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 | B | A | F | A | F | B | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 127 | 123 | 447 | 211 | 0 | 323 | 0 | 257 | 0 |
| N.S. |
1 | 0.97 | 3.52 | 1.66 | 0.00 | 2.54 | 0.00 | 2.02 | 0.00 |
| time (sec) |
N/A | 0.281 | 6.090 | 3.700 | 0.000 | 0.293 | 0.000 | 4.295 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | A | F | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 113 | 114 | 188 | 318 | 0 | 414 | 0 | 66 | 0 |
| N.S. |
1 | 1.01 | 1.66 | 2.81 | 0.00 | 3.66 | 0.00 | 0.58 | 0.00 |
| time (sec) |
N/A | 0.278 | 0.982 | 3.727 | 0.000 | 0.331 | 0.000 | 2.084 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | A | F | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 127 | 148 | 193 | 199 | 0 | 492 | 0 | 47 | 0 |
| N.S. |
1 | 1.17 | 1.52 | 1.57 | 0.00 | 3.87 | 0.00 | 0.37 | 0.00 |
| time (sec) |
N/A | 0.289 | 2.348 | 2.095 | 0.000 | 0.325 | 0.000 | 1.503 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | A | F | A | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 265 | 282 | 232 | 589 | 0 | 691 | 0 | 177 | 0 |
| N.S. |
1 | 1.06 | 0.88 | 2.22 | 0.00 | 2.61 | 0.00 | 0.67 | 0.00 |
| time (sec) |
N/A | 0.426 | 5.565 | 1.883 | 0.000 | 0.379 | 0.000 | 1.085 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | A | F | A | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 355 | 377 | 287 | 710 | 0 | 868 | 0 | 296 | 0 |
| N.S. |
1 | 1.06 | 0.81 | 2.00 | 0.00 | 2.45 | 0.00 | 0.83 | 0.00 |
| time (sec) |
N/A | 0.493 | 3.438 | 1.929 | 0.000 | 0.392 | 0.000 | 1.391 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-1) | A | F | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 439 | 466 | 292 | 746 | 0 | 1023 | 0 | 412 | 0 |
| N.S. |
1 | 1.06 | 0.67 | 1.70 | 0.00 | 2.33 | 0.00 | 0.94 | 0.00 |
| time (sec) |
N/A | 0.575 | 5.529 | 1.744 | 0.000 | 0.441 | 0.000 | 1.620 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | A | F(-1) | A | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 177 | 258 | 241 | 331 | 0 | 674 | 0 | 109 | 0 |
| N.S. |
1 | 1.46 | 1.36 | 1.87 | 0.00 | 3.81 | 0.00 | 0.62 | 0.00 |
| time (sec) |
N/A | 0.345 | 6.358 | 3.069 | 0.000 | 0.425 | 0.000 | 1.336 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 125 | 125 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.306 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 243 | 243 | 226 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.93 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.509 | 2.103 | 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 | 161 | 161 | 171 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.06 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.406 | 1.227 | 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 | 129 | 129 | 105 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.81 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.383 | 0.432 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 130 | 138 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.06 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.511 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 169 | 176 | 329 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.04 | 1.95 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.545 | 10.842 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 252 | 260 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.03 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.678 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 131 | 131 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.318 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 131 | 131 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.298 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 131 | 131 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.299 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 131 | 131 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.315 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 123 | 121 | 87 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.98 | 0.71 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.317 | 0.315 | 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 | 97 | 95 | 72 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.98 | 0.74 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.296 | 0.115 | 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 | 69 | 73 | 49 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.06 | 0.71 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.261 | 0.039 | 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 | 43 | 43 | 43 | 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 | 0.221 | 0.033 | 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 | 74 | 81 | 57 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.09 | 0.77 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.264 | 0.029 | 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 | 127 | 137 | 96 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.08 | 0.76 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.313 | 0.198 | 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 | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 106 | 106 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.267 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 106 | 106 | 910 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 8.58 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.264 | 6.330 | 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 | F | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 102 | 102 | 893 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 8.75 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.261 | 3.283 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 106 | 106 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.272 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | F | F | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 114 | 114 | 2072 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 18.18 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.276 | 27.339 | 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 | No | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 114 | 114 | 238 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 2.09 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.261 | 4.876 | 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 | No | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 111 | 111 | 229 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 2.06 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.261 | 9.022 | 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 | No | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 112 | 112 | 2164 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 19.32 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.267 | 17.523 | 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 | C | F(-2) | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 320 | 241 | 185 | 494 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.75 | 0.58 | 1.54 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.013 | 14.429 | 10.215 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F(-2) | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 346 | 257 | 191 | 501 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.74 | 0.55 | 1.45 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.117 | 1.244 | 10.760 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | C | F(-2) | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 274 | 208 | 169 | 141 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.76 | 0.62 | 0.51 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.773 | 1.832 | 9.347 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F(-2) | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 299 | 232 | 189 | 507 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.78 | 0.63 | 1.70 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.928 | 1.423 | 10.382 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F(-2) | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 320 | 243 | 224 | 382 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.76 | 0.70 | 1.19 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.986 | 2.130 | 10.122 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | C | F(-2) | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 357 | 266 | 93 | 496 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.75 | 0.26 | 1.39 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.650 | 12.830 | 17.606 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F(-2) | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 343 | 260 | 220 | 524 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.76 | 0.64 | 1.53 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.618 | 14.443 | 10.332 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F(-2) | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 311 | 236 | 118 | 265 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.76 | 0.38 | 0.85 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.585 | 12.012 | 11.140 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F(-2) | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 339 | 262 | 221 | 531 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.77 | 0.65 | 1.57 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.622 | 25.080 | 11.511 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F(-2) | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 375 | 284 | 127 | 405 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.76 | 0.34 | 1.08 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.647 | 13.324 | 11.109 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | F | C | C | F(-1) | F(-1) | F | F | F(-1) |
| verified |
N/A | N/A | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 405 | 0 | 316 | 1116 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.00 | 0.78 | 2.76 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.000 | 14.104 | 8.227 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | C | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 325 | 245 | 135 | 611 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.75 | 0.42 | 1.88 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.082 | 12.308 | 8.163 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | C | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 347 | 263 | 249 | 252 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.76 | 0.72 | 0.73 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.199 | 13.937 | 8.317 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | C | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 290 | 213 | 112 | 207 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.73 | 0.39 | 0.71 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.934 | 13.295 | 7.973 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | C | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 325 | 237 | 194 | 1100 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.73 | 0.60 | 3.38 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.085 | 23.234 | 9.772 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | C | F | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 335 | 247 | 130 | 976 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.74 | 0.39 | 2.91 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.107 | 12.942 | 9.795 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | C | F | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 371 | 272 | 261 | 1166 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.73 | 0.70 | 3.14 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.266 | 14.815 | 9.232 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | F | C | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | N/A | No | TBD | TBD | TBD | TBD | TBD |
| size | 413 | 313 | 0 | 705 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.76 | 0.00 | 1.71 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.811 | 0.000 | 8.546 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | F | C | F(-1) | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | N/A | No | TBD | TBD | TBD | TBD | TBD |
| size | 359 | 269 | 0 | 638 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.75 | 0.00 | 1.78 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.744 | 0.000 | 9.009 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | F | C | F | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | N/A | No | TBD | TBD | TBD | TBD | TBD |
| size | 355 | 263 | 0 | 262 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.74 | 0.00 | 0.74 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.742 | 0.000 | 8.095 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | F | C | F(-1) | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | N/A | No | TBD | TBD | TBD | TBD | TBD |
| size | 321 | 239 | 0 | 961 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.74 | 0.00 | 2.99 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.686 | 0.000 | 10.284 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | F | C | F | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | N/A | No | TBD | TBD | TBD | TBD | TBD |
