Detailed conclusion table per each integral is given by the table below. The elapsed time is in seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2) if the failure was due to an exception being raised, which could indicate a bug in the system. If the failure was due to integral not being evaluated within the time limit, then it is given as F.
In this table, the column N.S. means normalized size and is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To make the table fit the page, the name Mathematica was abbreviated to MMA
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 67 | 67 | 223 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 3.33 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.023 | 0.993 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | F | F | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 78 | 78 | 2791 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 35.78 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.088 | 25.004 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | F | F | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 78 | 78 | 2800 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 35.90 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.102 | 19.231 | 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(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 161 | 161 | 110 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.68 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.194 | 0.658 | 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 | 126 | 126 | 95 | 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 | 0.101 | 0.573 | 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 | 93 | 93 | 84 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.90 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.052 | 0.245 | 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 | 66 | 66 | 70 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.06 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.023 | 0.051 | 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(-1) | F | F | F(-1) |
| verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 77 | 77 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.074 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | F | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 77 | 77 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.089 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 162 | 162 | 116 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.72 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.213 | 0.710 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 129 | 129 | 108 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.84 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.106 | 0.514 | 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 | 99 | 99 | 130 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.31 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.048 | 0.357 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 69 | 69 | 130 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.88 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.024 | 0.124 | 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(-1) | F | F | F(-1) |
| verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 80 | 80 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.084 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | F | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 80 | 80 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.100 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 96 | 96 | 5109 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 53.22 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.079 | 22.639 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 43 | 43 | 2262 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 52.60 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.037 | 13.587 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 58 | 58 | 225 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 3.88 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.046 | 3.586 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | F | F | F | F | F(-1) | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 60 | 60 | 263 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 4.38 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.051 | 5.334 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 106 | 106 | 5111 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 48.22 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.103 | 7.113 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 46 | 46 | 183 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 3.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.047 | 1.324 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 60 | 60 | 234 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 3.90 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.091 | 2.745 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | F | F | F | F | F(-1) | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 65 | 65 | 274 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 4.22 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.100 | 3.316 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 130 | 130 | 5129 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 39.45 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.099 | 6.355 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 72 | 72 | 2282 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 31.69 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.040 | 6.230 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 78 | 78 | 227 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 2.91 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.081 | 0.381 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | F | F | F | F | F(-1) | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 80 | 80 | 265 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 3.31 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.087 | 0.584 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 131 | 131 | 5131 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 39.17 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.115 | 6.526 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 66 | 66 | 212 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 3.21 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.054 | 0.555 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 80 | 80 | 242 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 3.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.125 | 0.720 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | F | F | F | F | F(-1) | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 85 | 85 | 276 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 3.25 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.142 | 0.942 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 71 | 71 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.042 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 68 | 68 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.045 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 91 | 91 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.070 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 90 | 90 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.081 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 87 | 87 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.077 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 85 | 85 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.080 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 107 | 107 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.105 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 107 | 107 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.116 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 294 | 294 | 2746 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 9.34 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.351 | 25.231 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | F | F | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 