Detailed conclusion table per each integral is given by the table below. The elapsed time is in seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2) if the failure was due to an exception being raised, which could indicate a bug in the system. If the failure was due to integral not being evaluated within the time limit, then it is given as F.
In this table, the column N.S.
means normalized size and is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To make the table
fit the page, the name Mathematica
was abbreviated to MMA
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F(-1) | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 191 | 225 | 387 | 0 | 0 | 1855 | 0 | 0 | 123 | 0 |
N.S. |
1 | 1.18 | 2.03 | 0.00 | 0.00 | 9.71 | 0.00 | 0.00 | 0.64 | 0.00 |
time (sec) |
N/A | 0.876 | 3.856 | 0.000 | 0.000 | 0.406 | 0.000 | 0.000 | 0.196 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F(-1) | F | B | F(-1) | F(-1) | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 251 | 258 | 1844 | 0 | 0 | 3514 | 0 | 0 | 162 | 0 |
N.S. |
1 | 1.03 | 7.35 | 0.00 | 0.00 | 14.00 | 0.00 | 0.00 | 0.65 | 0.00 |
time (sec) |
N/A | 1.517 | 15.813 | 180.000 | 0.000 | 0.588 | 0.000 | 0.000 | 0.204 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F(-1) | F | B | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 194 | 200 | 1625 | 0 | 0 | 2977 | 0 | 0 | 103 | 0 |
N.S. |
1 | 1.03 | 8.38 | 0.00 | 0.00 | 15.35 | 0.00 | 0.00 | 0.53 | 0.00 |
time (sec) |
N/A | 0.998 | 15.607 | 180.000 | 0.000 | 0.505 | 0.000 | 0.000 | 0.194 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | F | B | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 126 | 126 | 372 | 764 | 0 | 896 | 0 | 0 | 49 | 0 |
N.S. |
1 | 1.00 | 2.95 | 6.06 | 0.00 | 7.11 | 0.00 | 0.00 | 0.39 | 0.00 |
time (sec) |
N/A | 0.471 | 3.072 | 6.622 | 0.000 | 0.282 | 0.000 | 0.000 | 0.193 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | F | B | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 135 | 135 | 381 | 708 | 0 | 1008 | 0 | 0 | 81 | 0 |
N.S. |
1 | 1.00 | 2.82 | 5.24 | 0.00 | 7.47 | 0.00 | 0.00 | 0.60 | 0.00 |
time (sec) |
N/A | 0.501 | 3.543 | 8.358 | 0.000 | 0.317 | 0.000 | 0.000 | 0.209 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F(-1) | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 197 | 219 | 401 | 0 | 0 | 1954 | 0 | 0 | 129 | 0 |
N.S. |
1 | 1.11 | 2.04 | 0.00 | 0.00 | 9.92 | 0.00 | 0.00 | 0.65 | 0.00 |
time (sec) |
N/A | 0.874 | 4.734 | 0.000 | 0.000 | 0.466 | 0.000 | 0.000 | 0.207 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F(-1) | F | B | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 271 | 313 | 478 | 0 | 0 | 3182 | 0 | 0 | 177 | 0 |
N.S. |
1 | 1.15 | 1.76 | 0.00 | 0.00 | 11.74 | 0.00 | 0.00 | 0.65 | 0.00 |
time (sec) |
N/A | 1.389 | 6.340 | 0.000 | 0.000 | 0.645 | 0.000 | 0.000 | 0.207 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F(-1) | F(-1) | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 260 | 272 | 1845 | 5128 | 0 | 3949 | 0 | 0 | 192 | 0 |
N.S. |
1 | 1.05 | 7.10 | 19.72 | 0.00 | 15.19 | 0.00 | 0.00 | 0.74 | 0.00 |
time (sec) |
N/A | 1.519 | 15.904 | 3409.480 | 0.000 | 0.640 | 0.000 | 0.000 | 0.233 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | F | B | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 184 | 190 | 396 | 1397 | 0 | 1304 | 0 | 0 | 123 | 0 |
N.S. |
1 | 1.03 | 2.15 | 7.59 | 0.00 | 7.09 | 0.00 | 0.00 | 0.67 | 0.00 |
time (sec) |
N/A | 0.885 | 4.209 | 12.431 | 0.000 | 0.376 | 0.000 | 0.000 | 0.216 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | F | B | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 191 | 197 | 412 | 1511 | 0 | 1474 | 0 | 0 | 59 | 0 |
N.S. |
1 | 1.03 | 2.16 | 7.91 | 0.00 | 7.72 | 0.00 | 0.00 | 0.31 | 0.00 |
