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 | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 30 | 26 | 538 | 114 | 0 | 28 | 146 | 28 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 19.21 | 4.07 | 0.00 | 1.00 | 5.21 | 1.00 |
time (sec) |
N/A | 0.401 | 15.879 | 0.412 | 0.968 | 0.091 | 0.000 | 0.187 | 0.255 | 3.728 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | F(-2) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 30 | 32 | 28 | 577 | 54 | 0 | 0 | 95 | 30 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 19.23 | 1.80 | 0.00 | 0.00 | 3.17 | 1.00 |
time (sec) |
N/A | 0.457 | 1.427 | 1.042 | 1.578 | 0.097 | 0.000 | 0.000 | 0.273 | 3.467 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 30 | 32 | 28 | 514 | 44 | 31 | 0 | 45 | 30 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 17.13 | 1.47 | 1.03 | 0.00 | 1.50 | 1.00 |
time (sec) |
N/A | 0.445 | 0.320 | 0.875 | 1.101 | 0.108 | 5.804 | 0.000 | 0.210 | 3.573 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | 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 | TBD |
size | 30 | 30 | 32 | 28 | 544 | 82 | 31 | 30 | 68 | 30 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 18.13 | 2.73 | 1.03 | 1.00 | 2.27 | 1.00 |
time (sec) |
N/A | 0.580 | 1.026 | 0.383 | 0.481 | 0.095 | 22.544 | 0.168 | 0.199 | 4.657 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 30 | 32 | 28 | 596 | 108 | 0 | 30 | 144 | 30 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 19.87 | 3.60 | 0.00 | 1.00 | 4.80 | 1.00 |
time (sec) |
N/A | 0.509 | 1.493 | 0.558 | 0.912 | 0.100 | 0.000 | 0.204 | 0.232 | 4.667 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 30 | 32 | 28 | 700 | 146 | 0 | 30 | 216 | 30 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 23.33 | 4.87 | 0.00 | 1.00 | 7.20 | 1.00 |
time (sec) |
N/A | 0.541 | 1.882 | 0.600 | 1.060 | 0.108 | 0.000 | 0.224 | 0.208 | 4.357 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 259 | 463 | 300 | 0 | 0 | 0 | 0 | 0 | 86 | 0 |
N.S. |
1 | 1.79 | 1.16 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.33 | 0.00 |
time (sec) |
N/A | 2.111 | 1.719 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.734 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 340 | 525 | 384 | 0 | 0 | 0 | 0 | 0 | 86 | 0 |
N.S. |
1 | 1.54 | 1.13 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.25 | 0.00 |
time (sec) |
N/A | 1.987 | 1.147 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.629 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F(-2) | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 241 | 275 | 0 | 0 | 0 | 0 | 0 | 0 | 84 | 0 |
N.S. |
1 | 1.14 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.35 | 0.00 |
time (sec) |
N/A | 3.991 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.510 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 233 | 231 | 246 | 0 | 0 | 0 | 0 | 0 | 860 | 0 |
N.S. |
1 | 0.99 | 1.06 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 3.69 | 0.00 |
time (sec) |
N/A | 1.056 | 1.061 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 1.309 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | F(-2) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 29 | 25 | 30 | 0 | 87 | 0 | 85 | 27 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 1.11 | 0.00 | 3.22 | 0.00 | 3.15 | 1.00 |
time (sec) |
N/A | 3.305 | 1.107 | 0.251 | 0.898 | 0.000 | 7.900 | 0.000 | 0.499 | 4.418 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 479 | 571 | 527 | 0 | 0 | 0 | 0 | 0 | 131 | 0 |
N.S. |
1 | 1.19 | 1.10 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.27 | 0.00 |
time (sec) |
