Detailed conclusion table per each integral is given by the table below. The elapsed time is in seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2) if the failure was due to an exception being raised, which could indicate a bug in the system. If the failure was due to integral not being evaluated within the time limit, then it is given as F.
In this table, the column N.S. means normalized size and is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To make the table
fit the page, the name Mathematica was abbreviated to MMA
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | B | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 67 | 67 | 223 | 0 | 0 | 0 | 0 | 0 | 36 | 0 |
| N.S. |
1 | 1.00 | 3.33 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.54 | 0.00 |
| time (sec) |
N/A | 0.283 | 1.051 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.196 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | F | F | F(-1) | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 78 | 78 | 2791 | 0 | 0 | 0 | 0 | 0 | 49 | 0 |
| N.S. |
1 | 1.00 | 35.78 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.63 | 0.00 |
| time (sec) |
N/A | 0.369 | 25.200 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.250 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | F | F | F(-1) | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 78 | 78 | 2800 | 0 | 0 | 0 | 0 | 0 | 53 | 0 |
| N.S. |
1 | 1.00 | 35.90 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.68 | 0.00 |
| time (sec) |
N/A | 0.396 | 20.240 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.251 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 161 | 178 | 110 | 0 | 0 | 0 | 0 | 0 | 25 | 0 |
| N.S. |
1 | 1.11 | 0.68 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.16 | 0.00 |
| time (sec) |
N/A | 0.910 | 0.719 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.208 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 126 | 134 | 95 | 0 | 0 | 0 | 0 | 0 | 25 | 0 |
| N.S. |
1 | 1.06 | 0.75 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.20 | 0.00 |
| time (sec) |
N/A | 0.573 | 0.638 | 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 | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 93 | 93 | 84 | 0 | 0 | 0 | 0 | 0 | 23 | 0 |
| N.S. |
1 | 1.00 | 0.90 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.25 | 0.00 |
| time (sec) |
N/A | 0.377 | 0.290 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.212 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 66 | 66 | 70 | 0 | 0 | 0 | 0 | 0 | 16 | 0 |
| N.S. |
1 | 1.00 | 1.06 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.24 | 0.00 |
| time (sec) |
N/A | 0.261 | 0.068 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.234 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | F | F | F | F(-1) | F | F | F | F(-1) |
| verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 77 | 77 | 0 | 0 | 0 | 0 | 0 | 0 | 23 | 0 |
| N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.30 | 0.00 |
| time (sec) |
N/A | 0.359 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.234 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | F | F | F | F(-1) | F | F | F | F(-1) |
| verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 77 | 77 | 0 | 0 | 0 | 0 | 0 | 0 | 25 | 0 |
| N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.32 | 0.00 |
| time (sec) |
N/A | 0.384 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.172 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 162 | 175 | 116 | 0 | 0 | 0 | 0 | 0 | 45 | 0 |
| N.S. |
1 | 1.08 | 0.72 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.28 | 0.00 |
| time (sec) |
N/A | 0.933 | 0.940 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.186 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 129 | 131 | 108 | 0 | 0 | 0 | 0 | 0 | 45 | 0 |
| N.S. |
1 | 1.02 | 0.84 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.35 | 0.00 |
| time (sec) |