time (sec) |
N/A | 0.810 | 4.075 | 16.950 | 0.000 | 0.347 | 0.000 | 0.000 | 0.219 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | F | B | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 201 | 214 | 411 | 1217 | 0 | 1644 | 0 | 0 | 103 | 0 |
N.S. |
1 | 1.06 | 2.04 | 6.05 | 0.00 | 8.18 | 0.00 | 0.00 | 0.51 | 0.00 |
time (sec) |
N/A | 0.866 | 5.708 | 20.452 | 0.000 | 0.489 | 0.000 | 0.000 | 0.213 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F(-1) | F | B | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 270 | 310 | 462 | 0 | 0 | 2984 | 0 | 0 | 167 | 0 |
N.S. |
1 | 1.15 | 1.71 | 0.00 | 0.00 | 11.05 | 0.00 | 0.00 | 0.62 | 0.00 |
time (sec) |
N/A | 1.389 | 7.882 | 0.000 | 0.000 | 0.743 | 0.000 | 0.000 | 0.220 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F(-1) | F | B | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 355 | 412 | 717 | 0 | 0 | 4858 | 0 | 0 | 231 | 0 |
N.S. |
1 | 1.16 | 2.02 | 0.00 | 0.00 | 13.68 | 0.00 | 0.00 | 0.65 | 0.00 |
time (sec) |
N/A | 2.016 | 11.053 | 0.000 | 0.000 | 1.635 | 0.000 | 0.000 | 0.221 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F | F | F | F(-1) |
verified |
N/A | No | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 129 | 143 | 0 | 0 | 0 | 0 | 0 | 0 | 27 | 0 |
N.S. |
1 | 1.11 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.21 | 0.00 |
time (sec) |
N/A | 0.386 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.233 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 320 | 318 | 454 | 0 | 0 | 0 | 0 | 0 | 102 | 0 |
N.S. |
1 | 0.99 | 1.42 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.32 | 0.00 |
time (sec) |
N/A | 1.483 | 22.702 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.198 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 193 | 195 | 310 | 0 | 0 | 0 | 0 | 0 | 71 | 0 |
N.S. |
1 | 1.01 | 1.61 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.37 | 0.00 |
time (sec) |
N/A | 0.725 | 21.687 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.192 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 117 | 117 | 101 | 0 | 0 | 0 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.00 | 0.86 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.34 | 0.00 |
time (sec) |
N/A | 0.406 | 0.575 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.190 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 74 | 74 | 70 | 0 | 0 | 0 | 0 | 0 | 14 | 0 |
N.S. |
1 | 1.00 | 0.95 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.19 | 0.00 |
time (sec) |
N/A | 0.268 | 0.104 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.174 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F | F | F | F(-1) |
verified |
N/A | No | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 100 | 114 | 0 | 0 | 0 | 0 | 0 | 0 | 27 | 0 |
N.S. |
1 | 1.14 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.27 | 0.00 |
time (sec) |
N/A | 0.344 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.186 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | No | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 100 | 114 | 0 | 0 | 0 | 0 | 0 | 0 | 43 | 0 |
N.S. |
1 | 1.14 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.43 | 0.00 |
time (sec) |
N/A | 0.347 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.181 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | No | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 100 | 114 | 0 | 0 | 0 | 0 | 0 | 0 | 59 | 0 |
N.S. |
1 | 1.14 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.59 | 0.00 |
time (sec) |
N/A | 0.340 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.184 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | No | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 134 | 150 | 0 | 0 | 0 | 0 | 0 | 0 | 63 | 0 |
N.S. |