N/A | 2.741 | 2.589 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.981 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 462 | 723 | 498 | 0 | 0 | 0 | 0 | 0 | 131 | 0 |
N.S. |
1 | 1.56 | 1.08 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.28 | 0.00 |
time (sec) |
N/A | 2.878 | 2.274 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.819 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F(-2) | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 363 | 567 | 0 | 0 | 0 | 0 | 0 | 0 | 129 | 0 |
N.S. |
1 | 1.56 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.36 | 0.00 |
time (sec) |
N/A | 4.060 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.706 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 351 | 331 | 387 | 0 | 0 | 0 | 0 | 0 | 1045 | 0 |
N.S. |
1 | 0.94 | 1.10 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 2.98 | 0.00 |
time (sec) |
N/A | 1.865 | 1.452 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 1.693 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | F(-2) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 31 | 27 | 30 | 0 | 133 | 0 | 130 | 29 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 1.03 | 0.00 | 4.59 | 0.00 | 4.48 | 1.00 |
time (sec) |
N/A | 4.526 | 1.009 | 0.254 | 0.858 | 0.000 | 8.339 | 0.000 | 0.739 | 3.997 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 65 | 50 | 72 | 0 | 0 | 0 | 0 | 0 | 30 | 0 |
N.S. |
1 | 0.77 | 1.11 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.46 | 0.00 |
time (sec) |
N/A | 0.386 | 0.079 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.313 | 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 | 253 | 184 | 182 | 0 | 0 | 0 | 0 | 0 | 30 | 0 |
N.S. |
1 | 0.73 | 0.72 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.12 | 0.00 |
time (sec) |
N/A | 0.670 | 0.721 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.277 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 379 | 279 | 241 | 0 | 0 | 0 | 0 | 0 | 28 | 0 |
N.S. |
1 | 0.74 | 0.64 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.07 | 0.00 |
time (sec) |
N/A | 1.086 | 0.919 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.231 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 253 | 184 | 214 | 0 | 0 | 0 | 0 | 0 | 27 | 0 |
N.S. |
1 | 0.73 | 0.85 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.11 | 0.00 |
time (sec) |
N/A | 0.822 | 0.547 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.247 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 31 | 27 | 29 | 29 | 29 | 0 | 30 | 29 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 1.00 | 1.00 | 1.00 | 0.00 | 1.03 | 1.00 |
time (sec) |
N/A | 1.025 | 0.317 | 0.232 | 0.357 | 0.105 | 4.468 | 0.000 | 0.237 | 3.790 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 31 | 27 | 29 | 29 | 31 | 0 | 30 | 29 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 1.00 | 1.00 | 1.07 | 0.00 | 1.03 | 1.00 |
time (sec) |
N/A | 0.595 | 0.289 | 0.256 | 0.359 | 0.098 | 6.333 | 0.000 | 0.294 | 3.773 |
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 | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 658 | 444 | 438 | 0 | 0 | 0 | 0 | 0 | 64 | 0 |
N.S. |
1 | 0.67 | 0.67 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.10 | 0.00 |
time (sec) |
N/A | 0.930 | 2.069 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.320 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 578 | 404 | 500 | 0 | 0 | 0 | 0 | 0 | 62 | 0 |
N.S. |
1 | 0.70 | 0.87 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.11 | 0.00 |
time (sec) |
N/A | 0.802 | 1.444 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.273 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 450 | 308 | 384 | 0 | 0 | 0 | 0 | 0 | 61 | 0 |