215 | 215 | 2131 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 9.91 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.206 | 23.744 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 156 | 156 | 1732 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 11.10 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.100 | 21.409 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 109 | 109 | 95 | 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 | 0.045 | 0.394 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 74 | 74 | 70 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.95 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.020 | 0.085 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 85 | 85 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.075 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 85 | 85 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.086 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 58 | 58 | 46 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.79 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.011 | 0.069 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 57 | 57 | 49 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.86 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.011 | 0.071 | 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 | A | A | A | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 77 | 77 | 76 | 60 | 57 | 60 | 144 | 62 | 111 |
| N.S. |
1 | 1.00 | 0.99 | 0.78 | 0.74 | 0.78 | 1.87 | 0.81 | 1.44 |
| time (sec) |
N/A | 0.043 | 0.174 | 1.623 | 0.215 | 0.272 | 0.168 | 0.304 | 9.827 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | A | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 55 | 55 | 60 | 47 | 48 | 46 | 92 | 47 | 68 |
| N.S. |
1 | 1.00 | 1.09 | 0.85 | 0.87 | 0.84 | 1.67 | 0.85 | 1.24 |
| time (sec) |
N/A | 0.034 | 0.092 | 1.177 | 0.199 | 0.293 | 0.128 | 0.291 | 8.726 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 39 | 39 | 35 | 33 | 36 | 34 | 66 | 32 | 68 |
| N.S. |
1 | 1.00 | 0.90 | 0.85 | 0.92 | 0.87 | 1.69 | 0.82 | 1.74 |
| time (sec) |
N/A | 0.010 | 0.102 | 0.495 | 0.205 | 0.305 | 0.098 | 0.279 | 6.488 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | A | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 16 | 16 | 27 | 17 | 16 | 18 | 19 | 16 | 25 |
| N.S. |
1 | 1.00 | 1.69 | 1.06 | 1.00 | 1.12 | 1.19 | 1.00 | 1.56 |
| time (sec) |
N/A | 0.006 | 0.021 | 0.276 | 0.199 | 0.273 | 0.061 | 0.289 | 5.989 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | A | A | B | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 17 | 17 | 43 | 22 | 29 | 38 | 51 | 25 | 85 |
| N.S. |
1 | 1.00 | 2.53 | 1.29 | 1.71 | 2.24 | 3.00 | 1.47 | 5.00 |
| time (sec) |
N/A | 0.015 | 0.033 | 0.613 | 0.219 | 0.319 | 2.589 | 0.288 | 6.294 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | B | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 26 | 26 | 52 | 33 | 40 | 62 | 0 | 58 | 28 |
| N.S. |
1 | 1.00 | 2.00 | 1.27 | 1.54 | 2.38 | 0.00 | 2.23 | 1.08 |
| time (sec) |
N/A | 0.027 | 0.070 | 0.928 | 0.195 | 0.305 | 0.000 | 0.322 | 6.267 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | B | F | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 48 | 48 | 91 | 50 | 60 | 96 | 0 | 86 | 81 |
| N.S. |
1 | 1.00 | 1.90 | 1.04 | 1.25 | 2.00 | 0.00 | 1.79 | 1.69 |
| time (sec) |
N/A | 0.038 | 0.072 | 1.355 | 0.187 | 0.280 | 0.000 | 0.299 | 6.603 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | B | F | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 64 | 64 | 115 | 61 | 73 | 128 | 0 | 114 | 111 |
| N.S. |
1 | 1.00 | 1.80 | 0.95 | 1.14 | 2.00 | 0.00 | 1.78 | 1.73 |
| time (sec) |
N/A | 0.040 | 0.079 | 1.493 | 0.210 | 0.319 | 0.000 | 0.311 | 6.328 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 112 | 112 | 91 | 95 | 94 | 90 | 221 | 102 | 157 |
| N.S. |
1 | 1.00 | 0.81 | 0.85 | 0.84 | 0.80 | 1.97 | 0.91 | 1.40 |
| time (sec) |
N/A | 0.077 | 0.343 | 1.921 | 0.191 | 0.278 | 0.240 | 0.288 | 10.064 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 101 | 101 | 117 | 89 | 84 | 84 | 211 | 82 | 85 |