1 | 1.12 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.47 | 0.00 |
time (sec) |
N/A | 0.396 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.193 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F | F | F | F(-1) |
verified |
N/A | No | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 131 | 145 | 0 | 0 | 0 | 0 | 0 | 0 | 26 | 0 |
N.S. |
1 | 1.11 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.20 | 0.00 |
time (sec) |
N/A | 0.362 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.167 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F | F | F | F(-1) |
verified |
N/A | No | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 131 | 145 | 0 | 0 | 0 | 0 | 0 | 0 | 38 | 0 |
N.S. |
1 | 1.11 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 0.376 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.161 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F | F | F | F(-1) |
verified |
N/A | No | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 136 | 152 | 0 | 0 | 0 | 0 | 0 | 0 | 54 | 0 |
N.S. |
1 | 1.12 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.40 | 0.00 |
time (sec) |
N/A | 0.389 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.185 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F | F | F | F(-1) |
verified |
N/A | No | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 136 | 152 | 0 | 0 | 0 | 0 | 0 | 0 | 70 | 0 |
N.S. |
1 | 1.12 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.51 | 0.00 |
time (sec) |
N/A | 0.387 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.195 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 62 | 111 | 196 | 0 | 0 | 0 | 0 | 0 | 50 | 0 |
N.S. |
1 | 1.79 | 3.16 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.81 | 0.00 |
time (sec) |
N/A | 0.304 | 7.969 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.188 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 64 | 122 | 272 | 0 | 0 | 0 | 0 | 0 | 50 | 0 |
N.S. |
1 | 1.91 | 4.25 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.78 | 0.00 |
time (sec) |
N/A | 0.306 | 8.815 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.190 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | A | A | F | A | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 45 | 0 | 35 | 54 | 0 | 43 | 49 | 41 |
N.S. |
1 | 1.00 | 1.61 | 0.00 | 1.25 | 1.93 | 0.00 | 1.54 | 1.75 | 1.46 |
time (sec) |
N/A | 0.209 | 0.044 | 0.000 | 0.194 | 0.085 | 0.000 | 0.384 | 0.185 | 17.679 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 122 | 122 | 252 | 0 | 0 | 0 | 0 | 0 | 50 | 0 |
N.S. |
1 | 1.00 | 2.07 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.41 | 0.00 |
time (sec) |
N/A | 0.308 | 9.008 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.203 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 106 | 106 | 245 | 0 | 0 | 0 | 0 | 0 | 45 | 0 |
N.S. |
1 | 1.00 | 2.31 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.42 | 0.00 |
time (sec) |
N/A | 0.294 | 2.632 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.210 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 65 | 65 | 53 | 0 | 0 | 0 | 0 | 0 | 19 | 0 |
N.S. |
1 | 1.00 | 0.82 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 0.215 | 0.074 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.196 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 94 | 94 | 276 | 0 | 0 | 0 | 0 | 0 | 51 | 0 |
N.S. |
1 | 1.00 | 2.94 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.54 | 0.00 |
time (sec) |
N/A | 0.293 | 10.895 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.218 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 114 | 114 | 270 | 0 | 0 | 0 | 0 | 0 | 52 | 0 |
N.S. |
1 | 1.00 | 2.37 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.46 | 0.00 |
time (sec) |
