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 | N/A | N/A | N/A | F(-2) | F(-2) | N/A | F(-2) | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 28 | 22 | 0 | 0 | 24 | 0 | 24 |
N.S. |
1 | 1.00 | 1.08 | 0.85 | 0.00 | 0.00 | 0.92 | 0.00 | 0.92 |
time (sec) |
N/A | 0.068 | 4.144 | 13.757 | 0.000 | 0.000 | 18.995 | 0.000 | 0.338 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | N/A | F(-1) | F(-2) | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 28 | 22 | 0 | 24 | 0 | 0 | 24 |
N.S. |
1 | 1.00 | 1.08 | 0.85 | 0.00 | 0.92 | 0.00 | 0.00 | 0.92 |
time (sec) |
N/A | 0.076 | 1.495 | 20.825 | 0.000 | 0.274 | 0.000 | 0.000 | 0.348 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | F(-2) | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 28 | 22 | 0 | 0 | 0 | 3 | 24 |
N.S. |
1 | 1.00 | 1.08 | 0.85 | 0.00 | 0.00 | 0.00 | 0.12 | 0.92 |
time (sec) |
N/A | 0.077 | 4.645 | 15.967 | 0.000 | 0.000 | 0.000 | 89.429 | 0.339 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | F(-2) | F(-1) | F(-2) | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 26 | 20 | 0 | 0 | 0 | 0 | 22 |
N.S. |
1 | 1.00 | 1.08 | 0.83 | 0.00 | 0.00 | 0.00 | 0.00 | 0.92 |
time (sec) |
N/A | 0.078 | 3.344 | 15.253 | 0.000 | 0.000 | 0.000 | 0.000 | 0.336 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | F(-2) | F(-1) | F(-2) | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 25 | 19 | 0 | 0 | 0 | 0 | 21 |
N.S. |
1 | 1.00 | 1.09 | 0.83 | 0.00 | 0.00 | 0.00 | 0.00 | 0.91 |
time (sec) |
N/A | 0.130 | 1.632 | 15.772 | 0.000 | 0.000 | 0.000 | 0.000 | 0.358 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | F(-2) | N/A | F(-2) | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 28 | 22 | 0 | 0 | 24 | 0 | 24 |
N.S. |
1 | 1.00 | 1.08 | 0.85 | 0.00 | 0.00 | 0.92 | 0.00 | 0.92 |
time (sec) |
N/A | 0.079 | 3.276 | 16.240 | 0.000 | 0.000 | 141.534 | 0.000 | 0.349 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | N/A | F(-1) | F(-2) | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 28 | 22 | 0 | 49 | 0 | 0 | 24 |
N.S. |
1 | 1.00 | 1.08 | 0.85 | 0.00 | 1.88 | 0.00 | 0.00 | 0.92 |
time (sec) |
N/A | 0.076 | 1.741 | 21.239 | 0.000 | 0.260 | 0.000 | 0.000 | 0.337 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | F(-2) | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 28 | 22 | 0 | 0 | 0 | 3 | 24 |
N.S. |
1 | 1.00 | 1.08 | 0.85 | 0.00 | 0.00 | 0.00 | 0.12 | 0.92 |
time (sec) |
N/A | 0.078 | 3.776 | 14.992 | 0.000 | 0.000 | 0.000 | 89.051 | 0.334 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | F(-2) | F(-1) | F(-2) | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 26 | 20 | 0 | 0 | 0 | 0 | 22 |
N.S. |
1 | 1.00 | 1.08 | 0.83 | 0.00 | 0.00 | 0.00 | 0.00 | 0.92 |
time (sec) |
N/A | 0.078 | 6.937 | 13.801 | 0.000 | 0.000 | 0.000 | 0.000 | 0.324 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | F(-2) | F(-1) | F(-2) | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 25 | 19 | 0 | 0 | 0 | 0 | 21 |
N.S. |
1 | 1.00 | 1.09 | 0.83 | 0.00 | 0.00 | 0.00 | 0.00 | 0.91 |
time (sec) |
N/A | 0.190 | 0.391 | 13.620 | 0.000 | 0.000 | 0.000 | 0.000 | 0.355 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | F(-2) | F(-1) | F(-2) | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 28 | 22 | 0 | 0 | 0 | 0 | 24 |
N.S. |
1 | 1.00 | 1.08 | 0.85 | 0.00 | 0.00 | 0.00 | 0.00 | 0.92 |
time (sec) |
N/A | 0.077 | 3.360 | 15.102 | 0.000 | 0.000 | 0.000 | 0.000 | 0.341 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | N/A | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 28 | 22 | 0 | 24 | 0 | 3 | 24 |
N.S. |
1 | 1.00 | 1.08 | 0.85 | 0.00 | 0.92 | 0.00 | 0.12 | 0.92 |
time (sec) |