| N.S. |
1 | 1.00 | 1.16 | 0.88 | 0.83 | 0.83 | 2.09 | 0.81 | 0.84 |
| time (sec) |
N/A | 0.067 | 0.208 | 1.602 | 0.198 | 0.291 | 0.195 | 0.284 | 6.530 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | A | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 71 | 71 | 59 | 64 | 62 | 55 | 107 | 60 | 103 |
| N.S. |
1 | 1.00 | 0.83 | 0.90 | 0.87 | 0.77 | 1.51 | 0.85 | 1.45 |
| time (sec) |
N/A | 0.036 | 0.359 | 1.281 | 0.201 | 0.299 | 0.124 | 0.308 | 9.571 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | A | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 50 | 50 | 46 | 43 | 46 | 45 | 78 | 43 | 44 |
| N.S. |
1 | 1.00 | 0.92 | 0.86 | 0.92 | 0.90 | 1.56 | 0.86 | 0.88 |
| time (sec) |
N/A | 0.011 | 0.149 | 0.460 | 0.196 | 0.293 | 0.091 | 0.305 | 6.938 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | A | A | A | F | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 35 | 35 | 76 | 40 | 44 | 54 | 0 | 49 | 125 |
| N.S. |
1 | 1.00 | 2.17 | 1.14 | 1.26 | 1.54 | 0.00 | 1.40 | 3.57 |
| time (sec) |
N/A | 0.041 | 0.059 | 0.700 | 0.219 | 0.296 | 0.000 | 0.294 | 6.780 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | A | A | B | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 34 | 34 | 76 | 46 | 52 | 77 | 0 | 74 | 105 |
| N.S. |
1 | 1.00 | 2.24 | 1.35 | 1.53 | 2.26 | 0.00 | 2.18 | 3.09 |
| time (sec) |
N/A | 0.047 | 0.481 | 1.072 | 0.199 | 0.317 | 0.000 | 0.306 | 6.248 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | A | A | B | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 59 | 59 | 133 | 73 | 89 | 129 | 0 | 118 | 92 |
| N.S. |
1 | 1.00 | 2.25 | 1.24 | 1.51 | 2.19 | 0.00 | 2.00 | 1.56 |
| time (sec) |
N/A | 0.055 | 0.748 | 1.393 | 0.204 | 0.313 | 0.000 | 0.324 | 6.498 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 82 | 82 | 132 | 76 | 89 | 149 | 0 | 156 | 136 |
| N.S. |
1 | 1.00 | 1.61 | 0.93 | 1.09 | 1.82 | 0.00 | 1.90 | 1.66 |
| time (sec) |
N/A | 0.065 | 0.175 | 1.812 | 0.200 | 0.307 | 0.000 | 0.315 | 6.127 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | A | A | B | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 110 | 110 | 255 | 114 | 147 | 229 | 0 | 217 | 178 |
| N.S. |
1 | 1.00 | 2.32 | 1.04 | 1.34 | 2.08 | 0.00 | 1.97 | 1.62 |
| time (sec) |
N/A | 0.082 | 0.130 | 1.977 | 0.197 | 0.290 | 0.000 | 0.330 | 6.306 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 171 | 193 | 147 | 145 | 145 | 138 | 393 | 150 | 417 |
| N.S. |
1 | 1.13 | 0.86 | 0.85 | 0.85 | 0.81 | 2.30 | 0.88 | 2.44 |
| time (sec) |
N/A | 0.160 | 1.558 | 2.730 | 0.209 | 0.301 | 0.387 | 0.311 | 8.362 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | A | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 160 | 180 | 117 | 124 | 121 | 118 | 284 | 124 | 328 |
| N.S. |
1 | 1.12 | 0.73 | 0.78 | 0.76 | 0.74 | 1.78 | 0.78 | 2.05 |
| time (sec) |
N/A | 0.152 | 1.228 | 1.998 | 0.205 | 0.309 | 0.263 | 0.304 | 7.696 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 121 | 121 | 100 | 104 | 97 | 93 | 233 | 96 | 313 |
| N.S. |
1 | 1.00 | 0.83 | 0.86 | 0.80 | 0.77 | 1.93 | 0.79 | 2.59 |
| time (sec) |
N/A | 0.086 | 0.454 | 1.661 | 0.233 | 0.283 | 0.180 | 0.294 | 7.718 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | A | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 90 | 90 | 71 | 76 | 74 | 71 | 128 | 72 | 127 |
| N.S. |
1 | 1.00 | 0.79 | 0.84 | 0.82 | 0.79 | 1.42 | 0.80 | 1.41 |
| time (sec) |
N/A | 0.047 | 0.215 | 1.067 | 0.208 | 0.290 | 0.130 | 0.295 | 6.716 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 74 | 74 | 81 | 69 | 71 | 79 | 0 | 108 | 259 |
| N.S. |
1 | 1.00 | 1.09 | 0.93 | 0.96 | 1.07 | 0.00 | 1.46 | 3.50 |
| time (sec) |
N/A | 0.083 | 1.148 | 0.686 | 0.201 | 0.353 | 0.000 | 0.323 | 6.475 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 68 | 68 | 87 | 61 | 68 | 99 | 0 | 137 | 194 |
| N.S. |
1 | 1.00 | 1.28 | 0.90 | 1.00 | 1.46 | 0.00 | 2.01 | 2.85 |
| time (sec) |
N/A | 0.093 | 1.056 | 1.132 | 0.204 | 0.301 | 0.000 | 0.334 | 6.551 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | B | F | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 79 | 79 | 152 | 86 | 102 | 155 | 0 | 134 | 234 |
