10.11 |
| time (sec) |
N/A | 1.576 | 1.191 | 22.293 | 0.000 | 0.297 | 0.000 | 0.000 | 6.180 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | B | F | F(-1) | B |
| verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 209 | 209 | 338 | 906 | 0 | 873 | 0 | 0 | 1355 |
| N.S. |
1 | 1.00 | 1.62 | 4.33 | 0.00 | 4.18 | 0.00 | 0.00 | 6.48 |
| time (sec) |
N/A | 1.253 | 6.275 | 0.592 | 0.000 | 0.263 | 0.000 | 0.000 | 48.591 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | B | F | F(-1) | B |
| verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 181 | 183 | 170 | 863 | 0 | 817 | 0 | 0 | 1229 |
| N.S. |
1 | 1.01 | 0.94 | 4.77 | 0.00 | 4.51 | 0.00 | 0.00 | 6.79 |
| time (sec) |
N/A | 1.070 | 1.758 | 0.288 | 0.000 | 0.257 | 0.000 | 0.000 | 23.985 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | B | F | F(-1) | B |
| verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 135 | 115 | 158 | 842 | 0 | 806 | 0 | 0 | 1141 |
| N.S. |
1 | 0.85 | 1.17 | 6.24 | 0.00 | 5.97 | 0.00 | 0.00 | 8.45 |
| time (sec) |
N/A | 0.685 | 1.107 | 0.317 | 0.000 | 0.260 | 0.000 | 0.000 | 10.706 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F(-2) | B | F | F(-1) | B |
| verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 128 | 116 | 116 | 831 | 0 | 756 | 0 | 0 | 1112 |
| N.S. |
1 | 0.91 | 0.91 | 6.49 | 0.00 | 5.91 | 0.00 | 0.00 | 8.69 |
| time (sec) |
N/A | 0.690 | 0.337 | 0.335 | 0.000 | 0.254 | 0.000 | 0.000 | 7.500 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F(-2) | B | F | F(-1) | B |
| verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 111 | 89 | 106 | 822 | 0 | 767 | 0 | 0 | 1099 |
| N.S. |
1 | 0.80 | 0.95 | 7.41 | 0.00 | 6.91 | 0.00 | 0.00 | 9.90 |
| time (sec) |
N/A | 0.554 | 0.121 | 0.293 | 0.000 | 0.255 | 0.000 | 0.000 | 5.697 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F(-1) | F | B | F | F(-1) | B |
| verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 116 | 106 | 111 | 0 | 0 | 1531 | 0 | 0 | 2260 |
| N.S. |
1 | 0.91 | 0.96 | 0.00 | 0.00 | 13.20 | 0.00 | 0.00 | 19.48 |
| time (sec) |
N/A | 0.948 | 0.188 | 180.000 | 0.000 | 0.314 | 0.000 | 0.000 | 4.979 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F(-1) | F | B | F | F(-1) | B |
| verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 149 | 135 | 186 | 0 | 0 | 1686 | 0 | 0 | 3623 |
| N.S. |
1 | 0.91 | 1.25 | 0.00 | 0.00 | 11.32 | 0.00 | 0.00 | 24.32 |
| time (sec) |
N/A | 1.221 | 0.413 | 180.000 | 0.000 | 0.300 | 0.000 | 0.000 | 5.233 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F(-1) | F | B | F | F(-1) | B |
| verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 189 | 191 | 168 | 0 | 0 | 1723 | 0 | 0 | 4660 |
| N.S. |
1 | 1.01 | 0.89 | 0.00 | 0.00 | 9.12 | 0.00 | 0.00 | 24.66 |
| time (sec) |
N/A | 1.606 | 1.713 | 180.000 | 0.000 | 0.335 | 0.000 | 0.000 | 5.290 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | B | F | F(-1) | B |
| verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 211 | 228 | 198 | 1240 | 0 | 1193 | 0 | 0 | 2384 |
| N.S. |
1 | 1.08 | 0.94 | 5.88 | 0.00 | 5.65 | 0.00 | 0.00 | 11.30 |
| time (sec) |
N/A | 1.374 | 3.922 | 0.656 | 0.000 | 0.269 | 0.000 | 0.000 | 54.572 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | B | F | F(-1) | B |
| verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 158 | 138 | 205 | 1194 | 0 | 1175 | 0 | 0 | 2165 |
| N.S. |
1 | 0.87 | 1.30 | 7.56 | 0.00 | 7.44 | 0.00 | 0.00 | 13.70 |
| time (sec) |
N/A | 0.865 | 2.306 | 0.113 | 0.000 | 0.260 | 0.000 | 0.000 | 27.906 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F(-2) | B | F | F(-1) | B |
| verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 158 | 161 | 138 | 1361 | 0 | 1122 | 0 | 0 | 2191 |
| N.S. |
1 | 1.02 | 0.87 | 8.61 | 0.00 | 7.10 | 0.00 | 0.00 | 13.87 |
| time (sec) |