N.S. |
1 | 0.68 | 0.85 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.14 | 0.00 |
time (sec) |
N/A | 0.635 | 1.392 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.275 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | F(-2) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 31 | 27 | 29 | 29 | 0 | 0 | 62 | 29 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 1.00 | 1.00 | 0.00 | 0.00 | 2.14 | 1.00 |
time (sec) |
N/A | 1.669 | 0.357 | 0.364 | 0.350 | 0.115 | 0.000 | 0.000 | 0.238 | 3.695 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | F(-2) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 31 | 27 | 29 | 29 | 0 | 0 | 61 | 29 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 1.00 | 1.00 | 0.00 | 0.00 | 2.10 | 1.00 |
time (sec) |
N/A | 1.598 | 0.744 | 0.227 | 0.366 | 0.093 | 0.000 | 0.000 | 0.298 | 3.749 |
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 | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 870 | 567 | 677 | 0 | 0 | 0 | 0 | 0 | 97 | 0 |
N.S. |
1 | 0.65 | 0.78 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.11 | 0.00 |
time (sec) |
N/A | 1.291 | 4.894 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.340 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 793 | 532 | 633 | 0 | 0 | 0 | 0 | 0 | 95 | 0 |
N.S. |
1 | 0.67 | 0.80 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.12 | 0.00 |
time (sec) |
N/A | 0.963 | 2.528 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.314 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 674 | 447 | 538 | 0 | 0 | 0 | 0 | 0 | 94 | 0 |
N.S. |
1 | 0.66 | 0.80 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.14 | 0.00 |
time (sec) |
N/A | 0.804 | 3.483 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.320 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | F(-2) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 31 | 27 | 29 | 54 | 0 | 0 | 95 | 29 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 1.00 | 1.86 | 0.00 | 0.00 | 3.28 | 1.00 |
time (sec) |
N/A | 2.273 | 0.366 | 0.234 | 0.383 | 0.097 | 0.000 | 0.000 | 0.283 | 3.627 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | F(-2) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 31 | 27 | 29 | 54 | 0 | 0 | 94 | 29 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 1.00 | 1.86 | 0.00 | 0.00 | 3.24 | 1.00 |
time (sec) |
N/A | 2.211 | 0.537 | 0.246 | 0.396 | 0.091 | 0.000 | 0.000 | 0.343 | 3.712 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 323 | 265 | 292 | 0 | 0 | 0 | 0 | 0 | 29 | 0 |
N.S. |
1 | 0.82 | 0.90 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 0.874 | 0.863 | 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 | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 211 | 170 | 212 | 0 | 0 | 0 | 0 | 0 | 29 | 0 |
N.S. |
1 | 0.81 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.14 | 0.00 |
time (sec) |
N/A | 0.549 | 0.535 | 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 | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 154 | 138 | 154 | 0 | 0 | 0 | 0 | 0 | 27 | 0 |
N.S. |
1 | 0.90 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.18 | 0.00 |
time (sec) |
N/A | 0.461 | 0.196 | 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 | A | A | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 44 | 43 | 56 | 53 | 0 | 213 | 0 | 0 | 26 | 0 |
N.S. |
1 | 0.98 | 1.27 | 1.20 | 0.00 | 4.84 | 0.00 | 0.00 | 0.59 | 0.00 |
time (sec) |
N/A | 0.237 | 0.030 | 0.109 | 0.000 | 0.106 | 0.000 | 0.000 | 0.187 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | 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 | TBD |