| size | 357 | 265 | 0 | 1141 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.74 | 0.00 | 3.20 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.730 | 0.000 | 8.912 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | F | C | F(-1) | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | N/A | No | TBD | TBD | TBD | TBD | TBD |
| size | 389 | 287 | 0 | 1007 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.74 | 0.00 | 2.59 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.755 | 0.000 | 9.694 | 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 | A | A | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 111 | 120 | 106 | 90 | 94 | 101 | 148 | 317 | 221 |
| N.S. |
1 | 1.08 | 0.95 | 0.81 | 0.85 | 0.91 | 1.33 | 2.86 | 1.99 |
| time (sec) |
N/A | 0.768 | 0.448 | 1.407 | 0.210 | 0.265 | 0.812 | 3.379 | 18.314 |
| 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 | 84 | 92 | 82 | 67 | 72 | 79 | 112 | 248 | 162 |
| N.S. |
1 | 1.10 | 0.98 | 0.80 | 0.86 | 0.94 | 1.33 | 2.95 | 1.93 |
| time (sec) |
N/A | 0.572 | 0.203 | 1.097 | 0.193 | 0.285 | 0.404 | 1.531 | 19.026 |
| 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 | 55 | 59 | 55 | 47 | 50 | 57 | 76 | 179 | 102 |
| N.S. |
1 | 1.07 | 1.00 | 0.85 | 0.91 | 1.04 | 1.38 | 3.25 | 1.85 |
| time (sec) |
N/A | 0.410 | 0.143 | 0.845 | 0.217 | 0.289 | 0.191 | 0.617 | 15.538 |
| 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 | 25 | 25 | 25 | 23 | 26 | 34 | 37 | 107 | 40 |
| N.S. |
1 | 1.00 | 1.00 | 0.92 | 1.04 | 1.36 | 1.48 | 4.28 | 1.60 |
| time (sec) |
N/A | 0.273 | 0.010 | 0.412 | 0.201 | 0.269 | 0.102 | 0.318 | 14.897 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 43 | 41 | 64 | 33 | 34 | 38 | 0 | 61 | 51 |
| N.S. |
1 | 0.95 | 1.49 | 0.77 | 0.79 | 0.88 | 0.00 | 1.42 | 1.19 |
| time (sec) |
N/A | 0.296 | 0.018 | 0.471 | 0.194 | 0.261 | 0.000 | 0.276 | 14.476 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 72 | 71 | 114 | 75 | 62 | 99 | 0 | 170 | 86 |
| N.S. |
1 | 0.99 | 1.58 | 1.04 | 0.86 | 1.38 | 0.00 | 2.36 | 1.19 |
| time (sec) |
N/A | 0.422 | 0.793 | 0.548 | 0.220 | 0.285 | 0.000 | 0.295 | 14.468 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 102 | 105 | 175 | 111 | 99 | 168 | 0 | 266 | 128 |
| N.S. |
1 | 1.03 | 1.72 | 1.09 | 0.97 | 1.65 | 0.00 | 2.61 | 1.25 |
| time (sec) |
N/A | 0.561 | 0.103 | 0.716 | 0.237 | 0.270 | 0.000 | 0.337 | 14.492 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 130 | 138 | 216 | 151 | 133 | 237 | 0 | 358 | 170 |
| N.S. |
1 | 1.06 | 1.66 | 1.16 | 1.02 | 1.82 | 0.00 | 2.75 | 1.31 |
| time (sec) |
N/A | 0.737 | 0.490 | 0.907 | 0.228 | 0.271 | 0.000 | 0.362 | 14.093 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 102 | 115 | 179 | 143 | 134 | 134 | 0 | 228 | 331 |
| N.S. |
1 | 1.13 | 1.75 | 1.40 | 1.31 | 1.31 | 0.00 | 2.24 | 3.25 |
| time (sec) |
N/A | 0.483 | 0.035 | 1.913 | 0.295 | 0.278 | 0.000 | 2.127 | 15.023 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 73 | 82 | 117 | 104 | 102 | 112 | 0 | 172 | 267 |
| N.S. |
1 | 1.12 | 1.60 | 1.42 | 1.40 | 1.53 | 0.00 | 2.36 | 3.66 |
| time (sec) |
N/A | 0.346 | 0.023 | 1.505 | 0.292 | 0.278 | 0.000 | 0.928 | 15.238 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | B | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 45 | 48 | 60 | 67 | 65 | 87 | 0 | 115 | 96 |
| N.S. |
1 | 1.07 | 1.33 | 1.49 | 1.44 | 1.93 | 0.00 | 2.56 | 2.13 |
| time (sec) |
N/A | 0.232 | 0.007 | 0.939 | 0.279 | 0.285 | 0.000 | 0.476 | 14.610 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | A | A | F | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 26 | 26 | 43 | 35 | 31 | 33 | 0 | 52 | 48 |
| N.S. |
1 | 1.00 | 1.65 | 1.35 | 1.19 | 1.27 | 0.00 | 2.00 | 1.85 |
| time (sec) |
N/A | 0.199 | 0.013 | 0.460 | 0.280 | 0.266 | 0.000 | 0.302 | 14.341 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | A | A | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 55 | 58 | 62 | 86 | 59 | 87 | 0 | 112 | 90 |
| N.S. |
1 | 1.05 | 1.13 | 1.56 | 1.07 | 1.58 | 0.00 | 2.04 | 1.64 |
| time (sec) |
N/A | 0.309 | 0.017 | 1.232 | 0.277 | 0.260 | 0.000 | 0.333 | 14.615 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | A | A | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 84 | 92 | 79 | 129 | 79 | 130 | 0 | 170 | 132 |
