Detailed conclusion table per each integral is given by the table below. The elapsed time is in seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2) if the failure was due to an exception being raised, which could indicate a bug in the system. If the failure was due to integral not being evaluated within the time limit, then it is given as F.
In this table, the column N.S. means normalized size and is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To make the table
fit the page, the name Mathematica was abbreviated to MMA
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F(-2) | B | F | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 241 | 275 | 220 | 329 | 0 | 2005 | 0 | 514 | 1117 | 2405 |
| N.S. |
1 | 1.14 | 0.91 | 1.37 | 0.00 | 8.32 | 0.00 | 2.13 | 4.63 | 9.98 |
| time (sec) |
N/A | 1.883 | 2.542 | 0.921 | 0.000 | 1.166 | 0.000 | 0.147 | 0.213 | 18.759 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F(-2) | B | F(-1) | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 182 | 218 | 157 | 510 | 0 | 965 | 0 | 510 | 997 | 708 |
| N.S. |
1 | 1.20 | 0.86 | 2.80 | 0.00 | 5.30 | 0.00 | 2.80 | 5.48 | 3.89 |
| time (sec) |
N/A | 0.773 | 1.283 | 1.062 | 0.000 | 0.145 | 0.000 | 0.138 | 0.206 | 19.860 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F | C | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 172 | 173 | 143 | 460 | 0 | 396 | 0 | 0 | 20 | 0 |
| N.S. |
1 | 1.01 | 0.83 | 2.67 | 0.00 | 2.30 | 0.00 | 0.00 | 0.12 | 0.00 |
| time (sec) |
N/A | 0.807 | 4.501 | 0.901 | 0.000 | 0.104 | 0.000 | 0.000 | 0.203 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F | C | F | F | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 62 | 62 | 61 | 239 | 0 | 351 | 0 | 0 | 13 | 55 |
| N.S. |
1 | 1.00 | 0.98 | 3.85 | 0.00 | 5.66 | 0.00 | 0.00 | 0.21 | 0.89 |
| time (sec) |
N/A | 0.290 | 0.143 | 1.337 | 0.000 | 0.132 | 0.000 | 0.000 | 0.202 | 16.419 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | F(-1) | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 128 | 128 | 89 | 169 | 0 | 0 | 0 | 0 | 20 | 0 |
| N.S. |
1 | 1.00 | 0.70 | 1.32 | 0.00 | 0.00 | 0.00 | 0.00 | 0.16 | 0.00 |
| time (sec) |
N/A | 0.741 | 17.002 | 0.714 | 0.000 | 0.000 | 0.000 | 0.000 | 0.200 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F | F(-1) | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 213 | 228 | 312 | 458 | 0 | 0 | 0 | 0 | 22 | 0 |
| N.S. |
1 | 1.07 | 1.46 | 2.15 | 0.00 | 0.00 | 0.00 | 0.00 | 0.10 | 0.00 |
| time (sec) |
N/A | 1.607 | 25.000 | 0.877 | 0.000 | 0.000 | 0.000 | 0.000 | 0.200 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | C | F | F | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 132 | 132 | 94 | 202 | 0 | 353 | 0 | 0 | 32 | 118 |
| N.S. |
1 | 1.00 | 0.71 | 1.53 | 0.00 | 2.67 | 0.00 | 0.00 | 0.24 | 0.89 |
| time (sec) |
N/A | 0.588 | 2.876 | 0.661 | 0.000 | 0.100 | 0.000 | 0.000 | 0.218 | 16.790 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F | C | F | F | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 62 | 62 | 61 | 126 | 0 | 143 | 0 | 0 | 26 | 55 |
| N.S. |
1 | 1.00 | 0.98 | 2.03 | 0.00 | 2.31 | 0.00 | 0.00 | 0.42 | 0.89 |
| time (sec) |
N/A | 0.286 | 0.123 | 0.344 | 0.000 | 0.093 | 0.000 | 0.000 | 0.184 | 16.691 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F | F(-1) | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 63 | 63 | 62 | 135 | 0 | 0 | 0 | 0 | 32 | 0 |
| N.S. |
1 | 1.00 | 0.98 | 2.14 | 0.00 | 0.00 | 0.00 | 0.00 | 0.51 | 0.00 |
| time (sec) |
N/A | 0.379 | 0.771 | 0.366 | 0.000 | 0.000 | 0.000 | 0.000 | 0.198 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | F | F(-1) | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 222 | 234 | 315 | 410 | 0 | 0 | 0 | 0 | 34 | 0 |
| N.S. |
1 | 1.05 | 1.42 | 1.85 | 0.00 | 0.00 | 0.00 | 0.00 | 0.15 | 0.00 |
| time (sec) |
N/A | 1.700 | 13.982 | 0.476 | 0.000 | 0.000 | 0.000 | 0.000 | 0.195 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | C | F | F(-1) | F | F(-2) | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 371 | 385 | 10847 | 4217 | 0 | 0 | 0 | 0 | 21 | 0 |
| N.S. |
1 | 1.04 | 29.24 | 11.37 | 0.00 | 0.00 | 0.00 | 0.00 | 0.06 | 0.00 |
| time (sec) |