N/A | 0.068 | 1.468 | 17.365 | 0.000 | 0.258 | 0.000 | 52.384 | 0.331 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | F(-2) | N/A | F(-2) | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 28 | 22 | 0 | 0 | 26 | 0 | 24 |
N.S. |
1 | 1.00 | 1.08 | 0.85 | 0.00 | 0.00 | 1.00 | 0.00 | 0.92 |
time (sec) |
N/A | 0.290 | 3.952 | 14.954 | 0.000 | 0.000 | 128.350 | 0.000 | 0.354 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | 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 | 26 | 26 | 28 | 22 | 0 | 0 | 26 | 3 | 24 |
N.S. |
1 | 1.00 | 1.08 | 0.85 | 0.00 | 0.00 | 1.00 | 0.12 | 0.92 |
time (sec) |
N/A | 0.178 | 3.209 | 13.642 | 0.000 | 0.000 | 62.975 | 151.578 | 0.334 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | 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 | 24 | 24 | 26 | 20 | 0 | 0 | 24 | 3 | 22 |
N.S. |
1 | 1.00 | 1.08 | 0.83 | 0.00 | 0.00 | 1.00 | 0.12 | 0.92 |
time (sec) |
N/A | 0.077 | 1.002 | 7.183 | 0.000 | 0.000 | 36.950 | 151.317 | 0.339 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | 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 | 23 | 23 | 25 | 19 | 0 | 0 | 22 | 3 | 21 |
N.S. |
1 | 1.00 | 1.09 | 0.83 | 0.00 | 0.00 | 0.96 | 0.13 | 0.91 |
time (sec) |
N/A | 0.025 | 0.189 | 9.730 | 0.000 | 0.000 | 12.614 | 143.927 | 0.340 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | 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 | 26 | 26 | 28 | 22 | 0 | 0 | 24 | 3 | 24 |
N.S. |
1 | 1.00 | 1.08 | 0.85 | 0.00 | 0.00 | 0.92 | 0.12 | 0.92 |
time (sec) |
N/A | 0.072 | 2.300 | 13.964 | 0.000 | 0.000 | 13.697 | 145.722 | 0.354 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | 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 | 26 | 26 | 28 | 22 | 0 | 0 | 26 | 3 | 24 |
N.S. |
1 | 1.00 | 1.08 | 0.85 | 0.00 | 0.00 | 1.00 | 0.12 | 0.92 |
time (sec) |
N/A | 0.136 | 2.355 | 15.606 | 0.000 | 0.000 | 18.158 | 147.543 | 0.340 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | 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 | 26 | 26 | 28 | 22 | 0 | 0 | 26 | 3 | 24 |
N.S. |
1 | 1.00 | 1.08 | 0.85 | 0.00 | 0.00 | 1.00 | 0.12 | 0.92 |
time (sec) |
N/A | 0.289 | 7.357 | 15.275 | 0.000 | 0.000 | 33.397 | 149.976 | 0.344 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | 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 | 26 | 26 | 28 | 22 | 0 | 0 | 26 | 3 | 24 |
N.S. |
1 | 1.00 | 1.08 | 0.85 | 0.00 | 0.00 | 1.00 | 0.12 | 0.92 |
time (sec) |
N/A | 0.432 | 18.291 | 15.665 | 0.000 | 0.000 | 58.848 | 147.842 | 0.337 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | N/A | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 28 | 22 | 0 | 51 | 0 | 3 | 24 |
N.S. |
1 | 1.00 | 1.08 | 0.85 | 0.00 | 1.96 | 0.00 | 0.12 | 0.92 |
time (sec) |
N/A | 0.078 | 1.683 | 12.276 | 0.000 | 0.271 | 0.000 | 52.336 | 0.354 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | F(-2) | N/A | F(-2) | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 28 | 22 | 0 | 0 | 26 | 0 | 24 |
N.S. |
1 | 1.00 | 1.08 | 0.85 | 0.00 | 0.00 | 1.00 | 0.00 | 0.92 |
time (sec) |
N/A | 0.080 | 6.823 | 8.767 | 0.000 | 0.000 | 154.485 | 0.000 | 0.334 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | 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 | 26 | 26 | 28 | 22 | 0 | 0 | 26 | 3 | 24 |
N.S. |
1 | 1.00 | 1.08 | 0.85 | 0.00 | 0.00 | 1.00 | 0.12 | 0.92 |
time (sec) |
N/A | 0.090 | 4.656 | 7.557 | 0.000 | 0.000 | 76.893 | 85.165 | 0.344 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F(-2) | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 129 | 129 | 128 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.99 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.145 | 0.160 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F(-2) | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 125 | 125 | 86 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.69 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.107 | 0.081 | 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) | F(-2) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 28 | 22 | 0 | 0 | 24 | 3 | 24 |