N/A | 0.304 | 9.569 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.213 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | F | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 43 | 43 | 48 | 0 | 0 | 41 | 0 | 0 | 51 | 43 |
N.S. |
1 | 1.00 | 1.12 | 0.00 | 0.00 | 0.95 | 0.00 | 0.00 | 1.19 | 1.00 |
time (sec) |
N/A | 0.243 | 0.191 | 0.000 | 0.000 | 0.091 | 0.000 | 0.000 | 0.221 | 17.666 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 90 | 113 | 271 | 0 | 0 | 0 | 0 | 0 | 52 | 0 |
N.S. |
1 | 1.26 | 3.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.58 | 0.00 |
time (sec) |
N/A | 0.300 | 9.926 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.220 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 88 | 111 | 199 | 0 | 0 | 0 | 0 | 0 | 52 | 0 |
N.S. |
1 | 1.26 | 2.26 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.59 | 0.00 |
time (sec) |
N/A | 0.299 | 9.163 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.212 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 81 | 117 | 198 | 0 | 0 | 0 | 0 | 0 | 52 | 0 |
N.S. |
1 | 1.44 | 2.44 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.64 | 0.00 |
time (sec) |
N/A | 0.314 | 9.019 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.195 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 83 | 120 | 274 | 0 | 0 | 0 | 0 | 0 | 52 | 0 |
N.S. |
1 | 1.45 | 3.30 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.63 | 0.00 |
time (sec) |
N/A | 0.314 | 9.323 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.208 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | A | A | F | B | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 39 | 39 | 69 | 0 | 38 | 43 | 0 | 753 | 51 | 52 |
N.S. |
1 | 1.00 | 1.77 | 0.00 | 0.97 | 1.10 | 0.00 | 19.31 | 1.31 | 1.33 |
time (sec) |
N/A | 0.246 | 3.530 | 0.000 | 0.285 | 0.076 | 0.000 | 0.430 | 0.199 | 0.254 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 83 | 120 | 254 | 0 | 0 | 0 | 0 | 0 | 52 | 0 |
N.S. |
1 | 1.45 | 3.06 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.63 | 0.00 |
time (sec) |
N/A | 0.317 | 9.530 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.183 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 81 | 119 | 254 | 0 | 0 | 0 | 0 | 0 | 47 | 0 |
N.S. |
1 | 1.47 | 3.14 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.58 | 0.00 |
time (sec) |
N/A | 0.309 | 11.119 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.176 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 81 | 81 | 77 | 0 | 0 | 0 | 0 | 0 | 21 | 0 |
N.S. |
1 | 1.00 | 0.95 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 0.285 | 0.104 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.171 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 72 | 120 | 278 | 0 | 0 | 0 | 0 | 0 | 53 | 0 |
N.S. |
1 | 1.67 | 3.86 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.74 | 0.00 |
time (sec) |
N/A | 0.318 | 12.987 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.200 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 118 | 272 | 0 | 0 | 0 | 0 | 0 | 54 | 0 |
N.S. |
1 | 1.53 | 3.53 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.70 | 0.00 |
time (sec) |
N/A | 0.307 | 11.536 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.203 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | F | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 45 | 45 | 55 | 0 | 0 | 43 | 0 | 0 | 53 | 45 |
N.S. |
1 | 1.00 | 1.22 | 0.00 | 0.00 | 0.96 | 0.00 | 0.00 | 1.18 | 1.00 |
time (sec) |
N/A | 0.249 | 0.231 | 0.000 | 0.000 | 0.090 | 0.000 | 0.000 | 0.186 | 17.637 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 115 | 117 | 273 | 0 | 0 | 0 | 0 | 0 | 54 | 0 |
N.S. |
1 | 1.02 | 2.37 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.47 | 0.00 |
time (sec) |
