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 | A | F | F | F(-2) | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 107 | 120 | 93 | 0 | 0 | 0 | 0 | 0 | 25 | 0 |
| N.S. |
1 | 1.12 | 0.87 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.23 | 0.00 |
| time (sec) |
N/A | 0.542 | 0.392 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.239 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F(-2) | F(-1) | F(-2) | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 121 | 134 | 103 | 0 | 0 | 0 | 0 | 0 | 25 | 0 |
| N.S. |
1 | 1.11 | 0.85 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.21 | 0.00 |
| time (sec) |
N/A | 0.531 | 0.335 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.222 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | F | F | F(-2) | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 98 | 106 | 143 | 0 | 0 | 0 | 0 | 0 | 23 | 0 |
| N.S. |
1 | 1.08 | 1.46 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.23 | 0.00 |
| time (sec) |
N/A | 0.430 | 3.730 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.230 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F(-2) | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 98 | 106 | 77 | 0 | 0 | 0 | 0 | 0 | 17 | 0 |
| N.S. |
1 | 1.08 | 0.79 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.17 | 0.00 |
| time (sec) |
N/A | 0.426 | 0.255 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.248 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F | F(-2) | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 71 | 71 | 115 | 229 | 0 | 0 | 0 | 0 | 25 | 0 |
| N.S. |
1 | 1.00 | 1.62 | 3.23 | 0.00 | 0.00 | 0.00 | 0.00 | 0.35 | 0.00 |
| time (sec) |
N/A | 0.329 | 1.608 | 0.656 | 0.000 | 0.000 | 0.000 | 0.000 | 0.231 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F(-2) | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 71 | 71 | 56 | 0 | 0 | 0 | 0 | 0 | 49 | 0 |
| N.S. |
1 | 1.00 | 0.79 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.69 | 0.00 |
| time (sec) |
N/A | 0.329 | 0.254 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.236 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F(-2) | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 98 | 102 | 66 | 0 | 0 | 0 | 0 | 0 | 51 | 0 |
| N.S. |
1 | 1.04 | 0.67 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.52 | 0.00 |
| time (sec) |
N/A | 0.400 | 0.280 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.243 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F(-2) | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 98 | 106 | 67 | 0 | 0 | 0 | 0 | 0 | 51 | 0 |
| N.S. |
1 | 1.08 | 0.68 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.52 | 0.00 |
| time (sec) |
N/A | 0.510 | 0.322 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.232 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F(-2) | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 121 | 130 | 89 | 0 | 0 | 0 | 0 | 0 | 51 | 0 |
| N.S. |
1 | 1.07 | 0.74 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.42 | 0.00 |
| time (sec) |
N/A | 0.822 | 0.321 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.235 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F(-2) | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 121 | 130 | 83 | 0 | 0 | 0 | 0 | 0 | 25 | 0 |
| N.S. |
1 | 1.07 | 0.69 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.21 | 0.00 |
| time (sec) |
N/A | 0.951 | 0.516 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.210 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F(-2) | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 98 | 106 | 75 | 0 | 0 | 0 | 0 | 0 | 25 | 0 |
| N.S. |
1 | 1.08 | 0.77 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.26 | 0.00 |
| time (sec) |
N/A | 0.554 | 0.338 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.218 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F(-2) | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 98 | 102 | 70 | 0 | 0 | 0 | 0 | 0 | 25 | 0 |
| N.S. |
1 | 1.04 | 0.71 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.26 | 0.00 |
| time (sec) |