N.S. |
1 | 1.00 | 1.08 | 0.85 | 0.00 | 0.00 | 0.92 | 0.12 | 0.92 |
time (sec) |
N/A | 0.084 | 3.777 | 12.046 | 0.000 | 0.000 | 34.595 | 80.860 | 0.339 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | 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 | 26 | 26 | 28 | 22 | 0 | 0 | 26 | 3 | 24 |
N.S. |
1 | 1.00 | 1.08 | 0.85 | 0.00 | 0.00 | 1.00 | 0.12 | 0.92 |
time (sec) |
N/A | 0.084 | 6.745 | 10.740 | 0.000 | 0.000 | 57.036 | 79.229 | 0.340 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | N/A | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 28 | 22 | 0 | 62 | 0 | 3 | 24 |
N.S. |
1 | 1.00 | 1.08 | 0.85 | 0.00 | 2.38 | 0.00 | 0.12 | 0.92 |
time (sec) |
N/A | 0.082 | 2.344 | 24.108 | 0.000 | 0.258 | 0.000 | 52.794 | 0.362 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | F(-2) | F(-1) | F(-2) | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 28 | 22 | 0 | 0 | 0 | 0 | 24 |
N.S. |
1 | 1.00 | 1.08 | 0.85 | 0.00 | 0.00 | 0.00 | 0.00 | 0.92 |
time (sec) |
N/A | 0.094 | 10.581 | 27.358 | 0.000 | 0.000 | 0.000 | 0.000 | 0.342 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | F(-2) | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 28 | 22 | 0 | 0 | 0 | 3 | 24 |
N.S. |
1 | 1.00 | 1.08 | 0.85 | 0.00 | 0.00 | 0.00 | 0.12 | 0.92 |
time (sec) |
N/A | 0.086 | 7.135 | 20.161 | 0.000 | 0.000 | 0.000 | 96.241 | 0.350 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F(-2) | F(-2) | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 263 | 263 | 272 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.03 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.445 | 0.952 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F(-2) | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 247 | 247 | 338 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.37 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.352 | 0.456 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F(-2) | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 248 | 248 | 261 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.05 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.206 | 0.926 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F(-2) | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 252 | 252 | 345 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.37 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.264 | 0.465 | 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) | F(-2) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 28 | 22 | 0 | 0 | 24 | 3 | 24 |
N.S. |
1 | 1.00 | 1.08 | 0.85 | 0.00 | 0.00 | 0.92 | 0.12 | 0.92 |
time (sec) |
N/A | 0.080 | 4.680 | 6.063 | 0.000 | 0.000 | 109.900 | 90.944 | 0.344 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | 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 | 26 | 26 | 28 | 22 | 0 | 0 | 26 | 3 | 24 |
N.S. |
1 | 1.00 | 1.08 | 0.85 | 0.00 | 0.00 | 1.00 | 0.12 | 0.92 |
time (sec) |
N/A | 0.081 | 7.355 | 6.541 | 0.000 | 0.000 | 176.904 | 87.683 | 0.339 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | N/A | 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 | 0 | 22 | 0 | 3 | 22 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 0.00 | 1.00 | 0.00 | 0.14 | 1.00 |
time (sec) |
N/A | 0.026 | 0.905 | 9.056 | 0.000 | 0.262 | 0.000 | 52.887 | 0.668 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | 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 | 24 | 20 | 0 | 0 | 31 | 3 | 22 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 0.00 | 0.00 | 1.41 | 0.14 | 1.00 |
