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 | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 768 | 881 | 65 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.15 | 0.08 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.226 | 10.062 | 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 | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 1032 | 1021 | 141 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.99 | 0.14 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.489 | 10.125 | 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(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 64 | 64 | 65 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.202 | 10.070 | 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(-2) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 64 | 64 | 65 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.204 | 10.062 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 59 | 59 | 161 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 2.73 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.190 | 10.198 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 62 | 62 | 141 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 2.27 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.210 | 10.133 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 64 | 64 | 141 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 2.20 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.209 | 10.145 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 123 | 144 | 130 | 133 | 0 | 475 | 0 | 134 | 144 |
| N.S. |
1 | 1.17 | 1.06 | 1.08 | 0.00 | 3.86 | 0.00 | 1.09 | 1.17 |
| time (sec) |
N/A | 0.280 | 0.536 | 5.954 | 0.000 | 0.278 | 0.000 | 0.274 | 9.483 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 99 | 98 | 100 | 83 | 0 | 348 | 0 | 116 | 95 |
| N.S. |
1 | 0.99 | 1.01 | 0.84 | 0.00 | 3.52 | 0.00 | 1.17 | 0.96 |
| time (sec) |
N/A | 0.235 | 0.273 | 5.837 | 0.000 | 0.324 | 0.000 | 0.273 | 9.294 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 87 | 86 | 86 | 90 | 0 | 302 | 0 | 93 | 84 |
| N.S. |
1 | 0.99 | 0.99 | 1.03 | 0.00 | 3.47 | 0.00 | 1.07 | 0.97 |
| time (sec) |
N/A | 0.219 | 0.251 | 5.819 | 0.000 | 0.413 | 0.000 | 0.265 | 9.137 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | A | F | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 132 | 155 | 124 | 146 | 0 | 862 | 0 | 139 | 3017 |
| N.S. |
1 | 1.17 | 0.94 | 1.11 | 0.00 | 6.53 | 0.00 | 1.05 | 22.86 |
| time (sec) |
N/A | 0.282 | 0.527 | 5.923 | 0.000 | 0.451 | 0.000 | 0.270 | 10.155 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | A | F | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 185 | 213 | 163 | 191 | 0 | 1236 | 0 | 257 | 3832 |
| N.S. |
1 | 1.15 | 0.88 | 1.03 | 0.00 | 6.68 | 0.00 | 1.39 | 20.71 |
| time (sec) |
N/A | 0.361 | 1.023 | 6.152 | 0.000 | 0.522 | 0.000 | 0.270 | 12.251 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | A | F(-1) | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 141 | 166 | 153 | 117 | 0 | 1077 | 0 | 298 | 0 |
| N.S. |
1 | 1.18 | 1.09 | 0.83 | 0.00 | 7.64 | 0.00 | 2.11 | 0.00 |
| time (sec) |
N/A | 0.323 | 4.186 | 24.895 | 0.000 | 1.194 | 0.000 | 0.374 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | B | F(-1) | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 93 | 97 | 112 | 81 | 0 | 426 | 0 | 244 | 0 |
| N.S. |
1 | 1.04 | 1.20 | 0.87 | 0.00 | 4.58 | 0.00 | 2.62 | 0.00 |
| time (sec) |
N/A | 0.238 | 2.026 | 20.282 | 0.000 | 0.353 | 0.000 | 0.993 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | B | F | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 104 | 108 | 124 | 90 | 0 | 467 | 0 | 237 | 0 |
| N.S. |
1 | 1.04 | 1.19 | 0.87 | 0.00 | 4.49 | 0.00 | 2.28 | 0.00 |