N/A | 0.439 | 0.272 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.221 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F(-2) | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 71 | 71 | 56 | 0 | 0 | 0 | 0 | 0 | 23 | 0 |
| N.S. |
1 | 1.00 | 0.79 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.32 | 0.00 |
| time (sec) |
N/A | 0.338 | 0.222 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.225 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F | F(-2) | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 71 | 71 | 100 | 229 | 0 | 0 | 0 | 0 | 17 | 0 |
| N.S. |
1 | 1.00 | 1.41 | 3.23 | 0.00 | 0.00 | 0.00 | 0.00 | 0.24 | 0.00 |
| time (sec) |
N/A | 0.335 | 0.848 | 0.673 | 0.000 | 0.000 | 0.000 | 0.000 | 0.217 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F(-2) | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 98 | 106 | 67 | 0 | 0 | 0 | 0 | 0 | 25 | 0 |
| N.S. |
1 | 1.08 | 0.68 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.26 | 0.00 |
| time (sec) |
N/A | 0.446 | 0.435 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.220 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | F | F | F(-2) | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 98 | 106 | 111 | 0 | 0 | 0 | 0 | 0 | 25 | 0 |
| N.S. |
1 | 1.08 | 1.13 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.26 | 0.00 |
| time (sec) |
N/A | 0.438 | 3.039 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.221 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F(-2) | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 121 | 134 | 103 | 0 | 0 | 0 | 0 | 0 | 25 | 0 |
| N.S. |
1 | 1.11 | 0.85 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.21 | 0.00 |
| time (sec) |
N/A | 0.543 | 0.457 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.227 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | B | B | F | F | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 13 | 13 | 13 | 42 | 35 | 53 | 0 | 0 | 9 | 35 |
| N.S. |
1 | 1.00 | 1.00 | 3.23 | 2.69 | 4.08 | 0.00 | 0.00 | 0.69 | 2.69 |
| time (sec) |
N/A | 0.345 | 0.084 | 1.033 | 0.147 | 0.080 | 0.000 | 0.000 | 0.221 | 0.928 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | C | A | F | B | B | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 31 | 84 | 23 | 0 | 69 | 95 | 0 | 0 | 39 | 0 |
| N.S. |
1 | 2.71 | 0.74 | 0.00 | 2.23 | 3.06 | 0.00 | 0.00 | 1.26 | 0.00 |
| time (sec) |
N/A | 0.620 | 0.093 | 0.000 | 0.140 | 0.092 | 0.000 | 0.000 | 0.241 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | C | A | F | B | B | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 50 | 114 | 29 | 0 | 103 | 253 | 0 | 0 | 17 | 0 |
| N.S. |
1 | 2.28 | 0.58 | 0.00 | 2.06 | 5.06 | 0.00 | 0.00 | 0.34 | 0.00 |
| time (sec) |
N/A | 0.948 | 0.133 | 0.000 | 0.152 | 0.128 | 0.000 | 0.000 | 0.225 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | B | B | B | B | F | F | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 13 | 13 | 35 | 42 | 54 | 55 | 0 | 0 | 9 | 23 |
| N.S. |
1 | 1.00 | 2.69 | 3.23 | 4.15 | 4.23 | 0.00 | 0.00 | 0.69 | 1.77 |
| time (sec) |
N/A | 0.642 | 0.095 | 1.062 | 0.155 | 0.084 | 0.000 | 0.000 | 0.213 | 0.858 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | C | A | F | B | B | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 31 | 74 | 21 | 0 | 109 | 97 | 0 | 0 | 13 | 0 |
| N.S. |
1 | 2.39 | 0.68 | 0.00 | 3.52 | 3.13 | 0.00 | 0.00 | 0.42 | 0.00 |
| time (sec) |
N/A | 0.668 | 0.078 | 0.000 | 0.162 | 0.082 | 0.000 | 0.000 | 0.233 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | C | A | F | B | B | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 50 | 99 | 44 | 0 | 163 | 259 | 0 | 0 | 17 | 0 |
| N.S. |
1 | 1.98 | 0.88 | 0.00 | 3.26 | 5.18 | 0.00 | 0.00 | 0.34 | 0.00 |
| time (sec) |
N/A | 0.597 | 0.277 | 0.000 | 0.155 | 0.094 | 0.000 | 0.000 | 0.229 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | B | B | C | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 52 | 52 | 60 | 50 | 122 | 167 | 585 | 87 | 141 | 178 |
| N.S. |
1 | 1.00 | 1.15 | 0.96 | 2.35 | 3.21 | 11.25 | 1.67 | 2.71 | 3.42 |
| time (sec) |
N/A | 0.360 | 0.151 | 1.017 | 0.124 | 0.121 | 16.342 | 0.135 | 0.229 | 1.185 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | B | B | C | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 53 | 53 | 62 | 52 | 119 | 174 | 586 | 88 | 143 | 177 |
| N.S. |
1 | 1.00 | 1.17 | 0.98 | 2.25 | 3.28 | 11.06 | 1.66 | 2.70 | 3.34 |
| time (sec) |
N/A | 0.374 | 0.220 | 1.088 | 0.113 | 0.106 | 16.232 | 0.135 | 0.220 | 1.108 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F(-2) | B | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 57 | 57 | 56 | 104 | 0 | 289 | 840 | 60 | 139 | 198 |
| N.S. |
1 | 1.00 | 0.98 | 1.82 | 0.00 | 5.07 | 14.74 | 1.05 | 2.44 | 3.47 |
| time (sec) |
N/A | 0.369 | 0.086 | 0.642 | 0.000 | 0.109 | 13.452 | 0.126 | 0.230 | 1.180 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F(-2) | B | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 59 | 59 | 56 | 109 | 0 | 299 | 840 | 62 | 143 | 199 |
| N.S. |
1 | 1.00 | 0.95 | 1.85 | 0.00 | 5.07 | 14.24 | 1.05 | 2.42 | 3.37 |
| time (sec) |
N/A | 0.357 | 0.118 | 0.649 | 0.000 | 0.112 | 12.908 | 0.131 | 0.227 | 0.354 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | B | B | F(-1) | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 25 | 25 | 25 | 58 | 62 | 134 | 0 | 96 | 110 | 103 |
| N.S. |
1 | 1.00 | 1.00 | 2.32 | 2.48 | 5.36 | 0.00 | 3.84 | 4.40 | 4.12 |
| time (sec) |
N/A | 0.289 | 0.286 | 1.044 | 0.236 | 0.108 | 0.000 | 0.141 | 0.217 | 0.928 |
| 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 | 25 | 25 | 25 | 55 | 0 | 129 | 0 | 100 | 103 | 105 |
| N.S. |
1 | 1.00 | 1.00 | 2.20 | 0.00 | 5.16 | 0.00 | 4.00 | 4.12 | 4.20 |
| time (sec) |
N/A | 0.285 | 0.111 | 1.004 | 0.000 | 0.093 | 0.000 | 0.143 | 0.217 | 0.903 |
| 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 | 62 | 62 | 63 | 59 | 0 | 249 | 0 | 53 | 105 | 636 |
| N.S. |
1 | 1.00 | 1.02 | 0.95 | 0.00 | 4.02 | 0.00 | 0.85 | 1.69 | 10.26 |
| time (sec) |
N/A | 0.477 | 0.187 | 0.753 | 0.000 | 0.339 | 0.000 | 0.125 | 0.230 | 6.450 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | C | A | A | B | B | F | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 58 | 71 | 77 | 58 | 141 | 172 | 0 | 90 | 130 | 539 |
| N.S. |
1 | 1.22 | 1.33 | 1.00 | 2.43 | 2.97 | 0.00 | 1.55 | 2.24 | 9.29 |
| time (sec) |
N/A | 0.568 | 1.107 | 1.096 | 0.126 | 0.308 | 0.000 | 0.140 | 0.218 | 2.913 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | B | B | B | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 19 | 19 | 24 | 39 | 64 | 70 | 238 | 41 | 56 | 56 |
| N.S. |
1 | 1.00 | 1.26 | 2.05 | 3.37 | 3.68 | 12.53 | 2.16 | 2.95 | 2.95 |
| time (sec) |
N/A | 0.378 | 0.043 | 0.484 | 0.121 | 0.104 | 3.035 | 0.131 | 0.222 | 0.891 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | B | A | A | B | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 8 | 8 | 17 | 15 | 14 | 17 | 41 | 14 | 29 | 14 |
| N.S. |
1 | 1.00 | 2.12 | 1.88 | 1.75 | 2.12 | 5.12 | 1.75 | 3.62 | 1.75 |
| time (sec) |
N/A | 0.518 | 0.022 | 0.503 | 0.039 | 0.078 | 0.416 | 0.140 | 0.233 | 0.049 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | A | B | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 8 | 8 | 18 | 13 | 14 | 17 | 12 | 14 | 27 | 14 |
| N.S. |
1 | 1.00 | 2.25 | 1.62 | 1.75 | 2.12 | 1.50 | 1.75 | 3.38 | 1.75 |
| time (sec) |
N/A | 0.517 | 0.033 | 0.501 | 0.030 | 0.102 | 0.311 | 0.124 | 0.214 | 0.810 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | B | B | B | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 19 | 19 | 24 | 39 | 102 | 70 | 61 | 38 | 51 | 56 |
| N.S. |
1 | 1.00 | 1.26 | 2.05 | 5.37 | 3.68 | 3.21 | 2.00 | 2.68 | 2.95 |
| time (sec) |
N/A | 0.442 | 0.055 | 1.009 | 0.136 | 0.096 | 0.886 | 0.128 | 0.224 | 0.119 |
| 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 | 74 | 79 | 127 | 84 | 0 | 598 | 0 | 71 | 266 | 704 |
| N.S. |
1 | 1.07 | 1.72 | 1.14 | 0.00 | 8.08 | 0.00 | 0.96 | 3.59 | 9.51 |
| time (sec) |
N/A | 0.875 | 0.592 | 0.829 | 0.000 | 0.355 | 0.000 | 0.128 | 0.229 | 6.603 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | C | A | A | B | B | F | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 69 | 87 | 106 | 86 | 158 | 401 | 0 | 109 | 333 | 613 |
| N.S. |
1 | 1.26 | 1.54 | 1.25 | 2.29 | 5.81 | 0.00 | 1.58 | 4.83 | 8.88 |
| time (sec) |
N/A | 0.694 | 1.593 | 1.108 | 0.119 | 0.326 | 0.000 | 0.132 | 0.211 | 3.179 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | B | B | F | B | F | F | F | F(-1) |
| verified |
N/A | N/A | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 263 | 0 | 1100 | 856 | 0 | 553 | 0 | 0 | 81 | 0 |
| N.S. |
1 | 0.00 | 4.18 | 3.25 | 0.00 | 2.10 | 0.00 | 0.00 | 0.31 | 0.00 |
| time (sec) |
N/A | 0.000 | 0.713 | 79.290 | 0.000 | 0.133 | 0.000 | 0.000 | 0.228 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | C | A | F | F | F | F | F | F | F(-1) |
| verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 91 | 164 | 96 | 0 | 0 | 0 | 0 | 0 | 362 | 0 |
| N.S. |
1 | 1.80 | 1.05 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 3.98 | 0.00 |
| time (sec) |
N/A | 0.412 | 0.332 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.249 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | A | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 9 | 9 | 9 | 10 | 9 | 9 | 8 | 23 | 9 | 9 |
| N.S. |
1 | 1.00 | 1.00 | 1.11 | 1.00 | 1.00 | 0.89 | 2.56 | 1.00 | 1.00 |
| time (sec) |
N/A | 0.154 | 0.036 | 0.526 | 0.032 | 0.085 | 0.052 | 0.122 | 0.226 | 0.050 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | B | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 37 | 37 | 36 | 37 | 46 | 42 | 78 | 74 | 66 | 39 |
| N.S. |
1 | 1.00 | 0.97 | 1.00 | 1.24 | 1.14 | 2.11 | 2.00 | 1.78 | 1.05 |
| time (sec) |
N/A | 0.195 | 0.048 | 1.486 | 0.038 | 0.089 | 0.091 | 0.123 | 0.219 | 0.821 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | C | A | A | B | B | B | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 35 | 51 | 63 | 36 | 69 | 97 | 66 | 134 | 57 | 53 |
| N.S. |
1 | 1.46 | 1.80 | 1.03 | 1.97 | 2.77 | 1.89 | 3.83 | 1.63 | 1.51 |
| time (sec) |
N/A | 0.213 | 0.116 | 7.446 | 0.034 | 0.092 | 0.117 | 0.125 | 0.208 | 0.101 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | B | B | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 72 | 75 | 87 | 90 | 103 | 168 | 265 | 208 | 217 | 143 |
| N.S. |
1 | 1.04 | 1.21 | 1.25 | 1.43 | 2.33 | 3.68 | 2.89 | 3.01 | 1.99 |
| time (sec) |
N/A | 0.283 | 0.096 | 27.409 | 0.038 | 0.110 | 0.168 | 0.126 | 0.219 | 0.893 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | C | B | A | B | B | B | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 61 | 83 | 133 | 60 | 191 | 298 | 172 | 344 | 139 | 117 |
| N.S. |
1 | 1.36 | 2.18 | 0.98 | 3.13 | 4.89 | 2.82 | 5.64 | 2.28 | 1.92 |
| time (sec) |
N/A | 0.358 | 0.195 | 185.487 | 0.047 | 0.084 | 0.200 | 0.121 | 0.195 | 0.881 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | C | A | A | F(-2) | A | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 38 | 47 | 46 | 39 | 0 | 148 | 105 | 35 | 48 | 35 |
| N.S. |
1 | 1.24 | 1.21 | 1.03 | 0.00 | 3.89 | 2.76 | 0.92 | 1.26 | 0.92 |
| time (sec) |
N/A | 0.358 | 0.037 | 0.921 | 0.000 | 0.106 | 1.677 | 0.124 | 0.209 | 0.102 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | B | F(-1) | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 17 | 17 | 17 | 27 | 29 | 62 | 0 | 26 | 39 | 22 |
| N.S. |
1 | 1.00 | 1.00 | 1.59 | 1.71 | 3.65 | 0.00 | 1.53 | 2.29 | 1.29 |
| time (sec) |
N/A | 0.301 | 0.023 | 5.338 | 0.037 | 0.085 | 0.000 | 0.142 | 0.234 | 0.853 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | C | A | B | F(-2) | B | F(-1) | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 77 | 85 | 96 | 146 | 0 | 1495 | 0 | 88 | 583 | 157 |
| N.S. |
1 | 1.10 | 1.25 | 1.90 | 0.00 | 19.42 | 0.00 | 1.14 | 7.57 | 2.04 |
| time (sec) |
N/A | 0.536 | 0.343 | 28.831 | 0.000 | 0.117 | 0.000 | 0.129 | 0.228 | 0.938 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | B | B | F(-1) | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 67 | 67 | 64 | 46 | 498 | 527 | 0 | 53 | 268 | 47 |
| N.S. |
1 | 1.00 | 0.96 | 0.69 | 7.43 | 7.87 | 0.00 | 0.79 | 4.00 | 0.70 |
| time (sec) |
N/A | 0.498 | 0.096 | 121.142 | 0.066 | 0.082 | 0.000 | 0.126 | 0.223 | 0.907 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | C | A | B | F(-2) | B | F(-1) | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 112 | 136 | 147 | 462 | 0 | 6874 | 0 | 236 | 1730 | 354 |
| N.S. |
1 | 1.21 | 1.31 | 4.12 | 0.00 | 61.38 | 0.00 | 2.11 | 15.45 | 3.16 |
| time (sec) |
N/A | 0.681 | 0.627 | 0.389 | 0.000 | 0.196 | 0.000 | 0.139 | 0.223 | 0.951 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 65 | 65 | 206 | 33 | 0 | 58 | 0 | 0 | 79 | 0 |
| N.S. |
1 | 1.00 | 3.17 | 0.51 | 0.00 | 0.89 | 0.00 | 0.00 | 1.22 | 0.00 |
| time (sec) |
N/A | 0.314 | 0.477 | 1.616 | 0.000 | 0.121 | 0.000 | 0.000 | 0.223 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 103 | 103 | 92 | 171 | 0 | 99 | 0 | 0 | 181 | 0 |
| N.S. |
1 | 1.00 | 0.89 | 1.66 | 0.00 | 0.96 | 0.00 | 0.00 | 1.76 | 0.00 |
| time (sec) |
N/A | 0.390 | 0.393 | 1.176 | 0.000 | 0.099 | 0.000 | 0.000 | 0.259 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | F | B | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 103 | 103 | 193 | 42 | 0 | 269 | 0 | 0 | 447 | 0 |
| N.S. |
1 | 1.00 | 1.87 | 0.41 | 0.00 | 2.61 | 0.00 | 0.00 | 4.34 | 0.00 |
| time (sec) |
N/A | 0.384 | 0.606 | 1.455 | 0.000 | 0.110 | 0.000 | 0.000 | 0.252 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 65 | 65 | 81 | 97 | 0 | 35 | 0 | 0 | 24 | 0 |
| N.S. |
1 | 1.00 | 1.25 | 1.49 | 0.00 | 0.54 | 0.00 | 0.00 | 0.37 | 0.00 |
| time (sec) |
N/A | 0.296 | 0.116 | 1.183 | 0.000 | 0.084 | 0.000 | 0.000 | 0.228 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | F | B | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 112 | 112 | 148 | 33 | 0 | 211 | 0 | 0 | 40 | 0 |
| N.S. |
1 | 1.00 | 1.32 | 0.29 | 0.00 | 1.88 | 0.00 | 0.00 | 0.36 | 0.00 |
| time (sec) |
N/A | 0.420 | 0.359 | 1.033 | 0.000 | 0.100 | 0.000 | 0.000 | 0.223 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | F | B | F | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 116 | 116 | 133 | 37 | 0 | 651 | 0 | 0 | 56 | 0 |
| N.S. |
1 | 1.00 | 1.15 | 0.32 | 0.00 | 5.61 | 0.00 | 0.00 | 0.48 | 0.00 |
| time (sec) |
N/A | 0.406 | 0.407 | 1.109 | 0.000 | 0.103 | 0.000 | 0.000 | 0.217 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | A | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 23 | 23 | 45 | 12 | 23 | 21 | 29 | 56 | 18 | 11 |
| N.S. |
1 | 1.00 | 1.96 | 0.52 | 1.00 | 0.91 | 1.26 | 2.43 | 0.78 | 0.48 |
| time (sec) |
N/A | 0.168 | 0.066 | 0.936 | 0.036 | 0.076 | 0.077 | 0.126 | 0.207 | 0.062 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | B | A | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 26 | 26 | 25 | 18 | 88 | 43 | 44 | 17 | 26 | 17 |
| N.S. |
1 | 1.00 | 0.96 | 0.69 | 3.38 | 1.65 | 1.69 | 0.65 | 1.00 | 0.65 |
| time (sec) |
N/A | 0.205 | 0.142 | 2.127 | 0.039 | 0.105 | 0.092 | 0.129 | 0.216 | 0.070 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | B | B | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 26 | 26 | 25 | 18 | 146 | 64 | 83 | 17 | 57 | 17 |
| N.S. |
1 | 1.00 | 0.96 | 0.69 | 5.62 | 2.46 | 3.19 | 0.65 | 2.19 | 0.65 |
| time (sec) |
N/A | 0.198 | 0.207 | 8.370 | 0.039 | 0.087 | 0.127 | 0.125 | 0.198 | 0.076 |
| 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 | 26 | 26 | 24 | 27 | 18 | 34 | 36 | 17 | 26 | 17 |
| N.S. |
1 | 1.00 | 0.92 | 1.04 | 0.69 | 1.31 | 1.38 | 0.65 | 1.00 | 0.65 |
| time (sec) |
N/A | 0.283 | 0.078 | 1.262 | 0.045 | 0.096 | 0.097 | 0.175 | 0.216 | 0.985 |
| 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 | 24 | 24 | 24 | 18 | 17 | 23 | 34 | 17 | 17 | 17 |
| N.S. |
1 | 1.00 | 1.00 | 0.75 | 0.71 | 0.96 | 1.42 | 0.71 | 0.71 | 0.71 |
| time (sec) |
N/A | 0.269 | 0.204 | 1.507 | 0.044 | 0.093 | 0.239 | 0.122 | 0.205 | 0.820 |
| 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 | 26 | 26 | 26 | 18 | 17 | 49 | 66 | 17 | 20 | 17 |
| N.S. |
1 | 1.00 | 1.00 | 0.69 | 0.65 | 1.88 | 2.54 | 0.65 | 0.77 | 0.65 |
| time (sec) |
N/A | 0.301 | 0.217 | 4.087 | 0.056 | 0.084 | 0.348 | 0.123 | 0.208 | 0.890 |
| 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 | 26 | 26 | 26 | 18 | 17 | 71 | 90 | 17 | 20 | 17 |
| N.S. |
1 | 1.00 | 1.00 | 0.69 | 0.65 | 2.73 | 3.46 | 0.65 | 0.77 | 0.65 |
| time (sec) |
N/A | 0.333 | 0.223 | 18.248 | 0.046 | 0.082 | 0.537 | 0.117 | 0.202 | 0.819 |
| 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 | 26 | 26 | 24 | 23 | 17 | 24 | 0 | 17 | 21 | 15 |
| N.S. |
1 | 1.00 | 0.92 | 0.88 | 0.65 | 0.92 | 0.00 | 0.65 | 0.81 | 0.58 |
| time (sec) |
N/A | 0.301 | 0.067 | 2.037 | 0.035 | 0.082 | 0.000 | 0.123 | 0.223 | 0.883 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | F | A | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 26 | 26 | 24 | 16 | 17 | 42 | 0 | 17 | 38 | 15 |
| N.S. |
1 | 1.00 | 0.92 | 0.62 | 0.65 | 1.62 | 0.00 | 0.65 | 1.46 | 0.58 |
| time (sec) |
N/A | 0.332 | 0.075 | 1.464 | 0.042 | 0.086 | 0.000 | 0.124 | 0.226 | 0.848 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | A | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 24 | 24 | 47 | 16 | 24 | 22 | 29 | 56 | 20 | 15 |
| N.S. |
1 | 1.00 | 1.96 | 0.67 | 1.00 | 0.92 | 1.21 | 2.33 | 0.83 | 0.62 |
| time (sec) |
N/A | 0.263 | 0.037 | 0.794 | 0.041 | 0.082 | 0.081 | 0.123 | 0.216 | 0.830 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | B | A | A | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 27 | 27 | 27 | 18 | 89 | 43 | 44 | 17 | 28 | 17 |
| N.S. |
1 | 1.00 | 1.00 | 0.67 | 3.30 | 1.59 | 1.63 | 0.63 | 1.04 | 0.63 |
| time (sec) |
N/A | 0.275 | 0.093 | 1.940 | 0.042 | 0.087 | 0.090 | 0.118 | 0.211 | 0.064 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | B | B | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 27 | 27 | 27 | 18 | 147 | 62 | 83 | 17 | 59 | 17 |
| N.S. |
1 | 1.00 | 1.00 | 0.67 | 5.44 | 2.30 | 3.07 | 0.63 | 2.19 | 0.63 |
| time (sec) |
N/A | 0.253 | 0.135 | 8.286 | 0.047 | 0.082 | 0.134 | 0.130 | 0.204 | 0.830 |
| 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 | 28 | 28 | 27 | 29 | 20 | 39 | 37 | 23 | 28 | 21 |
| N.S. |
1 | 1.00 | 0.96 | 1.04 | 0.71 | 1.39 | 1.32 | 0.82 | 1.00 | 0.75 |
| time (sec) |
N/A | 0.206 | 0.059 | 1.353 | 0.048 | 0.084 | 0.101 | 0.123 | 0.220 | 1.007 |
| 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 | 24 | 24 | 22 | 14 | 13 | 20 | 32 | 13 | 14 | 13 |
| N.S. |
1 | 1.00 | 0.92 | 0.58 | 0.54 | 0.83 | 1.33 | 0.54 | 0.58 | 0.54 |
| time (sec) |
N/A | 0.204 | 0.006 | 1.406 | 0.044 | 0.086 | 0.187 | 0.126 | 0.211 | 0.069 |
| 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 | 27 | 27 | 27 | 18 | 17 | 41 | 65 | 17 | 18 | 17 |
| N.S. |
1 | 1.00 | 1.00 | 0.67 | 0.63 | 1.52 | 2.41 | 0.63 | 0.67 | 0.63 |
| time (sec) |
N/A | 0.191 | 0.112 | 4.140 | 0.043 | 0.085 | 0.267 | 0.124 | 0.207 | 0.898 |
| 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 | 27 | 27 | 27 | 18 | 17 | 59 | 88 | 17 | 18 | 17 |
| N.S. |
1 | 1.00 | 1.00 | 0.67 | 0.63 | 2.19 | 3.26 | 0.63 | 0.67 | 0.63 |
| time (sec) |
N/A | 0.200 | 0.126 | 18.395 | 0.039 | 0.075 | 0.527 | 0.122 | 0.216 | 0.907 |
| 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 | 27 | 27 | 26 | 19 | 17 | 24 | 0 | 17 | 23 | 18 |
| N.S. |
1 | 1.00 | 0.96 | 0.70 | 0.63 | 0.89 | 0.00 | 0.63 | 0.85 | 0.67 |
| time (sec) |
N/A | 0.197 | 0.034 | 2.605 | 0.039 | 0.104 | 0.000 | 0.110 | 0.251 | 0.984 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | F | F(-2) | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 27 | 27 | 26 | 19 | 17 | 40 | 0 | 0 | 42 | 27 |
| N.S. |
1 | 1.00 | 0.96 | 0.70 | 0.63 | 1.48 | 0.00 | 0.00 | 1.56 | 1.00 |
| time (sec) |
N/A | 0.197 | 0.036 | 1.815 | 0.040 | 0.079 | 0.000 | 0.000 | 0.216 | 1.101 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | B | A | B | B | F | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 124 | 184 | 355 | 160 | 279 | 2040 | 0 | 240 | 789 | 495 |
| N.S. |
1 | 1.48 | 2.86 | 1.29 | 2.25 | 16.45 | 0.00 | 1.94 | 6.36 | 3.99 |
| time (sec) |
N/A | 0.492 | 1.324 | 190.172 | 0.141 | 0.116 | 0.000 | 0.135 | 0.221 | 0.593 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | B | B | F | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 100 | 106 | 79 | 84 | 210 | 207 | 0 | 110 | 243 | 145 |
| N.S. |
1 | 1.06 | 0.79 | 0.84 | 2.10 | 2.07 | 0.00 | 1.10 | 2.43 | 1.45 |
| time (sec) |
N/A | 0.619 | 0.234 | 60.389 | 0.047 | 0.082 | 0.000 | 0.137 | 0.244 | 0.917 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | B | A | B | B | F | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 58 | 92 | 194 | 64 | 120 | 502 | 0 | 117 | 267 | 233 |
| N.S. |
1 | 1.59 | 3.34 | 1.10 | 2.07 | 8.66 | 0.00 | 2.02 | 4.60 | 4.02 |
| time (sec) |
N/A | 0.361 | 1.292 | 14.189 | 0.130 | 0.108 | 0.000 | 0.135 | 0.220 | 0.225 |
| 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 | 29 | 29 | 26 | 26 | 43 | 42 | 0 | 31 | 62 | 33 |
| N.S. |
1 | 1.00 | 0.90 | 0.90 | 1.48 | 1.45 | 0.00 | 1.07 | 2.14 | 1.14 |
| time (sec) |
N/A | 0.290 | 0.035 | 3.704 | 0.033 | 0.094 | 0.000 | 0.121 | 0.211 | 0.945 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | B | A | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 11 | 11 | 12 | 12 | 11 | 30 | 19 | 21 | 22 | 40 |
| N.S. |
1 | 1.00 | 1.09 | 1.09 | 1.00 | 2.73 | 1.73 | 1.91 | 2.00 | 3.64 |
| time (sec) |
N/A | 0.155 | 0.007 | 1.121 | 0.046 | 0.083 | 0.178 | 0.121 | 0.217 | 0.086 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | B | B | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 11 | 11 | 11 | 27 | 28 | 27 | 32 | 22 | 26 | 25 |
| N.S. |
1 | 1.00 | 1.00 | 2.45 | 2.55 | 2.45 | 2.91 | 2.00 | 2.36 | 2.27 |
| time (sec) |
N/A | 0.247 | 0.006 | 0.802 | 0.058 | 0.096 | 0.134 | 0.125 | 0.224 | 0.093 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | C | C | A | A | B | F | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 62 | 80 | 502 | 101 | 100 | 362 | 0 | 97 | 254 | 132 |
| N.S. |
1 | 1.29 | 8.10 | 1.63 | 1.61 | 5.84 | 0.00 | 1.56 | 4.10 | 2.13 |
| time (sec) |
N/A | 0.642 | 1.585 | 2.553 | 0.136 | 0.104 | 0.000 | 0.132 | 0.215 | 1.137 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | B | B | B | A | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 48 | 45 | 42 | 78 | 117 | 543 | 651 | 75 | 1346 | 0 |
| N.S. |
1 | 0.94 | 0.88 | 1.62 | 2.44 | 11.31 | 13.56 | 1.56 | 28.04 | 0.00 |
| time (sec) |
N/A | 0.501 | 0.097 | 12.578 | 0.061 | 0.110 | 1.106 | 0.130 | 0.231 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | C | C | B | B | B | F | A | B | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 146 | 178 | 3430 | 357 | 375 | 2978 | 0 | 267 | 8290 | 0 |
| N.S. |
1 | 1.22 | 23.49 | 2.45 | 2.57 | 20.40 | 0.00 | 1.83 | 56.78 | 0.00 |
| time (sec) |
N/A | 1.541 | 7.157 | 90.606 | 0.153 | 0.129 | 0.000 | 0.164 | 0.231 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | B | B | B | A | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 95 | 83 | 83 | 176 | 297 | 2640 | 2162 | 152 | 6933 | 0 |
| N.S. |
1 | 0.87 | 0.87 | 1.85 | 3.13 | 27.79 | 22.76 | 1.60 | 72.98 | 0.00 |
| time (sec) |
N/A | 0.406 | 0.165 | 270.710 | 0.086 | 0.118 | 5.504 | 0.147 | 0.222 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | B | B | F | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 40 | 40 | 60 | 78 | 235 | 94 | 0 | 34 | 429 | 90 |
| N.S. |
1 | 1.00 | 1.50 | 1.95 | 5.88 | 2.35 | 0.00 | 0.85 | 10.72 | 2.25 |
| time (sec) |
N/A | 0.304 | 0.040 | 1.054 | 0.148 | 0.110 | 0.000 | 0.122 | 0.218 | 1.191 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | B | A | F | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 38 | 38 | 74 | 60 | 181 | 52 | 0 | 22 | 161 | 65 |
| N.S. |
1 | 1.00 | 1.95 | 1.58 | 4.76 | 1.37 | 0.00 | 0.58 | 4.24 | 1.71 |
| time (sec) |
N/A | 0.401 | 0.117 | 0.541 | 0.040 | 0.126 | 0.000 | 0.127 | 0.215 | 1.011 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | B | B | F | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 26 | 26 | 27 | 26 | 73 | 50 | 0 | 21 | 167 | 39 |
| N.S. |
1 | 1.00 | 1.04 | 1.00 | 2.81 | 1.92 | 0.00 | 0.81 | 6.42 | 1.50 |
| time (sec) |
N/A | 0.295 | 0.023 | 22.304 | 0.119 | 0.112 | 0.000 | 0.121 | 0.215 | 0.195 |
| 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 | 20 | 20 | 16 | 15 | 25 | 17 | 0 | 12 | 45 | 14 |
| N.S. |
1 | 1.00 | 0.80 | 0.75 | 1.25 | 0.85 | 0.00 | 0.60 | 2.25 | 0.70 |
| time (sec) |
N/A | 0.317 | 0.012 | 8.541 | 0.050 | 0.109 | 0.000 | 0.114 | 0.210 | 0.207 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | A | A | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 11 | 11 | 13 | 11 | 9 | 11 | 17 | 18 | 19 | 14 |
| N.S. |
1 | 1.00 | 1.18 | 1.00 | 0.82 | 1.00 | 1.55 | 1.64 | 1.73 | 1.27 |
| time (sec) |
N/A | 0.165 | 0.006 | 2.539 | 0.037 | 0.088 | 0.186 | 0.124 | 0.228 | 0.928 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | B | A | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 13 | 13 | 17 | 15 | 15 | 11 | 22 | 11 | 11 | 14 |
| N.S. |
1 | 1.00 | 1.31 | 1.15 | 1.15 | 0.85 | 1.69 | 0.85 | 0.85 | 1.08 |
| time (sec) |
N/A | 0.239 | 0.019 | 3.133 | 0.039 | 0.087 | 0.098 | 0.132 | 0.232 | 0.927 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | F | A | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 20 | 20 | 31 | 15 | 14 | 17 | 0 | 12 | 22 | 14 |
| N.S. |
1 | 1.00 | 1.55 | 0.75 | 0.70 | 0.85 | 0.00 | 0.60 | 1.10 | 0.70 |
| time (sec) |
N/A | 0.251 | 0.026 | 12.089 | 0.046 | 0.078 | 0.000 | 0.117 | 0.209 | 0.946 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | B | B | A | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 28 | 28 | 40 | 26 | 33 | 50 | 432 | 21 | 324 | 41 |
| N.S. |
1 | 1.00 | 1.43 | 0.93 | 1.18 | 1.79 | 15.43 | 0.75 | 11.57 | 1.46 |
| time (sec) |
N/A | 0.276 | 0.035 | 50.592 | 0.059 | 0.084 | 0.732 | 0.127 | 0.231 | 0.226 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | F | A | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 38 | 38 | 75 | 41 | 40 | 52 | 0 | 22 | 548 | 67 |
| N.S. |
1 | 1.00 | 1.97 | 1.08 | 1.05 | 1.37 | 0.00 | 0.58 | 14.42 | 1.76 |
| time (sec) |
N/A | 0.326 | 0.065 | 0.953 | 0.052 | 0.105 | 0.000 | 0.128 | 0.253 | 1.036 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | B | B | A | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 42 | 38 | 45 | 68 | 58 | 94 | 1445 | 34 | 847 | 94 |
| N.S. |
1 | 0.90 | 1.07 | 1.62 | 1.38 | 2.24 | 34.40 | 0.81 | 20.17 | 2.24 |
| time (sec) |
N/A | 0.276 | 0.087 | 0.846 | 0.050 | 0.091 | 2.322 | 0.126 | 0.343 | 1.055 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | B | B | F | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 42 | 40 | 60 | 78 | 235 | 94 | 0 | 34 | 429 | 94 |
| N.S. |
1 | 0.95 | 1.43 | 1.86 | 5.60 | 2.24 | 0.00 | 0.81 | 10.21 | 2.24 |
| time (sec) |
N/A | 0.291 | 0.037 | 0.827 | 0.123 | 0.097 | 0.000 | 0.117 | 0.224 | 0.176 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | B | A | F | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 38 | 38 | 75 | 60 | 181 | 52 | 0 | 22 | 161 | 67 |
| N.S. |
1 | 1.00 | 1.97 | 1.58 | 4.76 | 1.37 | 0.00 | 0.58 | 4.24 | 1.76 |
| time (sec) |
N/A | 0.477 | 0.057 | 1.418 | 0.048 | 0.106 | 0.000 | 0.129 | 0.216 | 0.916 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | B | B | F | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 28 | 26 | 27 | 26 | 73 | 50 | 0 | 21 | 167 | 41 |
| N.S. |
1 | 0.93 | 0.96 | 0.93 | 2.61 | 1.79 | 0.00 | 0.75 | 5.96 | 1.46 |
| time (sec) |
N/A | 0.413 | 0.021 | 22.391 | 0.125 | 0.096 | 0.000 | 0.128 | 0.221 | 0.171 |
| 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 | 20 | 20 | 16 | 15 | 25 | 17 | 0 | 12 | 45 | 14 |
| N.S. |
1 | 1.00 | 0.80 | 0.75 | 1.25 | 0.85 | 0.00 | 0.60 | 2.25 | 0.70 |
| time (sec) |
N/A | 0.512 | 0.005 | 8.107 | 0.040 | 0.090 | 0.000 | 0.128 | 0.237 | 0.892 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | A | A | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 11 | 11 | 13 | 11 | 9 | 11 | 17 | 18 | 19 | 14 |
| N.S. |
1 | 1.00 | 1.18 | 1.00 | 0.82 | 1.00 | 1.55 | 1.64 | 1.73 | 1.27 |
| time (sec) |
N/A | 0.241 | 0.004 | 2.344 | 0.032 | 0.106 | 0.196 | 0.123 | 0.233 | 0.788 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | B | A | B | A | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 11 | 13 | 17 | 15 | 15 | 11 | 22 | 11 | 12 | 14 |
| N.S. |
1 | 1.18 | 1.55 | 1.36 | 1.36 | 1.00 | 2.00 | 1.00 | 1.09 | 1.27 |
| time (sec) |
N/A | 0.393 | 0.019 | 3.127 | 0.056 | 0.107 | 0.108 | 0.124 | 0.227 | 0.141 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | F | A | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 20 | 20 | 31 | 15 | 14 | 17 | 0 | 12 | 22 | 14 |
| N.S. |
1 | 1.00 | 1.55 | 0.75 | 0.70 | 0.85 | 0.00 | 0.60 | 1.10 | 0.70 |
| time (sec) |
N/A | 0.351 | 0.025 | 12.233 | 0.050 | 0.094 | 0.000 | 0.124 | 0.224 | 0.101 |