time (sec) |
N/A | 0.025 | 3.983 | 3.711 | 0.000 | 0.000 | 41.865 | 108.416 | 0.536 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | 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 | 20 | 20 | 22 | 18 | 0 | 0 | 29 | 3 | 20 |
N.S. |
1 | 1.00 | 1.10 | 0.90 | 0.00 | 0.00 | 1.45 | 0.15 | 1.00 |
time (sec) |
N/A | 0.043 | 1.188 | 1.933 | 0.000 | 0.000 | 26.532 | 111.290 | 0.517 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | 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 | 19 | 19 | 21 | 17 | 0 | 0 | 27 | 3 | 19 |
N.S. |
1 | 1.00 | 1.11 | 0.89 | 0.00 | 0.00 | 1.42 | 0.16 | 1.00 |
time (sec) |
N/A | 0.020 | 2.436 | 1.875 | 0.000 | 0.000 | 21.657 | 108.650 | 0.564 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | F(-2) | N/A | F(-1) | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 24 | 20 | 0 | 0 | 27 | 0 | 22 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 0.00 | 0.00 | 1.23 | 0.00 | 1.00 |
time (sec) |
N/A | 0.023 | 1.929 | 2.745 | 0.000 | 0.000 | 16.428 | 0.000 | 0.550 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | F(-2) | N/A | F(-1) | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 24 | 20 | 0 | 0 | 27 | 0 | 22 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 0.00 | 0.00 | 1.23 | 0.00 | 1.00 |
time (sec) |
N/A | 0.023 | 0.857 | 2.848 | 0.000 | 0.000 | 19.434 | 0.000 | 0.550 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | N/A | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 26 | 22 | 0 | 37 | 0 | 3 | 24 |
N.S. |
1 | 1.00 | 1.08 | 0.92 | 0.00 | 1.54 | 0.00 | 0.12 | 1.00 |
time (sec) |
N/A | 0.036 | 0.775 | 8.549 | 0.000 | 0.257 | 0.000 | 53.604 | 0.561 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | 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 | 24 | 24 | 26 | 22 | 0 | 0 | 51 | 3 | 24 |
N.S. |
1 | 1.00 | 1.08 | 0.92 | 0.00 | 0.00 | 2.12 | 0.12 | 1.00 |
time (sec) |
N/A | 0.040 | 2.804 | 4.283 | 0.000 | 0.000 | 80.169 | 112.394 | 0.473 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | 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 | 24 | 20 | 0 | 0 | 49 | 3 | 22 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 0.00 | 0.00 | 2.23 | 0.14 | 1.00 |
time (sec) |
N/A | 0.088 | 0.883 | 1.980 | 0.000 | 0.000 | 51.417 | 109.500 | 0.452 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | 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 | 21 | 21 | 23 | 19 | 0 | 0 | 48 | 3 | 21 |
N.S. |
1 | 1.00 | 1.10 | 0.90 | 0.00 | 0.00 | 2.29 | 0.14 | 1.00 |
time (sec) |
N/A | 0.052 | 1.488 | 2.074 | 0.000 | 0.000 | 40.918 | 111.914 | 0.451 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | F(-2) | N/A | F(-1) | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 26 | 22 | 0 | 0 | 48 | 0 | 24 |
N.S. |
1 | 1.00 | 1.08 | 0.92 | 0.00 | 0.00 | 2.00 | 0.00 | 1.00 |
time (sec) |
N/A | 0.036 | 1.245 | 2.471 | 0.000 | 0.000 | 29.777 | 0.000 | 0.473 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | F(-2) | N/A | F(-1) | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 26 | 22 | 0 | 0 | 48 | 0 | 24 |
N.S. |
1 | 1.00 | 1.08 | 0.92 | 0.00 | 0.00 | 2.00 | 0.00 | 1.00 |
time (sec) |
N/A | 0.040 | 1.543 | 2.535 | 0.000 | 0.000 | 31.241 | 0.000 | 0.501 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | N/A | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 26 | 22 | 0 | 48 | 0 | 3 | 24 |
N.S. |
1 | 1.00 | 1.08 | 0.92 | 0.00 | 2.00 | 0.00 | 0.12 | 1.00 |
time (sec) |
N/A | 0.037 | 0.588 | 10.503 | 0.000 | 0.250 | 0.000 | 51.063 | 0.547 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | 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 | 24 | 24 | 26 | 22 | 0 | 0 | 70 | 3 | 24 |
N.S. |
1 | 1.00 | 1.08 | 0.92 | 0.00 | 0.00 | 2.92 | 0.12 | 1.00 |