| time (sec) |
N/A | 0.243 | 1.825 | 20.214 | 0.000 | 0.394 | 0.000 | 0.373 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | B | F | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 149 | 157 | 157 | 112 | 0 | 612 | 0 | 418 | 0 |
| N.S. |
1 | 1.05 | 1.05 | 0.75 | 0.00 | 4.11 | 0.00 | 2.81 | 0.00 |
| time (sec) |
N/A | 0.327 | 2.131 | 31.252 | 0.000 | 0.554 | 0.000 | 0.928 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | A | F | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 208 | 212 | 201 | 134 | 0 | 760 | 0 | 395 | 0 |
| N.S. |
1 | 1.02 | 0.97 | 0.64 | 0.00 | 3.65 | 0.00 | 1.90 | 0.00 |
| time (sec) |
N/A | 0.405 | 5.337 | 47.789 | 0.000 | 0.661 | 0.000 | 1.049 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | F | F | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 924 | 1033 | 159 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.12 | 0.17 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.491 | 10.164 | 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 | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 999 | 1036 | 169 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.04 | 0.17 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.433 | 10.178 | 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 | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 1060 | 1092 | 225 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.03 | 0.21 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.571 | 10.316 | 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 | F | F | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 1164 | 1107 | 159 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.95 | 0.14 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.550 | 10.171 | 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 | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 1162 | 1093 | 169 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.94 | 0.15 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.420 | 10.198 | 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 | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 1243 | 1170 | 226 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.94 | 0.18 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.535 | 10.310 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 64 | 64 | 170 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 2.66 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.201 | 10.217 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 64 | 64 | 170 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 2.66 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.198 | 10.186 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 59 | 59 | 328 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 5.56 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.181 | 10.296 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 62 | 62 | 226 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 3.65 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.202 | 10.330 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 64 | 64 | 226 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 3.53 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.208 | 10.320 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | A | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 123 | 112 | 118 | 116 | 243 | 242 | 226 | 143 | 134 |
| N.S. |
1 | 0.91 | 0.96 | 0.94 | 1.98 | 1.97 | 1.84 | 1.16 | 1.09 |
| time (sec) |
N/A | 0.217 | 0.644 | 0.093 | 0.294 | 0.432 | 24.897 | 0.273 | 10.008 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | A | A | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 90 | 86 | 97 | 91 | 159 | 191 | 144 | 105 | 93 |