N/A | 0.316 | 11.574 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.172 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 113 | 115 | 201 | 0 | 0 | 0 | 0 | 0 | 54 | 0 |
N.S. |
1 | 1.02 | 1.78 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.48 | 0.00 |
time (sec) |
N/A | 0.312 | 11.357 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.203 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 72 | 115 | 201 | 0 | 0 | 0 | 0 | 0 | 52 | 0 |
N.S. |
1 | 1.60 | 2.79 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.72 | 0.00 |
time (sec) |
N/A | 0.307 | 9.732 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.205 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 118 | 271 | 0 | 0 | 0 | 0 | 0 | 52 | 0 |
N.S. |
1 | 1.53 | 3.52 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.68 | 0.00 |
time (sec) |
N/A | 0.308 | 10.345 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.183 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | F | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 45 | 45 | 48 | 0 | 0 | 43 | 0 | 0 | 53 | 45 |
N.S. |
1 | 1.00 | 1.07 | 0.00 | 0.00 | 0.96 | 0.00 | 0.00 | 1.18 | 1.00 |
time (sec) |
N/A | 0.251 | 2.362 | 0.000 | 0.000 | 0.096 | 0.000 | 0.000 | 0.185 | 17.668 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 117 | 119 | 267 | 0 | 0 | 0 | 0 | 0 | 52 | 0 |
N.S. |
1 | 1.02 | 2.28 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.44 | 0.00 |
time (sec) |
N/A | 0.311 | 10.491 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.173 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 116 | 118 | 272 | 0 | 0 | 0 | 0 | 0 | 47 | 0 |
N.S. |
1 | 1.02 | 2.34 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.41 | 0.00 |
time (sec) |
N/A | 0.298 | 11.676 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.213 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 81 | 81 | 77 | 0 | 0 | 0 | 0 | 0 | 26 | 0 |
N.S. |
1 | 1.00 | 0.95 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.32 | 0.00 |
time (sec) |
N/A | 0.282 | 0.110 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.228 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 119 | 121 | 257 | 0 | 0 | 0 | 0 | 0 | 53 | 0 |
N.S. |
1 | 1.02 | 2.16 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.45 | 0.00 |
time (sec) |
N/A | 0.302 | 12.185 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.194 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 119 | 121 | 260 | 0 | 0 | 0 | 0 | 0 | 54 | 0 |
N.S. |
1 | 1.02 | 2.18 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.45 | 0.00 |
time (sec) |
N/A | 0.306 | 10.384 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.197 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | A | A | F | B | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 39 | 39 | 67 | 0 | 45 | 43 | 0 | 753 | 51 | 52 |
N.S. |
1 | 1.00 | 1.72 | 0.00 | 1.15 | 1.10 | 0.00 | 19.31 | 1.31 | 1.33 |
time (sec) |
N/A | 0.238 | 0.465 | 0.000 | 0.239 | 0.074 | 0.000 | 0.482 | 0.201 | 17.620 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 117 | 119 | 273 | 0 | 0 | 0 | 0 | 0 | 54 | 0 |
N.S. |
1 | 1.02 | 2.33 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.46 | 0.00 |
time (sec) |
N/A | 0.309 | 10.959 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.217 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 115 | 117 | 198 | 0 | 0 | 0 | 0 | 0 | 54 | 0 |
N.S. |
1 | 1.02 | 1.72 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.47 | 0.00 |
time (sec) |
N/A | 0.306 | 10.790 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.177 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 95 | 116 | 90 | 0 | 0 | 0 | 0 | 0 | 42 | 0 |
N.S. |
1 | 1.22 | 0.95 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.44 | 0.00 |