time (sec) |
N/A | 0.038 | 2.766 | 4.445 | 0.000 | 0.000 | 149.491 | 108.162 | 0.480 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | 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 | 24 | 20 | 0 | 0 | 68 | 3 | 22 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 0.00 | 0.00 | 3.09 | 0.14 | 1.00 |
time (sec) |
N/A | 0.136 | 0.955 | 2.187 | 0.000 | 0.000 | 96.844 | 104.838 | 0.462 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | 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 | 21 | 21 | 23 | 19 | 0 | 0 | 66 | 3 | 21 |
N.S. |
1 | 1.00 | 1.10 | 0.90 | 0.00 | 0.00 | 3.14 | 0.14 | 1.00 |
time (sec) |
N/A | 0.095 | 1.517 | 2.368 | 0.000 | 0.000 | 85.955 | 108.742 | 0.478 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | F(-2) | N/A | F(-1) | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 26 | 22 | 0 | 0 | 66 | 0 | 24 |
N.S. |
1 | 1.00 | 1.08 | 0.92 | 0.00 | 0.00 | 2.75 | 0.00 | 1.00 |
time (sec) |
N/A | 0.035 | 1.055 | 2.487 | 0.000 | 0.000 | 57.568 | 0.000 | 0.506 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | F(-2) | N/A | F(-1) | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 26 | 22 | 0 | 0 | 66 | 0 | 24 |
N.S. |
1 | 1.00 | 1.08 | 0.92 | 0.00 | 0.00 | 2.75 | 0.00 | 1.00 |
time (sec) |
N/A | 0.038 | 1.501 | 2.870 | 0.000 | 0.000 | 61.462 | 0.000 | 0.485 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | N/A | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 26 | 22 | 0 | 24 | 0 | 3 | 24 |
N.S. |
1 | 1.00 | 1.08 | 0.92 | 0.00 | 1.00 | 0.00 | 0.12 | 1.00 |
time (sec) |
N/A | 0.044 | 0.642 | 5.470 | 0.000 | 0.247 | 0.000 | 52.147 | 0.528 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | 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 | 24 | 24 | 26 | 22 | 0 | 0 | 22 | 3 | 24 |
N.S. |
1 | 1.00 | 1.08 | 0.92 | 0.00 | 0.00 | 0.92 | 0.12 | 1.00 |
time (sec) |
N/A | 0.093 | 3.689 | 2.205 | 0.000 | 0.000 | 9.675 | 108.096 | 0.462 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | 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 | 24 | 24 | 26 | 22 | 0 | 0 | 22 | 3 | 24 |
N.S. |
1 | 1.00 | 1.08 | 0.92 | 0.00 | 0.00 | 0.92 | 0.12 | 1.00 |
time (sec) |
N/A | 0.068 | 0.873 | 1.621 | 0.000 | 0.000 | 7.670 | 109.589 | 0.446 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | 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 | 24 | 20 | 0 | 0 | 20 | 3 | 22 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 0.00 | 0.00 | 0.91 | 0.14 | 1.00 |
time (sec) |
N/A | 0.040 | 0.810 | 1.151 | 0.000 | 0.000 | 5.064 | 107.694 | 0.467 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 18 | 15 | 0 | 14 | 15 | 14 | 14 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 0.00 | 0.78 | 0.83 | 0.78 | 0.78 |
time (sec) |
N/A | 0.019 | 0.004 | 2.537 | 0.000 | 0.245 | 7.275 | 0.278 | 0.442 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | 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 | 24 | 24 | 26 | 22 | 0 | 0 | 19 | 3 | 24 |
N.S. |
1 | 1.00 | 1.08 | 0.92 | 0.00 | 0.00 | 0.79 | 0.12 | 1.00 |
time (sec) |
N/A | 0.079 | 0.319 | 1.742 | 0.000 | 0.000 | 3.675 | 103.475 | 0.489 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | 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 | 24 | 24 | 26 | 22 | 0 | 0 | 20 | 3 | 24 |
N.S. |
1 | 1.00 | 1.08 | 0.92 | 0.00 | 0.00 | 0.83 | 0.12 | 1.00 |
time (sec) |
N/A | 0.077 | 0.600 | 1.579 | 0.000 | 0.000 | 5.196 | 107.729 | 0.494 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | 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 | 24 | 24 | 26 | 22 | 0 | 0 | 20 | 3 | 24 |
N.S. |
1 | 1.00 | 1.08 | 0.92 | 0.00 | 0.00 | 0.83 | 0.12 | 1.00 |
time (sec) |
N/A | 0.143 | 1.829 | 1.657 | 0.000 | 0.000 | 5.408 | 107.946 | 0.501 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | 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 | 24 | 24 | 26 | 22 | 0 | 0 | 20 | 3 | 24 |
