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(-2) | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 251 | 251 | 273 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.09 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.297 | 0.308 | 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(-2) | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 337 | 337 | 227 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.67 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.371 | 0.185 | 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(-2) | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 443 | 443 | 199 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.45 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.379 | 0.212 | 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(-2) | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 383 | 383 | 244 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.64 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.380 | 0.593 | 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 | A | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 89 | 89 | 101 | 0 | 0 | 277 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.13 | 0.00 | 0.00 | 3.11 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.067 | 0.130 | 0.000 | 0.000 | 0.330 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | A | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 113 | 113 | 116 | 0 | 0 | 337 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.03 | 0.00 | 0.00 | 2.98 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.043 | 0.102 | 0.000 | 0.000 | 0.330 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F(-2) | A | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 166 | 166 | 144 | 0 | 0 | 399 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.87 | 0.00 | 0.00 | 2.40 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.111 | 0.127 | 0.000 | 0.000 | 0.375 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F(-2) | A | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 230 | 230 | 182 | 0 | 0 | 520 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.79 | 0.00 | 0.00 | 2.26 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.178 | 0.147 | 0.000 | 0.000 | 0.380 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | A | A | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 251 | 251 | 163 | 0 | 199 | 125 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.65 | 0.00 | 0.79 | 0.50 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.402 | 0.298 | 0.000 | 0.262 | 0.330 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | A | A | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 148 | 148 | 113 | 0 | 105 | 66 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.76 | 0.00 | 0.71 | 0.45 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.223 | 0.147 | 0.000 | 0.300 | 0.300 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 301 | 301 | 310 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.03 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.412 | 1.204 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | F | F | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 489 | 489 | 255 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.52 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.521 | 0.636 | 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 | 406 | 406 | 316 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.78 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.427 | 1.882 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 248 | 248 | 217 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.88 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.150 | 0.381 | 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 | A | A | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 142 | 142 | 70 | 0 | 102 | 73 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.49 | 0.00 | 0.72 | 0.51 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.268 | 0.160 | 0.000 | 0.262 | 0.300 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | A | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 252 | 252 | 116 | 0 | 0 | 135 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.46 | 0.00 | 0.00 | 0.54 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.331 | 0.210 | 0.000 | 0.000 | 0.316 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | C | A | A | A | A | F(-1) |
| verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
| size | 34 | 34 | 27 | 119 | 27 | 27 | 29 | 28 | 0 |
| N.S. |
1 | 1.00 | 0.79 | 3.50 | 0.79 | 0.79 | 0.85 | 0.82 | 0.00 |
| time (sec) |
N/A | 0.027 | 0.018 | 0.425 | 0.260 | 0.283 | 1.214 | 0.349 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | A | B | B | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 211 | 211 | 156 | 1761 | 271 | 1222 | 6217 | 558 | 0 |
| N.S. |
1 | 1.00 | 0.74 | 8.35 | 1.28 | 5.79 | 29.46 | 2.64 | 0.00 |
| time (sec) |
N/A | 1.058 | 0.167 | 27.451 | 0.206 | 0.302 | 13.507 | 0.377 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | A | B | B | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 153 | 153 | 112 | 916 | 195 | 633 | 2820 | 396 | 0 |
| N.S. |
1 | 1.00 | 0.73 | 5.99 | 1.27 | 4.14 | 18.43 | 2.59 | 0.00 |
| time (sec) |
N/A | 0.132 | 0.100 | 5.717 | 0.195 | 0.299 | 5.452 | 0.368 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | A | B | B | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 95 | 95 | 68 | 343 | 119 | 235 | 920 | 234 | 0 |
| N.S. |
1 | 1.00 | 0.72 | 3.61 | 1.25 | 2.47 | 9.68 | 2.46 | 0.00 |
| time (sec) |
N/A | 0.076 | 0.054 | 0.901 | 0.190 | 0.292 | 2.709 | 0.343 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | B | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 46 | 46 | 32 | 68 | 57 | 52 | 141 | 95 | 0 |
| N.S. |
1 | 1.00 | 0.70 | 1.48 | 1.24 | 1.13 | 3.07 | 2.07 | 0.00 |
| time (sec) |
N/A | 0.010 | 0.008 | 0.004 | 0.185 | 0.289 | 2.176 | 0.331 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | N/A | B | N/A | N/A | N/A | N/A | N/A | N/A |
| verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 25 | 25 | 108 | 25 | 27 | 33 | 22 | 27 | 27 |
| N.S. |
1 | 1.00 | 4.32 | 1.00 | 1.08 | 1.32 | 0.88 | 1.08 | 1.08 |
| time (sec) |
N/A | 0.044 | 0.704 | 0.030 | 0.217 | 0.285 | 7.106 | 0.379 | 0.412 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | N/A | B | N/A | N/A | N/A | N/A | N/A | N/A |
| verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 25 | 25 | 108 | 25 | 27 | 44 | 24 | 27 | 27 |
| N.S. |
1 | 1.00 | 4.32 | 1.00 | 1.08 | 1.76 | 0.96 | 1.08 | 1.08 |
| time (sec) |
N/A | 0.042 | 0.137 | 0.044 | 0.221 | 0.283 | 162.221 | 0.419 | 0.451 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F(-2) | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 1198 | 1198 | 2215 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.85 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.016 | 7.313 | 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(-2) | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 860 | 860 | 1180 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.37 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.569 | 2.720 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | C | F(-2) | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
| size | 520 | 520 | 571 | 598 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.10 | 1.15 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.311 | 0.831 | 1.131 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 22 | 22 | 24 | 22 | 24 | 55 | 1 | 24 | 24 |
| N.S. |
1 | 1.00 | 1.09 | 1.00 | 1.09 | 2.50 | 0.05 | 1.09 | 1.09 |
| time (sec) |
N/A | 0.021 | 3.846 | 0.006 | 0.216 | 0.261 | 0.000 | 0.310 | 0.349 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 22 | 22 | 24 | 22 | 261 | 102 | 1 | 24 | 24 |
| N.S. |
1 | 1.00 | 1.09 | 1.00 | 11.86 | 4.64 | 0.05 | 1.09 | 1.09 |
| time (sec) |
N/A | 0.019 | 17.202 | 0.035 | 0.228 | 0.276 | 0.000 | 0.327 | 0.391 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | C | F | F | A | F | F(-1) |
| verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
| size | 185 | 185 | 171 | 313 | 0 | 0 | 316 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.92 | 1.69 | 0.00 | 0.00 | 1.71 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.133 | 0.070 | 0.338 | 0.000 | 0.000 | 75.860 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | C | F | F | A | F | F(-1) |
| verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
| size | 148 | 148 | 142 | 272 | 0 | 0 | 267 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.96 | 1.84 | 0.00 | 0.00 | 1.80 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.128 | 0.049 | 0.180 | 0.000 | 0.000 | 80.120 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | C | F | F | A | F | F(-1) |
| verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