time (sec) |
N/A | 0.532 | 1.596 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.188 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 129 | 129 | 352 | 0 | 0 | 0 | 0 | 0 | 52 | 0 |
N.S. |
1 | 1.00 | 2.73 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.40 | 0.00 |
time (sec) |
N/A | 0.339 | 12.549 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.181 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 107 | 107 | 0 | 0 | 0 | 0 | 0 | 0 | 90 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.84 | 0.00 |
time (sec) |
N/A | 0.308 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.203 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 107 | 107 | 0 | 0 | 0 | 0 | 0 | 0 | 65 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.61 | 0.00 |
time (sec) |
N/A | 0.285 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.237 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 105 | 105 | 0 | 0 | 0 | 0 | 0 | 0 | 38 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.36 | 0.00 |
time (sec) |
N/A | 0.264 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.195 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 104 | 104 | 120 | 0 | 0 | 0 | 0 | 0 | 14 | 0 |
N.S. |
1 | 1.00 | 1.15 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.13 | 0.00 |
time (sec) |
N/A | 0.254 | 0.228 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.180 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 107 | 107 | 0 | 0 | 0 | 0 | 0 | 0 | 29 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.27 | 0.00 |
time (sec) |
N/A | 0.304 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.204 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 109 | 109 | 0 | 0 | 0 | 0 | 0 | 0 | 39 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.36 | 0.00 |
time (sec) |
N/A | 0.304 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.208 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 109 | 109 | 0 | 0 | 0 | 0 | 0 | 0 | 49 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.45 | 0.00 |
time (sec) |
N/A | 0.299 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.207 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 257 | 255 | 190 | 0 | 0 | 0 | 0 | 0 | 95 | 0 |
N.S. |
1 | 0.99 | 0.74 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.37 | 0.00 |
time (sec) |
N/A | 0.935 | 12.993 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.215 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 160 | 159 | 133 | 0 | 0 | 0 | 0 | 0 | 59 | 0 |
N.S. |
1 | 0.99 | 0.83 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.37 | 0.00 |
time (sec) |
N/A | 0.556 | 4.544 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.189 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 85 | 85 | 0 | 0 | 0 | 0 | 0 | 0 | 27 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.32 | 0.00 |
time (sec) |
N/A | 0.290 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.182 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F | F | F | F | F(-1) |
verified |
N/A | No | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 99 | 131 | 236 | 0 | 0 | 0 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.32 | 2.38 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.40 | 0.00 |
time (sec) |
N/A | 0.344 | 4.906 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.186 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | No | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 104 | 130 | 319 | 0 | 0 | 0 | 0 | 0 | 50 | 0 |
N.S. |
1 | 1.25 | 3.07 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.48 | 0.00 |
time (sec) |
N/A | 0.351 | 6.303 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.183 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | No | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 104 | 136 | 414 | 0 | 0 | 0 | 0 | 0 | 60 | 0 |