N/A | 1.418 | 29.280 | 2.522 | 0.000 | 0.000 | 0.000 | 0.000 | 0.191 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 109 | 109 | 172 | 266 | 0 | 0 | 0 | 0 | 42 | 0 |
| N.S. |
1 | 1.00 | 1.58 | 2.44 | 0.00 | 0.00 | 0.00 | 0.00 | 0.39 | 0.00 |
| time (sec) |
N/A | 0.268 | 5.093 | 1.887 | 0.000 | 0.000 | 0.000 | 0.000 | 0.192 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 270 | 265 | 219 | 0 | 0 | 0 | 0 | 0 | 90 | 0 |
| N.S. |
1 | 0.98 | 0.81 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.33 | 0.00 |
| time (sec) |
N/A | 0.914 | 1.327 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.195 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 194 | 190 | 167 | 0 | 0 | 0 | 0 | 0 | 63 | 0 |
| N.S. |
1 | 0.98 | 0.86 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.32 | 0.00 |
| time (sec) |
N/A | 0.554 | 0.498 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.201 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 139 | 139 | 111 | 0 | 0 | 0 | 0 | 0 | 36 | 0 |
| N.S. |
1 | 1.00 | 0.80 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.26 | 0.00 |
| time (sec) |
N/A | 0.320 | 0.204 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.200 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | B | F | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 195 | 195 | 1590 | 0 | 0 | 0 | 0 | 0 | 27 | 0 |
| N.S. |
1 | 1.00 | 8.15 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.14 | 0.00 |
| time (sec) |
N/A | 0.553 | 19.833 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.219 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | B | F | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 306 | 306 | 1790 | 0 | 0 | 0 | 0 | 0 | 43 | 0 |
| N.S. |
1 | 1.00 | 5.85 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.14 | 0.00 |
| time (sec) |
N/A | 0.756 | 21.617 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.212 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | B | F | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 406 | 406 | 2298 | 0 | 0 | 0 | 0 | 0 | 59 | 0 |
| N.S. |
1 | 1.00 | 5.66 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.15 | 0.00 |
| time (sec) |
N/A | 0.959 | 25.073 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.218 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 142 | 142 | 249 | 0 | 0 | 0 | 0 | 0 | 97 | 0 |
| N.S. |
1 | 1.00 | 1.75 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.68 | 0.00 |
| time (sec) |
N/A | 0.480 | 0.587 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.203 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | F(-1) | F | F | B |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 73 | 73 | 110 | 0 | 0 | 0 | 0 | 0 | 35 | 127 |
| N.S. |
1 | 1.00 | 1.51 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.48 | 1.74 |
| time (sec) |
N/A | 0.359 | 0.264 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.222 | 18.130 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | 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 | TBD |
| size | 23 | 23 | 25 | 23 | 25 | 25 | 22 | 25 | 27 | 25 |
| N.S. |
1 | 1.00 | 1.09 | 1.00 | 1.09 | 1.09 | 0.96 | 1.09 | 1.17 | 1.09 |
| time (sec) |
N/A | 0.228 | 3.396 | 0.239 | 1.143 | 0.112 | 17.953 | 0.516 | 0.215 | 18.179 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | F | F | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 352 | 347 | 0 | 0 | 0 | 0 | 0 | 0 | 23 | 0 |
| N.S. |
1 | 0.99 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.07 | 0.00 |
| time (sec) |
N/A | 0.949 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.226 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | F | F | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 275 | 274 | 0 | 0 | 0 | 0 | 0 | 0 | 23 | 0 |
| N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.08 | 0.00 |
| time (sec) |
N/A | 0.615 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.224 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 221 | 220 | 193 | 0 | 0 | 0 | 0 | 0 | 21 | 0 |
| N.S. |
1 | 1.00 | 0.87 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.10 | 0.00 |
| time (sec) |
N/A | 0.436 | 0.606 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.221 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 104 | 104 | 120 | 0 | 0 | 0 | 0 | 0 | 14 | 0 |