| N.S. |
1 | 0.96 | 1.08 | 1.01 | 1.77 | 2.12 | 1.60 | 1.17 | 1.03 |
| time (sec) |
N/A | 0.205 | 0.171 | 0.075 | 0.303 | 0.435 | 17.849 | 0.280 | 9.655 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | A | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 84 | 78 | 80 | 77 | 108 | 155 | 107 | 87 | 68 |
| N.S. |
1 | 0.93 | 0.95 | 0.92 | 1.29 | 1.85 | 1.27 | 1.04 | 0.81 |
| time (sec) |
N/A | 0.200 | 0.261 | 0.083 | 0.287 | 0.453 | 17.144 | 0.328 | 9.611 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 59 | 66 | 82 | 84 | 67 | 166 | 85 | 163 | 57 |
| N.S. |
1 | 1.12 | 1.39 | 1.42 | 1.14 | 2.81 | 1.44 | 2.76 | 0.97 |
| time (sec) |
N/A | 0.191 | 0.205 | 0.082 | 0.289 | 0.307 | 4.533 | 0.471 | 9.554 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 46 | 50 | 47 | 48 | 49 | 60 | 73 | 250 | 91 |
| N.S. |
1 | 1.09 | 1.02 | 1.04 | 1.07 | 1.30 | 1.59 | 5.43 | 1.98 |
| time (sec) |
N/A | 0.190 | 0.149 | 0.069 | 0.208 | 0.356 | 1.178 | 0.592 | 9.221 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 74 | 78 | 69 | 70 | 84 | 85 | 109 | 310 | 126 |
| N.S. |
1 | 1.05 | 0.93 | 0.95 | 1.14 | 1.15 | 1.47 | 4.19 | 1.70 |
| time (sec) |
N/A | 0.218 | 0.199 | 0.087 | 0.203 | 0.284 | 1.211 | 0.806 | 9.431 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 104 | 108 | 93 | 94 | 118 | 109 | 143 | 370 | 168 |
| N.S. |
1 | 1.04 | 0.89 | 0.90 | 1.13 | 1.05 | 1.38 | 3.56 | 1.62 |
| time (sec) |
N/A | 0.242 | 0.225 | 0.104 | 0.202 | 0.326 | 1.293 | 0.989 | 9.704 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 134 | 138 | 113 | 118 | 152 | 133 | 177 | 430 | 210 |
| N.S. |
1 | 1.03 | 0.84 | 0.88 | 1.13 | 0.99 | 1.32 | 3.21 | 1.57 |
| time (sec) |
N/A | 0.269 | 0.255 | 0.141 | 0.211 | 0.362 | 1.382 | 1.487 | 10.113 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 150 | 143 | 108 | 113 | 158 | 131 | 1386 | 175 | 117 |
| N.S. |
1 | 0.95 | 0.72 | 0.75 | 1.05 | 0.87 | 9.24 | 1.17 | 0.78 |
| time (sec) |
N/A | 0.266 | 0.102 | 0.095 | 0.198 | 0.303 | 2.757 | 0.275 | 9.161 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 117 | 113 | 88 | 89 | 124 | 107 | 910 | 140 | 97 |
| N.S. |
1 | 0.97 | 0.75 | 0.76 | 1.06 | 0.91 | 7.78 | 1.20 | 0.83 |
| time (sec) |
N/A | 0.240 | 0.084 | 0.081 | 0.200 | 0.286 | 2.252 | 0.269 | 8.914 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 84 | 83 | 64 | 65 | 90 | 82 | 422 | 105 | 77 |
| N.S. |
1 | 0.99 | 0.76 | 0.77 | 1.07 | 0.98 | 5.02 | 1.25 | 0.92 |
| time (sec) |
N/A | 0.210 | 0.066 | 0.068 | 0.197 | 0.285 | 1.654 | 0.270 | 9.047 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 53 | 53 | 42 | 43 | 55 | 57 | 119 | 72 | 54 |
| N.S. |
1 | 1.00 | 0.79 | 0.81 | 1.04 | 1.08 | 2.25 | 1.36 | 1.02 |
| time (sec) |
N/A | 0.185 | 0.049 | 0.060 | 0.217 | 0.277 | 1.230 | 0.623 | 8.905 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 66 | 68 | 68 | 83 | 75 | 156 | 107 | 116 | 80 |
| N.S. |
1 | 1.03 | 1.03 | 1.26 | 1.14 | 2.36 | 1.62 | 1.76 | 1.21 |
| time (sec) |
N/A | 0.195 | 0.128 | 0.059 | 0.282 | 0.359 | 1.427 | 0.267 | 9.183 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | A | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 85 | 81 | 75 | 93 | 133 | 164 | 107 | 76 | 97 |
| N.S. |
1 | 0.95 | 0.88 | 1.09 | 1.56 | 1.93 | 1.26 | 0.89 | 1.14 |
| time (sec) |
N/A | 0.197 | 0.200 | 0.095 | 0.295 | 0.426 | 2.024 | 0.285 | 9.635 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | A | A | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 91 | 88 | 91 | 102 | 193 | 194 | 144 | 130 | 0 |
| N.S. |
1 | 0.97 | 1.00 | 1.12 | 2.12 | 2.13 | 1.58 | 1.43 | 0.00 |
| time (sec) |
N/A | 0.215 | 0.253 | 0.085 | 0.286 | 0.371 | 3.287 | 0.291 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | A | B | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 123 | 115 | 124 | 127 | 277 | 244 | 226 | 153 | 0 |