N.S. |
1 | 1.00 | 1.08 | 0.92 | 0.00 | 0.00 | 0.83 | 0.12 | 1.00 |
time (sec) |
N/A | 0.131 | 3.404 | 4.455 | 0.000 | 0.000 | 7.183 | 109.257 | 0.491 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | N/A | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 26 | 22 | 0 | 39 | 0 | 3 | 24 |
N.S. |
1 | 1.00 | 1.08 | 0.92 | 0.00 | 1.62 | 0.00 | 0.12 | 1.00 |
time (sec) |
N/A | 0.047 | 1.423 | 9.633 | 0.000 | 0.257 | 0.000 | 52.150 | 0.544 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | 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 | 24 | 24 | 26 | 22 | 0 | 0 | 32 | 3 | 24 |
N.S. |
1 | 1.00 | 1.08 | 0.92 | 0.00 | 0.00 | 1.33 | 0.12 | 1.00 |
time (sec) |
N/A | 0.046 | 3.592 | 7.579 | 0.000 | 0.000 | 15.147 | 118.133 | 0.483 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 157 | 157 | 111 | 93 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.71 | 0.59 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.163 | 0.363 | 25.514 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F(-2) | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 156 | 156 | 234 | 82 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.50 | 0.53 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.158 | 0.164 | 25.740 | 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(-2) | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 151 | 151 | 108 | 93 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.72 | 0.62 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.140 | 0.311 | 25.052 | 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) | F(-2) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 26 | 22 | 0 | 0 | 29 | 3 | 24 |
N.S. |
1 | 1.00 | 1.08 | 0.92 | 0.00 | 0.00 | 1.21 | 0.12 | 1.00 |
time (sec) |
N/A | 0.044 | 1.074 | 3.253 | 0.000 | 0.000 | 5.277 | 116.899 | 0.519 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | N/A | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 26 | 22 | 0 | 50 | 0 | 3 | 24 |
N.S. |
1 | 1.00 | 1.08 | 0.92 | 0.00 | 2.08 | 0.00 | 0.12 | 1.00 |
time (sec) |
N/A | 0.048 | 1.398 | 7.799 | 0.000 | 0.268 | 0.000 | 54.135 | 0.538 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | 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 | 24 | 24 | 26 | 22 | 0 | 0 | 41 | 3 | 24 |
N.S. |
1 | 1.00 | 1.08 | 0.92 | 0.00 | 0.00 | 1.71 | 0.12 | 1.00 |
time (sec) |
N/A | 0.047 | 6.621 | 8.124 | 0.000 | 0.000 | 31.006 | 128.672 | 0.503 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F(-2) | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 310 | 310 | 287 | 168 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.93 | 0.54 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.360 | 0.599 | 2.763 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F(-2) | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 256 | 256 | 359 | 157 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.40 | 0.61 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.365 | 0.604 | 2.562 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F(-2) | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 133 | 133 | 185 | 96 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.39 | 0.72 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.137 | 0.452 | 1.477 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F(-2) | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 254 | 254 | 359 | 157 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.41 | 0.62 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.273 | 0.563 | 1.819 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F(-2) | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 296 | 296 | 287 | 168 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.97 | 0.57 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.274 | 0.613 | 2.097 | 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) | F(-2) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 26 | 22 | 0 | 0 | 37 | 3 | 24 |