N/A | 0.844 | 0.815 | 0.099 | 0.000 | 0.265 | 0.000 | 0.000 | 13.324 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F(-2) | B | F | F(-1) | B |
| verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 134 | 112 | 121 | 1174 | 0 | 1125 | 0 | 0 | 2100 |
| N.S. |
1 | 0.84 | 0.90 | 8.76 | 0.00 | 8.40 | 0.00 | 0.00 | 15.67 |
| time (sec) |
N/A | 0.723 | 0.419 | 0.081 | 0.000 | 0.256 | 0.000 | 0.000 | 7.757 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F(-1) | F | B | F | F(-1) | B |
| verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 138 | 143 | 220 | 0 | 0 | 2255 | 0 | 0 | 3333 |
| N.S. |
1 | 1.04 | 1.59 | 0.00 | 0.00 | 16.34 | 0.00 | 0.00 | 24.15 |
| time (sec) |
N/A | 1.213 | 0.210 | 180.000 | 0.000 | 0.358 | 0.000 | 0.000 | 12.240 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F(-1) | F | B | F | F(-1) | B |
| verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 151 | 137 | 233 | 0 | 0 | 2375 | 0 | 0 | 3366 |
| N.S. |
1 | 0.91 | 1.54 | 0.00 | 0.00 | 15.73 | 0.00 | 0.00 | 22.29 |
| time (sec) |
N/A | 1.350 | 0.540 | 180.000 | 0.000 | 0.366 | 0.000 | 0.000 | 12.183 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F(-1) | F | B | F(-1) | F(-1) | B |
| verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 192 | 209 | 268 | 0 | 0 | 2398 | 0 | 0 | 4304 |
| N.S. |
1 | 1.09 | 1.40 | 0.00 | 0.00 | 12.49 | 0.00 | 0.00 | 22.42 |
| time (sec) |
N/A | 1.736 | 1.516 | 180.000 | 0.000 | 0.407 | 0.000 | 0.000 | 13.522 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F(-1) | F(-1) | B | F(-1) | F(-1) | B |
| verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 237 | 242 | 185 | 0 | 0 | 2507 | 0 | 0 | 4455 |
| N.S. |
1 | 1.02 | 0.78 | 0.00 | 0.00 | 10.58 | 0.00 | 0.00 | 18.80 |
| time (sec) |
N/A | 2.203 | 3.850 | 180.000 | 0.000 | 0.496 | 0.000 | 0.000 | 12.401 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F(-2) | B | F | F(-1) | B |
| verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 167 | 145 | 143 | 1552 | 0 | 1569 | 0 | 0 | 2862 |
| N.S. |
1 | 0.87 | 0.86 | 9.29 | 0.00 | 9.40 | 0.00 | 0.00 | 17.14 |
| time (sec) |
N/A | 0.869 | 1.032 | 0.592 | 0.000 | 0.293 | 0.000 | 0.000 | 13.047 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | B | F | F(-1) | B |
| verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 229 | 245 | 162 | 443 | 0 | 789 | 0 | 0 | 938 |
| N.S. |
1 | 1.07 | 0.71 | 1.93 | 0.00 | 3.45 | 0.00 | 0.00 | 4.10 |
| time (sec) |
N/A | 1.367 | 5.349 | 0.123 | 0.000 | 0.261 | 0.000 | 0.000 | 14.011 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | A | F | F(-1) | B |
| verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 500 | 540 | 184 | 1641 | 0 | 789 | 0 | 0 | 791 |
| N.S. |
1 | 1.08 | 0.37 | 3.28 | 0.00 | 1.58 | 0.00 | 0.00 | 1.58 |
| time (sec) |
N/A | 1.263 | 3.314 | 0.108 | 0.000 | 0.260 | 0.000 | 0.000 | 9.207 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | B | F | F(-1) | B |
| verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 140 | 140 | 159 | 377 | 0 | 743 | 0 | 0 | 827 |
| N.S. |
1 | 1.00 | 1.14 | 2.69 | 0.00 | 5.31 | 0.00 | 0.00 | 5.91 |
| time (sec) |
N/A | 0.740 | 0.790 | 0.089 | 0.000 | 0.253 | 0.000 | 0.000 | 5.679 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | B | F | F(-1) | B |
| verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 424 | 448 | 108 | 1577 | 0 | 745 | 0 | 0 | 730 |
| N.S. |
1 | 1.06 | 0.25 | 3.72 | 0.00 | 1.76 | 0.00 | 0.00 | 1.72 |
| time (sec) |
N/A | 0.759 | 0.214 | 0.074 | 0.000 | 0.260 | 0.000 | 0.000 | 6.148 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F(-2) | B | F | F(-1) | B |
| verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 87 | 75 | 107 | 339 | 0 | 693 | 0 | 0 | 781 |
| N.S. |
1 | 0.86 | 1.23 | 3.90 | 0.00 | 7.97 | 0.00 | 0.00 | 8.98 |
| time (sec) |