N/A | 0.577 | 0.564 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.169 | 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 | 99 | 99 | 130 | 0 | 0 | 0 | 0 | 0 | 43 | 0 |
| N.S. |
1 | 1.00 | 1.31 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.43 | 0.00 |
| time (sec) |
N/A | 0.389 | 0.400 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.164 | 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 | 69 | 69 | 130 | 0 | 0 | 0 | 0 | 0 | 36 | 0 |
| N.S. |
1 | 1.00 | 1.88 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.52 | 0.00 |
| time (sec) |
N/A | 0.271 | 0.143 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.172 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | F | F | F | F(-1) | F | F | F | F(-1) |
| verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 80 | 80 | 0 | 0 | 0 | 0 | 0 | 0 | 43 | 0 |
| N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.54 | 0.00 |
| time (sec) |
N/A | 0.387 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.166 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | F | F | F | F(-1) | F | F | F | F(-1) |
| verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 80 | 80 | 0 | 0 | 0 | 0 | 0 | 0 | 45 | 0 |
| N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.56 | 0.00 |
| time (sec) |
N/A | 0.409 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.175 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 96 | 96 | 5109 | 0 | 0 | 0 | 0 | 0 | 47 | 0 |
| N.S. |
1 | 1.00 | 53.22 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.49 | 0.00 |
| time (sec) |
N/A | 0.437 | 22.832 | 0.000 | 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 | C | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 43 | 43 | 2262 | 0 | 0 | 0 | 0 | 0 | 20 | 0 |
| N.S. |
1 | 1.00 | 52.60 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.47 | 0.00 |
| time (sec) |
N/A | 0.242 | 13.859 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.161 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | B | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 58 | 58 | 225 | 0 | 0 | 0 | 0 | 0 | 30 | 0 |
| N.S. |
1 | 1.00 | 3.88 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.52 | 0.00 |
| time (sec) |
N/A | 0.280 | 3.841 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.178 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | B | F | F | F | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 60 | 60 | 263 | 0 | 0 | 0 | 0 | 0 | 40 | 0 |
| N.S. |
1 | 1.00 | 4.38 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.67 | 0.00 |
| time (sec) |
N/A | 0.271 | 6.065 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.164 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 106 | 106 | 5111 | 0 | 0 | 0 | 0 | 0 | 51 | 0 |
| N.S. |
1 | 1.00 | 48.22 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.48 | 0.00 |
| time (sec) |
N/A | 0.486 | 7.275 | 0.000 | 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 | C | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 46 | 46 | 183 | 0 | 0 | 0 | 0 | 0 | 23 | 0 |
| N.S. |
1 | 1.00 | 3.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.50 | 0.00 |
| time (sec) |
N/A | 0.254 | 1.009 | 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 | B | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 60 | 60 | 234 | 0 | 0 | 0 | 0 | 0 | 36 | 0 |
| N.S. |
1 | 1.00 | 3.90 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.60 | 0.00 |
| time (sec) |
N/A | 0.368 | 2.745 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.183 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | B | F | F | F | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 65 | 65 | 274 | 0 | 0 | 0 | 0 | 0 | 46 | 0 |
| N.S. |
1 | 1.00 | 4.22 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.71 | 0.00 |
| time (sec) |
N/A | 0.374 | 4.975 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.173 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 121 | 130 | 5129 | 0 | 0 | 0 | 0 | 0 | 51 | 0 |
| N.S. |
1 | 1.07 | 42.39 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.42 | 0.00 |
| time (sec) |