N.S. |
1 | 1.00 | 1.08 | 0.92 | 0.00 | 0.00 | 1.54 | 0.12 | 1.00 |
time (sec) |
N/A | 0.046 | 2.040 | 3.766 | 0.000 | 0.000 | 10.942 | 125.499 | 0.530 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | N/A | F(-1) | F(-2) | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 28 | 22 | 0 | 24 | 0 | 0 | 24 |
N.S. |
1 | 1.00 | 1.08 | 0.85 | 0.00 | 0.92 | 0.00 | 0.00 | 0.92 |
time (sec) |
N/A | 0.076 | 1.264 | 11.497 | 0.000 | 0.256 | 0.000 | 0.000 | 0.352 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | F(-2) | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 28 | 22 | 0 | 0 | 0 | 3 | 24 |
N.S. |
1 | 1.00 | 1.08 | 0.85 | 0.00 | 0.00 | 0.00 | 0.12 | 0.92 |
time (sec) |
N/A | 0.071 | 3.880 | 5.571 | 0.000 | 0.000 | 0.000 | 123.403 | 0.340 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | F(-2) | F(-1) | F(-2) | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 26 | 20 | 0 | 0 | 0 | 0 | 22 |
N.S. |
1 | 1.00 | 1.08 | 0.83 | 0.00 | 0.00 | 0.00 | 0.00 | 0.92 |
time (sec) |
N/A | 0.134 | 4.579 | 3.505 | 0.000 | 0.000 | 0.000 | 0.000 | 0.329 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | F(-2) | F(-1) | F(-2) | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 25 | 19 | 0 | 0 | 0 | 0 | 21 |
N.S. |
1 | 1.00 | 1.09 | 0.83 | 0.00 | 0.00 | 0.00 | 0.00 | 0.91 |
time (sec) |
N/A | 0.076 | 0.245 | 3.582 | 0.000 | 0.000 | 0.000 | 0.000 | 0.361 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | F(-2) | N/A | F(-2) | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 28 | 22 | 0 | 0 | 24 | 0 | 24 |
N.S. |
1 | 1.00 | 1.08 | 0.85 | 0.00 | 0.00 | 0.92 | 0.00 | 0.92 |
time (sec) |
N/A | 0.070 | 3.300 | 3.889 | 0.000 | 0.000 | 168.429 | 0.000 | 0.340 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | N/A | F(-1) | F(-2) | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 28 | 22 | 0 | 24 | 0 | 0 | 24 |
N.S. |
1 | 1.00 | 1.08 | 0.85 | 0.00 | 0.92 | 0.00 | 0.00 | 0.92 |
time (sec) |
N/A | 0.078 | 1.440 | 9.154 | 0.000 | 0.252 | 0.000 | 0.000 | 0.344 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | F(-2) | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 28 | 22 | 0 | 0 | 0 | 3 | 24 |
N.S. |
1 | 1.00 | 1.08 | 0.85 | 0.00 | 0.00 | 0.00 | 0.12 | 0.92 |
time (sec) |
N/A | 0.081 | 4.285 | 4.161 | 0.000 | 0.000 | 0.000 | 122.427 | 0.343 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | F(-2) | F(-1) | F(-2) | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 26 | 20 | 0 | 0 | 0 | 0 | 22 |
N.S. |
1 | 1.00 | 1.08 | 0.83 | 0.00 | 0.00 | 0.00 | 0.00 | 0.92 |
time (sec) |
N/A | 0.197 | 3.008 | 2.926 | 0.000 | 0.000 | 0.000 | 0.000 | 0.333 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | F(-2) | F(-1) | F(-2) | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 25 | 19 | 0 | 0 | 0 | 0 | 21 |
N.S. |
1 | 1.00 | 1.09 | 0.83 | 0.00 | 0.00 | 0.00 | 0.00 | 0.91 |
time (sec) |
N/A | 0.130 | 1.745 | 2.869 | 0.000 | 0.000 | 0.000 | 0.000 | 0.334 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | F(-2) | F(-1) | F(-2) | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 28 | 22 | 0 | 0 | 0 | 0 | 24 |
N.S. |
1 | 1.00 | 1.08 | 0.85 | 0.00 | 0.00 | 0.00 | 0.00 | 0.92 |
time (sec) |
N/A | 0.075 | 3.116 | 3.763 | 0.000 | 0.000 | 0.000 | 0.000 | 0.362 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | N/A | F(-1) | F(-2) | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 28 | 22 | 0 | 49 | 0 | 0 | 24 |
N.S. |
1 | 1.00 | 1.08 | 0.85 | 0.00 | 1.88 | 0.00 | 0.00 | 0.92 |
