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 | 61 | 61 | 181 | 0 | 0 | 0 | 0 | 0 | 37 | 0 |
| N.S. |
1 | 1.00 | 2.97 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.61 | 0.00 |
| time (sec) |
N/A | 0.330 | 0.161 | 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 | B | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 61 | 61 | 391 | 0 | 0 | 0 | 0 | 0 | 65 | 0 |
| N.S. |
1 | 1.00 | 6.41 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.07 | 0.00 |
| time (sec) |
N/A | 0.316 | 0.838 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.474 | 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 | 178 | 174 | 130 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.98 | 0.73 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.644 | 5.258 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.255 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F(-2) | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 93 | 103 | 77 | 0 | 0 | 0 | 112 | 0 | 706 | 0 |
| N.S. |
1 | 1.11 | 0.83 | 0.00 | 0.00 | 0.00 | 1.20 | 0.00 | 7.59 | 0.00 |
| time (sec) |
N/A | 0.386 | 0.116 | 0.000 | 0.000 | 0.000 | 2.374 | 0.000 | 0.275 | 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 | 64 | 64 | 382 | 0 | 0 | 0 | 0 | 0 | 65 | 0 |
| N.S. |
1 | 1.00 | 5.97 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.02 | 0.00 |
| time (sec) |
N/A | 0.328 | 0.802 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.497 | 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 | 64 | 64 | 1294 | 0 | 0 | 0 | 0 | 0 | 112 | 0 |
| N.S. |
1 | 1.00 | 20.22 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.75 | 0.00 |
| time (sec) |
N/A | 0.328 | 1.224 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.692 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F(-2) | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 187 | 187 | 214 | 0 | 0 | 0 | 185 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.14 | 0.00 | 0.00 | 0.00 | 0.99 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.653 | 5.416 | 0.000 | 0.000 | 0.000 | 3.321 | 0.000 | 0.288 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F(-2) | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 90 | 90 | 97 | 0 | 0 | 0 | 114 | 0 | 501 | 0 |
| N.S. |
1 | 1.00 | 1.08 | 0.00 | 0.00 | 0.00 | 1.27 | 0.00 | 5.57 | 0.00 |
| time (sec) |
N/A | 0.378 | 0.115 | 0.000 | 0.000 | 0.000 | 1.493 | 0.000 | 0.297 | 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 | 61 | 61 | 181 | 0 | 0 | 0 | 0 | 0 | 21 | 0 |
| N.S. |
1 | 1.00 | 2.97 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.34 | 0.00 |
| time (sec) |
N/A | 0.327 | 0.374 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.266 | 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 | 61 | 61 | 364 | 0 | 0 | 0 | 0 | 0 | 34 | 0 |
| N.S. |
1 | 1.00 | 5.97 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.56 | 0.00 |
| time (sec) |
N/A | 0.322 | 0.935 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.361 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F(-2) | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 187 | 187 | 146 | 0 | 0 | 0 | 182 | 0 | 56 | 0 |
| N.S. |
1 | 1.00 | 0.78 | 0.00 | 0.00 | 0.00 | 0.97 | 0.00 | 0.30 | 0.00 |
| time (sec) |
N/A | 0.672 | 5.260 | 0.000 | 0.000 | 0.000 | 2.130 | 0.000 | 0.242 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F(-2) | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 90 | 90 | 83 | 0 | 0 | 0 | 112 | 0 | 31 | 0 |
| N.S. |
1 | 1.00 | 0.92 | 0.00 | 0.00 | 0.00 | 1.24 | 0.00 | 0.34 | 0.00 |
| time (sec) |
N/A | 0.382 | 0.139 | 0.000 | 0.000 | 0.000 | 1.178 | 0.000 | 0.230 | 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 | 61 | 61 | 181 | 0 | 0 | 0 | 0 | 0 | 30 | 0 |
| N.S. |
1 | 1.00 | 2.97 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.49 | 0.00 |
| time (sec) |
N/A | 0.331 | 0.544 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.224 | 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 | 61 | 61 | 391 | 0 | 0 | 0 | 0 | 0 | 52 | 0 |
| N.S. |
1 | 1.00 | 6.41 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.85 | 0.00 |
| time (sec) |
N/A | 0.322 | 0.872 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.240 | 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 | 187 | 183 | 140 | 0 | 0 | 0 | 0 | 0 | 113 | 0 |
| N.S. |
1 | 0.98 | 0.75 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.60 | 0.00 |
| time (sec) |
N/A | 0.654 | 5.313 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.254 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F(-2) | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 93 | 103 | 77 | 0 | 0 | 0 | 112 | 0 | 69 | 0 |
| N.S. |
1 | 1.11 | 0.83 | 0.00 | 0.00 | 0.00 | 1.20 | 0.00 | 0.74 | 0.00 |
| time (sec) |
N/A | 0.389 | 0.146 | 0.000 | 0.000 | 0.000 | 2.561 | 0.000 | 0.211 | 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 | 64 | 64 | 382 | 0 | 0 | 0 | 0 | 0 | 64 | 0 |
| N.S. |
1 | 1.00 | 5.97 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | 0.00 |
| time (sec) |