size | 28 | 28 | 30 | 26 | 28 | 39 | 27 | 28 | 29 | 28 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 1.00 | 1.39 | 0.96 | 1.00 | 1.04 | 1.00 |
time (sec) |
N/A | 0.297 | 1.906 | 0.301 | 0.343 | 0.099 | 6.211 | 9.736 | 0.201 | 3.744 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | 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 | TBD |
size | 28 | 28 | 30 | 26 | 28 | 41 | 29 | 28 | 29 | 28 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 1.00 | 1.46 | 1.04 | 1.00 | 1.04 | 1.00 |
time (sec) |
N/A | 0.295 | 1.067 | 0.316 | 0.347 | 0.107 | 28.555 | 9.739 | 0.203 | 3.847 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 379 | 279 | 291 | 0 | 0 | 0 | 0 | 0 | 34 | 0 |
N.S. |
1 | 0.74 | 0.77 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 0.697 | 0.841 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.222 | 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 | 253 | 184 | 213 | 0 | 0 | 0 | 0 | 0 | 34 | 0 |
N.S. |
1 | 0.73 | 0.84 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.13 | 0.00 |
time (sec) |
N/A | 0.572 | 0.592 | 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 | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 182 | 152 | 153 | 0 | 0 | 0 | 0 | 0 | 32 | 0 |
N.S. |
1 | 0.84 | 0.84 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.18 | 0.00 |
time (sec) |
N/A | 0.608 | 0.230 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.221 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 61 | 57 | 57 | 54 | 0 | 221 | 0 | 0 | 31 | 0 |
N.S. |
1 | 0.93 | 0.93 | 0.89 | 0.00 | 3.62 | 0.00 | 0.00 | 0.51 | 0.00 |
time (sec) |
N/A | 0.392 | 0.037 | 0.110 | 0.000 | 0.099 | 0.000 | 0.000 | 0.209 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | 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 | TBD |
size | 29 | 29 | 31 | 27 | 29 | 42 | 29 | 29 | 34 | 29 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 1.00 | 1.45 | 1.00 | 1.00 | 1.17 | 1.00 |
time (sec) |
N/A | 0.497 | 0.446 | 0.296 | 0.354 | 0.111 | 6.290 | 9.700 | 0.227 | 3.853 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | 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 | TBD |
size | 29 | 29 | 31 | 27 | 29 | 44 | 31 | 29 | 34 | 29 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 1.00 | 1.52 | 1.07 | 1.00 | 1.17 | 1.00 |
time (sec) |
N/A | 0.510 | 0.457 | 0.330 | 0.353 | 0.109 | 28.553 | 9.833 | 0.225 | 3.856 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | 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 | TBD |
size | 29 | 29 | 31 | 27 | 29 | 56 | 31 | 29 | 59 | 29 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 1.00 | 1.93 | 1.07 | 1.00 | 2.03 | 1.00 |
time (sec) |
N/A | 0.526 | 0.804 | 0.346 | 0.380 | 0.106 | 63.591 | 9.774 | 0.252 | 3.688 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | 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 | TBD |
size | 27 | 27 | 29 | 25 | 27 | 54 | 29 | 27 | 57 | 27 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 1.00 | 2.00 | 1.07 | 1.00 | 2.11 | 1.00 |
time (sec) |
N/A | 0.391 | 0.586 | 0.280 | 0.374 | 0.110 | 60.512 | 9.827 | 0.218 | 3.597 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | 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 | TBD |
size | 26 | 26 | 28 | 24 | 26 | 53 | 27 | 26 | 56 | 26 |
N.S. |
1 | 1.00 | 1.08 | 0.92 | 1.00 | 2.04 | 1.04 | 1.00 | 2.15 | 1.00 |
time (sec) |
N/A | 0.298 | 0.128 | 0.322 | 0.366 | 0.092 | 40.727 | 9.736 | 0.218 | 3.664 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 31 | 27 | 29 | 55 | 0 | 29 | 57 | 29 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 1.00 | 1.90 | 0.00 | 1.00 | 1.97 | 1.00 |
time (sec) |