N/A | 0.446 | 6.603 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.178 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 63 | 72 | 2282 | 0 | 0 | 0 | 0 | 0 | 24 | 0 |
| N.S. |
1 | 1.14 | 36.22 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.38 | 0.00 |
| time (sec) |
N/A | 0.238 | 6.348 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.175 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | B | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 78 | 78 | 227 | 0 | 0 | 0 | 0 | 0 | 34 | 0 |
| N.S. |
1 | 1.00 | 2.91 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.44 | 0.00 |
| time (sec) |
N/A | 0.371 | 0.632 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.190 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | B | F | F | F | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 80 | 80 | 265 | 0 | 0 | 0 | 0 | 0 | 44 | 0 |
| N.S. |
1 | 1.00 | 3.31 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.55 | 0.00 |
| time (sec) |
N/A | 0.378 | 1.062 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.181 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 131 | 131 | 5131 | 0 | 0 | 0 | 0 | 0 | 54 | 0 |
| N.S. |
1 | 1.00 | 39.17 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.41 | 0.00 |
| time (sec) |
N/A | 0.523 | 6.810 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.194 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 66 | 66 | 212 | 0 | 0 | 0 | 0 | 0 | 26 | 0 |
| N.S. |
1 | 1.00 | 3.21 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.39 | 0.00 |
| time (sec) |
N/A | 0.275 | 0.841 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.197 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | B | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 80 | 80 | 242 | 0 | 0 | 0 | 0 | 0 | 39 | 0 |
| N.S. |
1 | 1.00 | 3.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.49 | 0.00 |
| time (sec) |
N/A | 0.507 | 1.155 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.200 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | B | F | F | F | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 85 | 85 | 276 | 0 | 0 | 0 | 0 | 0 | 49 | 0 |
| N.S. |
1 | 1.00 | 3.25 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.58 | 0.00 |
| time (sec) |
N/A | 0.521 | 1.603 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.200 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | F | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 71 | 71 | 0 | 0 | 0 | 0 | 0 | 0 | 21 | 0 |
| N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.30 | 0.00 |
| time (sec) |
N/A | 0.265 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.182 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | F | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 68 | 68 | 0 | 0 | 0 | 0 | 0 | 0 | 27 | 0 |
| N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.40 | 0.00 |
| time (sec) |
N/A | 0.267 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.167 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | F | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 91 | 91 | 0 | 0 | 0 | 0 | 0 | 0 | 25 | 0 |
| N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.27 | 0.00 |
| time (sec) |
N/A | 0.363 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.170 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | F | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 90 | 90 | 0 | 0 | 0 | 0 | 0 | 0 | 27 | 0 |
| N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.30 | 0.00 |
| time (sec) |
N/A | 0.374 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.180 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | F | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 87 | 87 | 0 | 0 | 0 | 0 | 0 | 0 | 23 | 0 |
| N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.26 | 0.00 |
| time (sec) |
N/A | 0.355 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.169 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | F | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 85 | 85 | 0 | 0 | 0 | 0 | 0 | 0 | 28 | 0 |