| N.S. |
1 | 0.93 | 1.01 | 1.03 | 2.25 | 1.98 | 1.84 | 1.24 | 0.00 |
| time (sec) |
N/A | 0.246 | 0.281 | 0.096 | 0.285 | 0.401 | 7.141 | 0.297 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | A | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 123 | 110 | 123 | 116 | 240 | 243 | 253 | 144 | 130 |
| N.S. |
1 | 0.89 | 1.00 | 0.94 | 1.95 | 1.98 | 2.06 | 1.17 | 1.06 |
| time (sec) |
N/A | 0.215 | 0.255 | 0.085 | 0.297 | 0.691 | 33.529 | 0.287 | 10.272 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 115 | 103 | 98 | 96 | 171 | 203 | 216 | 121 | 105 |
| N.S. |
1 | 0.90 | 0.85 | 0.83 | 1.49 | 1.77 | 1.88 | 1.05 | 0.91 |
| time (sec) |
N/A | 0.217 | 0.486 | 0.089 | 0.287 | 0.311 | 55.222 | 0.332 | 10.183 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 110 | 97 | 103 | 99 | 134 | 195 | 187 | 225 | 95 |
| N.S. |
1 | 0.88 | 0.94 | 0.90 | 1.22 | 1.77 | 1.70 | 2.05 | 0.86 |
| time (sec) |
N/A | 0.214 | 0.349 | 0.093 | 0.286 | 0.291 | 16.511 | 0.485 | 10.131 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 76 | 84 | 91 | 108 | 80 | 213 | 114 | 254 | 72 |
| N.S. |
1 | 1.11 | 1.20 | 1.42 | 1.05 | 2.80 | 1.50 | 3.34 | 0.95 |
| time (sec) |
N/A | 0.201 | 0.338 | 0.096 | 0.283 | 0.315 | 9.839 | 0.840 | 10.370 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 46 | 50 | 49 | 48 | 49 | 84 | 189 | 370 | 122 |
| N.S. |
1 | 1.09 | 1.07 | 1.04 | 1.07 | 1.83 | 4.11 | 8.04 | 2.65 |
| time (sec) |
N/A | 0.189 | 0.235 | 0.088 | 0.197 | 0.310 | 3.388 | 0.939 | 10.106 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 74 | 78 | 71 | 70 | 84 | 109 | 258 | 430 | 164 |
| N.S. |
1 | 1.05 | 0.96 | 0.95 | 1.14 | 1.47 | 3.49 | 5.81 | 2.22 |
| time (sec) |
N/A | 0.218 | 0.291 | 0.111 | 0.217 | 0.300 | 3.547 | 1.307 | 10.253 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 104 | 108 | 94 | 94 | 118 | 134 | 326 | 490 | 206 |
| N.S. |
1 | 1.04 | 0.90 | 0.90 | 1.13 | 1.29 | 3.13 | 4.71 | 1.98 |
| time (sec) |
N/A | 0.242 | 0.343 | 0.165 | 0.196 | 0.354 | 3.767 | 2.031 | 10.679 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 134 | 138 | 115 | 118 | 152 | 157 | 393 | 550 | 248 |
| N.S. |
1 | 1.03 | 0.86 | 0.88 | 1.13 | 1.17 | 2.93 | 4.10 | 1.85 |
| time (sec) |
N/A | 0.263 | 0.409 | 0.263 | 0.200 | 0.398 | 3.927 | 2.047 | 11.330 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 150 | 143 | 110 | 115 | 158 | 155 | 3351 | 175 | 137 |
| N.S. |
1 | 0.95 | 0.73 | 0.77 | 1.05 | 1.03 | 22.34 | 1.17 | 0.91 |
| time (sec) |
N/A | 0.275 | 0.113 | 0.103 | 0.206 | 0.304 | 5.607 | 0.275 | 9.059 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 117 | 113 | 89 | 91 | 124 | 132 | 2304 | 140 | 118 |
| N.S. |
1 | 0.97 | 0.76 | 0.78 | 1.06 | 1.13 | 19.69 | 1.20 | 1.01 |
| time (sec) |
N/A | 0.248 | 0.095 | 0.085 | 0.206 | 0.289 | 4.205 | 0.274 | 9.021 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 84 | 83 | 66 | 67 | 90 | 106 | 1340 | 105 | 97 |
| N.S. |
1 | 0.99 | 0.79 | 0.80 | 1.07 | 1.26 | 15.95 | 1.25 | 1.15 |
| time (sec) |
N/A | 0.219 | 0.075 | 0.078 | 0.212 | 0.297 | 3.147 | 0.268 | 8.964 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 53 | 53 | 44 | 45 | 55 | 80 | 498 | 72 | 77 |
| N.S. |
1 | 1.00 | 0.83 | 0.85 | 1.04 | 1.51 | 9.40 | 1.36 | 1.45 |
| time (sec) |
N/A | 0.186 | 0.052 | 0.067 | 0.211 | 0.299 | 2.366 | 0.273 | 8.993 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | B | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 86 | 89 | 81 | 99 | 91 | 203 | 184 | 140 | 0 |
| N.S. |
1 | 1.03 | 0.94 | 1.15 | 1.06 | 2.36 | 2.14 | 1.63 | 0.00 |
| time (sec) |