N/A | 0.412 | 0.072 | 0.982 | 0.000 | 0.268 | 0.000 | 0.000 | 5.484 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F(-2) | B | F | F(-2) | B |
| verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 402 | 425 | 87 | 1557 | 0 | 717 | 0 | 0 | 708 |
| N.S. |
1 | 1.06 | 0.22 | 3.87 | 0.00 | 1.78 | 0.00 | 0.00 | 1.76 |
| time (sec) |
N/A | 0.625 | 0.056 | 0.148 | 0.000 | 0.259 | 0.000 | 0.000 | 6.412 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F(-1) | F | B | F | F(-2) | B |
| verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 116 | 106 | 111 | 0 | 0 | 1488 | 0 | 0 | 2028 |
| N.S. |
1 | 0.91 | 0.96 | 0.00 | 0.00 | 12.83 | 0.00 | 0.00 | 17.48 |
| time (sec) |
N/A | 0.887 | 0.157 | 180.000 | 0.000 | 0.283 | 0.000 | 0.000 | 5.210 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | F(-1) | F | B | F | F(-1) | B |
| verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 461 | 495 | 142 | 0 | 0 | 1660 | 0 | 0 | 2145 |
| N.S. |
1 | 1.07 | 0.31 | 0.00 | 0.00 | 3.60 | 0.00 | 0.00 | 4.65 |
| time (sec) |
N/A | 1.354 | 0.840 | 180.000 | 0.000 | 0.301 | 0.000 | 0.000 | 8.018 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F(-1) | F | B | F | F(-2) | B |
| verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 194 | 200 | 203 | 0 | 0 | 1685 | 0 | 0 | 3399 |
| N.S. |
1 | 1.03 | 1.05 | 0.00 | 0.00 | 8.69 | 0.00 | 0.00 | 17.52 |
| time (sec) |
N/A | 1.456 | 3.292 | 180.000 | 0.000 | 0.347 | 0.000 | 0.000 | 0.678 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F(-1) | B | F | F(-1) | B |
| verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 282 | 285 | 311 | 1836 | 0 | 2076 | 0 | 0 | 2930 |
| N.S. |
1 | 1.01 | 1.10 | 6.51 | 0.00 | 7.36 | 0.00 | 0.00 | 10.39 |
| time (sec) |
N/A | 1.669 | 6.452 | 0.118 | 0.000 | 0.298 | 0.000 | 0.000 | 16.956 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F(-1) | B | F | F(-1) | B |
| verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 226 | 228 | 252 | 1978 | 0 | 2034 | 0 | 0 | 2282 |
| N.S. |
1 | 1.01 | 1.12 | 8.75 | 0.00 | 9.00 | 0.00 | 0.00 | 10.10 |
| time (sec) |
N/A | 1.233 | 3.325 | 0.082 | 0.000 | 0.293 | 0.000 | 0.000 | 9.511 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F(-1) | B | F | F(-1) | B |
| verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 165 | 173 | 243 | 1772 | 0 | 2011 | 0 | 0 | 2869 |
| N.S. |
1 | 1.05 | 1.47 | 10.74 | 0.00 | 12.19 | 0.00 | 0.00 | 17.39 |
| time (sec) |
N/A | 0.887 | 1.187 | 0.092 | 0.000 | 0.280 | 0.000 | 0.000 | 7.419 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | B | F | F(-1) | B |
| verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 125 | 129 | 119 | 1937 | 0 | 1971 | 0 | 0 | 2239 |
| N.S. |
1 | 1.03 | 0.95 | 15.50 | 0.00 | 15.77 | 0.00 | 0.00 | 17.91 |
| time (sec) |
N/A | 0.647 | 0.169 | 0.081 | 0.000 | 0.274 | 0.000 | 0.000 | 6.664 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F(-2) | B | F | F(-1) | B |
| verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 116 | 126 | 100 | 1747 | 0 | 1955 | 0 | 0 | 2844 |
| N.S. |
1 | 1.09 | 0.86 | 15.06 | 0.00 | 16.85 | 0.00 | 0.00 | 24.52 |
| time (sec) |
N/A | 0.594 | 0.171 | 0.081 | 0.000 | 0.283 | 0.000 | 0.000 | 7.165 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F(-2) | B | F | F(-1) | B |
| verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 120 | 123 | 105 | 1932 | 0 | 1949 | 0 | 0 | 2236 |
| N.S. |
1 | 1.02 | 0.88 | 16.10 | 0.00 | 16.24 | 0.00 | 0.00 | 18.63 |
| time (sec) |
N/A | 0.558 | 0.096 | 0.074 | 0.000 | 0.277 | 0.000 | 0.000 | 7.246 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F(-1) | F | B | F | F(-1) | B |
| verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 150 | 174 | 165 | 0 | 0 | 4100 | 0 | 0 | 6384 |
| N.S. |
1 | 1.16 | 1.10 | 0.00 | 0.00 | 27.33 | 0.00 | 0.00 | 42.56 |
| time (sec) |
N/A | 1.246 | 1.228 | 180.000 | 0.000 | 0.346 | 0.000 | 0.000 | 5.192 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F(-1) | F | B | F | F(-1) | B |
| verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 192 | 222 | 184 | 0 | 0 | 4248 | 0 | 0 | 7971 |
| N.S. |
1 | 1.16 | 0.96 | 0.00 | 0.00 | 22.12 | 0.00 | 0.00 | 41.52 |
| time (sec) |
N/A | 1.608 | 3.558 | 180.000 | 0.000 | 0.385 | 0.000 | 0.000 | 5.564 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F(-1) | F(-1) | B | F | F(-1) | B |
| verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 241 | 280 | 259 | 0 | 0 | 4381 | 0 | 0 | 6216 |
| N.S. |
1 | 1.16 | 1.07 | 0.00 | 0.00 | 18.18 | 0.00 | 0.00 | 25.79 |
| time (sec) |
N/A | 2.012 | 5.845 | 180.000 | 0.000 | 0.554 | 0.000 | 0.000 | 5.902 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F(-1) | B | F | F(-1) | B |
| verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 291 | 319 | 353 | 2209 | 0 | 3401 | 0 | 0 | 4681 |
| N.S. |
1 | 1.10 | 1.21 | 7.59 | 0.00 | 11.69 | 0.00 | 0.00 | 16.09 |
| time (sec) |
N/A | 1.771 | 5.973 | 0.091 | 0.000 | 0.334 | 0.000 | 0.000 | 16.329 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F(-1) | B | F | F(-1) | B |
| verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 226 | 255 | 308 | 2379 | 0 | 3383 | 0 | 0 | 3739 |
| N.S. |
1 | 1.13 | 1.36 | 10.53 | 0.00 | 14.97 | 0.00 | 0.00 | 16.54 |
| time (sec) |
N/A | 1.239 | 3.262 | 0.153 | 0.000 | 0.309 | 0.000 | 0.000 | 13.169 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F(-1) | B | F | F(-1) | B |
| verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 172 | 209 | 220 | 2165 | 0 | 3324 | 0 | 0 | 4638 |
| N.S. |
1 | 1.22 | 1.28 | 12.59 | 0.00 | 19.33 | 0.00 | 0.00 | 26.97 |
| time (sec) |
N/A | 0.968 | 1.550 | 0.155 | 0.000 | 0.313 | 0.000 | 0.000 | 11.643 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | B | F | F(-1) | B |
| verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 157 | 176 | 122 | 2323 | 0 | 3320 | 0 | 0 | 3708 |
| N.S. |
1 | 1.12 | 0.78 | 14.80 | 0.00 | 21.15 | 0.00 | 0.00 | 23.62 |
| time (sec) |
N/A | 0.868 | 0.188 | 0.134 | 0.000 | 0.307 | 0.000 | 0.000 | 9.971 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F(-2) | B | F | F(-1) | B |
| verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 155 | 183 | 103 | 2157 | 0 | 3289 | 0 | 0 | 4630 |
| N.S. |
1 | 1.18 | 0.66 | 13.92 | 0.00 | 21.22 | 0.00 | 0.00 | 29.87 |
| time (sec) |
N/A | 0.804 | 0.164 | 0.110 | 0.000 | 0.314 | 0.000 | 0.000 | 11.353 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F(-2) | B | F | F(-1) | B |
| verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 152 | 170 | 108 | 2318 | 0 | 3296 | 0 | 0 | 3703 |
| N.S. |
1 | 1.12 | 0.71 | 15.25 | 0.00 | 21.68 | 0.00 | 0.00 | 24.36 |
| time (sec) |
N/A | 0.783 | 0.099 | 0.164 | 0.000 | 0.305 | 0.000 | 0.000 | 10.764 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F(-1) | F | B | F | F(-1) | B |
| verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 195 | 246 | 237 | 0 | 0 | 6876 | 0 | 0 | 13727 |
| N.S. |
1 | 1.26 | 1.22 | 0.00 | 0.00 | 35.26 | 0.00 | 0.00 | 70.39 |
| time (sec) |
N/A | 1.705 | 2.379 | 180.000 | 0.000 | 0.488 | 0.000 | 0.000 | 6.137 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F(-1) | F | B | F | F(-1) | B |
| verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 245 | 295 | 232 | 0 | 0 | 7108 | 0 | 0 | 14956 |
| N.S. |
1 | 1.20 | 0.95 | 0.00 | 0.00 | 29.01 | 0.00 | 0.00 | 61.04 |
| time (sec) |
N/A | 2.115 | 5.034 | 180.000 | 0.000 | 0.588 | 0.000 | 0.000 | 5.547 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F(-2) | B | F | F(-1) | B |
| verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 194 | 223 | 108 | 3082 | 0 | 4720 | 0 | 0 | 5307 |
| N.S. |
1 | 1.15 | 0.56 | 15.89 | 0.00 | 24.33 | 0.00 | 0.00 | 27.36 |
| time (sec) |