| N.S. |
1 | 1.10 | 0.94 | 1.54 | 0.94 | 1.55 | 0.00 | 2.02 | 1.57 |
| time (sec) |
N/A | 0.426 | 0.024 | 1.215 | 0.273 | 0.267 | 0.000 | 0.335 | 14.831 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | A | A | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 111 | 119 | 92 | 162 | 100 | 179 | 0 | 225 | 174 |
| N.S. |
1 | 1.07 | 0.83 | 1.46 | 0.90 | 1.61 | 0.00 | 2.03 | 1.57 |
| time (sec) |
N/A | 0.561 | 0.028 | 1.694 | 0.288 | 0.283 | 0.000 | 0.370 | 14.660 |
| 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 | 185 | 217 | 173 | 133 | 174 | 181 | 314 | 489 | 344 |
| N.S. |
1 | 1.17 | 0.94 | 0.72 | 0.94 | 0.98 | 1.70 | 2.64 | 1.86 |
| time (sec) |
N/A | 0.361 | 1.166 | 6.163 | 0.196 | 0.309 | 2.475 | 5.918 | 17.871 |
| 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 | 149 | 172 | 138 | 113 | 139 | 146 | 252 | 415 | 280 |
| N.S. |
1 | 1.15 | 0.93 | 0.76 | 0.93 | 0.98 | 1.69 | 2.79 | 1.88 |
| time (sec) |
N/A | 0.332 | 0.675 | 3.736 | 0.194 | 0.291 | 1.493 | 3.306 | 17.893 |
| 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 | 115 | 133 | 105 | 93 | 108 | 115 | 189 | 341 | 215 |
| N.S. |
1 | 1.16 | 0.91 | 0.81 | 0.94 | 1.00 | 1.64 | 2.97 | 1.87 |
| time (sec) |
N/A | 0.301 | 0.326 | 2.283 | 0.199 | 0.292 | 0.983 | 1.693 | 17.834 |
| 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 | 87 | 92 | 74 | 75 | 75 | 82 | 126 | 267 | 151 |
| N.S. |
1 | 1.06 | 0.85 | 0.86 | 0.86 | 0.94 | 1.45 | 3.07 | 1.74 |
| time (sec) |
N/A | 0.281 | 0.385 | 1.513 | 0.197 | 0.304 | 0.275 | 0.742 | 16.451 |
| 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 | 43 | 42 | 40 | 42 | 51 | 60 | 191 | 81 |
| N.S. |
1 | 0.91 | 0.89 | 0.85 | 0.89 | 1.09 | 1.28 | 4.06 | 1.72 |
| time (sec) |
N/A | 0.229 | 0.046 | 0.720 | 0.204 | 0.269 | 0.183 | 0.357 | 13.203 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 61 | 70 | 54 | 48 | 62 | 68 | 0 | 101 | 96 |
| N.S. |
1 | 1.15 | 0.89 | 0.79 | 1.02 | 1.11 | 0.00 | 1.66 | 1.57 |
| time (sec) |
N/A | 0.262 | 0.147 | 0.692 | 0.192 | 0.277 | 0.000 | 0.302 | 14.380 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 92 | 116 | 89 | 92 | 72 | 113 | 0 | 209 | 98 |
| N.S. |
1 | 1.26 | 0.97 | 1.00 | 0.78 | 1.23 | 0.00 | 2.27 | 1.07 |
| time (sec) |
N/A | 0.324 | 0.561 | 0.753 | 0.195 | 0.282 | 0.000 | 0.330 | 14.267 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 126 | 174 | 139 | 136 | 122 | 203 | 0 | 360 | 164 |
| N.S. |
1 | 1.38 | 1.10 | 1.08 | 0.97 | 1.61 | 0.00 | 2.86 | 1.30 |
| time (sec) |
N/A | 0.374 | 3.247 | 1.136 | 0.195 | 0.280 | 0.000 | 0.367 | 14.336 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 157 | 157 | 132 | 167 | 150 | 184 | 0 | 282 | 403 |
| N.S. |
1 | 1.00 | 0.84 | 1.06 | 0.96 | 1.17 | 0.00 | 1.80 | 2.57 |
| time (sec) |
N/A | 0.407 | 1.259 | 3.656 | 0.290 | 0.278 | 0.000 | 2.302 | 15.420 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 116 | 116 | 107 | 129 | 118 | 151 | 0 | 220 | 332 |
| N.S. |
1 | 1.00 | 0.92 | 1.11 | 1.02 | 1.30 | 0.00 | 1.90 | 2.86 |
| time (sec) |
N/A | 0.353 | 0.618 | 2.356 | 0.280 | 0.294 | 0.000 | 1.045 | 15.413 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 70 | 70 | 66 | 91 | 82 | 115 | 0 | 158 | 227 |
| N.S. |
1 | 1.00 | 0.94 | 1.30 | 1.17 | 1.64 | 0.00 | 2.26 | 3.24 |
| time (sec) |
N/A | 0.327 | 0.224 | 1.267 | 0.283 | 0.275 | 0.000 | 0.571 | 14.663 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | C | A | A | F | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 48 | 48 | 39 | 47 | 47 | 44 | 0 | 80 | 58 |
| N.S. |
1 | 1.00 | 0.81 | 0.98 | 0.98 | 0.92 | 0.00 | 1.67 | 1.21 |
| time (sec) |
N/A | 0.269 | 0.622 | 1.126 | 0.286 | 0.269 | 0.000 | 0.295 | 14.139 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | A | A | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 85 | 85 | 70 | 111 | 76 | 102 | 0 | 176 | 118 |
| N.S. |
1 | 1.00 | 0.82 | 1.31 | 0.89 | 1.20 | 0.00 | 2.07 | 1.39 |
| time (sec) |
N/A | 0.321 | 0.262 | 1.317 | 0.268 | 0.285 | 0.000 | 0.319 | 14.001 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | A | A | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 122 | 122 | 84 | 154 | 96 | 152 | 0 | 273 | 191 |
| N.S. |
1 | 1.00 | 0.69 | 1.26 | 0.79 | 1.25 | 0.00 | 2.24 | 1.57 |
| time (sec) |
N/A | 0.348 | 0.375 | 2.064 | 0.276 | 0.272 | 0.000 | 0.356 | 13.700 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | A | A | F(-1) | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 153 | 153 | 94 | 187 | 116 | 206 | 0 | 366 | 258 |