| N.S. |
1 | 1.00 | 1.15 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.13 | 0.00 |
| time (sec) |
N/A | 0.256 | 0.415 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.204 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | 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 | TBD |
| size | 19 | 19 | 21 | 19 | 21 | 21 | 19 | 21 | 21 | 23 |
| N.S. |
1 | 1.00 | 1.11 | 1.00 | 1.11 | 1.11 | 1.00 | 1.11 | 1.11 | 1.21 |
| time (sec) |
N/A | 0.203 | 3.965 | 0.330 | 0.870 | 0.090 | 4.957 | 0.183 | 0.216 | 17.016 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | F | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 103 | 103 | 0 | 0 | 0 | 0 | 0 | 0 | 27 | 0 |
| N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.26 | 0.00 |
| time (sec) |
N/A | 0.622 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.212 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | 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 | TBD |
| size | 23 | 23 | 25 | 23 | 25 | 25 | 22 | 25 | 27 | 27 |
| N.S. |
1 | 1.00 | 1.09 | 1.00 | 1.09 | 1.09 | 0.96 | 1.09 | 1.17 | 1.17 |
| time (sec) |
N/A | 0.330 | 4.094 | 0.519 | 1.125 | 0.107 | 9.284 | 0.244 | 0.207 | 17.175 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 298 | 298 | 167 | 0 | 0 | 0 | 0 | 0 | 90 | 0 |
| N.S. |
1 | 1.00 | 0.56 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.30 | 0.00 |
| time (sec) |
N/A | 1.721 | 2.648 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.214 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 213 | 203 | 135 | 0 | 0 | 0 | 0 | 0 | 63 | 0 |
| N.S. |
1 | 0.95 | 0.63 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.30 | 0.00 |
| time (sec) |
N/A | 0.993 | 2.170 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.202 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 149 | 148 | 105 | 0 | 0 | 0 | 0 | 0 | 36 | 0 |
| N.S. |
1 | 0.99 | 0.70 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.24 | 0.00 |
| time (sec) |
N/A | 0.548 | 0.813 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.199 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | B | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 204 | 216 | 1665 | 0 | 0 | 0 | 0 | 0 | 27 | 0 |
| N.S. |
1 | 1.06 | 8.16 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.13 | 0.00 |
| time (sec) |
N/A | 0.817 | 20.992 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.211 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | B | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 321 | 320 | 1872 | 0 | 0 | 0 | 0 | 0 | 43 | 0 |
| N.S. |
1 | 1.00 | 5.83 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.13 | 0.00 |
| time (sec) |
N/A | 0.933 | 24.213 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.223 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | B | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 432 | 418 | 2406 | 0 | 0 | 0 | 0 | 0 | 59 | 0 |
| N.S. |
1 | 0.97 | 5.57 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.14 | 0.00 |
| time (sec) |
N/A | 1.052 | 26.526 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.189 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 116 | 118 | 64 | 68 | 146 | 77 | 314 | 95 | 85 | 292 |
| N.S. |
1 | 1.02 | 0.55 | 0.59 | 1.26 | 0.66 | 2.71 | 0.82 | 0.73 | 2.52 |
| time (sec) |
N/A | 0.583 | 0.905 | 93.085 | 0.036 | 0.086 | 0.271 | 0.134 | 0.173 | 18.259 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 83 | 83 | 54 | 57 | 86 | 63 | 196 | 77 | 69 | 250 |
| N.S. |
1 | 1.00 | 0.65 | 0.69 | 1.04 | 0.76 | 2.36 | 0.93 | 0.83 | 3.01 |
| time (sec) |
N/A | 0.446 | 1.207 | 12.292 | 0.034 | 0.085 | 0.175 | 0.133 | 0.166 | 18.516 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 52 | 47 | 42 | 44 | 77 | 46 | 133 | 59 | 53 | 125 |
| N.S. |
1 | 0.90 | 0.81 | 0.85 | 1.48 | 0.88 | 2.56 | 1.13 | 1.02 | 2.40 |
| time (sec) |
N/A | 0.315 | 0.541 | 10.347 | 0.032 | 0.088 | 0.122 | 0.128 | 0.168 | 19.041 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 29 | 29 | 25 | 22 | 37 | 26 | 70 | 22 | 24 | 54 |
| N.S. |
1 | 1.00 | 0.86 | 0.76 | 1.28 | 0.90 | 2.41 | 0.76 | 0.83 | 1.86 |