N/A | 0.330 | 0.846 | 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 | B | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 64 | 64 | 1294 | 0 | 0 | 0 | 0 | 0 | 110 | 0 |
| N.S. |
1 | 1.00 | 20.22 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.72 | 0.00 |
| time (sec) |
N/A | 0.318 | 1.104 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.268 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | C | F(-2) | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 395 | 385 | 168 | 0 | 0 | 0 | 243 | 0 | 0 | 0 |
| N.S. |
1 | 0.97 | 0.43 | 0.00 | 0.00 | 0.00 | 0.62 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.449 | 5.317 | 0.000 | 0.000 | 0.000 | 91.679 | 0.000 | 0.316 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | C | F(-2) | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 197 | 188 | 140 | 0 | 0 | 0 | 175 | 0 | 0 | 0 |
| N.S. |
1 | 0.95 | 0.71 | 0.00 | 0.00 | 0.00 | 0.89 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.767 | 5.223 | 0.000 | 0.000 | 0.000 | 20.709 | 0.000 | 0.241 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | C | F(-2) | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 89 | 89 | 94 | 0 | 0 | 0 | 107 | 0 | 1336 | 0 |
| N.S. |
1 | 1.00 | 1.06 | 0.00 | 0.00 | 0.00 | 1.20 | 0.00 | 15.01 | 0.00 |
| time (sec) |
N/A | 0.396 | 0.083 | 0.000 | 0.000 | 0.000 | 2.618 | 0.000 | 0.211 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | C | F | F | B |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 46 | 46 | 46 | 0 | 0 | 0 | 46 | 0 | 96 | 47 |
| N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 1.00 | 0.00 | 2.09 | 1.02 |
| time (sec) |
N/A | 0.284 | 0.003 | 0.000 | 0.000 | 0.000 | 0.893 | 0.000 | 0.217 | 1.490 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | B | F | F | F | F(-2) | F | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 59 | 59 | 180 | 0 | 0 | 0 | 0 | 0 | 21 | 0 |
| N.S. |
1 | 1.00 | 3.05 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.36 | 0.00 |
| time (sec) |
N/A | 0.326 | 0.490 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.226 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | B | F | F | F | F(-2) | F | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 59 | 59 | 180 | 0 | 0 | 0 | 0 | 0 | 34 | 0 |
| N.S. |
1 | 1.00 | 3.05 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.58 | 0.00 |
| time (sec) |
N/A | 0.324 | 0.387 | 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 | B | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 59 | 59 | 180 | 0 | 0 | 0 | 0 | 0 | 47 | 0 |
| N.S. |
1 | 1.00 | 3.05 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.80 | 0.00 |
| time (sec) |
N/A | 0.321 | 0.500 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.291 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | F(-2) | F | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 93 | 93 | 94 | 0 | 0 | 0 | 0 | 0 | 56 | 0 |
| N.S. |
1 | 1.00 | 1.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.60 | 0.00 |
| time (sec) |
N/A | 0.345 | 0.178 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.240 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F | B | B | F(-2) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 193 | 160 | 218 | 1290 | 0 | 478 | 2822 | 0 | 461 | 0 |
| N.S. |
1 | 0.83 | 1.13 | 6.68 | 0.00 | 2.48 | 14.62 | 0.00 | 2.39 | 0.00 |
| time (sec) |
N/A | 0.511 | 0.215 | 1.970 | 0.000 | 0.130 | 47.156 | 0.000 | 0.227 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F | A | B | F(-2) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 127 | 109 | 113 | 588 | 0 | 231 | 1035 | 0 | 269 | 0 |
| N.S. |
1 | 0.86 | 0.89 | 4.63 | 0.00 | 1.82 | 8.15 | 0.00 | 2.12 | 0.00 |
| time (sec) |
N/A | 0.395 | 0.143 | 1.352 | 0.000 | 0.117 | 15.862 | 0.000 | 0.216 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F | A | B | F(-2) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 72 | 58 | 82 | 199 | 0 | 85 | 311 | 0 | 125 | 0 |
| N.S. |
1 | 0.81 | 1.14 | 2.76 | 0.00 | 1.18 | 4.32 | 0.00 | 1.74 | 0.00 |
| time (sec) |
N/A | 0.301 | 0.178 | 0.992 | 0.000 | 0.087 | 2.272 | 0.000 | 0.236 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F | A | B | F | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 18 | 18 | 18 | 47 | 0 | 31 | 42 | 0 | 34 | 75 |
| N.S. |
1 | 1.00 | 1.00 | 2.61 | 0.00 | 1.72 | 2.33 | 0.00 | 1.89 | 4.17 |
| time (sec) |
N/A | 0.233 | 0.058 | 0.924 | 0.000 | 0.102 | 0.804 | 0.000 | 0.224 | 1.043 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | F(-2) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 53 | 53 | 52 | 0 | 0 | 0 | 0 | 0 | 34 | 0 |
| N.S. |
1 | 1.00 | 0.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.64 | 0.00 |
| time (sec) |
N/A | 0.285 | 0.073 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.222 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | F(-2) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 54 | 54 | 53 | 0 | 0 | 0 | 0 | 0 | 125 | 0 |
| N.S. |
1 | 1.00 | 0.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 2.31 | 0.00 |
| time (sec) |