| N.S. |
1 | 1.00 | 0.61 | 1.22 | 0.76 | 1.35 | 0.00 | 2.39 | 1.69 |
| time (sec) |
N/A | 0.391 | 0.399 | 3.218 | 0.280 | 0.274 | 0.000 | 0.397 | 13.750 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 250 | 229 | 228 | 273 | 268 | 293 | 0 | 1768 | 631 |
| N.S. |
1 | 0.92 | 0.91 | 1.09 | 1.07 | 1.17 | 0.00 | 7.07 | 2.52 |
| time (sec) |
N/A | 0.421 | 3.910 | 2.182 | 0.205 | 0.344 | 0.000 | 5.760 | 15.150 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 170 | 157 | 156 | 184 | 183 | 205 | 0 | 1052 | 395 |
| N.S. |
1 | 0.92 | 0.92 | 1.08 | 1.08 | 1.21 | 0.00 | 6.19 | 2.32 |
| time (sec) |
N/A | 0.356 | 6.228 | 1.683 | 0.234 | 0.342 | 0.000 | 3.414 | 15.602 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 108 | 99 | 98 | 115 | 110 | 129 | 0 | 560 | 227 |
| N.S. |
1 | 0.92 | 0.91 | 1.06 | 1.02 | 1.19 | 0.00 | 5.19 | 2.10 |
| time (sec) |
N/A | 0.308 | 0.362 | 1.239 | 0.218 | 0.321 | 0.000 | 1.527 | 15.085 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 59 | 58 | 52 | 57 | 57 | 69 | 0 | 289 | 115 |
| N.S. |
1 | 0.98 | 0.88 | 0.97 | 0.97 | 1.17 | 0.00 | 4.90 | 1.95 |
| time (sec) |
N/A | 0.277 | 0.143 | 0.722 | 0.241 | 0.277 | 0.000 | 0.614 | 14.914 |
| 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 | 35 | 34 | 19 | 33 | 19 | 19 | 82 | 114 | 71 |
| N.S. |
1 | 0.97 | 0.54 | 0.94 | 0.54 | 0.54 | 2.34 | 3.26 | 2.03 |
| time (sec) |
N/A | 0.220 | 0.109 | 0.279 | 0.213 | 0.266 | 2.924 | 0.348 | 14.699 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 94 | 100 | 82 | 75 | 68 | 75 | 0 | 257 | 93 |
| N.S. |
1 | 1.06 | 0.87 | 0.80 | 0.72 | 0.80 | 0.00 | 2.73 | 0.99 |
| time (sec) |
N/A | 0.316 | 0.150 | 0.617 | 0.219 | 0.286 | 0.000 | 0.311 | 14.753 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 157 | 165 | 151 | 126 | 144 | 263 | 0 | 403 | 174 |
| N.S. |
1 | 1.05 | 0.96 | 0.80 | 0.92 | 1.68 | 0.00 | 2.57 | 1.11 |
| time (sec) |
N/A | 0.402 | 0.981 | 0.937 | 0.203 | 0.349 | 0.000 | 0.351 | 14.726 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | B | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 234 | 246 | 220 | 193 | 289 | 576 | 0 | 649 | 290 |
| N.S. |
1 | 1.05 | 0.94 | 0.82 | 1.24 | 2.46 | 0.00 | 2.77 | 1.24 |
| time (sec) |
N/A | 0.526 | 4.503 | 1.216 | 0.213 | 0.428 | 0.000 | 0.392 | 15.273 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | B | F(-2) | A | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 198 | 271 | 907 | 411 | 0 | 603 | 0 | 746 | 9148 |
| N.S. |
1 | 1.37 | 4.58 | 2.08 | 0.00 | 3.05 | 0.00 | 3.77 | 46.20 |
| time (sec) |
N/A | 0.687 | 6.529 | 1.540 | 0.000 | 0.612 | 0.000 | 2.107 | 16.738 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | B | F(-2) | A | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 126 | 146 | 287 | 234 | 0 | 444 | 0 | 476 | 6062 |
| N.S. |
1 | 1.16 | 2.28 | 1.86 | 0.00 | 3.52 | 0.00 | 3.78 | 48.11 |
| time (sec) |
N/A | 0.788 | 1.911 | 0.880 | 0.000 | 0.408 | 0.000 | 0.902 | 16.056 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 76 | 88 | 115 | 108 | 0 | 253 | 0 | 140 | 121 |
| N.S. |
1 | 1.16 | 1.51 | 1.42 | 0.00 | 3.33 | 0.00 | 1.84 | 1.59 |
| time (sec) |
N/A | 0.650 | 0.329 | 0.808 | 0.000 | 0.321 | 0.000 | 0.486 | 14.406 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 106 | 125 | 147 | 115 | 0 | 362 | 0 | 582 | 1002 |
| N.S. |
1 | 1.18 | 1.39 | 1.08 | 0.00 | 3.42 | 0.00 | 5.49 | 9.45 |
| time (sec) |
N/A | 0.739 | 0.608 | 0.755 | 0.000 | 0.302 | 0.000 | 0.384 | 16.551 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | A | F(-2) | B | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 177 | 222 | 416 | 184 | 0 | 742 | 0 | 1073 | 3859 |
| N.S. |
1 | 1.25 | 2.35 | 1.04 | 0.00 | 4.19 | 0.00 | 6.06 | 21.80 |
| time (sec) |
N/A | 1.342 | 6.439 | 0.905 | 0.000 | 0.315 | 0.000 | 0.483 | 23.381 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 255 | 231 | 230 | 287 | 321 | 423 | 0 | 1696 | 760 |
| N.S. |
1 | 0.91 | 0.90 | 1.13 | 1.26 | 1.66 | 0.00 | 6.65 | 2.98 |
| time (sec) |
N/A | 0.421 | 0.915 | 3.602 | 0.205 | 0.365 | 0.000 | 5.906 | 16.976 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 179 | 165 | 163 | 200 | 227 | 312 | 0 | 1023 | 505 |
| N.S. |
1 | 0.92 | 0.91 | 1.12 | 1.27 | 1.74 | 0.00 | 5.72 | 2.82 |
| time (sec) |
N/A | 0.367 | 1.510 | 2.539 | 0.205 | 0.331 | 0.000 | 3.435 | 15.729 |