| time (sec) |
N/A | 0.188 | 0.032 | 0.631 | 0.033 | 0.082 | 0.083 | 0.123 | 0.178 | 17.980 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | B | C | B | A | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 33 | 33 | 83 | 32 | 82 | 66 | 88 | 35 | 49 | 46 |
| N.S. |
1 | 1.00 | 2.52 | 0.97 | 2.48 | 2.00 | 2.67 | 1.06 | 1.48 | 1.39 |
| time (sec) |
N/A | 0.258 | 2.372 | 0.370 | 0.115 | 0.086 | 0.565 | 0.129 | 0.161 | 17.974 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | B | A | B | B | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 30 | 30 | 74 | 38 | 217 | 104 | 158 | 37 | 72 | 56 |
| N.S. |
1 | 1.00 | 2.47 | 1.27 | 7.23 | 3.47 | 5.27 | 1.23 | 2.40 | 1.87 |
| time (sec) |
N/A | 0.279 | 2.523 | 0.467 | 0.038 | 0.070 | 1.157 | 0.129 | 0.177 | 17.985 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | C | B | B | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 60 | 63 | 96 | 62 | 389 | 154 | 571 | 79 | 126 | 136 |
| N.S. |
1 | 1.05 | 1.60 | 1.03 | 6.48 | 2.57 | 9.52 | 1.32 | 2.10 | 2.27 |
| time (sec) |
N/A | 0.385 | 4.222 | 0.561 | 0.041 | 0.078 | 2.472 | 0.141 | 0.178 | 18.058 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | C | B | B | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 92 | 99 | 109 | 75 | 561 | 206 | 1061 | 107 | 178 | 97 |
| N.S. |
1 | 1.08 | 1.18 | 0.82 | 6.10 | 2.24 | 11.53 | 1.16 | 1.93 | 1.05 |
| time (sec) |
N/A | 0.508 | 5.702 | 0.754 | 0.047 | 0.074 | 5.277 | 0.144 | 0.176 | 18.225 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | C | B | B | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 126 | 135 | 124 | 85 | 733 | 256 | 1700 | 135 | 246 | 119 |
| N.S. |
1 | 1.07 | 0.98 | 0.67 | 5.82 | 2.03 | 13.49 | 1.07 | 1.95 | 0.94 |
| time (sec) |
N/A | 0.645 | 5.879 | 0.952 | 0.051 | 0.079 | 10.234 | 0.156 | 0.180 | 19.260 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 152 | 148 | 89 | 255 | 256 | 103 | 629 | 147 | 119 | 452 |
| N.S. |
1 | 0.97 | 0.59 | 1.68 | 1.68 | 0.68 | 4.14 | 0.97 | 0.78 | 2.97 |
| time (sec) |
N/A | 0.693 | 4.408 | 1.172 | 0.039 | 0.097 | 0.545 | 0.157 | 0.168 | 19.950 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 118 | 113 | 79 | 211 | 209 | 87 | 530 | 127 | 103 | 284 |
| N.S. |
1 | 0.96 | 0.67 | 1.79 | 1.77 | 0.74 | 4.49 | 1.08 | 0.87 | 2.41 |
| time (sec) |
N/A | 0.557 | 7.843 | 0.916 | 0.040 | 0.092 | 0.397 | 0.143 | 0.164 | 19.835 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | B | A | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 85 | 77 | 69 | 70 | 158 | 71 | 340 | 107 | 87 | 220 |
| N.S. |
1 | 0.91 | 0.81 | 0.82 | 1.86 | 0.84 | 4.00 | 1.26 | 1.02 | 2.59 |
| time (sec) |
N/A | 0.419 | 9.191 | 282.368 | 0.038 | 0.096 | 0.272 | 0.137 | 0.167 | 20.688 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 64 | 58 | 39 | 37 | 81 | 54 | 206 | 50 | 46 | 36 |
| N.S. |
1 | 0.91 | 0.61 | 0.58 | 1.27 | 0.84 | 3.22 | 0.78 | 0.72 | 0.56 |
| time (sec) |
N/A | 0.330 | 0.062 | 14.439 | 0.033 | 0.081 | 0.178 | 0.130 | 0.163 | 18.376 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 52 | 47 | 43 | 44 | 77 | 46 | 133 | 59 | 53 | 125 |
| N.S. |
1 | 0.90 | 0.83 | 0.85 | 1.48 | 0.88 | 2.56 | 1.13 | 1.02 | 2.40 |
| time (sec) |
N/A | 0.325 | 0.934 | 10.418 | 0.031 | 0.095 | 0.122 | 0.126 | 0.172 | 20.408 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | B | A | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 57 | 62 | 71 | 55 | 218 | 105 | 454 | 97 | 76 | 118 |
| N.S. |
1 | 1.09 | 1.25 | 0.96 | 3.82 | 1.84 | 7.96 | 1.70 | 1.33 | 2.07 |
| time (sec) |
N/A | 0.438 | 0.360 | 0.583 | 0.114 | 0.093 | 1.035 | 0.130 | 0.175 | 17.068 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | B | B | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 72 | 79 | 121 | 53 | 364 | 158 | 473 | 57 | 110 | 90 |
| N.S. |
1 | 1.10 | 1.68 | 0.74 | 5.06 | 2.19 | 6.57 | 0.79 | 1.53 | 1.25 |
| time (sec) |
N/A | 0.428 | 8.169 | 0.780 | 0.120 | 0.081 | 2.114 | 0.143 | 0.163 | 19.202 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | B | A | B | B | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 34 | 34 | 81 | 53 | 557 | 168 | 354 | 57 | 112 | 92 |
| N.S. |
1 | 1.00 | 2.38 | 1.56 | 16.38 | 4.94 | 10.41 | 1.68 | 3.29 | 2.71 |