N.S. |
1 | 1.31 | 3.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.58 | 0.00 |
time (sec) |
N/A | 0.363 | 9.218 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.184 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 107 | 107 | 1736 | 0 | 0 | 0 | 0 | 0 | 38 | 0 |
N.S. |
1 | 1.00 | 16.22 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.36 | 0.00 |
time (sec) |
N/A | 0.290 | 6.610 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.192 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 107 | 107 | 886 | 0 | 0 | 0 | 0 | 0 | 38 | 0 |
N.S. |
1 | 1.00 | 8.28 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.36 | 0.00 |
time (sec) |
N/A | 0.286 | 6.612 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.223 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 112 | 112 | 942 | 0 | 0 | 0 | 0 | 0 | 88 | 0 |
N.S. |
1 | 1.00 | 8.41 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.79 | 0.00 |
time (sec) |
N/A | 0.284 | 6.836 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.220 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 171 | 179 | 143 | 148 | 175 | 145 | 386 | 148 | 233 | 183 |
N.S. |
1 | 1.05 | 0.84 | 0.87 | 1.02 | 0.85 | 2.26 | 0.87 | 1.36 | 1.07 |
time (sec) |
N/A | 0.576 | 1.774 | 24.220 | 0.037 | 0.092 | 0.232 | 0.132 | 0.207 | 17.811 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 106 | 109 | 90 | 115 | 112 | 90 | 199 | 93 | 136 | 108 |
N.S. |
1 | 1.03 | 0.85 | 1.08 | 1.06 | 0.85 | 1.88 | 0.88 | 1.28 | 1.02 |
time (sec) |
N/A | 0.361 | 0.894 | 0.300 | 0.034 | 0.082 | 0.197 | 0.136 | 0.196 | 17.687 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 53 | 53 | 52 | 52 | 57 | 48 | 94 | 46 | 61 | 52 |
N.S. |
1 | 1.00 | 0.98 | 0.98 | 1.08 | 0.91 | 1.77 | 0.87 | 1.15 | 0.98 |
time (sec) |
N/A | 0.221 | 0.129 | 2.072 | 0.031 | 0.081 | 0.103 | 0.120 | 0.195 | 17.581 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 27 | 17 | 16 | 18 | 19 | 16 | 18 | 25 |
N.S. |
1 | 1.00 | 1.69 | 1.06 | 1.00 | 1.12 | 1.19 | 1.00 | 1.12 | 1.56 |
time (sec) |
N/A | 0.154 | 0.003 | 0.395 | 0.026 | 0.073 | 0.064 | 0.121 | 0.205 | 17.543 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 65 | 71 | 67 | 76 | 0 | 255 | 425 | 83 | 116 | 342 |
N.S. |
1 | 1.09 | 1.03 | 1.17 | 0.00 | 3.92 | 6.54 | 1.28 | 1.78 | 5.26 |
time (sec) |
N/A | 0.326 | 0.190 | 0.675 | 0.000 | 0.103 | 16.525 | 0.138 | 0.199 | 18.874 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 98 | 104 | 96 | 142 | 0 | 394 | 0 | 152 | 289 | 214 |
N.S. |
1 | 1.06 | 0.98 | 1.45 | 0.00 | 4.02 | 0.00 | 1.55 | 2.95 | 2.18 |
time (sec) |
N/A | 0.378 | 0.430 | 1.013 | 0.000 | 0.095 | 0.000 | 0.142 | 0.194 | 17.751 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 164 | 183 | 157 | 351 | 0 | 793 | 0 | 411 | 973 | 477 |
N.S. |
1 | 1.12 | 0.96 | 2.14 | 0.00 | 4.84 | 0.00 | 2.51 | 5.93 | 2.91 |
time (sec) |
N/A | 0.614 | 0.631 | 1.491 | 0.000 | 0.116 | 0.000 | 0.163 | 0.195 | 18.920 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 314 | 323 | 249 | 325 | 314 | 247 | 729 | 269 | 457 | 358 |
N.S. |
1 | 1.03 | 0.79 | 1.04 | 1.00 | 0.79 | 2.32 | 0.86 | 1.46 | 1.14 |
time (sec) |
N/A | 1.011 | 3.677 | 0.402 | 0.044 | 0.091 | 0.407 | 1.349 | 0.184 | 18.075 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 217 | 224 | 160 | 216 | 208 | 163 | 459 | 172 | 276 | 221 |
N.S. |
1 | 1.03 | 0.74 | 1.00 | 0.96 | 0.75 | 2.12 | 0.79 | 1.27 | 1.02 |
time (sec) |
N/A | 0.658 | 2.658 | 0.362 | 0.038 | 0.089 | 0.354 | 0.133 | 0.183 | 17.846 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 107 | 110 | 90 | 115 | 112 | 89 | 199 | 93 | 136 | 108 |
N.S. |
1 | 1.03 | 0.84 | 1.07 | 1.05 | 0.83 | 1.86 | 0.87 | 1.27 | 1.01 |
time (sec) |