N/A | 0.334 | 0.606 | 0.447 | 0.387 | 0.108 | 0.000 | 9.692 | 0.216 | 3.907 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 31 | 27 | 29 | 57 | 0 | 29 | 59 | 29 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 1.00 | 1.97 | 0.00 | 1.00 | 2.03 | 1.00 |
time (sec) |
N/A | 0.315 | 0.622 | 0.363 | 0.381 | 0.109 | 0.000 | 9.757 | 0.225 | 3.859 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | 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 | TBD |
size | 30 | 30 | 32 | 28 | 30 | 42 | 31 | 30 | 33 | 30 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 1.00 | 1.40 | 1.03 | 1.00 | 1.10 | 1.00 |
time (sec) |
N/A | 0.282 | 0.529 | 0.312 | 0.368 | 0.103 | 78.944 | 9.600 | 0.232 | 4.090 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | F(-2) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 31 | 29 | 32 | 43 | 0 | 0 | 71 | 31 |
N.S. |
1 | 1.00 | 1.07 | 1.00 | 1.10 | 1.48 | 0.00 | 0.00 | 2.45 | 1.07 |
time (sec) |
N/A | 0.262 | 0.580 | 0.164 | 0.928 | 0.102 | 0.000 | 0.000 | 0.382 | 3.581 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | F(-2) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 29 | 27 | 32 | 31 | 0 | 0 | 46 | 29 |
N.S. |
1 | 1.00 | 1.07 | 1.00 | 1.19 | 1.15 | 0.00 | 0.00 | 1.70 | 1.07 |
time (sec) |
N/A | 0.233 | 0.392 | 0.139 | 0.874 | 0.098 | 0.000 | 0.000 | 0.320 | 3.623 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | 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 | TBD |
size | 16 | 16 | 18 | 16 | 18 | 18 | 15 | 0 | 20 | 18 |
N.S. |
1 | 1.00 | 1.12 | 1.00 | 1.12 | 1.12 | 0.94 | 0.00 | 1.25 | 1.12 |
time (sec) |
N/A | 0.193 | 0.029 | 0.126 | 0.348 | 0.109 | 27.750 | 0.000 | 0.242 | 3.343 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | 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 | TBD |
size | 29 | 29 | 31 | 29 | 34 | 33 | 27 | 33 | 35 | 31 |
N.S. |
1 | 1.00 | 1.07 | 1.00 | 1.17 | 1.14 | 0.93 | 1.14 | 1.21 | 1.07 |
time (sec) |
N/A | 0.282 | 1.002 | 0.201 | 0.367 | 0.105 | 69.985 | 9.810 | 0.257 | 3.661 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 31 | 29 | 32 | 45 | 0 | 32 | 42 | 31 |
N.S. |
1 | 1.00 | 1.07 | 1.00 | 1.10 | 1.55 | 0.00 | 1.10 | 1.45 | 1.07 |
time (sec) |
N/A | 0.276 | 1.259 | 0.214 | 0.413 | 0.114 | 0.000 | 9.622 | 0.272 | 3.695 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 31 | 33 | 29 | 31 | 44 | 0 | 0 | 70 | 31 |
N.S. |
1 | 1.00 | 1.06 | 0.94 | 1.00 | 1.42 | 0.00 | 0.00 | 2.26 | 1.00 |
time (sec) |
N/A | 0.322 | 0.926 | 0.219 | 0.408 | 0.104 | 0.000 | 0.000 | 0.334 | 3.901 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 31 | 33 | 29 | 31 | 31 | 0 | 0 | 33 | 31 |
N.S. |
1 | 1.00 | 1.06 | 0.94 | 1.00 | 1.00 | 0.00 | 0.00 | 1.06 | 1.00 |
time (sec) |
N/A | 0.313 | 0.241 | 0.195 | 0.415 | 0.119 | 0.000 | 0.000 | 0.248 | 3.748 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | 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 | TBD |
size | 31 | 31 | 33 | 29 | 31 | 46 | 32 | 31 | 37 | 31 |
N.S. |
1 | 1.00 | 1.06 | 0.94 | 1.00 | 1.48 | 1.03 | 1.00 | 1.19 | 1.00 |
time (sec) |
N/A | 0.311 | 0.643 | 0.310 | 0.414 | 0.104 | 78.968 | 10.071 | 0.219 | 3.812 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 31 | 33 | 29 | 31 | 58 | 0 | 31 | 62 | 31 |
N.S. |
1 | 1.00 | 1.06 | 0.94 | 1.00 | 1.87 | 0.00 | 1.00 | 2.00 | 1.00 |
time (sec) |
N/A | 0.371 | 0.916 | 0.467 | 0.391 | 0.117 | 0.000 | 10.291 | 0.205 | 3.814 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 177 | 173 | 122 | 123 | 178 | 140 | 0 | 0 | 185 | 0 |
N.S. |
1 | 0.98 | 0.69 | 0.69 | 1.01 | 0.79 | 0.00 | 0.00 | 1.05 | 0.00 |
time (sec) |
N/A | 0.602 | 0.074 | 0.290 | 0.032 | 0.097 | 0.000 | 0.000 | 0.202 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 161 | 157 | 140 | 215 | 196 | 136 | 0 | 0 | 189 | 0 |