| time (sec) |
N/A | 0.311 | 3.691 | 0.682 | 0.047 | 0.078 | 4.510 | 0.145 | 0.170 | 20.691 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | C | B | B | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 67 | 67 | 117 | 87 | 816 | 222 | 1074 | 121 | 180 | 99 |
| N.S. |
1 | 1.00 | 1.75 | 1.30 | 12.18 | 3.31 | 16.03 | 1.81 | 2.69 | 1.48 |
| time (sec) |
N/A | 0.420 | 3.924 | 0.910 | 0.058 | 0.082 | 8.779 | 0.148 | 0.166 | 17.930 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | C | B | B | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 98 | 103 | 121 | 116 | 1073 | 278 | 1717 | 153 | 248 | 121 |
| N.S. |
1 | 1.05 | 1.23 | 1.18 | 10.95 | 2.84 | 17.52 | 1.56 | 2.53 | 1.23 |
| time (sec) |
N/A | 0.548 | 4.575 | 1.077 | 0.067 | 0.087 | 16.648 | 0.168 | 0.165 | 18.127 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | C | B | B | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 132 | 139 | 133 | 110 | 1332 | 332 | 2509 | 185 | 302 | 143 |
| N.S. |
1 | 1.05 | 1.01 | 0.83 | 10.09 | 2.52 | 19.01 | 1.40 | 2.29 | 1.08 |
| time (sec) |
N/A | 0.705 | 4.832 | 1.485 | 0.075 | 0.086 | 29.198 | 0.159 | 0.187 | 18.883 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 180 | 174 | 109 | 297 | 301 | 119 | 838 | 187 | 151 | 403 |
| N.S. |
1 | 0.97 | 0.61 | 1.65 | 1.67 | 0.66 | 4.66 | 1.04 | 0.84 | 2.24 |
| time (sec) |
N/A | 0.819 | 9.211 | 1.378 | 0.042 | 0.097 | 1.038 | 0.163 | 0.165 | 19.116 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | B | A | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 145 | 139 | 89 | 276 | 282 | 103 | 740 | 147 | 135 | 372 |
| N.S. |
1 | 0.96 | 0.61 | 1.90 | 1.94 | 0.71 | 5.10 | 1.01 | 0.93 | 2.57 |
| time (sec) |
N/A | 0.664 | 9.360 | 1.137 | 0.039 | 0.097 | 0.756 | 0.162 | 0.173 | 20.834 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | B | A | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 112 | 103 | 89 | 255 | 256 | 87 | 631 | 147 | 119 | 301 |
| N.S. |
1 | 0.92 | 0.79 | 2.28 | 2.29 | 0.78 | 5.63 | 1.31 | 1.06 | 2.69 |
| time (sec) |
N/A | 0.501 | 8.308 | 1.131 | 0.040 | 0.095 | 0.538 | 0.145 | 0.168 | 20.745 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 91 | 84 | 49 | 140 | 132 | 70 | 398 | 70 | 62 | 143 |
| N.S. |
1 | 0.92 | 0.54 | 1.54 | 1.45 | 0.77 | 4.37 | 0.77 | 0.68 | 1.57 |
| time (sec) |
N/A | 0.407 | 0.058 | 0.464 | 0.035 | 0.081 | 0.371 | 0.140 | 0.178 | 19.305 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | B | A | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 85 | 77 | 69 | 160 | 158 | 71 | 340 | 107 | 87 | 220 |
| N.S. |
1 | 0.91 | 0.81 | 1.88 | 1.86 | 0.84 | 4.00 | 1.26 | 1.02 | 2.59 |
| time (sec) |
N/A | 0.418 | 8.747 | 0.721 | 0.035 | 0.084 | 0.272 | 0.131 | 0.185 | 20.099 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 82 | 82 | 54 | 89 | 86 | 63 | 196 | 77 | 69 | 250 |
| N.S. |
1 | 1.00 | 0.66 | 1.09 | 1.05 | 0.77 | 2.39 | 0.94 | 0.84 | 3.05 |
| time (sec) |
N/A | 0.436 | 0.988 | 0.504 | 0.034 | 0.089 | 0.174 | 0.129 | 0.162 | 18.155 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | B | A | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 94 | 102 | 153 | 68 | 433 | 129 | 1168 | 111 | 118 | 219 |
| N.S. |
1 | 1.09 | 1.63 | 0.72 | 4.61 | 1.37 | 12.43 | 1.18 | 1.26 | 2.33 |
| time (sec) |
N/A | 0.550 | 8.958 | 1.557 | 0.124 | 0.088 | 1.994 | 0.132 | 0.179 | 19.190 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | B | B | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 92 | 101 | 149 | 87 | 594 | 184 | 1282 | 96 | 172 | 218 |
| N.S. |
1 | 1.10 | 1.62 | 0.95 | 6.46 | 2.00 | 13.93 | 1.04 | 1.87 | 2.37 |
| time (sec) |
N/A | 0.561 | 9.546 | 1.791 | 0.127 | 0.088 | 4.031 | 0.144 | 0.171 | 18.629 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | B | C | B | B | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 106 | 116 | 249 | 97 | 785 | 235 | 1282 | 105 | 192 | 203 |
| N.S. |
1 | 1.09 | 2.35 | 0.92 | 7.41 | 2.22 | 12.09 | 0.99 | 1.81 | 1.92 |
| time (sec) |
N/A | 0.570 | 8.674 | 1.633 | 0.136 | 0.092 | 7.931 | 0.159 | 0.186 | 18.798 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | B | A | B | B | B | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 34 | 34 | 93 | 64 | 1045 | 222 | 619 | 73 | 148 | 116 |