| N.S. |
1 | 1.00 | 1.92 | 1.09 | 1.29 | 1.96 | 0.00 | 1.70 | 2.96 |
| time (sec) |
N/A | 0.099 | 2.221 | 1.276 | 0.202 | 0.326 | 0.000 | 0.323 | 6.638 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | A | A | A | F | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 109 | 109 | 525 | 99 | 118 | 191 | 0 | 190 | 150 |
| N.S. |
1 | 1.00 | 4.82 | 0.91 | 1.08 | 1.75 | 0.00 | 1.74 | 1.38 |
| time (sec) |
N/A | 0.141 | 7.680 | 1.846 | 0.255 | 0.307 | 0.000 | 0.313 | 6.534 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | A | A | A | F(-1) | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 134 | 134 | 322 | 129 | 162 | 238 | 0 | 254 | 203 |
| N.S. |
1 | 1.00 | 2.40 | 0.96 | 1.21 | 1.78 | 0.00 | 1.90 | 1.51 |
| time (sec) |
N/A | 0.150 | 7.766 | 2.648 | 0.202 | 0.311 | 0.000 | 0.337 | 6.674 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | A | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 137 | 137 | 106 | 116 | 113 | 106 | 240 | 108 | 114 |
| N.S. |
1 | 1.00 | 0.77 | 0.85 | 0.82 | 0.77 | 1.75 | 0.79 | 0.83 |
| time (sec) |
N/A | 0.113 | 0.488 | 1.596 | 0.203 | 0.298 | 0.198 | 0.284 | 6.633 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 110 | 110 | 98 | 143 | 0 | 333 | 0 | 149 | 1075 |
| N.S. |
1 | 1.00 | 0.89 | 1.30 | 0.00 | 3.03 | 0.00 | 1.35 | 9.77 |
| time (sec) |
N/A | 0.198 | 0.527 | 0.598 | 0.000 | 0.323 | 0.000 | 0.306 | 6.856 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 82 | 82 | 78 | 112 | 0 | 291 | 0 | 112 | 1004 |
| N.S. |
1 | 1.00 | 0.95 | 1.37 | 0.00 | 3.55 | 0.00 | 1.37 | 12.24 |
| time (sec) |
N/A | 0.125 | 0.218 | 0.474 | 0.000 | 0.308 | 0.000 | 0.295 | 7.251 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 61 | 61 | 56 | 71 | 0 | 231 | 1192 | 77 | 623 |
| N.S. |
1 | 1.00 | 0.92 | 1.16 | 0.00 | 3.79 | 19.54 | 1.26 | 10.21 |
| time (sec) |
N/A | 0.079 | 0.144 | 0.451 | 0.000 | 0.339 | 101.692 | 0.322 | 7.068 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 50 | 50 | 47 | 54 | 0 | 192 | 155 | 58 | 101 |
| N.S. |
1 | 1.00 | 0.94 | 1.08 | 0.00 | 3.84 | 3.10 | 1.16 | 2.02 |
| time (sec) |
N/A | 0.048 | 0.024 | 0.316 | 0.000 | 0.323 | 10.828 | 0.317 | 6.635 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 40 | 40 | 40 | 39 | 0 | 148 | 100 | 48 | 45 |
| N.S. |
1 | 1.00 | 1.00 | 0.98 | 0.00 | 3.70 | 2.50 | 1.20 | 1.12 |
| time (sec) |
N/A | 0.024 | 0.012 | 0.247 | 0.000 | 0.313 | 1.723 | 0.308 | 6.448 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | F | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 53 | 53 | 62 | 53 | 0 | 239 | 0 | 63 | 122 |
| N.S. |
1 | 1.00 | 1.17 | 1.00 | 0.00 | 4.51 | 0.00 | 1.19 | 2.30 |
| time (sec) |
N/A | 0.048 | 0.105 | 0.447 | 0.000 | 0.356 | 0.000 | 0.310 | 6.643 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | B | F | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 62 | 62 | 91 | 77 | 0 | 302 | 0 | 98 | 179 |
| N.S. |
1 | 1.00 | 1.47 | 1.24 | 0.00 | 4.87 | 0.00 | 1.58 | 2.89 |
| time (sec) |
N/A | 0.088 | 0.243 | 0.511 | 0.000 | 0.345 | 0.000 | 0.313 | 6.755 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | B | F | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 84 | 84 | 144 | 112 | 0 | 490 | 0 | 141 | 531 |
| N.S. |
1 | 1.00 | 1.71 | 1.33 | 0.00 | 5.83 | 0.00 | 1.68 | 6.32 |
| time (sec) |
N/A | 0.188 | 0.433 | 0.693 | 0.000 | 0.412 | 0.000 | 0.313 | 6.979 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | B | F | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 112 | 112 | 125 | 156 | 0 | 577 | 0 | 194 | 586 |
| N.S. |
1 | 1.00 | 1.12 | 1.39 | 0.00 | 5.15 | 0.00 | 1.73 | 5.23 |
| time (sec) |
N/A | 0.307 | 1.293 | 0.692 | 0.000 | 0.443 | 0.000 | 0.311 | 6.946 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 169 | 169 | 115 | 183 | 0 | 580 | 0 | 184 | 4368 |
| N.S. |
1 | 1.00 | 0.68 | 1.08 | 0.00 | 3.43 | 0.00 | 1.09 | 25.85 |
| time (sec) |
N/A | 0.270 | 0.841 | 0.805 | 0.000 | 0.538 | 0.000 | 0.310 | 11.962 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 124 | 124 | 94 | 142 | 0 | 483 | 0 | 204 | 2578 |
| N.S. |
1 | 1.00 | 0.76 | 1.15 | 0.00 | 3.90 | 0.00 | 1.65 | 20.79 |
| time (sec) |