N.S. |
1 | 0.98 | 0.87 | 1.34 | 1.22 | 0.84 | 0.00 | 0.00 | 1.17 | 0.00 |
time (sec) |
N/A | 0.570 | 0.114 | 0.216 | 0.033 | 0.098 | 0.000 | 0.000 | 0.197 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 138 | 137 | 101 | 105 | 139 | 119 | 0 | 0 | 145 | 0 |
N.S. |
1 | 0.99 | 0.73 | 0.76 | 1.01 | 0.86 | 0.00 | 0.00 | 1.05 | 0.00 |
time (sec) |
N/A | 0.426 | 0.071 | 0.220 | 0.027 | 0.096 | 0.000 | 0.000 | 0.177 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 122 | 121 | 120 | 197 | 156 | 114 | 0 | 0 | 149 | 0 |
N.S. |
1 | 0.99 | 0.98 | 1.61 | 1.28 | 0.93 | 0.00 | 0.00 | 1.22 | 0.00 |
time (sec) |
N/A | 0.433 | 0.092 | 0.213 | 0.035 | 0.088 | 0.000 | 0.000 | 0.184 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 94 | 99 | 76 | 76 | 91 | 94 | 0 | 0 | 103 | 0 |
N.S. |
1 | 1.05 | 0.81 | 0.81 | 0.97 | 1.00 | 0.00 | 0.00 | 1.10 | 0.00 |
time (sec) |
N/A | 0.466 | 0.056 | 0.110 | 0.032 | 0.102 | 0.000 | 0.000 | 0.183 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 264 | 274 | 129 | 128 | 0 | 0 | 0 | 0 | 91 | 0 |
N.S. |
1 | 1.04 | 0.49 | 0.48 | 0.00 | 0.00 | 0.00 | 0.00 | 0.34 | 0.00 |
time (sec) |
N/A | 0.986 | 0.136 | 0.504 | 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 | A | A | A | A | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 75 | 76 | 105 | 102 | 63 | 132 | 0 | 0 | 80 | 0 |
N.S. |
1 | 1.01 | 1.40 | 1.36 | 0.84 | 1.76 | 0.00 | 0.00 | 1.07 | 0.00 |
time (sec) |
N/A | 0.304 | 0.080 | 0.122 | 0.106 | 0.105 | 0.000 | 0.000 | 0.190 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 251 | 258 | 100 | 135 | 0 | 0 | 0 | 0 | 70 | 0 |
N.S. |
1 | 1.03 | 0.40 | 0.54 | 0.00 | 0.00 | 0.00 | 0.00 | 0.28 | 0.00 |
time (sec) |
N/A | 0.888 | 0.078 | 0.364 | 0.000 | 0.000 | 0.000 | 0.000 | 0.191 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 94 | 97 | 128 | 141 | 85 | 139 | 0 | 0 | 100 | 0 |
N.S. |
1 | 1.03 | 1.36 | 1.50 | 0.90 | 1.48 | 0.00 | 0.00 | 1.06 | 0.00 |
time (sec) |
N/A | 0.317 | 0.165 | 0.142 | 0.114 | 0.133 | 0.000 | 0.000 | 0.185 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 261 | 267 | 192 | 214 | 305 | 231 | 0 | 0 | 336 | 0 |
N.S. |
1 | 1.02 | 0.74 | 0.82 | 1.17 | 0.89 | 0.00 | 0.00 | 1.29 | 0.00 |
time (sec) |
N/A | 0.638 | 0.186 | 0.257 | 0.036 | 0.123 | 0.000 | 0.000 | 0.194 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 301 | 266 | 214 | 364 | 332 | 227 | 0 | 0 | 343 | 0 |
N.S. |
1 | 0.88 | 0.71 | 1.21 | 1.10 | 0.75 | 0.00 | 0.00 | 1.14 | 0.00 |
time (sec) |
N/A | 0.703 | 0.224 | 0.239 | 0.034 | 0.107 | 0.000 | 0.000 | 0.194 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 214 | 226 | 163 | 182 | 247 | 198 | 0 | 0 | 271 | 0 |
N.S. |
1 | 1.06 | 0.76 | 0.85 | 1.15 | 0.93 | 0.00 | 0.00 | 1.27 | 0.00 |
time (sec) |
N/A | 0.866 | 0.148 | 0.247 | 0.040 | 0.100 | 0.000 | 0.000 | 0.191 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 233 | 246 | 183 | 304 | 273 | 195 | 0 | 0 | 278 | 0 |
N.S. |
1 | 1.06 | 0.79 | 1.30 | 1.17 | 0.84 | 0.00 | 0.00 | 1.19 | 0.00 |
time (sec) |
N/A | 0.700 | 0.199 | 0.240 | 0.034 | 0.098 | 0.000 | 0.000 | 0.205 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 162 | 180 | 130 | 138 | 180 | 163 | 0 | 0 | 204 | 0 |
N.S. |
1 | 1.11 | 0.80 | 0.85 | 1.11 | 1.01 | 0.00 | 0.00 | 1.26 | 0.00 |
time (sec) |
N/A | 0.596 | 0.120 | 0.171 | 0.033 | 0.092 | 0.000 | 0.000 | 0.205 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 342 | 372 | 228 | 223 | 0 | 0 | 0 | 0 | 193 | 0 |
N.S. |
1 | 1.09 | 0.67 | 0.65 | 0.00 | 0.00 | 0.00 | 0.00 | 0.56 | 0.00 |
time (sec) |