| size | 107 | 107 | 105 | 233 | 0 | 0 | 218 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.98 | 2.18 | 0.00 | 0.00 | 2.04 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.083 | 0.036 | 0.127 | 0.000 | 0.000 | 53.551 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | C | F | F | A | F | F(-1) |
| verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
| size | 69 | 69 | 66 | 188 | 0 | 0 | 163 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.96 | 2.72 | 0.00 | 0.00 | 2.36 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.053 | 0.023 | 0.109 | 0.000 | 0.000 | 42.526 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | C | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
| size | 39 | 39 | 37 | 151 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.95 | 3.87 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.051 | 0.006 | 0.076 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | C | F | F | C | F | F(-1) |
| verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
| size | 44 | 44 | 63 | 181 | 0 | 0 | 173 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.43 | 4.11 | 0.00 | 0.00 | 3.93 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.044 | 0.025 | 0.095 | 0.000 | 0.000 | 6.043 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | C | F | F | A | F | F(-1) |
| verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
| size | 95 | 95 | 88 | 221 | 0 | 0 | 216 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.93 | 2.33 | 0.00 | 0.00 | 2.27 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.101 | 0.057 | 0.128 | 0.000 | 0.000 | 37.151 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | C | F | F | A | F | F(-1) |
| verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
| size | 135 | 135 | 124 | 264 | 0 | 0 | 265 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.92 | 1.96 | 0.00 | 0.00 | 1.96 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.120 | 0.133 | 0.184 | 0.000 | 0.000 | 42.968 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | F | A | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 170 | 170 | 156 | 204 | 210 | 0 | 299 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.92 | 1.20 | 1.24 | 0.00 | 1.76 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.128 | 0.056 | 0.127 | 0.243 | 0.000 | 82.828 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | F | A | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 136 | 136 | 125 | 168 | 164 | 0 | 253 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.92 | 1.24 | 1.21 | 0.00 | 1.86 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.110 | 0.044 | 0.049 | 0.226 | 0.000 | 79.519 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | F | A | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 98 | 98 | 99 | 126 | 112 | 0 | 207 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.01 | 1.29 | 1.14 | 0.00 | 2.11 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.081 | 0.028 | 0.036 | 0.238 | 0.000 | 52.730 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | F | A | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 63 | 63 | 64 | 88 | 69 | 0 | 156 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.02 | 1.40 | 1.10 | 0.00 | 2.48 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.055 | 0.022 | 0.033 | 0.232 | 0.000 | 43.429 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 36 | 36 | 34 | 59 | 43 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.94 | 1.64 | 1.19 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.075 | 0.006 | 0.027 | 0.246 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | F | C | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 41 | 41 | 54 | 81 | 67 | 0 | 170 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.32 | 1.98 | 1.63 | 0.00 | 4.15 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.053 | 0.018 | 0.042 | 0.217 | 0.000 | 5.953 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | F | A | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 84 | 84 | 77 | 115 | 96 | 0 | 206 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.92 | 1.37 | 1.14 | 0.00 | 2.45 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.093 | 0.061 | 0.046 | 0.229 | 0.000 | 37.730 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | F | A | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 121 | 121 | 110 | 157 | 151 | 0 | 252 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.91 | 1.30 | 1.25 | 0.00 | 2.08 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.111 | 0.096 | 0.057 | 0.227 | 0.000 | 42.654 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | B | F(-2) | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 17 | 17 | 17 | 14 | 52 | 39 | 0 | 0 | 13 |