| N.S. |
1 | 1.00 | 2.74 | 1.88 | 30.74 | 6.53 | 18.21 | 2.15 | 4.35 | 3.41 |
| time (sec) |
N/A | 0.319 | 4.577 | 1.747 | 0.065 | 0.082 | 15.480 | 0.159 | 0.232 | 17.947 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | C | B | B | B | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 69 | 67 | 135 | 110 | 1389 | 276 | 1717 | 153 | 245 | 121 |
| N.S. |
1 | 0.97 | 1.96 | 1.59 | 20.13 | 4.00 | 24.88 | 2.22 | 3.55 | 1.75 |
| time (sec) |
N/A | 0.430 | 5.583 | 1.941 | 0.075 | 0.080 | 28.006 | 0.164 | 0.185 | 18.992 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | C | B | B | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 101 | 103 | 145 | 143 | 1734 | 332 | 2509 | 185 | 302 | 143 |
| N.S. |
1 | 1.02 | 1.44 | 1.42 | 17.17 | 3.29 | 24.84 | 1.83 | 2.99 | 1.42 |
| time (sec) |
N/A | 0.551 | 6.215 | 2.368 | 0.089 | 0.081 | 46.280 | 0.180 | 0.191 | 19.380 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | C | B | B | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 132 | 139 | 157 | 133 | 2078 | 386 | 3451 | 217 | 352 | 165 |
| N.S. |
1 | 1.05 | 1.19 | 1.01 | 15.74 | 2.92 | 26.14 | 1.64 | 2.67 | 1.25 |
| time (sec) |
N/A | 0.707 | 8.787 | 2.427 | 0.103 | 0.084 | 73.352 | 0.197 | 0.184 | 20.784 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | C | B | B | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 166 | 175 | 209 | 174 | 2422 | 440 | 4542 | 249 | 406 | 187 |
| N.S. |
1 | 1.05 | 1.26 | 1.05 | 14.59 | 2.65 | 27.36 | 1.50 | 2.45 | 1.13 |
| time (sec) |
N/A | 0.859 | 9.395 | 2.950 | 0.129 | 0.092 | 117.211 | 0.195 | 0.167 | 21.828 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | B | A | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 118 | 123 | 175 | 79 | 720 | 156 | 2108 | 128 | 147 | 290 |
| N.S. |
1 | 1.04 | 1.48 | 0.67 | 6.10 | 1.32 | 17.86 | 1.08 | 1.25 | 2.46 |
| time (sec) |
N/A | 0.665 | 14.044 | 9.956 | 0.130 | 0.087 | 3.797 | 0.138 | 0.189 | 20.505 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | B | A | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 92 | 99 | 155 | 68 | 424 | 128 | 1170 | 111 | 121 | 216 |
| N.S. |
1 | 1.08 | 1.68 | 0.74 | 4.61 | 1.39 | 12.72 | 1.21 | 1.32 | 2.35 |
| time (sec) |
N/A | 0.544 | 12.260 | 1.521 | 0.126 | 0.086 | 1.999 | 0.144 | 0.166 | 19.141 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | B | A | B | A | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 56 | 60 | 129 | 57 | 210 | 101 | 456 | 94 | 77 | 118 |
| N.S. |
1 | 1.07 | 2.30 | 1.02 | 3.75 | 1.80 | 8.14 | 1.68 | 1.38 | 2.11 |
| time (sec) |
N/A | 0.417 | 6.417 | 0.555 | 0.113 | 0.086 | 1.039 | 0.132 | 0.177 | 17.942 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | B | C | B | A | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 32 | 32 | 79 | 32 | 77 | 64 | 90 | 35 | 50 | 45 |
| N.S. |
1 | 1.00 | 2.47 | 1.00 | 2.41 | 2.00 | 2.81 | 1.09 | 1.56 | 1.41 |
| time (sec) |
N/A | 0.262 | 1.989 | 0.357 | 0.110 | 0.079 | 0.581 | 0.132 | 0.256 | 17.484 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 16 | 16 | 16 | 17 | 16 | 24 | 49 | 16 | 24 | 35 |
| N.S. |
1 | 1.00 | 1.00 | 1.06 | 1.00 | 1.50 | 3.06 | 1.00 | 1.50 | 2.19 |
| time (sec) |
N/A | 0.283 | 0.018 | 0.591 | 0.033 | 0.079 | 0.576 | 0.127 | 0.252 | 16.998 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | C | B | A | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 53 | 50 | 98 | 54 | 142 | 56 | 328 | 73 | 71 | 74 |
| N.S. |
1 | 0.94 | 1.85 | 1.02 | 2.68 | 1.06 | 6.19 | 1.38 | 1.34 | 1.40 |
| time (sec) |
N/A | 0.408 | 1.181 | 0.534 | 0.039 | 0.081 | 1.206 | 0.132 | 0.289 | 17.801 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | B | A | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 85 | 84 | 118 | 51 | 211 | 83 | 614 | 99 | 107 | 89 |
| N.S. |
1 | 0.99 | 1.39 | 0.60 | 2.48 | 0.98 | 7.22 | 1.16 | 1.26 | 1.05 |
| time (sec) |
N/A | 0.536 | 1.616 | 0.768 | 0.039 | 0.080 | 2.447 | 0.144 | 0.179 | 17.895 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | C | B | A | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 118 | 118 | 154 | 77 | 319 | 111 | 1307 | 125 | 143 | 96 |
