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 | C | C | F(-1) | B | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 410 | 410 | 237 | 226 | 0 | 1251 | 0 | 0 | 22 | 0 |
| N.S. |
1 | 1.00 | 0.58 | 0.55 | 0.00 | 3.05 | 0.00 | 0.00 | 0.05 | 0.00 |
| time (sec) |
N/A | 1.000 | 0.190 | 0.698 | 0.000 | 0.138 | 0.000 | 0.000 | 0.158 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | C | F | B | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 718 | 729 | 363 | 877 | 0 | 2050 | 0 | 0 | 754 | 0 |
| N.S. |
1 | 1.02 | 0.51 | 1.22 | 0.00 | 2.86 | 0.00 | 0.00 | 1.05 | 0.00 |
| time (sec) |
N/A | 1.768 | 0.160 | 0.980 | 0.000 | 0.125 | 0.000 | 0.000 | 0.213 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | C | F | B | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 373 | 376 | 203 | 594 | 0 | 1276 | 0 | 0 | 87 | 0 |
| N.S. |
1 | 1.01 | 0.54 | 1.59 | 0.00 | 3.42 | 0.00 | 0.00 | 0.23 | 0.00 |
| time (sec) |
N/A | 0.879 | 0.121 | 0.869 | 0.000 | 0.143 | 0.000 | 0.000 | 0.186 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | C | F | B | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 695 | 725 | 387 | 395 | 0 | 2135 | 0 | 0 | 30 | 0 |
| N.S. |
1 | 1.04 | 0.56 | 0.57 | 0.00 | 3.07 | 0.00 | 0.00 | 0.04 | 0.00 |
| time (sec) |
N/A | 1.983 | 0.131 | 0.834 | 0.000 | 0.174 | 0.000 | 0.000 | 0.160 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | C | F | B | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 739 | 832 | 387 | 226 | 0 | 2048 | 0 | 0 | 29 | 0 |
| N.S. |
1 | 1.13 | 0.52 | 0.31 | 0.00 | 2.77 | 0.00 | 0.00 | 0.04 | 0.00 |
| time (sec) |
N/A | 2.315 | 0.139 | 0.764 | 0.000 | 0.136 | 0.000 | 0.000 | 0.161 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | C | F | B | F(-1) | F(-2) | F | F(-1) |
| verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 697 | 846 | 411 | 338 | 0 | 1773 | 0 | 0 | 31 | 0 |
| N.S. |
1 | 1.21 | 0.59 | 0.48 | 0.00 | 2.54 | 0.00 | 0.00 | 0.04 | 0.00 |
| time (sec) |
N/A | 2.178 | 0.365 | 0.878 | 0.000 | 0.142 | 0.000 | 0.000 | 0.155 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | C | F | B | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 784 | 1146 | 397 | 6251 | 0 | 2980 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.46 | 0.51 | 7.97 | 0.00 | 3.80 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 3.452 | 0.382 | 2.064 | 0.000 | 0.164 | 0.000 | 0.000 | 0.319 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | C | F | B | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 1105 | 1142 | 675 | 4708 | 0 | 4691 | 0 | 0 | 114 | 0 |
| N.S. |
1 | 1.03 | 0.61 | 4.26 | 0.00 | 4.25 | 0.00 | 0.00 | 0.10 | 0.00 |
| time (sec) |
N/A | 3.630 | 0.367 | 1.762 | 0.000 | 0.173 | 0.000 | 0.000 | 0.210 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | B | C | C | F | B | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 776 | 1596 | 429 | 3281 | 0 | 2962 | 0 | 0 | 1448 | 0 |
| N.S. |
1 | 2.06 | 0.55 | 4.23 | 0.00 | 3.82 | 0.00 | 0.00 | 1.87 | 0.00 |
| time (sec) |
N/A | 3.901 | 0.429 | 1.632 | 0.000 | 0.163 | 0.000 | 0.000 | 0.262 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | C | F | B | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 781 | 863 | 423 | 2238 | 0 | 2972 | 0 | 0 | 114 | 0 |
| N.S. |
1 | 1.10 | 0.54 | 2.87 | 0.00 | 3.81 | 0.00 | 0.00 | 0.15 | 0.00 |
| time (sec) |
N/A | 2.100 | 0.305 | 1.526 | 0.000 | 0.158 | 0.000 | 0.000 | 0.209 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | C | F | B | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 1147 | 1813 | 669 | 1416 | 0 | 4691 | 0 | 0 | 110 | 0 |
| N.S. |
1 | 1.58 | 0.58 | 1.23 | 0.00 | 4.09 | 0.00 | 0.00 | 0.10 | 0.00 |
| time (sec) |
N/A | 4.975 | 0.307 | 1.382 | 0.000 | 0.185 | 0.000 | 0.000 | 0.214 | 0.000 |