N/A | 1.125 | 0.391 | 0.436 | 0.000 | 0.000 | 0.000 | 0.000 | 0.201 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | B | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 141 | 144 | 128 | 178 | 134 | 236 | 0 | 0 | 170 | 0 |
N.S. |
1 | 1.02 | 0.91 | 1.26 | 0.95 | 1.67 | 0.00 | 0.00 | 1.21 | 0.00 |
time (sec) |
N/A | 0.559 | 0.158 | 0.195 | 0.113 | 0.123 | 0.000 | 0.000 | 0.190 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 321 | 329 | 173 | 196 | 0 | 0 | 0 | 0 | 169 | 0 |
N.S. |
1 | 1.02 | 0.54 | 0.61 | 0.00 | 0.00 | 0.00 | 0.00 | 0.53 | 0.00 |
time (sec) |
N/A | 1.251 | 0.270 | 0.517 | 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 | A | A | A | A | F | F | B | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 140 | 168 | 133 | 191 | 126 | 216 | 0 | 0 | 167 | 0 |
N.S. |
1 | 1.20 | 0.95 | 1.36 | 0.90 | 1.54 | 0.00 | 0.00 | 1.19 | 0.00 |
time (sec) |
N/A | 0.863 | 0.153 | 0.184 | 0.104 | 0.139 | 0.000 | 0.000 | 0.194 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 365 | 365 | 276 | 319 | 451 | 334 | 0 | 0 | 512 | 0 |
N.S. |
1 | 1.00 | 0.76 | 0.87 | 1.24 | 0.92 | 0.00 | 0.00 | 1.40 | 0.00 |
time (sec) |
N/A | 0.980 | 0.269 | 0.263 | 0.038 | 0.101 | 0.000 | 0.000 | 0.212 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 399 | 442 | 294 | 538 | 487 | 330 | 0 | 0 | 522 | 0 |
N.S. |
1 | 1.11 | 0.74 | 1.35 | 1.22 | 0.83 | 0.00 | 0.00 | 1.31 | 0.00 |
time (sec) |
N/A | 0.895 | 0.357 | 0.289 | 0.037 | 0.104 | 0.000 | 0.000 | 0.204 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 307 | 313 | 236 | 273 | 374 | 289 | 0 | 0 | 422 | 0 |
N.S. |
1 | 1.02 | 0.77 | 0.89 | 1.22 | 0.94 | 0.00 | 0.00 | 1.37 | 0.00 |
time (sec) |
N/A | 1.000 | 0.205 | 0.260 | 0.035 | 0.097 | 0.000 | 0.000 | 0.188 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 311 | 328 | 256 | 430 | 409 | 286 | 0 | 0 | 432 | 0 |
N.S. |
1 | 1.05 | 0.82 | 1.38 | 1.32 | 0.92 | 0.00 | 0.00 | 1.39 | 0.00 |
time (sec) |
N/A | 0.855 | 0.259 | 0.257 | 0.037 | 0.101 | 0.000 | 0.000 | 0.200 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 241 | 253 | 193 | 211 | 287 | 241 | 0 | 0 | 330 | 0 |
N.S. |
1 | 1.05 | 0.80 | 0.88 | 1.19 | 1.00 | 0.00 | 0.00 | 1.37 | 0.00 |
time (sec) |
N/A | 1.133 | 0.157 | 0.177 | 0.033 | 0.097 | 0.000 | 0.000 | 0.188 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 509 | 508 | 344 | 348 | 0 | 0 | 0 | 0 | 322 | 0 |
N.S. |
1 | 1.00 | 0.68 | 0.68 | 0.00 | 0.00 | 0.00 | 0.00 | 0.63 | 0.00 |
time (sec) |
N/A | 1.507 | 0.697 | 0.467 | 0.000 | 0.000 | 0.000 | 0.000 | 0.199 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 214 | 217 | 182 | 273 | 222 | 327 | 0 | 0 | 272 | 0 |
N.S. |
1 | 1.01 | 0.85 | 1.28 | 1.04 | 1.53 | 0.00 | 0.00 | 1.27 | 0.00 |
time (sec) |
N/A | 0.805 | 0.212 | 0.196 | 0.117 | 0.140 | 0.000 | 0.000 | 0.188 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 402 | 480 | 278 | 293 | 0 | 0 | 0 | 0 | 276 | 0 |
N.S. |
1 | 1.19 | 0.69 | 0.73 | 0.00 | 0.00 | 0.00 | 0.00 | 0.69 | 0.00 |
time (sec) |
N/A | 2.063 | 0.501 | 0.556 | 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 | A | A | A | A | F | F | B | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 208 | 198 | 184 | 270 | 197 | 322 | 0 | 0 | 260 | 0 |
N.S. |
1 | 0.95 | 0.88 | 1.30 | 0.95 | 1.55 | 0.00 | 0.00 | 1.25 | 0.00 |
time (sec) |
N/A | 0.948 | 0.224 | 0.208 | 0.111 | 0.166 | 0.000 | 0.000 | 0.194 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F(-2) | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 627 | 627 | 524 | 364 | 0 | 0 | 0 | 0 | 65 | 0 |
N.S. |
1 | 1.00 | 0.84 | 0.58 | 0.00 | 0.00 | 0.00 | 0.00 | 0.10 | 0.00 |
time (sec) |
N/A | 1.477 | 0.790 | 23.088 | 0.000 | 0.000 | 0.000 | 0.000 | 0.222 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 521 | 521 | 512 | 2111 | 0 | 0 | 0 | 0 | 49 | 0 |