N/A | 1.059 | 0.306 | 0.110 | 0.000 | 0.334 | 0.000 | 0.000 | 24.326 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | A | B | F | F(-1) | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 202 | 198 | 106 | 211 | 158 | 608 | 0 | 0 | 130 |
| N.S. |
1 | 0.98 | 0.52 | 1.04 | 0.78 | 3.01 | 0.00 | 0.00 | 0.64 |
| time (sec) |
N/A | 0.635 | 0.562 | 0.081 | 0.362 | 0.238 | 0.000 | 0.000 | 6.953 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | A | B | F | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 184 | 180 | 94 | 200 | 147 | 592 | 0 | 0 | 114 |
| N.S. |
1 | 0.98 | 0.51 | 1.09 | 0.80 | 3.22 | 0.00 | 0.00 | 0.62 |
| time (sec) |
N/A | 0.535 | 0.265 | 0.030 | 0.373 | 0.245 | 0.000 | 0.000 | 6.018 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | A | B | F | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 166 | 162 | 79 | 189 | 135 | 583 | 0 | 0 | 153 |
| N.S. |
1 | 0.98 | 0.48 | 1.14 | 0.81 | 3.51 | 0.00 | 0.00 | 0.92 |
| time (sec) |
N/A | 0.433 | 0.089 | 0.056 | 0.361 | 0.245 | 0.000 | 0.000 | 5.815 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | A | B | F | F(-1) | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 150 | 145 | 61 | 178 | 124 | 561 | 0 | 0 | 141 |
| N.S. |
1 | 0.97 | 0.41 | 1.19 | 0.83 | 3.74 | 0.00 | 0.00 | 0.94 |
| time (sec) |
N/A | 0.343 | 0.049 | 0.141 | 0.644 | 0.240 | 0.000 | 0.000 | 5.220 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | A | B | F | F(-1) | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 166 | 162 | 69 | 189 | 135 | 615 | 0 | 0 | 102 |
| N.S. |
1 | 0.98 | 0.42 | 1.14 | 0.81 | 3.70 | 0.00 | 0.00 | 0.61 |
| time (sec) |
N/A | 0.455 | 0.112 | 0.063 | 0.289 | 0.243 | 0.000 | 0.000 | 5.882 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | A | B | F | F(-1) | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 184 | 180 | 72 | 200 | 146 | 631 | 0 | 0 | 114 |
| N.S. |
1 | 0.98 | 0.39 | 1.09 | 0.79 | 3.43 | 0.00 | 0.00 | 0.62 |
| time (sec) |
N/A | 0.559 | 0.114 | 0.066 | 0.291 | 0.244 | 0.000 | 0.000 | 5.991 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | A | B | F | F(-1) | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 202 | 198 | 72 | 211 | 159 | 648 | 0 | 0 | 128 |
| N.S. |
1 | 0.98 | 0.36 | 1.04 | 0.79 | 3.21 | 0.00 | 0.00 | 0.63 |
| time (sec) |
N/A | 0.676 | 0.114 | 0.062 | 0.285 | 0.236 | 0.000 | 0.000 | 7.072 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | A | B | F | F(-1) | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 268 | 246 | 133 | 250 | 217 | 1037 | 0 | 0 | 995 |
| N.S. |
1 | 0.92 | 0.50 | 0.93 | 0.81 | 3.87 | 0.00 | 0.00 | 3.71 |
| time (sec) |
N/A | 0.842 | 1.201 | 0.096 | 0.277 | 0.266 | 0.000 | 0.000 | 8.314 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | A | B | F | F(-1) | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 249 | 227 | 120 | 238 | 205 | 1030 | 0 | 0 | 986 |
| N.S. |
1 | 0.91 | 0.48 | 0.96 | 0.82 | 4.14 | 0.00 | 0.00 | 3.96 |
| time (sec) |
N/A | 0.737 | 0.757 | 0.056 | 0.278 | 0.253 | 0.000 | 0.000 | 6.418 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | A | B | F | F(-1) | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 223 | 201 | 99 | 212 | 186 | 1005 | 0 | 0 | 954 |
| N.S. |
1 | 0.90 | 0.44 | 0.95 | 0.83 | 4.51 | 0.00 | 0.00 | 4.28 |
| time (sec) |
N/A | 0.588 | 0.297 | 0.050 | 0.281 | 0.271 | 0.000 | 0.000 | 5.840 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | A | B | F | F(-1) | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 204 | 182 | 85 | 200 | 173 | 997 | 0 | 0 | 937 |
| N.S. |
1 | 0.89 | 0.42 | 0.98 | 0.85 | 4.89 | 0.00 | 0.00 | 4.59 |
| time (sec) |
N/A | 0.487 | 0.136 | 0.050 | 0.298 | 0.250 | 0.000 | 0.000 | 5.058 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | A | B | F | F(-1) | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 204 | 182 | 166 | 200 | 173 | 1023 | 0 | 0 | 949 |
| N.S. |