| N.S. |
1 | 1.00 | 1.31 | 0.65 | 2.70 | 0.94 | 11.08 | 1.06 | 1.21 | 0.81 |
| time (sec) |
N/A | 0.666 | 2.131 | 1.060 | 0.043 | 0.086 | 5.033 | 0.142 | 0.180 | 17.803 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | B | A | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 148 | 159 | 276 | 124 | 1304 | 238 | 3641 | 191 | 224 | 372 |
| N.S. |
1 | 1.07 | 1.86 | 0.84 | 8.81 | 1.61 | 24.60 | 1.29 | 1.51 | 2.51 |
| time (sec) |
N/A | 0.827 | 12.539 | 86.333 | 0.138 | 0.145 | 13.167 | 0.159 | 0.194 | 20.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | B | A | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 135 | 137 | 243 | 125 | 903 | 210 | 2312 | 144 | 198 | 291 |
| N.S. |
1 | 1.01 | 1.80 | 0.93 | 6.69 | 1.56 | 17.13 | 1.07 | 1.47 | 2.16 |
| time (sec) |
N/A | 0.680 | 12.138 | 10.127 | 0.134 | 0.090 | 7.640 | 0.150 | 0.183 | 20.247 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | B | A | B | B | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 90 | 98 | 210 | 85 | 590 | 185 | 1282 | 96 | 172 | 217 |
| N.S. |
1 | 1.09 | 2.33 | 0.94 | 6.56 | 2.06 | 14.24 | 1.07 | 1.91 | 2.41 |
| time (sec) |
N/A | 0.536 | 12.033 | 1.860 | 0.127 | 0.080 | 4.042 | 0.146 | 0.186 | 19.584 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | B | B | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 70 | 77 | 119 | 53 | 361 | 158 | 473 | 55 | 110 | 89 |
| N.S. |
1 | 1.10 | 1.70 | 0.76 | 5.16 | 2.26 | 6.76 | 0.79 | 1.57 | 1.27 |
| time (sec) |
N/A | 0.423 | 2.351 | 0.788 | 0.121 | 0.088 | 2.114 | 0.143 | 0.172 | 17.744 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | B | A | B | B | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 29 | 29 | 70 | 38 | 215 | 104 | 158 | 37 | 70 | 54 |
| N.S. |
1 | 1.00 | 2.41 | 1.31 | 7.41 | 3.59 | 5.45 | 1.28 | 2.41 | 1.86 |
| time (sec) |
N/A | 0.287 | 1.607 | 0.473 | 0.038 | 0.073 | 1.190 | 0.134 | 0.169 | 16.932 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | C | B | A | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 52 | 49 | 98 | 54 | 142 | 55 | 328 | 73 | 71 | 74 |
| N.S. |
1 | 0.94 | 1.88 | 1.04 | 2.73 | 1.06 | 6.31 | 1.40 | 1.37 | 1.42 |
| time (sec) |
N/A | 0.385 | 0.838 | 0.499 | 0.039 | 0.072 | 1.228 | 0.139 | 0.196 | 17.748 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 38 | 32 | 29 | 30 | 28 | 37 | 286 | 28 | 49 | 63 |
| N.S. |
1 | 0.84 | 0.76 | 0.79 | 0.74 | 0.97 | 7.53 | 0.74 | 1.29 | 1.66 |
| time (sec) |
N/A | 0.302 | 0.053 | 0.866 | 0.033 | 0.075 | 1.333 | 0.134 | 0.178 | 17.092 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | C | B | A | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 76 | 67 | 138 | 77 | 335 | 86 | 1418 | 125 | 143 | 128 |
| N.S. |
1 | 0.88 | 1.82 | 1.01 | 4.41 | 1.13 | 18.66 | 1.64 | 1.88 | 1.68 |
| time (sec) |
N/A | 0.415 | 1.497 | 1.123 | 0.044 | 0.077 | 5.040 | 0.145 | 0.194 | 18.383 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | C | B | A | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 111 | 103 | 174 | 89 | 427 | 113 | 2213 | 151 | 153 | 119 |
| N.S. |
1 | 0.93 | 1.57 | 0.80 | 3.85 | 1.02 | 19.94 | 1.36 | 1.38 | 1.07 |
| time (sec) |
N/A | 0.533 | 1.938 | 1.648 | 0.045 | 0.079 | 10.293 | 0.145 | 0.173 | 17.262 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | C | B | A | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 144 | 139 | 193 | 100 | 519 | 143 | 3186 | 177 | 215 | 180 |
| N.S. |
1 | 0.97 | 1.34 | 0.69 | 3.60 | 0.99 | 22.12 | 1.23 | 1.49 | 1.25 |
| time (sec) |
N/A | 0.693 | 7.342 | 2.473 | 0.049 | 0.081 | 21.262 | 0.160 | 0.187 | 20.630 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | B | A | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 161 | 175 | 303 | 156 | 1496 | 285 | 3643 | 176 | 280 | 364 |
| N.S. |
1 | 1.09 | 1.88 | 0.97 | 9.29 | 1.77 | 22.63 | 1.09 | 1.74 | 2.26 |
| time (sec) |
N/A | 0.843 | 17.483 | 86.113 | 0.145 | 0.105 | 24.311 | 0.164 | 0.202 | 24.922 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | B | A | B | B | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 124 | 136 | 270 | 102 | 1096 | 256 | 2314 | 128 | 254 | 290 |
| N.S. |
1 | 1.10 | 2.18 | 0.82 | 8.84 | 2.06 | 18.66 | 1.03 | 2.05 | 2.34 |