N/A | 0.287 | 0.093 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.237 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | F(-2) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 56 | 56 | 55 | 0 | 0 | 0 | 0 | 0 | 269 | 0 |
| N.S. |
1 | 1.00 | 0.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 4.80 | 0.00 |
| time (sec) |
N/A | 0.293 | 0.083 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.268 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | F | F | F | F | F(-2) | F | F | F(-1) |
| verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 164 | 181 | 0 | 0 | 0 | 0 | 0 | 0 | 86 | 0 |
| N.S. |
1 | 1.10 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.52 | 0.00 |
| time (sec) |
N/A | 0.519 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.205 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F | A | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 57 | 57 | 55 | 334 | 0 | 108 | 0 | 0 | 144 | 0 |
| N.S. |
1 | 1.00 | 0.96 | 5.86 | 0.00 | 1.89 | 0.00 | 0.00 | 2.53 | 0.00 |
| time (sec) |
N/A | 0.312 | 0.597 | 6.151 | 0.000 | 0.136 | 0.000 | 0.000 | 0.226 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F | A | B | F(-2) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 253 | 231 | 136 | 1059 | 0 | 400 | 2746 | 0 | 341 | 0 |
| N.S. |
1 | 0.91 | 0.54 | 4.19 | 0.00 | 1.58 | 10.85 | 0.00 | 1.35 | 0.00 |
| time (sec) |
N/A | 0.664 | 0.479 | 1.397 | 0.000 | 0.117 | 15.894 | 0.000 | 0.273 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F | A | B | F(-2) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 127 | 113 | 94 | 434 | 0 | 173 | 959 | 0 | 173 | 0 |
| N.S. |
1 | 0.89 | 0.74 | 3.42 | 0.00 | 1.36 | 7.55 | 0.00 | 1.36 | 0.00 |
| time (sec) |
N/A | 0.424 | 0.223 | 1.004 | 0.000 | 0.093 | 2.492 | 0.000 | 0.218 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | F | F | A | B | F | F | B |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 50 | 50 | 55 | 0 | 0 | 68 | 250 | 0 | 58 | 64 |
| N.S. |
1 | 1.00 | 1.10 | 0.00 | 0.00 | 1.36 | 5.00 | 0.00 | 1.16 | 1.28 |
| time (sec) |
N/A | 0.295 | 0.065 | 0.000 | 0.000 | 0.081 | 0.832 | 0.000 | 0.209 | 1.098 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | F | F | F | F(-2) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 94 | 95 | 153 | 0 | 0 | 0 | 0 | 0 | 72 | 0 |
| N.S. |
1 | 1.01 | 1.63 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.77 | 0.00 |
| time (sec) |
N/A | 0.360 | 6.671 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.203 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | F | F | F | F(-2) | F | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 127 | 127 | 212 | 0 | 0 | 0 | 0 | 0 | 58 | 0 |
| N.S. |
1 | 1.00 | 1.67 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.46 | 0.00 |
| time (sec) |
N/A | 0.417 | 8.595 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.259 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | F | F | F | F(-2) | F | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 130 | 131 | 333 | 0 | 0 | 0 | 0 | 0 | 173 | 0 |
| N.S. |
1 | 1.01 | 2.56 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.33 | 0.00 |
| time (sec) |
N/A | 0.431 | 8.827 | 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 | C | F | F | F | F(-2) | F | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 132 | 133 | 6405 | 0 | 0 | 0 | 0 | 0 | 341 | 0 |
| N.S. |
1 | 1.01 | 48.52 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 2.58 | 0.00 |
| time (sec) |
N/A | 0.436 | 37.052 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.259 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | B | F | F | F | F(-2) | F | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 81 | 81 | 190 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 2.35 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.388 | 0.487 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.301 | 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 | 34 | 34 | 164 | 0 | 0 | 0 | 0 | 0 | 23 | 0 |
| N.S. |
1 | 1.00 | 4.82 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.68 | 0.00 |
| time (sec) |
N/A | 0.267 | 0.283 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.204 | 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 | 34 | 34 | 164 | 0 | 0 | 0 | 0 | 0 | 23 | 0 |
| N.S. |
1 | 1.00 | 4.82 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.68 | 0.00 |
| time (sec) |
N/A | 0.262 | 0.288 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.204 | 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 | 56 | 56 | 164 | 0 | 0 | 0 | 0 | 0 | 23 | 0 |
| N.S. |
1 | 1.00 | 2.93 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.41 | 0.00 |
| time (sec) |
N/A | 0.323 | 0.457 | 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(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 56 | 56 | 164 | 0 | 0 | 0 | 0 | 0 | 23 | 0 |
| N.S. |
1 | 1.00 | 2.93 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.41 | 0.00 |
| time (sec) |
N/A | 0.317 | 0.355 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.256 | 0.000 |