N/A | 0.223 | 0.178 | 0.068 | 0.306 | 0.305 | 2.181 | 0.279 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | A | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 121 | 107 | 105 | 147 | 163 | 190 | 202 | 115 | 0 |
| N.S. |
1 | 0.88 | 0.87 | 1.21 | 1.35 | 1.57 | 1.67 | 0.95 | 0.00 |
| time (sec) |
N/A | 0.219 | 0.204 | 0.108 | 0.306 | 0.336 | 3.240 | 0.293 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | A | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 112 | 105 | 92 | 115 | 207 | 216 | 216 | 145 | 78 |
| N.S. |
1 | 0.94 | 0.82 | 1.03 | 1.85 | 1.93 | 1.93 | 1.29 | 0.70 |
| time (sec) |
N/A | 0.216 | 0.298 | 0.102 | 0.293 | 0.323 | 5.378 | 0.299 | 10.150 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | A | B | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 123 | 112 | 117 | 127 | 275 | 246 | 253 | 173 | 0 |
| N.S. |
1 | 0.91 | 0.95 | 1.03 | 2.24 | 2.00 | 2.06 | 1.41 | 0.00 |
| time (sec) |
N/A | 0.225 | 0.388 | 0.109 | 0.300 | 0.298 | 10.454 | 0.305 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | A | B | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 159 | 140 | 150 | 151 | 354 | 298 | 287 | 214 | 0 |
| N.S. |
1 | 0.88 | 0.94 | 0.95 | 2.23 | 1.87 | 1.81 | 1.35 | 0.00 |
| time (sec) |
N/A | 0.253 | 0.354 | 0.116 | 0.278 | 0.335 | 31.778 | 0.304 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | A | A | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 90 | 88 | 105 | 99 | 178 | 192 | 150 | 111 | 99 |
| N.S. |
1 | 0.98 | 1.17 | 1.10 | 1.98 | 2.13 | 1.67 | 1.23 | 1.10 |
| time (sec) |
N/A | 0.206 | 0.434 | 0.083 | 0.285 | 0.332 | 14.385 | 0.283 | 9.850 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | A | A | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 59 | 57 | 80 | 82 | 109 | 146 | 66 | 79 | 59 |
| N.S. |
1 | 0.97 | 1.36 | 1.39 | 1.85 | 2.47 | 1.12 | 1.34 | 1.00 |
| time (sec) |
N/A | 0.189 | 0.101 | 0.073 | 0.285 | 0.304 | 14.104 | 0.273 | 9.557 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | A | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 43 | 48 | 76 | 69 | 54 | 130 | 71 | 66 | 35 |
| N.S. |
1 | 1.12 | 1.77 | 1.60 | 1.26 | 3.02 | 1.65 | 1.53 | 0.81 |
| time (sec) |
N/A | 0.178 | 0.108 | 0.075 | 0.279 | 0.320 | 2.951 | 0.290 | 9.299 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 43 | 48 | 39 | 44 | 48 | 39 | 65 | 124 | 35 |
| N.S. |
1 | 1.12 | 0.91 | 1.02 | 1.12 | 0.91 | 1.51 | 2.88 | 0.81 |
| time (sec) |
N/A | 0.188 | 0.125 | 0.064 | 0.206 | 0.309 | 1.054 | 0.452 | 9.004 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 72 | 76 | 60 | 67 | 83 | 62 | 100 | 180 | 58 |
| N.S. |
1 | 1.06 | 0.83 | 0.93 | 1.15 | 0.86 | 1.39 | 2.50 | 0.81 |
| time (sec) |
N/A | 0.209 | 0.159 | 0.071 | 0.222 | 0.312 | 1.056 | 0.660 | 9.044 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 101 | 106 | 93 | 91 | 118 | 86 | 133 | 236 | 102 |
| N.S. |
1 | 1.05 | 0.92 | 0.90 | 1.17 | 0.85 | 1.32 | 2.34 | 1.01 |
| time (sec) |
N/A | 0.236 | 0.194 | 0.080 | 0.194 | 0.302 | 1.181 | 0.866 | 9.091 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 82 | 81 | 56 | 62 | 85 | 59 | 338 | 99 | 53 |
| N.S. |
1 | 0.99 | 0.68 | 0.76 | 1.04 | 0.72 | 4.12 | 1.21 | 0.65 |
| time (sec) |
N/A | 0.202 | 0.075 | 0.066 | 0.197 | 0.283 | 1.464 | 0.320 | 9.703 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | A | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 51 | 51 | 34 | 39 | 49 | 36 | 70 | 66 | 67 |
| N.S. |
1 | 1.00 | 0.67 | 0.76 | 0.96 | 0.71 | 1.37 | 1.29 | 1.31 |
| time (sec) |
N/A | 0.171 | 0.049 | 0.058 | 0.197 | 0.287 | 1.077 | 0.280 | 9.422 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 47 | 47 | 71 | 73 | 58 | 131 | 39 | 80 | 65 |
| N.S. |
1 | 1.00 | 1.51 | 1.55 | 1.23 | 2.79 | 0.83 | 1.70 | 1.38 |
| time (sec) |