1 | 0.89 | 0.81 | 0.98 | 0.85 | 5.01 | 0.00 | 0.00 | 4.65 |
| time (sec) |
N/A | 0.489 | 0.831 | 0.061 | 0.289 | 0.278 | 0.000 | 0.000 | 5.639 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | A | B | F | F(-1) | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 223 | 201 | 77 | 212 | 185 | 1050 | 0 | 0 | 968 |
| N.S. |
1 | 0.90 | 0.35 | 0.95 | 0.83 | 4.71 | 0.00 | 0.00 | 4.34 |
| time (sec) |
N/A | 0.589 | 0.217 | 0.059 | 0.412 | 0.254 | 0.000 | 0.000 | 6.161 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | A | B | F | F(-1) | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 249 | 227 | 81 | 231 | 206 | 1065 | 0 | 0 | 983 |
| N.S. |
1 | 0.91 | 0.33 | 0.93 | 0.83 | 4.28 | 0.00 | 0.00 | 3.95 |
| time (sec) |
N/A | 0.722 | 0.250 | 0.054 | 0.422 | 0.269 | 0.000 | 0.000 | 6.606 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | A | B | F | F(-1) | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 328 | 305 | 164 | 308 | 280 | 1431 | 0 | 0 | 1796 |
| N.S. |
1 | 0.93 | 0.50 | 0.94 | 0.85 | 4.36 | 0.00 | 0.00 | 5.48 |
| time (sec) |
N/A | 1.217 | 3.171 | 0.209 | 0.357 | 0.295 | 0.000 | 0.000 | 11.570 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | A | B | F | F(-1) | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 299 | 278 | 144 | 279 | 258 | 1427 | 0 | 0 | 1729 |
| N.S. |
1 | 0.93 | 0.48 | 0.93 | 0.86 | 4.77 | 0.00 | 0.00 | 5.78 |
| time (sec) |
N/A | 1.060 | 1.476 | 0.059 | 0.327 | 0.296 | 0.000 | 0.000 | 9.669 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | A | B | F | F(-1) | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 272 | 249 | 120 | 250 | 238 | 1388 | 0 | 0 | 1742 |
| N.S. |
1 | 0.92 | 0.44 | 0.92 | 0.88 | 5.10 | 0.00 | 0.00 | 6.40 |
| time (sec) |
N/A | 0.867 | 0.840 | 0.054 | 0.303 | 0.294 | 0.000 | 0.000 | 7.788 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | A | B | F | F(-1) | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 245 | 222 | 101 | 225 | 216 | 1385 | 0 | 0 | 1674 |
| N.S. |
1 | 0.91 | 0.41 | 0.92 | 0.88 | 5.65 | 0.00 | 0.00 | 6.83 |
| time (sec) |
N/A | 0.722 | 0.366 | 0.054 | 0.310 | 0.288 | 0.000 | 0.000 | 5.900 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | A | B | F | F(-1) | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 245 | 219 | 192 | 226 | 214 | 1398 | 0 | 0 | 1767 |
| N.S. |
1 | 0.89 | 0.78 | 0.92 | 0.87 | 5.71 | 0.00 | 0.00 | 7.21 |
| time (sec) |
N/A | 0.682 | 2.033 | 0.056 | 0.292 | 0.288 | 0.000 | 0.000 | 5.831 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | A | B | F | F(-1) | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 245 | 222 | 91 | 225 | 215 | 1424 | 0 | 0 | 1752 |
| N.S. |
1 | 0.91 | 0.37 | 0.92 | 0.88 | 5.81 | 0.00 | 0.00 | 7.15 |
| time (sec) |
N/A | 0.701 | 0.318 | 0.058 | 0.295 | 0.290 | 0.000 | 0.000 | 6.257 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | A | B | F | F(-1) | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 270 | 250 | 103 | 243 | 235 | 1428 | 0 | 0 | 1777 |
| N.S. |
1 | 0.93 | 0.38 | 0.90 | 0.87 | 5.29 | 0.00 | 0.00 | 6.58 |
| time (sec) |
N/A | 0.901 | 0.548 | 0.065 | 0.293 | 0.288 | 0.000 | 0.000 | 7.326 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | A | B | F | F(-1) | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 299 | 281 | 103 | 267 | 259 | 1468 | 0 | 0 | 1795 |
| N.S. |
1 | 0.94 | 0.34 | 0.89 | 0.87 | 4.91 | 0.00 | 0.00 | 6.00 |
| time (sec) |
N/A | 1.071 | 0.585 | 0.064 | 0.407 | 0.295 | 0.000 | 0.000 | 9.748 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | A | B | F | F(-1) | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 326 | 308 | 104 | 289 | 279 | 1472 | 0 | 0 | 1821 |
| N.S. |
1 | 0.94 | 0.32 | 0.89 | 0.86 | 4.52 | 0.00 | 0.00 | 5.59 |
| time (sec) |