| N.S. |
1 | 1.00 | 1.00 | 0.82 | 3.06 | 2.29 | 0.00 | 0.00 | 0.76 |
| time (sec) |
N/A | 0.047 | 0.011 | 0.794 | 0.298 | 0.297 | 0.000 | 0.000 | 0.495 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | B | F(-2) | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 16 | 16 | 17 | 13 | 45 | 50 | 0 | 0 | 12 |
| N.S. |
1 | 1.00 | 1.06 | 0.81 | 2.81 | 3.12 | 0.00 | 0.00 | 0.75 |
| time (sec) |
N/A | 0.044 | 0.010 | 0.480 | 0.301 | 0.303 | 0.000 | 0.000 | 0.397 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | B | F(-2) | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 20 | 20 | 21 | 19 | 64 | 55 | 0 | 0 | 18 |
| N.S. |
1 | 1.00 | 1.05 | 0.95 | 3.20 | 2.75 | 0.00 | 0.00 | 0.90 |
| time (sec) |
N/A | 0.051 | 0.009 | 0.508 | 0.314 | 0.303 | 0.000 | 0.000 | 0.410 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | A | C | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 14 | 14 | 16 | 11 | 72 | 13 | 82 | 0 | 10 |
| N.S. |
1 | 1.00 | 1.14 | 0.79 | 5.14 | 0.93 | 5.86 | 0.00 | 0.71 |
| time (sec) |
N/A | 0.053 | 0.004 | 0.777 | 0.188 | 0.314 | 4.883 | 0.000 | 0.377 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | A | C | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 17 | 17 | 21 | 12 | 81 | 14 | 92 | 0 | 11 |
| N.S. |
1 | 1.00 | 1.24 | 0.71 | 4.76 | 0.82 | 5.41 | 0.00 | 0.65 |
| time (sec) |
N/A | 0.061 | 0.005 | 0.667 | 0.199 | 0.310 | 5.017 | 0.000 | 0.340 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | B | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 26 | 26 | 23 | 0 | 0 | 89 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.88 | 0.00 | 0.00 | 3.42 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.066 | 0.009 | 0.000 | 0.000 | 0.283 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | B | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 171 | 171 | 140 | 256 | 253 | 193 | 333 | 339 | 0 |
| N.S. |
1 | 1.00 | 0.82 | 1.50 | 1.48 | 1.13 | 1.95 | 1.98 | 0.00 |
| time (sec) |
N/A | 0.154 | 0.110 | 54.990 | 0.212 | 0.294 | 8.482 | 0.429 | 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 | 142 | 142 | 101 | 181 | 180 | 135 | 241 | 241 | 0 |
| N.S. |
1 | 1.00 | 0.71 | 1.27 | 1.27 | 0.95 | 1.70 | 1.70 | 0.00 |
| time (sec) |
N/A | 0.139 | 0.079 | 12.181 | 0.199 | 0.286 | 4.897 | 0.422 | 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 | 90 | 113 | 61 | 105 | 109 | 76 | 156 | 146 | 0 |
| N.S. |
1 | 1.26 | 0.68 | 1.17 | 1.21 | 0.84 | 1.73 | 1.62 | 0.00 |
| time (sec) |
N/A | 0.084 | 0.046 | 1.743 | 0.197 | 0.296 | 3.007 | 0.395 | 0.000 |
| 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 | 38 | 38 | 29 | 48 | 48 | 42 | 82 | 64 | 0 |
| N.S. |
1 | 1.00 | 0.76 | 1.26 | 1.26 | 1.11 | 2.16 | 1.68 | 0.00 |
| time (sec) |
N/A | 0.012 | 0.008 | 0.114 | 0.193 | 0.296 | 2.072 | 0.338 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | A | F | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 77 | 77 | 141 | 0 | 0 | 77 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.83 | 0.00 | 0.00 | 1.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.136 | 0.304 | 0.000 | 0.000 | 0.288 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | A | A | F | B | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 69 | 69 | 89 | 0 | 97 | 89 | 0 | 202 | 0 |
| N.S. |
1 | 1.00 | 1.29 | 0.00 | 1.41 | 1.29 | 0.00 | 2.93 | 0.00 |
| time (sec) |
N/A | 0.077 | 0.280 | 0.000 | 0.204 | 0.318 | 0.000 | 0.350 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | A | A | F | B | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 150 | 150 | 137 | 0 | 152 | 167 | 0 | 633 | 0 |
| N.S. |
1 | 1.00 | 0.91 | 0.00 | 1.01 | 1.11 | 0.00 | 4.22 | 0.00 |
| time (sec) |
N/A | 0.155 | 0.275 | 0.000 | 0.205 | 0.314 | 0.000 | 0.362 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | A | A | F(-1) | B | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 188 | 188 | 178 | 0 | 210 | 242 | 0 | 1102 | 0 |
| N.S. |
1 | 1.00 | 0.95 | 0.00 | 1.12 | 1.29 | 0.00 | 5.86 | 0.00 |
| time (sec) |
N/A | 0.159 | 0.292 | 0.000 | 0.217 | 0.319 | 0.000 | 0.370 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | B | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 372 | 372 | 285 | 617 | 578 | 592 | 760 | 995 | 0 |