N/A | 0.149 | 0.426 | 0.763 | 0.000 | 0.436 | 0.000 | 0.347 | 10.052 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 87 | 87 | 83 | 121 | 0 | 403 | 0 | 124 | 2562 |
| N.S. |
1 | 1.00 | 0.95 | 1.39 | 0.00 | 4.63 | 0.00 | 1.43 | 29.45 |
| time (sec) |
N/A | 0.092 | 0.195 | 0.535 | 0.000 | 0.330 | 0.000 | 0.305 | 9.987 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 66 | 66 | 67 | 99 | 0 | 266 | 0 | 90 | 123 |
| N.S. |
1 | 1.00 | 1.02 | 1.50 | 0.00 | 4.03 | 0.00 | 1.36 | 1.86 |
| time (sec) |
N/A | 0.046 | 0.101 | 0.401 | 0.000 | 0.300 | 0.000 | 0.295 | 6.443 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 65 | 65 | 66 | 98 | 0 | 268 | 1474 | 95 | 148 |
| N.S. |
1 | 1.00 | 1.02 | 1.51 | 0.00 | 4.12 | 22.68 | 1.46 | 2.28 |
| time (sec) |
N/A | 0.039 | 0.073 | 0.409 | 0.000 | 0.322 | 35.754 | 0.310 | 6.712 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | B | F | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 93 | 93 | 99 | 123 | 0 | 511 | 0 | 134 | 1356 |
| N.S. |
1 | 1.00 | 1.06 | 1.32 | 0.00 | 5.49 | 0.00 | 1.44 | 14.58 |
| time (sec) |
N/A | 0.135 | 0.272 | 0.672 | 0.000 | 0.509 | 0.000 | 0.329 | 7.614 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | B | F | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 123 | 123 | 127 | 144 | 0 | 784 | 0 | 234 | 1471 |
| N.S. |
1 | 1.00 | 1.03 | 1.17 | 0.00 | 6.37 | 0.00 | 1.90 | 11.96 |
| time (sec) |
N/A | 0.237 | 0.606 | 0.638 | 0.000 | 0.511 | 0.000 | 0.326 | 7.424 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | B | F | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 168 | 168 | 171 | 181 | 0 | 1174 | 0 | 215 | 1576 |
| N.S. |
1 | 1.00 | 1.02 | 1.08 | 0.00 | 6.99 | 0.00 | 1.28 | 9.38 |
| time (sec) |
N/A | 0.391 | 0.805 | 0.841 | 0.000 | 0.738 | 0.000 | 0.312 | 7.637 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 243 | 243 | 164 | 330 | 0 | 1090 | 0 | 516 | 6640 |
| N.S. |
1 | 1.00 | 0.67 | 1.36 | 0.00 | 4.49 | 0.00 | 2.12 | 27.33 |
| time (sec) |
N/A | 0.451 | 4.081 | 1.447 | 0.000 | 0.404 | 0.000 | 0.306 | 15.547 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 179 | 179 | 144 | 286 | 0 | 945 | 0 | 256 | 5945 |
| N.S. |
1 | 1.00 | 0.80 | 1.60 | 0.00 | 5.28 | 0.00 | 1.43 | 33.21 |
| time (sec) |
N/A | 0.293 | 3.113 | 1.035 | 0.000 | 0.363 | 0.000 | 0.300 | 15.061 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 144 | 144 | 136 | 269 | 0 | 819 | 0 | 234 | 5756 |
| N.S. |
1 | 1.00 | 0.94 | 1.87 | 0.00 | 5.69 | 0.00 | 1.62 | 39.97 |
| time (sec) |
N/A | 0.171 | 0.459 | 0.708 | 0.000 | 0.361 | 0.000 | 0.299 | 14.843 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 118 | 118 | 94 | 213 | 0 | 516 | 0 | 182 | 318 |
| N.S. |
1 | 1.00 | 0.80 | 1.81 | 0.00 | 4.37 | 0.00 | 1.54 | 2.69 |
| time (sec) |
N/A | 0.105 | 0.302 | 0.660 | 0.000 | 0.342 | 0.000 | 0.319 | 6.937 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F(-2) | B | F(-1) | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 103 | 103 | 94 | 221 | 0 | 490 | 0 | 189 | 310 |
| N.S. |
1 | 1.00 | 0.91 | 2.15 | 0.00 | 4.76 | 0.00 | 1.83 | 3.01 |
| time (sec) |
N/A | 0.083 | 0.230 | 0.641 | 0.000 | 0.334 | 0.000 | 0.298 | 6.994 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F(-2) | B | F(-1) | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 102 | 102 | 93 | 248 | 0 | 516 | 0 | 215 | 349 |
| N.S. |
1 | 1.00 | 0.91 | 2.43 | 0.00 | 5.06 | 0.00 | 2.11 | 3.42 |
| time (sec) |
N/A | 0.073 | 0.144 | 0.598 | 0.000 | 0.327 | 0.000 | 0.272 | 6.859 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | B | F | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 145 | 145 | 140 | 270 | 0 | 1027 | 0 | 246 | 2191 |
| N.S. |
1 | 1.00 | 0.97 | 1.86 | 0.00 | 7.08 | 0.00 | 1.70 | 15.11 |
| time (sec) |
N/A | 0.259 | 0.700 | 0.930 | 0.000 | 0.828 | 0.000 | 0.305 | 11.481 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | B | F | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 187 | 187 | 174 | 294 | 0 | 1436 | 0 | 280 | 2295 |
| N.S. |
1 | 1.00 | 0.93 | 1.57 | 0.00 | 7.68 | 0.00 | 1.50 | 12.27 |
| time (sec) |
N/A | 0.435 | 1.126 | 1.057 | 0.000 | 0.960 | 0.000 | 0.326 | 8.699 |