time (sec) |
N/A | 0.077 | 1.701 | 12.808 | 0.000 | 0.257 | 0.000 | 0.000 | 0.351 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | F(-2) | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 28 | 22 | 0 | 0 | 0 | 3 | 24 |
N.S. |
1 | 1.00 | 1.08 | 0.85 | 0.00 | 0.00 | 0.00 | 0.12 | 0.92 |
time (sec) |
N/A | 0.077 | 3.634 | 5.083 | 0.000 | 0.000 | 0.000 | 124.483 | 0.335 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | F(-2) | F(-1) | F(-2) | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 26 | 20 | 0 | 0 | 0 | 0 | 22 |
N.S. |
1 | 1.00 | 1.08 | 0.83 | 0.00 | 0.00 | 0.00 | 0.00 | 0.92 |
time (sec) |
N/A | 0.250 | 5.435 | 3.204 | 0.000 | 0.000 | 0.000 | 0.000 | 0.344 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | F(-2) | F(-1) | F(-2) | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 25 | 19 | 0 | 0 | 0 | 0 | 21 |
N.S. |
1 | 1.00 | 1.09 | 0.83 | 0.00 | 0.00 | 0.00 | 0.00 | 0.91 |
time (sec) |
N/A | 0.184 | 0.408 | 3.665 | 0.000 | 0.000 | 0.000 | 0.000 | 0.347 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | F(-2) | F(-1) | F(-2) | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 28 | 22 | 0 | 0 | 0 | 0 | 24 |
N.S. |
1 | 1.00 | 1.08 | 0.85 | 0.00 | 0.00 | 0.00 | 0.00 | 0.92 |
time (sec) |
N/A | 0.073 | 3.351 | 4.730 | 0.000 | 0.000 | 0.000 | 0.000 | 0.339 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | N/A | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 28 | 22 | 0 | 24 | 0 | 3 | 24 |
N.S. |
1 | 1.00 | 1.08 | 0.85 | 0.00 | 0.92 | 0.00 | 0.12 | 0.92 |
time (sec) |
N/A | 0.069 | 1.365 | 13.726 | 0.000 | 0.256 | 0.000 | 53.841 | 0.352 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | F(-2) | F(-1) | F(-2) | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 28 | 22 | 0 | 0 | 0 | 0 | 24 |
N.S. |
1 | 1.00 | 1.08 | 0.85 | 0.00 | 0.00 | 0.00 | 0.00 | 0.92 |
time (sec) |
N/A | 0.322 | 4.019 | 6.365 | 0.000 | 0.000 | 0.000 | 0.000 | 0.348 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | F(-2) | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 28 | 22 | 0 | 0 | 0 | 3 | 24 |
N.S. |
1 | 1.00 | 1.08 | 0.85 | 0.00 | 0.00 | 0.00 | 0.12 | 0.92 |
time (sec) |
N/A | 0.164 | 3.038 | 4.425 | 0.000 | 0.000 | 0.000 | 227.558 | 0.335 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | F(-2) | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 26 | 20 | 0 | 0 | 0 | 3 | 22 |
N.S. |
1 | 1.00 | 1.08 | 0.83 | 0.00 | 0.00 | 0.00 | 0.12 | 0.92 |
time (sec) |
N/A | 0.069 | 1.006 | 4.000 | 0.000 | 0.000 | 0.000 | 224.849 | 0.337 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | 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 | 23 | 23 | 25 | 19 | 0 | 0 | 22 | 3 | 21 |
N.S. |
1 | 1.00 | 1.09 | 0.83 | 0.00 | 0.00 | 0.96 | 0.13 | 0.91 |
time (sec) |
N/A | 0.022 | 0.184 | 5.217 | 0.000 | 0.000 | 120.182 | 213.370 | 0.339 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | 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 | 26 | 26 | 28 | 22 | 0 | 0 | 24 | 3 | 24 |
N.S. |
1 | 1.00 | 1.08 | 0.85 | 0.00 | 0.00 | 0.92 | 0.12 | 0.92 |
time (sec) |
N/A | 0.064 | 2.222 | 5.536 | 0.000 | 0.000 | 141.358 | 215.084 | 0.354 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | 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 | 26 | 26 | 28 | 22 | 0 | 0 | 26 | 3 | 24 |
N.S. |
1 | 1.00 | 1.08 | 0.85 | 0.00 | 0.00 | 1.00 | 0.12 | 0.92 |
time (sec) |
N/A | 0.134 | 2.561 | 5.742 | 0.000 | 0.000 | 171.522 | 223.397 | 0.362 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | 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 | 26 | 26 | 28 | 22 | 0 | 0 | 26 | 3 | 24 |
N.S. |
1 | 1.00 | 1.08 | 0.85 | 0.00 | 0.00 | 1.00 | 0.12 | 0.92 |
time (sec) |
N/A | 0.267 | 8.137 | 5.900 | 0.000 | 0.000 | 168.999 | 224.385 | 0.344 |