| N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.33 | 0.00 |
| time (sec) |
N/A | 0.372 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.164 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | F | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 107 | 107 | 0 | 0 | 0 | 0 | 0 | 0 | 27 | 0 |
| N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.25 | 0.00 |
| time (sec) |
N/A | 0.475 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.166 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | F | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 107 | 107 | 0 | 0 | 0 | 0 | 0 | 0 | 28 | 0 |
| N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.26 | 0.00 |
| time (sec) |
N/A | 0.485 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.168 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | B | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 294 | 284 | 2746 | 0 | 0 | 0 | 0 | 0 | 23 | 0 |
| N.S. |
1 | 0.97 | 9.34 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.08 | 0.00 |
| time (sec) |
N/A | 1.421 | 30.796 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.175 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | B | F | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 215 | 213 | 2131 | 0 | 0 | 0 | 0 | 0 | 23 | 0 |
| N.S. |
1 | 0.99 | 9.91 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.11 | 0.00 |
| time (sec) |
N/A | 0.945 | 26.917 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.173 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | B | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 156 | 158 | 1732 | 0 | 0 | 0 | 0 | 0 | 23 | 0 |
| N.S. |
1 | 1.01 | 11.10 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.15 | 0.00 |
| time (sec) |
N/A | 0.595 | 24.011 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.161 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 109 | 109 | 95 | 0 | 0 | 0 | 0 | 0 | 21 | 0 |
| N.S. |
1 | 1.00 | 0.87 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.19 | 0.00 |
| time (sec) |
N/A | 0.390 | 0.418 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.174 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 74 | 74 | 70 | 0 | 0 | 0 | 0 | 0 | 14 | 0 |
| N.S. |
1 | 1.00 | 0.95 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.19 | 0.00 |
| time (sec) |
N/A | 0.265 | 0.135 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.173 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | F | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 85 | 85 | 0 | 0 | 0 | 0 | 0 | 0 | 21 | 0 |
| N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.25 | 0.00 |
| time (sec) |
N/A | 0.367 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.172 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | F | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 85 | 85 | 0 | 0 | 0 | 0 | 0 | 0 | 23 | 0 |
| N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.27 | 0.00 |
| time (sec) |
N/A | 0.390 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.176 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 58 | 58 | 46 | 0 | 0 | 0 | 0 | 0 | 12 | 0 |
| N.S. |
1 | 1.00 | 0.79 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.21 | 0.00 |
| time (sec) |
N/A | 0.201 | 0.113 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.162 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 57 | 57 | 49 | 0 | 0 | 0 | 0 | 0 | 14 | 0 |
| N.S. |
1 | 1.00 | 0.86 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.25 | 0.00 |
| time (sec) |
N/A | 0.204 | 0.118 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.170 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 77 | 79 | 76 | 60 | 57 | 60 | 144 | 62 | 72 | 111 |
| N.S. |
1 | 1.03 | 0.99 | 0.78 | 0.74 | 0.78 | 1.87 | 0.81 | 0.94 | 1.44 |
| time (sec) |
N/A | 0.388 | 0.271 | 2.511 | 0.029 | 0.081 | 0.160 | 0.122 | 0.167 | 19.642 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | A | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 55 | 53 | 60 | 47 | 48 | 46 | 92 | 47 | 55 | 68 |
| N.S. |