N/A | 0.174 | 0.076 | 0.058 | 0.282 | 0.289 | 1.156 | 0.273 | 9.460 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | A | A | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 61 | 61 | 80 | 93 | 121 | 144 | 66 | 64 | 94 |
| N.S. |
1 | 1.00 | 1.31 | 1.52 | 1.98 | 2.36 | 1.08 | 1.05 | 1.54 |
| time (sec) |
N/A | 0.190 | 0.127 | 0.084 | 0.263 | 0.290 | 2.104 | 0.289 | 10.069 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | A | A | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 93 | 92 | 101 | 112 | 200 | 201 | 150 | 125 | 0 |
| N.S. |
1 | 0.99 | 1.09 | 1.20 | 2.15 | 2.16 | 1.61 | 1.34 | 0.00 |
| time (sec) |
N/A | 0.210 | 0.244 | 0.088 | 0.277 | 0.406 | 4.095 | 0.294 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | A | A | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 118 | 113 | 159 | 140 | 215 | 304 | 177 | 144 | 134 |
| N.S. |
1 | 0.96 | 1.35 | 1.19 | 1.82 | 2.58 | 1.50 | 1.22 | 1.14 |
| time (sec) |
N/A | 0.220 | 0.548 | 0.114 | 0.294 | 0.430 | 34.409 | 0.290 | 10.336 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | A | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 86 | 82 | 139 | 115 | 144 | 249 | 264 | 105 | 90 |
| N.S. |
1 | 0.95 | 1.62 | 1.34 | 1.67 | 2.90 | 3.07 | 1.22 | 1.05 |
| time (sec) |
N/A | 0.201 | 0.328 | 0.103 | 0.277 | 0.510 | 16.943 | 0.274 | 9.820 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | B | A | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 52 | 58 | 75 | 75 | 69 | 200 | 75 | 69 | 54 |
| N.S. |
1 | 1.12 | 1.44 | 1.44 | 1.33 | 3.85 | 1.44 | 1.33 | 1.04 |
| time (sec) |
N/A | 0.185 | 0.132 | 0.066 | 0.289 | 0.456 | 4.103 | 0.272 | 9.467 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | A | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 42 | 46 | 36 | 46 | 46 | 46 | 68 | 66 | 46 |
| N.S. |
1 | 1.10 | 0.86 | 1.10 | 1.10 | 1.10 | 1.62 | 1.57 | 1.10 |
| time (sec) |
N/A | 0.189 | 0.111 | 0.091 | 0.224 | 0.314 | 0.479 | 0.313 | 8.939 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 68 | 74 | 60 | 69 | 81 | 73 | 85 | 188 | 66 |
| N.S. |
1 | 1.09 | 0.88 | 1.01 | 1.19 | 1.07 | 1.25 | 2.76 | 0.97 |
| time (sec) |
N/A | 0.210 | 0.167 | 0.095 | 0.200 | 0.288 | 2.250 | 0.531 | 8.977 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 100 | 104 | 81 | 94 | 116 | 98 | 114 | 303 | 91 |
| N.S. |
1 | 1.04 | 0.81 | 0.94 | 1.16 | 0.98 | 1.14 | 3.03 | 0.91 |
| time (sec) |
N/A | 0.235 | 0.213 | 0.105 | 0.202 | 0.286 | 2.646 | 0.696 | 9.204 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 126 | 132 | 104 | 118 | 151 | 121 | 146 | 414 | 154 |
| N.S. |
1 | 1.05 | 0.83 | 0.94 | 1.20 | 0.96 | 1.16 | 3.29 | 1.22 |
| time (sec) |
N/A | 0.257 | 0.243 | 0.116 | 0.194 | 0.302 | 3.056 | 1.192 | 9.346 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 111 | 107 | 80 | 91 | 128 | 95 | 561 | 146 | 79 |
| N.S. |
1 | 0.96 | 0.72 | 0.82 | 1.15 | 0.86 | 5.05 | 1.32 | 0.71 |
| time (sec) |
N/A | 0.234 | 0.096 | 0.110 | 0.234 | 0.289 | 2.920 | 0.282 | 10.138 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 79 | 77 | 57 | 66 | 90 | 70 | 267 | 106 | 81 |
| N.S. |
1 | 0.97 | 0.72 | 0.84 | 1.14 | 0.89 | 3.38 | 1.34 | 1.03 |
| time (sec) |
N/A | 0.199 | 0.076 | 0.091 | 0.190 | 0.307 | 2.613 | 0.272 | 9.695 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | A | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 45 | 45 | 33 | 43 | 53 | 47 | 65 | 62 | 38 |
| N.S. |
1 | 1.00 | 0.73 | 0.96 | 1.18 | 1.04 | 1.44 | 1.38 | 0.84 |
| time (sec) |
N/A | 0.169 | 0.050 | 0.086 | 0.193 | 0.279 | 2.456 | 0.273 | 9.212 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 59 | 59 | 71 | 79 | 80 | 195 | 206 | 108 | 60 |
| N.S. |
1 | 1.00 | 1.20 | 1.34 | 1.36 | 3.31 | 3.49 | 1.83 | 1.02 |
| time (sec) |