N/A | 1.222 | 0.726 | 0.066 | 0.400 | 0.298 | 0.000 | 0.000 | 11.722 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | A | B | F | F(-1) | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 150 | 145 | 61 | 178 | 124 | 561 | 0 | 0 | 141 |
| N.S. |
1 | 0.97 | 0.41 | 1.19 | 0.83 | 3.74 | 0.00 | 0.00 | 0.94 |
| time (sec) |
N/A | 0.353 | 0.035 | 0.000 | 0.359 | 0.237 | 0.000 | 0.000 | 0.003 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | A | B | F | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 162 | 157 | 82 | 202 | 136 | 569 | 0 | 0 | 94 |
| N.S. |
1 | 0.97 | 0.51 | 1.25 | 0.84 | 3.51 | 0.00 | 0.00 | 0.58 |
| time (sec) |
N/A | 0.357 | 0.158 | 0.173 | 0.293 | 0.244 | 0.000 | 0.000 | 5.698 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F(-2) | B | F | F(-1) | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 208 | 197 | 83 | 273 | 0 | 653 | 0 | 0 | 120 |
| N.S. |
1 | 0.95 | 0.40 | 1.31 | 0.00 | 3.14 | 0.00 | 0.00 | 0.58 |
| time (sec) |
N/A | 0.388 | 0.089 | 0.275 | 0.000 | 0.244 | 0.000 | 0.000 | 5.522 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F(-2) | B | F | F(-1) | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 214 | 203 | 84 | 285 | 0 | 657 | 0 | 0 | 122 |
| N.S. |
1 | 0.95 | 0.39 | 1.33 | 0.00 | 3.07 | 0.00 | 0.00 | 0.57 |
| time (sec) |
N/A | 0.385 | 0.161 | 0.182 | 0.000 | 0.245 | 0.000 | 0.000 | 5.701 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | B | F(-1) | F(-1) | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 300 | 290 | 243 | 284 | 225 | 2908 | 0 | 0 | 4082 |
| N.S. |
1 | 0.97 | 0.81 | 0.95 | 0.75 | 9.69 | 0.00 | 0.00 | 13.61 |
| time (sec) |
N/A | 1.491 | 2.264 | 0.115 | 0.334 | 0.384 | 0.000 | 0.000 | 12.019 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | B | F(-1) | F(-1) | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 271 | 255 | 222 | 255 | 202 | 2856 | 0 | 0 | 4927 |
| N.S. |
1 | 0.94 | 0.82 | 0.94 | 0.75 | 10.54 | 0.00 | 0.00 | 18.18 |
| time (sec) |
N/A | 1.175 | 0.963 | 0.076 | 0.280 | 0.365 | 0.000 | 0.000 | 7.463 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | A | B | F | F(-1) | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 250 | 226 | 155 | 241 | 185 | 2796 | 0 | 0 | 3693 |
| N.S. |
1 | 0.90 | 0.62 | 0.96 | 0.74 | 11.18 | 0.00 | 0.00 | 14.77 |
| time (sec) |
N/A | 0.975 | 0.186 | 0.083 | 0.288 | 0.315 | 0.000 | 0.000 | 9.264 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | A | B | F | F(-1) | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 232 | 201 | 227 | 225 | 171 | 2730 | 0 | 0 | 4299 |
| N.S. |
1 | 0.87 | 0.98 | 0.97 | 0.74 | 11.77 | 0.00 | 0.00 | 18.53 |
| time (sec) |
N/A | 0.732 | 0.280 | 0.076 | 0.283 | 0.310 | 0.000 | 0.000 | 6.043 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | A | B | F | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 232 | 201 | 204 | 224 | 170 | 2726 | 0 | 0 | 3216 |
| N.S. |
1 | 0.87 | 0.88 | 0.97 | 0.73 | 11.75 | 0.00 | 0.00 | 13.86 |
| time (sec) |
N/A | 0.723 | 0.192 | 0.084 | 0.299 | 0.283 | 0.000 | 0.000 | 7.658 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | A | B | F | F(-1) | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 232 | 201 | 227 | 225 | 170 | 2730 | 0 | 0 | 4102 |
| N.S. |
1 | 0.87 | 0.98 | 0.97 | 0.73 | 11.77 | 0.00 | 0.00 | 17.68 |
| time (sec) |
N/A | 0.729 | 0.193 | 0.094 | 0.405 | 0.320 | 0.000 | 0.000 | 6.386 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | A | B | F | F(-1) | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 250 | 226 | 131 | 241 | 185 | 2872 | 0 | 0 | 3829 |
| N.S. |
1 | 0.90 | 0.52 | 0.96 | 0.74 | 11.49 | 0.00 | 0.00 | 15.32 |
| time (sec) |
N/A | 0.954 | 0.560 | 0.073 | 0.390 | 0.314 | 0.000 | 0.000 | 6.604 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | B | F | F(-1) | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 271 | 254 | 222 | 255 | 201 | 2946 | 0 | 0 | 4806 |
| N.S. |