1 | 0.96 | 1.09 | 0.85 | 0.87 | 0.84 | 1.67 | 0.85 | 1.00 | 1.24 |
| time (sec) |
N/A | 0.311 | 0.150 | 1.431 | 0.033 | 0.085 | 0.114 | 0.125 | 0.170 | 18.201 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 39 | 39 | 35 | 33 | 36 | 34 | 66 | 32 | 37 | 68 |
| N.S. |
1 | 1.00 | 0.90 | 0.85 | 0.92 | 0.87 | 1.69 | 0.82 | 0.95 | 1.74 |
| time (sec) |
N/A | 0.198 | 0.160 | 0.660 | 0.031 | 0.090 | 0.087 | 0.119 | 0.175 | 17.593 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | A | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 16 | 16 | 27 | 17 | 16 | 18 | 19 | 16 | 18 | 25 |
| N.S. |
1 | 1.00 | 1.69 | 1.06 | 1.00 | 1.12 | 1.19 | 1.00 | 1.12 | 1.56 |
| time (sec) |
N/A | 0.155 | 0.029 | 0.251 | 0.037 | 0.084 | 0.054 | 0.121 | 0.159 | 16.491 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | B | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 17 | 17 | 17 | 22 | 29 | 38 | 51 | 25 | 21 | 85 |
| N.S. |
1 | 1.00 | 1.00 | 1.29 | 1.71 | 2.24 | 3.00 | 1.47 | 1.24 | 5.00 |
| time (sec) |
N/A | 0.236 | 0.010 | 0.280 | 0.033 | 0.093 | 2.356 | 0.121 | 0.161 | 16.555 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | B | F | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 26 | 26 | 26 | 33 | 40 | 62 | 0 | 58 | 40 | 28 |
| N.S. |
1 | 1.00 | 1.00 | 1.27 | 1.54 | 2.38 | 0.00 | 2.23 | 1.54 | 1.08 |
| time (sec) |
N/A | 0.292 | 0.093 | 0.527 | 0.029 | 0.159 | 0.000 | 0.125 | 0.175 | 17.278 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | B | F | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 48 | 49 | 91 | 50 | 60 | 96 | 0 | 86 | 58 | 81 |
| N.S. |
1 | 1.02 | 1.90 | 1.04 | 1.25 | 2.00 | 0.00 | 1.79 | 1.21 | 1.69 |
| time (sec) |
N/A | 0.376 | 0.138 | 0.768 | 0.028 | 0.085 | 0.000 | 0.132 | 0.163 | 17.021 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | B | F | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 64 | 62 | 115 | 61 | 73 | 128 | 0 | 114 | 76 | 111 |
| N.S. |
1 | 0.97 | 1.80 | 0.95 | 1.14 | 2.00 | 0.00 | 1.78 | 1.19 | 1.73 |
| time (sec) |
N/A | 0.397 | 0.123 | 0.764 | 0.034 | 0.086 | 0.000 | 0.129 | 0.173 | 17.118 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 112 | 112 | 91 | 95 | 94 | 90 | 221 | 102 | 135 | 157 |
| N.S. |
1 | 1.00 | 0.81 | 0.85 | 0.84 | 0.80 | 1.97 | 0.91 | 1.21 | 1.40 |
| time (sec) |
N/A | 0.508 | 0.595 | 8.162 | 0.029 | 0.087 | 0.238 | 0.128 | 0.176 | 19.401 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 101 | 91 | 117 | 89 | 84 | 84 | 211 | 82 | 105 | 85 |
| N.S. |
1 | 0.90 | 1.16 | 0.88 | 0.83 | 0.83 | 2.09 | 0.81 | 1.04 | 0.84 |
| time (sec) |
N/A | 0.451 | 0.410 | 3.803 | 0.032 | 0.100 | 0.179 | 0.130 | 0.163 | 16.761 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | A | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 71 | 77 | 59 | 64 | 62 | 55 | 107 | 60 | 79 | 103 |
| N.S. |
1 | 1.08 | 0.83 | 0.90 | 0.87 | 0.77 | 1.51 | 0.85 | 1.11 | 1.45 |
| time (sec) |
N/A | 0.305 | 0.548 | 1.858 | 0.032 | 0.088 | 0.118 | 0.119 | 0.168 | 18.485 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | A | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 50 | 50 | 46 | 43 | 46 | 45 | 78 | 43 | 50 | 44 |
| N.S. |
1 | 1.00 | 0.92 | 0.86 | 0.92 | 0.90 | 1.56 | 0.86 | 1.00 | 0.88 |
| time (sec) |
N/A | 0.202 | 0.230 | 0.717 | 0.026 | 0.091 | 0.094 | 0.120 | 0.161 | 16.541 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | F | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 35 | 35 | 48 | 40 | 44 | 54 | 0 | 49 | 44 | 125 |
| N.S. |
1 | 1.00 | 1.37 | 1.14 | 1.26 | 1.54 | 0.00 | 1.40 | 1.26 | 3.57 |
| time (sec) |
N/A | 0.338 | 0.041 | 0.339 | 0.032 | 0.091 | 0.000 | 0.131 | 0.163 | 16.865 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | B | A | A | B | F | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 34 | 34 | 76 | 46 | 52 | 77 | 0 | 74 | 56 | 105 |
| N.S. |
1 | 1.00 | 2.24 | 1.35 | 1.53 | 2.26 | 0.00 | 2.18 | 1.65 | 3.09 |
| time (sec) |