| N.S. |
1 | 1.00 | 0.77 | 1.66 | 1.55 | 1.59 | 2.04 | 2.67 | 0.00 |
| time (sec) |
N/A | 0.343 | 0.185 | 205.349 | 0.233 | 0.310 | 38.319 | 0.622 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | A | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 298 | 298 | 207 | 439 | 417 | 419 | 552 | 715 | 0 |
| N.S. |
1 | 1.00 | 0.69 | 1.47 | 1.40 | 1.41 | 1.85 | 2.40 | 0.00 |
| time (sec) |
N/A | 0.343 | 0.147 | 50.855 | 0.234 | 0.315 | 12.604 | 0.523 | 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 | 226 | 226 | 125 | 261 | 257 | 244 | 352 | 435 | 0 |
| N.S. |
1 | 1.00 | 0.55 | 1.15 | 1.14 | 1.08 | 1.56 | 1.92 | 0.00 |
| time (sec) |
N/A | 0.209 | 0.092 | 10.749 | 0.205 | 0.324 | 9.277 | 0.452 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | B | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 69 | 69 | 67 | 119 | 117 | 124 | 184 | 198 | 0 |
| N.S. |
1 | 1.00 | 0.97 | 1.72 | 1.70 | 1.80 | 2.67 | 2.87 | 0.00 |
| time (sec) |
N/A | 0.036 | 0.016 | 0.387 | 0.196 | 0.329 | 6.767 | 0.421 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | F | F | A | F | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 129 | 129 | 502 | 0 | 0 | 178 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 3.89 | 0.00 | 0.00 | 1.38 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.223 | 0.400 | 0.000 | 0.000 | 0.314 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | A | F | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 138 | 138 | 157 | 0 | 0 | 266 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.14 | 0.00 | 0.00 | 1.93 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.235 | 0.510 | 0.000 | 0.000 | 0.296 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | B | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 214 | 214 | 207 | 0 | 0 | 535 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.97 | 0.00 | 0.00 | 2.50 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.329 | 0.488 | 0.000 | 0.000 | 0.296 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | B | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 346 | 346 | 240 | 0 | 0 | 810 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.69 | 0.00 | 0.00 | 2.34 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.499 | 0.598 | 0.000 | 0.000 | 0.307 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | A | B | B | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 59 | 59 | 73 | 174 | 76 | 159 | 398 | 132 | 0 |
| N.S. |
1 | 1.00 | 1.24 | 2.95 | 1.29 | 2.69 | 6.75 | 2.24 | 0.00 |
| time (sec) |
N/A | 0.055 | 0.062 | 4.804 | 0.184 | 0.304 | 8.569 | 0.325 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | A | B | B | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 59 | 59 | 73 | 169 | 76 | 159 | 398 | 132 | 0 |
| N.S. |
1 | 1.00 | 1.24 | 2.86 | 1.29 | 2.69 | 6.75 | 2.24 | 0.00 |
| time (sec) |
N/A | 0.072 | 0.059 | 1.324 | 0.195 | 0.313 | 2.856 | 0.324 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | A | B | B | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 59 | 59 | 73 | 174 | 76 | 159 | 398 | 132 | 0 |
| N.S. |
1 | 1.00 | 1.24 | 2.95 | 1.29 | 2.69 | 6.75 | 2.24 | 0.00 |
| time (sec) |
N/A | 0.053 | 0.063 | 0.362 | 0.185 | 0.316 | 0.858 | 0.317 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | B | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 53 | 53 | 54 | 68 | 56 | 64 | 131 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.02 | 1.28 | 1.06 | 1.21 | 2.47 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.061 | 0.061 | 0.217 | 0.193 | 0.310 | 2.282 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | B | B | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 71 | 71 | 72 | 135 | 0 | 140 | 495 | 389 | 0 |
| N.S. |
1 | 1.00 | 1.01 | 1.90 | 0.00 | 1.97 | 6.97 | 5.48 | 0.00 |
| time (sec) |
N/A | 0.051 | 0.076 | 0.224 | 0.000 | 0.314 | 2.037 | 0.338 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | B | B | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 71 | 71 | 72 | 135 | 0 | 140 | 495 | 390 | 0 |
| N.S. |
1 | 1.00 | 1.01 | 1.90 | 0.00 | 1.97 | 6.97 | 5.49 | 0.00 |
| time (sec) |
N/A | 0.053 | 0.070 | 0.377 | 0.000 | 0.301 | 3.419 | 0.337 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | A | B | B | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 59 | 59 | 73 | 169 | 76 | 159 | 398 | 132 | 0 |
| N.S. |
1 | 1.00 | 1.24 | 2.86 | 1.29 | 2.69 | 6.75 | 2.24 | 0.00 |