N/A | 0.359 | 0.837 | 0.276 | 0.040 | 0.084 | 0.158 | 0.136 | 0.175 | 17.656 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 50 | 50 | 46 | 43 | 46 | 45 | 78 | 43 | 50 | 44 |
N.S. |
1 | 1.00 | 0.92 | 0.86 | 0.92 | 0.90 | 1.56 | 0.86 | 1.00 | 0.88 |
time (sec) |
N/A | 0.200 | 0.056 | 1.362 | 0.032 | 0.082 | 0.110 | 0.132 | 0.171 | 17.534 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 93 | 104 | 89 | 119 | 0 | 375 | 4032 | 130 | 219 | 2629 |
N.S. |
1 | 1.12 | 0.96 | 1.28 | 0.00 | 4.03 | 43.35 | 1.40 | 2.35 | 28.27 |
time (sec) |
N/A | 0.499 | 0.989 | 0.995 | 0.000 | 0.107 | 147.311 | 0.138 | 0.199 | 20.752 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 129 | 160 | 134 | 218 | 0 | 675 | 0 | 241 | 627 | 5776 |
N.S. |
1 | 1.24 | 1.04 | 1.69 | 0.00 | 5.23 | 0.00 | 1.87 | 4.86 | 44.78 |
time (sec) |
N/A | 0.613 | 0.913 | 1.149 | 0.000 | 0.116 | 0.000 | 0.143 | 0.203 | 23.360 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 196 | 217 | 202 | 467 | 0 | 1027 | 0 | 586 | 1590 | 641 |
N.S. |
1 | 1.11 | 1.03 | 2.38 | 0.00 | 5.24 | 0.00 | 2.99 | 8.11 | 3.27 |
time (sec) |
N/A | 0.713 | 1.262 | 1.608 | 0.000 | 0.132 | 0.000 | 0.179 | 0.194 | 19.141 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 305 | 339 | 346 | 933 | 0 | 1724 | 0 | 1264 | 2911 | 1220 |
N.S. |
1 | 1.11 | 1.13 | 3.06 | 0.00 | 5.65 | 0.00 | 4.14 | 9.54 | 4.00 |
time (sec) |
N/A | 1.159 | 1.805 | 2.710 | 0.000 | 0.167 | 0.000 | 0.180 | 0.220 | 20.123 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 400 | 509 | 552 | 489 | 477 | 375 | 1217 | 410 | 732 | 574 |
N.S. |
1 | 1.27 | 1.38 | 1.22 | 1.19 | 0.94 | 3.04 | 1.02 | 1.83 | 1.44 |
time (sec) |
N/A | 1.663 | 6.456 | 0.458 | 0.045 | 0.108 | 0.564 | 0.157 | 26.622 | 18.310 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 315 | 324 | 246 | 325 | 314 | 253 | 729 | 269 | 457 | 358 |
N.S. |
1 | 1.03 | 0.78 | 1.03 | 1.00 | 0.80 | 2.31 | 0.85 | 1.45 | 1.14 |
time (sec) |
N/A | 0.987 | 3.752 | 0.438 | 0.039 | 0.095 | 0.369 | 0.148 | 0.185 | 17.965 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 171 | 179 | 142 | 182 | 175 | 148 | 386 | 148 | 233 | 183 |
N.S. |
1 | 1.05 | 0.83 | 1.06 | 1.02 | 0.87 | 2.26 | 0.87 | 1.36 | 1.07 |
time (sec) |
N/A | 0.559 | 1.676 | 0.375 | 0.038 | 0.089 | 0.228 | 0.136 | 0.180 | 17.745 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 90 | 93 | 71 | 76 | 74 | 71 | 128 | 72 | 92 | 127 |
N.S. |
1 | 1.03 | 0.79 | 0.84 | 0.82 | 0.79 | 1.42 | 0.80 | 1.02 | 1.41 |
time (sec) |
N/A | 0.328 | 0.086 | 274.339 | 0.035 | 0.082 | 0.136 | 0.126 | 0.163 | 17.568 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 156 | 170 | 137 | 229 | 0 | 578 | 0 | 244 | 466 | 5902 |
N.S. |
1 | 1.09 | 0.88 | 1.47 | 0.00 | 3.71 | 0.00 | 1.56 | 2.99 | 37.83 |
time (sec) |
N/A | 0.833 | 2.529 | 3.179 | 0.000 | 0.131 | 0.000 | 0.144 | 0.194 | 22.334 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 208 | 234 | 152 | 302 | 0 | 1062 | 0 | 564 | 1138 | 8953 |
N.S. |
1 | 1.12 | 0.73 | 1.45 | 0.00 | 5.11 | 0.00 | 2.71 | 5.47 | 43.04 |
time (sec) |
N/A | 1.059 | 2.736 | 3.608 | 0.000 | 0.142 | 0.000 | 0.164 | 0.188 | 25.466 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | F(-2) | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 255 | 306 | 521 | 670 | 0 | 1707 | 0 | 858 | 2592 | 11848 |
N.S. |
1 | 1.20 | 2.04 | 2.63 | 0.00 | 6.69 | 0.00 | 3.36 | 10.16 | 46.46 |
time (sec) |
N/A | 1.229 | 5.619 | 3.602 | 0.000 | 0.168 | 0.000 | 0.194 | 0.193 | 27.055 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 325 | 372 | 345 | 1154 | 0 | 2136 | 0 | 1613 | 3856 | 1423 |
N.S. |
1 | 1.14 | 1.06 | 3.55 | 0.00 | 6.57 | 0.00 | 4.96 | 11.86 | 4.38 |
time (sec) |
N/A | 1.495 | 5.978 | 4.721 | 0.000 | 0.215 | 0.000 | 0.206 | 0.562 | 20.555 |