N/A | 0.195 | 0.107 | 0.063 | 0.270 | 0.257 | 3.840 | 0.272 | 9.449 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | A | B | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 92 | 86 | 91 | 127 | 162 | 248 | 262 | 107 | 0 |
| N.S. |
1 | 0.93 | 0.99 | 1.38 | 1.76 | 2.70 | 2.85 | 1.16 | 0.00 |
| time (sec) |
N/A | 0.220 | 0.251 | 0.104 | 0.278 | 0.279 | 6.588 | 0.307 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | A | A | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 123 | 117 | 113 | 155 | 243 | 314 | 180 | 148 | 0 |
| N.S. |
1 | 0.95 | 0.92 | 1.26 | 1.98 | 2.55 | 1.46 | 1.20 | 0.00 |
| time (sec) |
N/A | 0.240 | 0.269 | 0.119 | 0.274 | 0.279 | 11.330 | 0.309 | 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 | 105 | 101 | 115 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.96 | 1.10 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.270 | 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 | A | F | F | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 84 | 84 | 106 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.26 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.240 | 0.267 | 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 | 100 | 100 | 100 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.234 | 0.258 | 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 | 84 | 84 | 106 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.26 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.246 | 0.244 | 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 | 98 | 98 | 100 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.219 | 0.251 | 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 | 79 | 79 | 104 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.32 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.229 | 0.091 | 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 | 97 | 97 | 95 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.223 | 0.234 | 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 | 82 | 82 | 106 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.29 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.215 | 0.263 | 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 | No | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 85 | 85 | 110 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.29 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.207 | 0.102 | 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 | 84 | 84 | 106 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.26 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.230 | 0.351 | 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(-2) | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 91 | 91 | 111 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.22 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.287 | 0.489 | 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(-2) | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 91 | 91 | 111 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.22 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.284 | 0.486 | 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 | 91 | 91 | 111 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.22 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.284 | 0.427 | 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 | 89 | 89 | 111 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.25 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.281 | 0.459 | 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 | 89 | 89 | 111 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.25 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.260 | 0.535 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |