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 | C | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 634 | 634 | 792 | 635 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.25 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.612 | 1.555 | 1.609 | 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 | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
size | 839 | 839 | 777 | 897 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.93 | 1.07 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.634 | 1.319 | 31.119 | 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 | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 792 | 792 | 719 | 813 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.91 | 1.03 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.380 | 6.079 | 24.162 | 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 | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 804 | 804 | 734 | 828 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.91 | 1.03 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.521 | 6.391 | 20.609 | 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 | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 846 | 846 | 821 | 900 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.97 | 1.06 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.468 | 6.719 | 37.202 | 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 | F(-1) | F(-2) | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
size | 737 | 737 | 1097 | 3551 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.49 | 4.82 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.653 | 6.634 | 5.517 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | B | F(-1) | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 231 | 220 | 192 | 1169 | 0 | 1217 | 0 | 0 | 0 |
N.S. |
1 | 0.95 | 0.83 | 5.06 | 0.00 | 5.27 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.590 | 0.667 | 0.551 | 0.000 | 0.364 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | B | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 177 | 166 | 183 | 1126 | 0 | 1233 | 0 | 0 | 0 |
N.S. |
1 | 0.94 | 1.03 | 6.36 | 0.00 | 6.97 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.360 | 0.834 | 0.625 | 0.000 | 0.375 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
size | 772 | 772 | 1204 | 1225 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.56 | 1.59 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.715 | 6.075 | 2.445 | 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 | F(-1) | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
size | 834 | 834 | 1261 | 1455 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.51 | 1.74 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.833 | 6.086 | 2.692 | 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 | F(-1) | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
size | 1224 | 1224 | 1185 | 1752 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.97 | 1.43 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 4.136 | 11.031 | 49.457 | 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 | F(-1) | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
size | 1234 | 1234 | 1193 | 1222 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.97 | 0.99 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 3.106 | 11.030 | 23.198 | 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 | F(-1) | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
size | 1234 | 1234 | 1161 | 1778 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.94 | 1.44 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.986 | 10.354 | 29.030 | 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 | F(-2) | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 22 | 18 | 0 | 20 | 19 | 20 | 20 |
N.S. |
1 | 1.00 | 1.10 | 0.90 | 0.00 | 1.00 | 0.95 | 1.00 | 1.00 |
time (sec) |
N/A | 0.191 | 6.366 | 1.063 | 0.000 | 0.256 | 1.717 | 0.332 | 3.232 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 22 | 18 | 0 | 20 | 19 | 20 | 20 |
N.S. |
1 | 1.00 | 1.10 | 0.90 | 0.00 | 1.00 | 0.95 | 1.00 | 1.00 |
time (sec) |
N/A | 0.199 | 2.906 | 1.158 | 0.000 | 0.268 | 1.065 | 0.307 | 3.317 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F(-2) | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 101 | 101 | 556 | 0 | 0 | 332 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 5.50 | 0.00 | 0.00 | 3.29 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.402 | 13.469 | 0.000 | 0.000 | 0.286 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 182 | 176 | 633 | 0 | 0 | 724 | 0 | 0 | 0 |
N.S. |
1 | 0.97 | 3.48 | 0.00 | 0.00 | 3.98 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.375 | 1.869 | 0.000 | 0.000 | 0.326 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | B | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 284 | 270 | 685 | 0 | 0 | 1360 | 0 | 0 | 0 |
N.S. |
1 | 0.95 | 2.41 | 0.00 | 0.00 | 4.79 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.155 | 3.004 | 0.000 | 0.000 | 0.386 | 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 | 558 | 544 | 397 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.97 | 0.71 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.474 | 0.867 | 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 | 353 | 350 | 293 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.99 | 0.83 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.740 | 0.323 | 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 | 198 | 205 | 186 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.04 | 0.94 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.422 | 0.427 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | 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 | 23 | 23 | 25 | 23 | 25 | 25 | 20 | 25 | 25 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 1.09 | 1.09 | 0.87 | 1.09 | 1.09 |
time (sec) |
N/A | 0.241 | 2.856 | 2.470 | 0.284 | 0.269 | 16.244 | 0.278 | 3.551 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 25 | 23 | 25 | 36 | 0 | 25 | 25 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 1.09 | 1.57 | 0.00 | 1.09 | 1.09 |
time (sec) |
N/A | 0.235 | 2.293 | 1.375 | 0.318 | 0.270 | 0.000 | 0.280 | 3.194 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 25 | 23 | 25 | 47 | 0 | 25 | 25 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 1.09 | 2.04 | 0.00 | 1.09 | 1.09 |
time (sec) |
N/A | 0.237 | 3.602 | 2.325 | 0.286 | 0.277 | 0.000 | 0.279 | 3.308 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 609 | 609 | 453 | 632 | 684 | 586 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.74 | 1.04 | 1.12 | 0.96 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.395 | 0.370 | 0.809 | 0.217 | 0.271 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 359 | 359 | 299 | 402 | 429 | 380 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.83 | 1.12 | 1.19 | 1.06 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.471 | 0.276 | 0.752 | 0.211 | 0.275 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 168 | 168 | 174 | 203 | 218 | 209 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.04 | 1.21 | 1.30 | 1.24 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.792 | 0.156 | 0.347 | 0.205 | 0.269 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 51 | 55 | 84 | 78 | 72 | 96 | 0 | 111 | 0 |
N.S. |
1 | 1.08 | 1.65 | 1.53 | 1.41 | 1.88 | 0.00 | 2.18 | 0.00 |
time (sec) |
N/A | 0.390 | 0.094 | 0.348 | 0.202 | 0.256 | 0.000 | 0.386 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 763 | 763 | 623 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.82 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.762 | 0.434 | 0.000 | 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 | F(-2) | 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 | 20 | 0 | 34 | 20 | 22 | 22 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 0.00 | 1.55 | 0.91 | 1.00 | 1.00 |
time (sec) |
N/A | 0.208 | 15.372 | 0.669 | 0.000 | 0.260 | 1.637 | 0.399 | 3.075 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | 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 | 20 | 0 | 34 | 20 | 22 | 22 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 0.00 | 1.55 | 0.91 | 1.00 | 1.00 |
time (sec) |
N/A | 0.206 | 8.229 | 0.783 | 0.000 | 0.263 | 1.097 | 0.332 | 3.106 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | 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 | 20 | 0 | 54 | 20 | 22 | 22 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 0.00 | 2.45 | 0.91 | 1.00 | 1.00 |
time (sec) |
N/A | 0.213 | 13.235 | 1.615 | 0.000 | 0.264 | 7.622 | 0.326 | 3.172 |
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 | 20 | 107 | 65 | 20 | 22 | 22 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 4.86 | 2.95 | 0.91 | 1.00 | 1.00 |
time (sec) |
N/A | 0.210 | 26.794 | 1.655 | 0.719 | 0.271 | 167.634 | 0.335 | 3.356 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 388 | 388 | 254 | 380 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.65 | 0.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.001 | 0.417 | 2.646 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 139 | 180 | 125 | 178 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.29 | 0.90 | 1.28 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.560 | 0.174 | 0.944 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 54 | 57 | 46 | 56 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.06 | 0.85 | 1.04 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.412 | 0.057 | 0.054 | 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 | 20 | 20 | 22 | 20 | 22 | 29 | 17 | 22 | 22 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 1.10 | 1.45 | 0.85 | 1.10 | 1.10 |
time (sec) |
N/A | 0.211 | 0.567 | 0.825 | 0.270 | 0.258 | 9.359 | 0.281 | 2.866 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 22 | 20 | 22 | 53 | 0 | 22 | 22 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 1.10 | 2.65 | 0.00 | 1.10 | 1.10 |
time (sec) |
N/A | 0.216 | 2.607 | 0.738 | 0.269 | 0.242 | 0.000 | 0.283 | 2.836 |
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 | 20 | 22 | 22 | 19 | 22 | 22 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 1.00 | 1.00 | 0.86 | 1.00 | 1.00 |
time (sec) |
N/A | 0.221 | 0.982 | 1.175 | 0.263 | 0.246 | 0.470 | 0.313 | 2.792 |
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 | 20 | 22 | 39 | 20 | 22 | 22 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 1.00 | 1.77 | 0.91 | 1.00 | 1.00 |
time (sec) |
N/A | 0.216 | 0.812 | 1.336 | 0.267 | 0.248 | 0.729 | 0.298 | 2.819 |
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 | 20 | 22 | 63 | 20 | 22 | 22 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 1.00 | 2.86 | 0.91 | 1.00 | 1.00 |
time (sec) |
N/A | 0.223 | 1.422 | 1.342 | 0.287 | 0.298 | 3.052 | 0.301 | 2.964 |
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 | 20 | 22 | 87 | 20 | 22 | 22 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 1.00 | 3.95 | 0.91 | 1.00 | 1.00 |
time (sec) |
N/A | 0.227 | 2.805 | 1.339 | 0.268 | 0.308 | 34.561 | 0.304 | 2.958 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
size | 510 | 510 | 663 | 1102 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.30 | 2.16 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.190 | 2.580 | 1.985 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
size | 257 | 257 | 338 | 465 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.32 | 1.81 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.802 | 1.001 | 1.117 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 90 | 86 | 80 | 125 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.96 | 0.89 | 1.39 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.767 | 0.334 | 0.073 | 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 | 20 | 20 | 22 | 20 | 816 | 57 | 19 | 22 | 22 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 40.80 | 2.85 | 0.95 | 1.10 | 1.10 |
time (sec) |
N/A | 0.210 | 17.947 | 0.895 | 1.318 | 0.251 | 89.470 | 0.314 | 2.964 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 22 | 20 | 1078 | 98 | 0 | 22 | 22 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 53.90 | 4.90 | 0.00 | 1.10 | 1.10 |
time (sec) |
N/A | 0.210 | 29.873 | 0.662 | 1.766 | 0.274 | 0.000 | 0.304 | 2.901 |
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 | 20 | 596 | 36 | 20 | 22 | 22 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 27.09 | 1.64 | 0.91 | 1.00 | 1.00 |
time (sec) |
N/A | 0.223 | 10.789 | 1.214 | 0.808 | 0.251 | 0.872 | 0.302 | 3.170 |
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 | 20 | 580 | 67 | 22 | 22 | 22 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 26.36 | 3.05 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.215 | 10.972 | 1.308 | 1.099 | 0.296 | 1.978 | 0.312 | 3.178 |
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 | 20 | 857 | 108 | 22 | 22 | 22 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 38.95 | 4.91 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.227 | 16.339 | 1.521 | 1.988 | 0.262 | 15.244 | 0.327 | 3.268 |
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 | 20 | 1117 | 149 | 22 | 22 | 22 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 50.77 | 6.77 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.222 | 24.975 | 1.393 | 2.985 | 0.271 | 170.436 | 0.334 | 3.409 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 672 | 672 | 536 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.80 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.673 | 4.906 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 322 | 322 | 317 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.457 | 1.973 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 102 | 104 | 100 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.02 | 0.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.756 | 0.142 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | F(-1) | N/A | F(-2) | F(-2) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 0 | 20 | 0 | 0 | 19 | 22 | 22 |
N.S. |
1 | 1.00 | 0.00 | 0.91 | 0.00 | 0.00 | 0.86 | 1.00 | 1.00 |
time (sec) |
N/A | 0.219 | 0.000 | 1.408 | 0.000 | 0.000 | 1.588 | 12.583 | 3.091 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | F(-1) | N/A | N/A | F(-2) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 0 | 20 | 22 | 0 | 20 | 22 | 22 |
N.S. |
1 | 1.00 | 0.00 | 0.91 | 1.00 | 0.00 | 0.91 | 1.00 | 1.00 |
time (sec) |
N/A | 0.226 | 0.000 | 0.926 | 0.544 | 0.000 | 41.816 | 12.374 | 3.183 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F | F(-2) | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
size | 442 | 442 | 812 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.84 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.016 | 1.994 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | F | F | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
size | 140 | 151 | 269 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.08 | 1.92 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.871 | 0.398 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | F(-1) | N/A | F(-2) | F(-2) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 0 | 20 | 0 | 0 | 19 | 22 | 22 |
N.S. |
1 | 1.00 | 0.00 | 0.91 | 0.00 | 0.00 | 0.86 | 1.00 | 1.00 |
time (sec) |
N/A | 0.225 | 0.000 | 1.372 | 0.000 | 0.000 | 37.428 | 19.146 | 3.354 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | F(-1) | N/A | N/A | F(-2) | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 0 | 20 | 22 | 0 | 0 | 22 | 22 |
N.S. |
1 | 1.00 | 0.00 | 0.91 | 1.00 | 0.00 | 0.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.226 | 0.000 | 1.216 | 0.708 | 0.000 | 0.000 | 19.263 | 3.176 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 608 | 608 | 530 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.87 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.373 | 0.815 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 287 | 287 | 213 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.74 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.765 | 0.418 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | F | F | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 88 | 96 | 100 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.09 | 1.14 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.416 | 0.072 | 0.000 | 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 | F(-2) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 24 | 20 | 22 | 0 | 20 | 22 | 22 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 1.00 | 0.00 | 0.91 | 1.00 | 1.00 |
time (sec) |
N/A | 0.220 | 0.182 | 1.359 | 0.500 | 0.000 | 5.045 | 12.922 | 3.076 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 24 | 20 | 22 | 0 | 22 | 22 | 22 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 1.00 | 0.00 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.222 | 0.227 | 1.068 | 0.533 | 0.000 | 151.692 | 12.693 | 3.113 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
size | 358 | 358 | 268 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.75 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.051 | 1.260 | 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(-2) | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 120 | 129 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.08 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.812 | 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 | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 24 | 20 | 22 | 0 | 20 | 22 | 22 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 1.00 | 0.00 | 0.91 | 1.00 | 1.00 |
time (sec) |
N/A | 0.227 | 0.196 | 1.406 | 0.509 | 0.000 | 36.247 | 0.419 | 3.985 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | F(-2) | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 24 | 20 | 22 | 0 | 0 | 22 | 22 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 1.00 | 0.00 | 0.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.239 | 0.250 | 1.210 | 0.559 | 0.000 | 0.000 | 0.421 | 3.784 |