| time (sec) |
N/A | 0.057 | 0.061 | 2.615 | 0.191 | 0.299 | 5.027 | 0.307 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | A | B | B | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 59 | 59 | 73 | 169 | 76 | 159 | 398 | 132 | 0 |
| N.S. |
1 | 1.00 | 1.24 | 2.86 | 1.29 | 2.69 | 6.75 | 2.24 | 0.00 |
| time (sec) |
N/A | 0.064 | 0.059 | 0.697 | 0.187 | 0.305 | 1.509 | 0.344 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | A | B | B | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 57 | 57 | 53 | 144 | 68 | 138 | 323 | 110 | 0 |
| N.S. |
1 | 1.00 | 0.93 | 2.53 | 1.19 | 2.42 | 5.67 | 1.93 | 0.00 |
| time (sec) |
N/A | 0.025 | 0.083 | 0.194 | 0.189 | 0.280 | 0.474 | 0.314 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | B | B | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 67 | 67 | 67 | 127 | 0 | 130 | 348 | 186 | 0 |
| N.S. |
1 | 1.00 | 1.00 | 1.90 | 0.00 | 1.94 | 5.19 | 2.78 | 0.00 |
| time (sec) |
N/A | 0.058 | 0.070 | 0.208 | 0.000 | 0.290 | 2.181 | 0.384 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | B | B | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 71 | 71 | 72 | 135 | 0 | 140 | 495 | 390 | 0 |
| N.S. |
1 | 1.00 | 1.01 | 1.90 | 0.00 | 1.97 | 6.97 | 5.49 | 0.00 |
| time (sec) |
N/A | 0.055 | 0.072 | 0.223 | 0.000 | 0.289 | 2.571 | 0.352 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | B | B | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 71 | 71 | 72 | 135 | 0 | 140 | 495 | 390 | 0 |
| N.S. |
1 | 1.00 | 1.01 | 1.90 | 0.00 | 1.97 | 6.97 | 5.49 | 0.00 |
| time (sec) |
N/A | 0.056 | 0.066 | 0.747 | 0.000 | 0.295 | 5.035 | 0.353 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | A | B | B | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 103 | 103 | 118 | 583 | 148 | 489 | 1634 | 744 | 0 |
| N.S. |
1 | 1.00 | 1.15 | 5.66 | 1.44 | 4.75 | 15.86 | 7.22 | 0.00 |
| time (sec) |
N/A | 0.109 | 0.177 | 15.649 | 0.192 | 0.301 | 26.357 | 0.374 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | A | B | B | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 103 | 103 | 118 | 588 | 148 | 488 | 1625 | 744 | 0 |
| N.S. |
1 | 1.00 | 1.15 | 5.71 | 1.44 | 4.74 | 15.78 | 7.22 | 0.00 |
| time (sec) |
N/A | 0.130 | 0.170 | 5.228 | 0.192 | 0.305 | 7.097 | 0.378 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | A | B | B | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 102 | 102 | 116 | 577 | 148 | 488 | 1622 | 744 | 0 |
| N.S. |
1 | 1.00 | 1.14 | 5.66 | 1.45 | 4.78 | 15.90 | 7.29 | 0.00 |
| time (sec) |
N/A | 0.105 | 0.163 | 1.789 | 0.181 | 0.301 | 1.726 | 0.313 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | B | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 104 | 104 | 90 | 122 | 114 | 115 | 216 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.87 | 1.17 | 1.10 | 1.11 | 2.08 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.105 | 0.136 | 1.444 | 0.326 | 0.293 | 2.439 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F(-2) | B | B | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 135 | 135 | 120 | 474 | 0 | 457 | 2118 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.89 | 3.51 | 0.00 | 3.39 | 15.69 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.121 | 0.215 | 1.149 | 0.000 | 0.303 | 3.299 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F(-2) | B | B | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 135 | 135 | 121 | 475 | 0 | 457 | 2127 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.90 | 3.52 | 0.00 | 3.39 | 15.76 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.116 | 0.205 | 1.099 | 0.000 | 0.303 | 4.816 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | A | B | F(-1) | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 105 | 105 | 124 | 586 | 152 | 497 | 0 | 746 | 0 |
| N.S. |
1 | 1.00 | 1.18 | 5.58 | 1.45 | 4.73 | 0.00 | 7.10 | 0.00 |
| time (sec) |
N/A | 0.111 | 0.174 | 9.098 | 0.187 | 0.303 | 0.000 | 0.346 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | A | B | A | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 105 | 105 | 124 | 581 | 152 | 497 | 240 | 746 | 0 |
| N.S. |
1 | 1.00 | 1.18 | 5.53 | 1.45 | 4.73 | 2.29 | 7.10 | 0.00 |
| time (sec) |
N/A | 0.109 | 0.173 | 3.028 | 0.185 | 0.282 | 83.393 | 0.366 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | A | B | A | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 113 | 113 | 107 | 509 | 144 | 466 | 211 | 244 | 0 |
| N.S. |
1 | 1.00 | 0.95 | 4.50 | 1.27 | 4.12 | 1.87 | 2.16 | 0.00 |
| time (sec) |
N/A | 0.049 | 0.115 | 1.010 | 0.183 | 0.316 | 2.283 | 0.344 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F(-2) | B | A | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 123 | 123 | 121 | 471 | 0 | 455 | 209 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.98 | 3.83 | 0.00 | 3.70 | 1.70 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.113 | 0.198 | 1.108 | 0.000 | 0.319 | 3.285 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F(-2) | B | A | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 127 | 127 | 127 | 478 | 0 | 466 | 233 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.00 | 3.76 | 0.00 | 3.67 | 1.83 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.112 | 0.204 | 1.119 | 0.000 | 0.299 | 18.042 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F(-2) | B | A | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 127 | 127 | 127 | 478 | 0 | 466 | 233 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.00 | 3.76 | 0.00 | 3.67 | 1.83 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.115 | 0.198 | 1.096 | 0.000 | 0.332 | 139.218 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F(-2) | B | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 127 | 127 | 127 | 473 | 0 | 466 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.00 | 3.72 | 0.00 | 3.67 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.115 | 0.206 | 3.262 | 0.000 | 0.319 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | A | B | B | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 147 | 147 | 172 | 1249 | 218 | 1011 | 4100 | 1609 | 0 |
| N.S. |
1 | 1.00 | 1.17 | 8.50 | 1.48 | 6.88 | 27.89 | 10.95 | 0.00 |
| time (sec) |
N/A | 0.244 | 0.241 | 40.921 | 0.190 | 0.321 | 92.425 | 0.372 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | A | B | F(-1) | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 149 | 149 | 178 | 1262 | 222 | 1022 | 0 | 1611 | 0 |
| N.S. |
1 | 1.00 | 1.19 | 8.47 | 1.49 | 6.86 | 0.00 | 10.81 | 0.00 |
| time (sec) |
N/A | 0.277 | 0.240 | 15.464 | 0.186 | 0.338 | 0.000 | 0.476 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | A | B | A | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 149 | 149 | 178 | 1267 | 222 | 1024 | 357 | 1611 | 0 |
| N.S. |
1 | 1.00 | 1.19 | 8.50 | 1.49 | 6.87 | 2.40 | 10.81 | 0.00 |
| time (sec) |
N/A | 0.231 | 0.230 | 5.648 | 0.196 | 0.336 | 86.831 | 0.375 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | A | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 152 | 152 | 132 | 177 | 172 | 169 | 299 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.87 | 1.16 | 1.13 | 1.11 | 1.97 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.111 | 0.240 | 3.322 | 0.188 | 0.346 | 2.913 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F(-2) | B | A | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 191 | 191 | 181 | 1039 | 0 | 981 | 347 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.95 | 5.44 | 0.00 | 5.14 | 1.82 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.283 | 0.272 | 3.593 | 0.000 | 0.361 | 46.140 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F(-2) | B | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 191 | 191 | 181 | 1039 | 0 | 980 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.95 | 5.44 | 0.00 | 5.13 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.268 | 0.282 | 3.445 | 0.000 | 0.319 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | A | B | F(-1) | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 151 | 151 | 184 | 1269 | 228 | 1023 | 0 | 1611 | 0 |
| N.S. |
1 | 1.00 | 1.22 | 8.40 | 1.51 | 6.77 | 0.00 | 10.67 | 0.00 |
| time (sec) |
N/A | 0.275 | 0.230 | 26.564 | 0.191 | 0.359 | 0.000 | 0.354 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | A | B | F(-1) | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 148 | 148 | 176 | 1257 | 224 | 1022 | 0 | 1611 | 0 |
| N.S. |
1 | 1.00 | 1.19 | 8.49 | 1.51 | 6.91 | 0.00 | 10.89 | 0.00 |
| time (sec) |
N/A | 0.272 | 0.229 | 9.671 | 0.194 | 0.319 | 0.000 | 0.326 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | A | B | A | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 169 | 169 | 159 | 1108 | 220 | 983 | 325 | 379 | 0 |
| N.S. |
1 | 1.00 | 0.94 | 6.56 | 1.30 | 5.82 | 1.92 | 2.24 | 0.00 |
| time (sec) |
N/A | 0.062 | 0.162 | 3.408 | 0.187 | 0.306 | 3.895 | 0.308 | 0.000 |