N.S. |
1 | 1.00 | 0.98 | 4.05 | 0.00 | 0.00 | 0.00 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 1.305 | 0.390 | 1.454 | 0.000 | 0.000 | 0.000 | 0.000 | 0.232 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F(-2) | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 544 | 544 | 457 | 284 | 0 | 0 | 0 | 0 | 52 | 0 |
N.S. |
1 | 1.00 | 0.84 | 0.52 | 0.00 | 0.00 | 0.00 | 0.00 | 0.10 | 0.00 |
time (sec) |
N/A | 1.661 | 0.370 | 10.496 | 0.000 | 0.000 | 0.000 | 0.000 | 0.221 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 449 | 449 | 447 | 386 | 0 | 0 | 0 | 0 | 37 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.86 | 0.00 | 0.00 | 0.00 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 1.630 | 0.097 | 0.403 | 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 | C | F(-2) | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 501 | 501 | 397 | 232 | 0 | 0 | 0 | 0 | 46 | 0 |
N.S. |
1 | 1.00 | 0.79 | 0.46 | 0.00 | 0.00 | 0.00 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 1.319 | 0.216 | 0.370 | 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 | C | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 472 | 489 | 410 | 381 | 0 | 0 | 0 | 0 | 44 | 0 |
N.S. |
1 | 1.04 | 0.87 | 0.81 | 0.00 | 0.00 | 0.00 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 1.400 | 0.195 | 0.555 | 0.000 | 0.000 | 0.000 | 0.000 | 0.252 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F(-2) | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 543 | 543 | 549 | 331 | 0 | 0 | 0 | 0 | 58 | 0 |
N.S. |
1 | 1.00 | 1.01 | 0.61 | 0.00 | 0.00 | 0.00 | 0.00 | 0.11 | 0.00 |
time (sec) |
N/A | 1.372 | 0.938 | 10.626 | 0.000 | 0.000 | 0.000 | 0.000 | 0.310 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 531 | 550 | 518 | 466 | 0 | 0 | 0 | 0 | 65 | 0 |
N.S. |
1 | 1.04 | 0.98 | 0.88 | 0.00 | 0.00 | 0.00 | 0.00 | 0.12 | 0.00 |
time (sec) |
N/A | 2.107 | 0.345 | 0.599 | 0.000 | 0.000 | 0.000 | 0.000 | 0.374 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F(-2) | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 624 | 624 | 657 | 424 | 0 | 0 | 0 | 0 | 75 | 0 |
N.S. |
1 | 1.00 | 1.05 | 0.68 | 0.00 | 0.00 | 0.00 | 0.00 | 0.12 | 0.00 |
time (sec) |
N/A | 1.834 | 1.033 | 12.450 | 0.000 | 0.000 | 0.000 | 0.000 | 0.415 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 562 | 562 | 694 | 2132 | 0 | 0 | 0 | 0 | 123 | 0 |
N.S. |
1 | 1.00 | 1.23 | 3.79 | 0.00 | 0.00 | 0.00 | 0.00 | 0.22 | 0.00 |
time (sec) |
N/A | 1.477 | 1.194 | 1.540 | 0.000 | 0.000 | 0.000 | 0.000 | 0.324 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 113 | 113 | 123 | 399 | 0 | 537 | 0 | 0 | 90 | 0 |
N.S. |
1 | 1.00 | 1.09 | 3.53 | 0.00 | 4.75 | 0.00 | 0.00 | 0.80 | 0.00 |
time (sec) |
N/A | 0.301 | 0.246 | 2.260 | 0.000 | 0.124 | 0.000 | 0.000 | 0.321 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 581 | 598 | 754 | 505 | 0 | 0 | 0 | 0 | 138 | 0 |
N.S. |
1 | 1.03 | 1.30 | 0.87 | 0.00 | 0.00 | 0.00 | 0.00 | 0.24 | 0.00 |
time (sec) |
N/A | 1.848 | 1.063 | 0.628 | 0.000 | 0.000 | 0.000 | 0.000 | 0.468 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 616 | 634 | 792 | 635 | 0 | 0 | 0 | 0 | 168 | 0 |
N.S. |
1 | 1.03 | 1.29 | 1.03 | 0.00 | 0.00 | 0.00 | 0.00 | 0.27 | 0.00 |
time (sec) |
N/A | 2.221 | 1.409 | 0.800 | 0.000 | 0.000 | 0.000 | 0.000 | 0.764 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F(-2) | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 839 | 839 | 777 | 897 | 0 | 0 | 0 | 0 | 149 | 0 |
N.S. |
1 | 1.00 | 0.93 | 1.07 | 0.00 | 0.00 | 0.00 | 0.00 | 0.18 | 0.00 |
time (sec) |
N/A | 2.613 | 1.203 | 12.946 | 0.000 | 0.000 | 0.000 | 0.000 | 0.338 | 0.000 |