| time (sec) |
N/A | 0.664 | 13.304 | 10.160 | 0.137 | 0.089 | 14.218 | 0.156 | 0.181 | 20.171 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | B | C | B | B | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 103 | 113 | 239 | 97 | 781 | 233 | 1284 | 105 | 192 | 200 |
| N.S. |
1 | 1.10 | 2.32 | 0.94 | 7.58 | 2.26 | 12.47 | 1.02 | 1.86 | 1.94 |
| time (sec) |
N/A | 0.544 | 4.127 | 1.704 | 0.130 | 0.084 | 8.142 | 0.149 | 0.190 | 18.266 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | B | A | B | B | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 33 | 33 | 81 | 53 | 554 | 168 | 354 | 57 | 111 | 90 |
| N.S. |
1 | 1.00 | 2.45 | 1.61 | 16.79 | 5.09 | 10.73 | 1.73 | 3.36 | 2.73 |
| time (sec) |
N/A | 0.294 | 3.322 | 0.703 | 0.050 | 0.083 | 4.534 | 0.147 | 0.189 | 17.664 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | C | B | B | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 58 | 61 | 92 | 62 | 387 | 154 | 573 | 79 | 126 | 134 |
| N.S. |
1 | 1.05 | 1.59 | 1.07 | 6.67 | 2.66 | 9.88 | 1.36 | 2.17 | 2.31 |
| time (sec) |
N/A | 0.374 | 3.187 | 0.551 | 0.042 | 0.074 | 2.544 | 0.142 | 0.188 | 17.712 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | B | A | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 83 | 82 | 134 | 51 | 211 | 82 | 614 | 99 | 104 | 89 |
| N.S. |
1 | 0.99 | 1.61 | 0.61 | 2.54 | 0.99 | 7.40 | 1.19 | 1.25 | 1.07 |
| time (sec) |
N/A | 0.492 | 1.499 | 0.737 | 0.038 | 0.074 | 2.438 | 0.145 | 0.194 | 17.639 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | B | C | B | A | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 75 | 66 | 154 | 77 | 335 | 85 | 1418 | 125 | 141 | 128 |
| N.S. |
1 | 0.88 | 2.05 | 1.03 | 4.47 | 1.13 | 18.91 | 1.67 | 1.88 | 1.71 |
| time (sec) |
N/A | 0.410 | 2.086 | 1.091 | 0.044 | 0.078 | 5.099 | 0.155 | 0.183 | 17.788 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 59 | 44 | 41 | 40 | 40 | 47 | 687 | 40 | 69 | 89 |
| N.S. |
1 | 0.75 | 0.69 | 0.68 | 0.68 | 0.80 | 11.64 | 0.68 | 1.17 | 1.51 |
| time (sec) |
N/A | 0.296 | 0.140 | 1.307 | 0.037 | 0.075 | 3.942 | 0.150 | 0.245 | 18.495 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | C | B | A | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 97 | 79 | 193 | 100 | 519 | 106 | 3186 | 177 | 213 | 180 |
| N.S. |
1 | 0.81 | 1.99 | 1.03 | 5.35 | 1.09 | 32.85 | 1.82 | 2.20 | 1.86 |
| time (sec) |
N/A | 0.425 | 7.427 | 2.402 | 0.050 | 0.084 | 21.188 | 0.151 | 0.210 | 19.635 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | C | B | A | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 131 | 115 | 213 | 110 | 610 | 133 | 4335 | 203 | 251 | 190 |
| N.S. |
1 | 0.88 | 1.63 | 0.84 | 4.66 | 1.02 | 33.09 | 1.55 | 1.92 | 1.45 |
| time (sec) |
N/A | 0.538 | 10.494 | 3.250 | 0.054 | 0.084 | 38.476 | 0.171 | 0.198 | 18.950 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | C | B | A | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 167 | 151 | 233 | 123 | 703 | 163 | 5661 | 229 | 285 | 185 |
| N.S. |
1 | 0.90 | 1.40 | 0.74 | 4.21 | 0.98 | 33.90 | 1.37 | 1.71 | 1.11 |
| time (sec) |
N/A | 0.677 | 11.505 | 4.753 | 0.063 | 0.084 | 66.831 | 0.170 | 0.169 | 18.113 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | A | F(-1) | A | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 137 | 142 | 104 | 79 | 0 | 179 | 0 | 136 | 91 | 0 |
| N.S. |
1 | 1.04 | 0.76 | 0.58 | 0.00 | 1.31 | 0.00 | 0.99 | 0.66 | 0.00 |
| time (sec) |
N/A | 0.726 | 2.252 | 1.620 | 0.000 | 0.082 | 0.000 | 0.200 | 0.177 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | A | F | A | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 103 | 105 | 94 | 69 | 0 | 152 | 0 | 136 | 89 | 0 |
| N.S. |
1 | 1.02 | 0.91 | 0.67 | 0.00 | 1.48 | 0.00 | 1.32 | 0.86 | 0.00 |
| time (sec) |
N/A | 0.594 | 1.467 | 1.485 | 0.000 | 0.085 | 0.000 | 0.201 | 0.185 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | A | F | A | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 69 | 68 | 82 | 59 | 0 | 109 | 0 | 99 | 43 | 0 |
| N.S. |
1 | 0.99 | 1.19 | 0.86 | 0.00 | 1.58 | 0.00 | 1.43 | 0.62 | 0.00 |
| time (sec) |
N/A | 0.435 | 1.096 | 0.776 | 0.000 | 0.079 | 0.000 | 0.166 | 0.193 | 0.000 |