N/A | 0.329 | 0.791 | 0.527 | 0.032 | 0.088 | 0.000 | 0.135 | 0.179 | 17.257 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | B | A | A | B | F | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 59 | 59 | 133 | 73 | 89 | 129 | 0 | 118 | 86 | 92 |
| N.S. |
1 | 1.00 | 2.25 | 1.24 | 1.51 | 2.19 | 0.00 | 2.00 | 1.46 | 1.56 |
| time (sec) |
N/A | 0.428 | 1.245 | 0.774 | 0.037 | 0.087 | 0.000 | 0.141 | 0.162 | 16.517 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | F | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 82 | 87 | 132 | 76 | 89 | 149 | 0 | 156 | 101 | 136 |
| N.S. |
1 | 1.06 | 1.61 | 0.93 | 1.09 | 1.82 | 0.00 | 1.90 | 1.23 | 1.66 |
| time (sec) |
N/A | 0.531 | 0.295 | 0.993 | 0.034 | 0.098 | 0.000 | 0.134 | 0.166 | 16.708 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | B | A | A | B | F | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 110 | 100 | 255 | 114 | 147 | 229 | 0 | 217 | 143 | 178 |
| N.S. |
1 | 0.91 | 2.32 | 1.04 | 1.34 | 2.08 | 0.00 | 1.97 | 1.30 | 1.62 |
| time (sec) |
N/A | 0.558 | 0.207 | 1.064 | 0.036 | 0.088 | 0.000 | 0.147 | 0.166 | 17.098 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 171 | 171 | 147 | 145 | 145 | 138 | 393 | 150 | 207 | 417 |
| N.S. |
1 | 1.00 | 0.86 | 0.85 | 0.85 | 0.81 | 2.30 | 0.88 | 1.21 | 2.44 |
| time (sec) |
N/A | 0.850 | 2.645 | 44.801 | 0.037 | 0.092 | 0.373 | 0.141 | 0.165 | 18.345 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | A | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 160 | 189 | 117 | 124 | 121 | 118 | 284 | 124 | 168 | 328 |
| N.S. |
1 | 1.18 | 0.73 | 0.78 | 0.76 | 0.74 | 1.78 | 0.78 | 1.05 | 2.05 |
| time (sec) |
N/A | 0.689 | 1.988 | 15.904 | 0.035 | 0.086 | 0.267 | 0.133 | 0.177 | 18.123 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 121 | 129 | 100 | 104 | 97 | 93 | 233 | 96 | 129 | 313 |
| N.S. |
1 | 1.07 | 0.83 | 0.86 | 0.80 | 0.77 | 1.93 | 0.79 | 1.07 | 2.59 |
| time (sec) |
N/A | 0.458 | 0.884 | 6.001 | 0.035 | 0.087 | 0.176 | 0.131 | 0.162 | 17.212 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | A | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 90 | 93 | 71 | 76 | 74 | 71 | 128 | 72 | 92 | 127 |
| N.S. |
1 | 1.03 | 0.79 | 0.84 | 0.82 | 0.79 | 1.42 | 0.80 | 1.02 | 1.41 |
| time (sec) |
N/A | 0.330 | 0.356 | 176.177 | 0.027 | 0.087 | 0.122 | 0.119 | 0.162 | 16.817 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | F | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 74 | 74 | 68 | 69 | 71 | 79 | 0 | 108 | 82 | 259 |
| N.S. |
1 | 1.00 | 0.92 | 0.93 | 0.96 | 1.07 | 0.00 | 1.46 | 1.11 | 3.50 |
| time (sec) |
N/A | 0.528 | 0.032 | 0.461 | 0.037 | 0.094 | 0.000 | 0.138 | 0.163 | 17.191 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | F | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 68 | 70 | 87 | 61 | 68 | 99 | 0 | 137 | 87 | 194 |
| N.S. |
1 | 1.03 | 1.28 | 0.90 | 1.00 | 1.46 | 0.00 | 2.01 | 1.28 | 2.85 |
| time (sec) |
N/A | 0.522 | 1.969 | 0.638 | 0.035 | 0.091 | 0.000 | 0.138 | 0.163 | 17.283 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | B | F | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 79 | 81 | 152 | 86 | 102 | 155 | 0 | 134 | 104 | 234 |
| N.S. |
1 | 1.03 | 1.92 | 1.09 | 1.29 | 1.96 | 0.00 | 1.70 | 1.32 | 2.96 |
| time (sec) |
N/A | 0.534 | 3.911 | 0.839 | 0.035 | 0.093 | 0.000 | 0.122 | 0.170 | 17.205 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | B | A | A | A | F | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 109 | 115 | 525 | 99 | 118 | 191 | 0 | 190 | 129 | 150 |
| N.S. |
1 | 1.06 | 4.82 | 0.91 | 1.08 | 1.75 | 0.00 | 1.74 | 1.18 | 1.38 |
| time (sec) |
N/A | 0.695 | 8.937 | 1.095 | 0.037 | 0.106 | 0.000 | 0.144 | 0.179 | 17.200 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | B | A | A | A | F(-1) | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 134 | 130 | 322 | 129 | 162 | 238 | 0 | 254 | 168 | 203 |
| N.S. |
1 | 0.97 | 2.40 | 0.96 | 1.21 | 1.78 | 0.00 | 1.90 | 1.25 | 1.51 |
| time (sec) |
N/A | 0.821 | 9.048 | 1.346 | 0.036 | 0.090 | 0.000 | 0.156 | 0.163 | 17.325 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | A | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 137 | 145 | 106 | 116 | 113 | 106 | 240 | 108 | 142 | 114 |
| N.S. |
1 | 1.06 | 0.77 | 0.85 | 0.82 | 0.77 | 1.75 | 0.79 | 1.04 | 0.83 |
| time (sec) |
N/A | 0.479 | 0.871 | 12.488 | 0.032 | 0.090 | 0.211 | 0.123 | 0.170 | 17.456 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 110 | 133 | 98 | 143 | 0 | 333 | 0 | 149 | 167 | 1075 |
| N.S. |
1 | 1.21 | 0.89 | 1.30 | 0.00 | 3.03 | 0.00 | 1.35 | 1.52 | 9.77 |
| time (sec) |
N/A | 0.743 | 0.827 | 0.589 | 0.000 | 0.106 | 0.000 | 0.132 | 0.168 | 17.428 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 82 | 99 | 78 | 112 | 0 | 291 | 0 | 112 | 111 | 1004 |
| N.S. |
1 | 1.21 | 0.95 | 1.37 | 0.00 | 3.55 | 0.00 | 1.37 | 1.35 | 12.24 |
| time (sec) |
N/A | 0.512 | 0.332 | 0.399 | 0.000 | 0.107 | 0.000 | 0.126 | 0.166 | 17.629 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 61 | 70 | 56 | 71 | 0 | 231 | 1192 | 77 | 79 | 623 |
| N.S. |
1 | 1.15 | 0.92 | 1.16 | 0.00 | 3.79 | 19.54 | 1.26 | 1.30 | 10.21 |
| time (sec) |
N/A | 0.369 | 0.199 | 0.276 | 0.000 | 0.104 | 100.475 | 0.120 | 0.177 | 17.234 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 50 | 56 | 47 | 54 | 0 | 192 | 155 | 58 | 62 | 101 |
| N.S. |
1 | 1.12 | 0.94 | 1.08 | 0.00 | 3.84 | 3.10 | 1.16 | 1.24 | 2.02 |
| time (sec) |
N/A | 0.276 | 0.060 | 0.178 | 0.000 | 0.097 | 10.299 | 0.129 | 0.169 | 17.433 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 40 | 46 | 40 | 39 | 0 | 148 | 100 | 48 | 45 | 45 |
| N.S. |
1 | 1.15 | 1.00 | 0.98 | 0.00 | 3.70 | 2.50 | 1.20 | 1.12 | 1.12 |
| time (sec) |
N/A | 0.214 | 0.030 | 0.122 | 0.000 | 0.100 | 1.657 | 0.124 | 0.166 | 17.106 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | F | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 53 | 59 | 62 | 53 | 0 | 239 | 0 | 63 | 70 | 122 |
| N.S. |
1 | 1.11 | 1.17 | 1.00 | 0.00 | 4.51 | 0.00 | 1.19 | 1.32 | 2.30 |
| time (sec) |
N/A | 0.336 | 0.187 | 0.274 | 0.000 | 0.126 | 0.000 | 0.129 | 0.182 | 17.173 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F(-2) | B | F | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 62 | 73 | 91 | 77 | 0 | 302 | 0 | 98 | 97 | 179 |
| N.S. |
1 | 1.18 | 1.47 | 1.24 | 0.00 | 4.87 | 0.00 | 1.58 | 1.56 | 2.89 |
| time (sec) |
N/A | 0.439 | 0.444 | 0.315 | 0.000 | 0.122 | 0.000 | 0.126 | 0.162 | 17.460 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F(-2) | B | F | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 84 | 103 | 144 | 112 | 0 | 490 | 0 | 141 | 141 | 531 |
| N.S. |
1 | 1.23 | 1.71 | 1.33 | 0.00 | 5.83 | 0.00 | 1.68 | 1.68 | 6.32 |
| time (sec) |
N/A | 0.707 | 0.731 | 0.408 | 0.000 | 0.193 | 0.000 | 0.134 | 0.177 | 17.267 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F(-2) | B | F | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 112 | 136 | 125 | 156 | 0 | 577 | 0 | 194 | 184 | 586 |
| N.S. |
1 | 1.21 | 1.12 | 1.39 | 0.00 | 5.15 | 0.00 | 1.73 | 1.64 | 5.23 |
| time (sec) |
N/A | 0.985 | 2.055 | 0.487 | 0.000 | 0.199 | 0.000 | 0.137 | 0.177 | 17.313 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 169 | 188 | 115 | 183 | 0 | 580 | 0 | 184 | 426 | 4368 |
| N.S. |
1 | 1.11 | 0.68 | 1.08 | 0.00 | 3.43 | 0.00 | 1.09 | 2.52 | 25.85 |
| time (sec) |
N/A | 0.966 | 1.318 | 0.796 | 0.000 | 0.126 | 0.000 | 0.125 | 0.175 | 20.705 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 124 | 149 | 94 | 142 | 0 | 483 | 0 | 204 | 365 | 2578 |
| N.S. |
1 | 1.20 | 0.76 | 1.15 | 0.00 | 3.90 | 0.00 | 1.65 | 2.94 | 20.79 |
| time (sec) |
N/A | 0.685 | 0.767 | 0.604 | 0.000 | 0.120 | 0.000 | 0.134 | 0.169 | 19.109 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 87 | 118 | 83 | 121 | 0 | 403 | 0 | 124 | 267 | 2562 |
| N.S. |
1 | 1.36 | 0.95 | 1.39 | 0.00 | 4.63 | 0.00 | 1.43 | 3.07 | 29.45 |
| time (sec) |
N/A | 0.502 | 0.294 | 0.337 | 0.000 | 0.169 | 0.000 | 0.135 | 0.166 | 19.046 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 66 | 72 | 67 | 99 | 0 | 266 | 0 | 90 | 133 | 123 |
| N.S. |
1 | 1.09 | 1.02 | 1.50 | 0.00 | 4.03 | 0.00 | 1.36 | 2.02 | 1.86 |
| time (sec) |
N/A | 0.328 | 0.161 | 0.282 | 0.000 | 0.103 | 0.000 | 0.127 | 0.175 | 16.444 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 65 | 71 | 66 | 98 | 0 | 268 | 1474 | 95 | 133 | 148 |
| N.S. |
1 | 1.09 | 1.02 | 1.51 | 0.00 | 4.12 | 22.68 | 1.46 | 2.05 | 2.28 |
| time (sec) |
N/A | 0.314 | 0.114 | 0.213 | 0.000 | 0.098 | 37.350 | 0.130 | 0.177 | 16.916 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F(-2) | B | F | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 93 | 124 | 99 | 123 | 0 | 511 | 0 | 134 | 291 | 1356 |
| N.S. |
1 | 1.33 | 1.06 | 1.32 | 0.00 | 5.49 | 0.00 | 1.44 | 3.13 | 14.58 |
| time (sec) |
N/A | 0.624 | 0.411 | 0.453 | 0.000 | 0.271 | 0.000 | 0.131 | 0.172 | 17.683 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F(-2) | B | F | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 123 | 149 | 127 | 144 | 0 | 784 | 0 | 234 | 366 | 1471 |
| N.S. |
1 | 1.21 | 1.03 | 1.17 | 0.00 | 6.37 | 0.00 | 1.90 | 2.98 | 11.96 |
| time (sec) |
N/A | 0.888 | 1.042 | 0.524 | 0.000 | 0.271 | 0.000 | 0.135 | 0.171 | 17.563 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F(-2) | B | F | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 168 | 187 | 171 | 181 | 0 | 1174 | 0 | 215 | 448 | 1576 |
| N.S. |
1 | 1.11 | 1.02 | 1.08 | 0.00 | 6.99 | 0.00 | 1.28 | 2.67 | 9.38 |
| time (sec) |
N/A | 1.281 | 1.271 | 0.609 | 0.000 | 0.485 | 0.000 | 0.138 | 0.173 | 17.271 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 243 | 274 | 164 | 330 | 0 | 1090 | 0 | 516 | 953 | 6640 |
| N.S. |
1 | 1.13 | 0.67 | 1.36 | 0.00 | 4.49 | 0.00 | 2.12 | 3.92 | 27.33 |
| time (sec) |
N/A | 1.527 | 5.943 | 1.455 | 0.000 | 0.159 | 0.000 | 0.138 | 0.193 | 22.663 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 179 | 221 | 144 | 286 | 0 | 945 | 0 | 256 | 864 | 5945 |
| N.S. |
1 | 1.23 | 0.80 | 1.60 | 0.00 | 5.28 | 0.00 | 1.43 | 4.83 | 33.21 |
| time (sec) |
N/A | 1.116 | 5.061 | 1.005 | 0.000 | 0.160 | 0.000 | 0.135 | 0.186 | 22.144 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 144 | 196 | 136 | 269 | 0 | 819 | 0 | 234 | 759 | 5756 |
| N.S. |
1 | 1.36 | 0.94 | 1.87 | 0.00 | 5.69 | 0.00 | 1.62 | 5.27 | 39.97 |
| time (sec) |
N/A | 0.780 | 0.819 | 0.623 | 0.000 | 0.157 | 0.000 | 0.128 | 0.182 | 21.957 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 118 | 140 | 94 | 213 | 0 | 516 | 0 | 182 | 493 | 318 |
| N.S. |
1 | 1.19 | 0.80 | 1.81 | 0.00 | 4.37 | 0.00 | 1.54 | 4.18 | 2.69 |
| time (sec) |
N/A | 0.529 | 0.467 | 0.548 | 0.000 | 0.108 | 0.000 | 0.126 | 0.180 | 16.945 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F(-2) | B | F(-1) | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 103 | 122 | 94 | 221 | 0 | 490 | 0 | 189 | 379 | 310 |
| N.S. |
1 | 1.18 | 0.91 | 2.15 | 0.00 | 4.76 | 0.00 | 1.83 | 3.68 | 3.01 |
| time (sec) |
N/A | 0.475 | 0.356 | 0.490 | 0.000 | 0.102 | 0.000 | 0.136 | 0.194 | 16.896 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F(-2) | B | F(-1) | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 102 | 123 | 93 | 248 | 0 | 516 | 0 | 215 | 457 | 349 |
| N.S. |
1 | 1.21 | 0.91 | 2.43 | 0.00 | 5.06 | 0.00 | 2.11 | 4.48 | 3.42 |
| time (sec) |
N/A | 0.486 | 0.309 | 0.422 | 0.000 | 0.104 | 0.000 | 0.123 | 0.215 | 17.080 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F(-2) | B | F | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 145 | 195 | 140 | 270 | 0 | 1027 | 0 | 246 | 806 | 2191 |
| N.S. |
1 | 1.34 | 0.97 | 1.86 | 0.00 | 7.08 | 0.00 | 1.70 | 5.56 | 15.11 |
| time (sec) |
N/A | 0.967 | 1.127 | 0.721 | 0.000 | 0.605 | 0.000 | 0.141 | 0.203 | 19.569 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F(-2) | B | F | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 187 | 230 | 174 | 294 | 0 | 1436 | 0 | 280 | 999 | 2295 |
| N.S. |
1 | 1.23 | 0.93 | 1.57 | 0.00 | 7.68 | 0.00 | 1.50 | 5.34 | 12.27 |
| time (sec) |
N/A | 1.410 | 1.903 | 0.816 | 0.000 | 0.579 | 0.000 | 0.143 | 0.210 | 18.060 |