1 | 0.94 | 0.82 | 0.94 | 0.74 | 10.87 | 0.00 | 0.00 | 17.73 |
| time (sec) |
N/A | 1.179 | 1.952 | 0.079 | 0.400 | 0.376 | 0.000 | 0.000 | 6.646 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | B | F | F(-1) | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 300 | 289 | 248 | 277 | 223 | 3006 | 0 | 0 | 4207 |
| N.S. |
1 | 0.96 | 0.83 | 0.92 | 0.74 | 10.02 | 0.00 | 0.00 | 14.02 |
| time (sec) |
N/A | 1.469 | 3.864 | 0.067 | 0.533 | 0.399 | 0.000 | 0.000 | 8.366 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | A | B | F(-1) | F(-1) | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 399 | 365 | 442 | 311 | 311 | 5522 | 0 | 0 | 12117 |
| N.S. |
1 | 0.91 | 1.11 | 0.78 | 0.78 | 13.84 | 0.00 | 0.00 | 30.37 |
| time (sec) |
N/A | 1.879 | 2.064 | 0.162 | 0.284 | 0.831 | 0.000 | 0.000 | 10.781 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | A | B | F(-1) | F(-1) | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 358 | 327 | 375 | 296 | 296 | 5439 | 0 | 0 | 8642 |
| N.S. |
1 | 0.91 | 1.05 | 0.83 | 0.83 | 15.19 | 0.00 | 0.00 | 24.14 |
| time (sec) |
N/A | 1.478 | 1.313 | 0.149 | 0.284 | 0.584 | 0.000 | 0.000 | 14.917 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | A | B | F | F(-1) | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 318 | 288 | 157 | 281 | 277 | 5353 | 0 | 0 | 11104 |
| N.S. |
1 | 0.91 | 0.49 | 0.88 | 0.87 | 16.83 | 0.00 | 0.00 | 34.92 |
| time (sec) |
N/A | 1.120 | 1.801 | 0.151 | 0.295 | 0.482 | 0.000 | 0.000 | 7.646 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | A | B | F | F(-1) | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 312 | 278 | 151 | 276 | 268 | 5291 | 0 | 0 | 7761 |
| N.S. |
1 | 0.89 | 0.48 | 0.88 | 0.86 | 16.96 | 0.00 | 0.00 | 24.88 |
| time (sec) |
N/A | 1.079 | 1.376 | 0.071 | 0.294 | 0.424 | 0.000 | 0.000 | 13.557 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | A | B | F | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 316 | 281 | 182 | 278 | 270 | 5309 | 0 | 0 | 10520 |
| N.S. |
1 | 0.89 | 0.58 | 0.88 | 0.85 | 16.80 | 0.00 | 0.00 | 33.29 |
| time (sec) |
N/A | 1.042 | 0.770 | 0.073 | 0.295 | 0.401 | 0.000 | 0.000 | 8.078 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | A | B | F | F(-1) | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 317 | 287 | 166 | 281 | 277 | 5341 | 0 | 0 | 8282 |
| N.S. |
1 | 0.91 | 0.52 | 0.89 | 0.87 | 16.85 | 0.00 | 0.00 | 26.13 |
| time (sec) |
N/A | 1.141 | 0.669 | 0.071 | 0.283 | 0.496 | 0.000 | 0.000 | 12.967 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | A | B | F | F(-1) | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 358 | 326 | 195 | 296 | 315 | 5555 | 0 | 0 | 12063 |
| N.S. |
1 | 0.91 | 0.54 | 0.83 | 0.88 | 15.52 | 0.00 | 0.00 | 33.70 |
| time (sec) |
N/A | 1.519 | 1.889 | 0.069 | 0.322 | 0.641 | 0.000 | 0.000 | 8.816 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | A | B | F | F(-1) | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 397 | 363 | 230 | 310 | 342 | 5640 | 0 | 0 | 6886 |
| N.S. |
1 | 0.91 | 0.58 | 0.78 | 0.86 | 14.21 | 0.00 | 0.00 | 17.35 |
| time (sec) |
N/A | 1.937 | 4.795 | 0.080 | 0.364 | 0.967 | 0.000 | 0.000 | 10.785 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | A | B | F(-1) | F(-1) | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 493 | 465 | 723 | 373 | 449 | 8468 | 0 | 0 | 18832 |
| N.S. |
1 | 0.94 | 1.47 | 0.76 | 0.91 | 17.18 | 0.00 | 0.00 | 38.20 |
| time (sec) |
N/A | 2.638 | 6.483 | 0.540 | 0.439 | 2.960 | 0.000 | 0.000 | 22.947 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | A | B | F(-1) | F(-1) | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 444 | 419 | 403 | 356 | 434 | 8384 | 0 | 0 | 13319 |
| N.S. |
1 | 0.94 | 0.91 | 0.80 | 0.98 | 18.88 | 0.00 | 0.00 | 30.00 |
| time (sec) |
N/A | 2.119 | 5.724 | 0.496 | 0.635 | 1.912 | 0.000 | 0.000 | 23.407 |