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 | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 22 | 18 | 0 | 20 | 19 | 20 | 61 | 20 |
N.S. |
1 | 1.00 | 1.10 | 0.90 | 0.00 | 1.00 | 0.95 | 1.00 | 3.05 | 1.00 |
time (sec) |
N/A | 0.220 | 4.999 | 2.157 | 0.000 | 0.124 | 9.138 | 0.277 | 0.267 | 0.537 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | F(-2) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 22 | 18 | 0 | 20 | 19 | 0 | 48 | 20 |
N.S. |
1 | 1.00 | 1.10 | 0.90 | 0.00 | 1.00 | 0.95 | 0.00 | 2.40 | 1.00 |
time (sec) |
N/A | 0.206 | 2.832 | 1.768 | 0.000 | 0.115 | 4.676 | 0.000 | 0.289 | 0.494 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F(-2) | B | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 71 | 71 | 73 | 0 | 0 | 294 | 0 | 0 | 123 | 0 |
N.S. |
1 | 1.00 | 1.03 | 0.00 | 0.00 | 4.14 | 0.00 | 0.00 | 1.73 | 0.00 |
time (sec) |
N/A | 0.267 | 0.079 | 0.000 | 0.000 | 0.163 | 0.000 | 0.000 | 0.289 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | B | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 146 | 147 | 190 | 0 | 0 | 686 | 0 | 0 | 276 | 0 |
N.S. |
1 | 1.01 | 1.30 | 0.00 | 0.00 | 4.70 | 0.00 | 0.00 | 1.89 | 0.00 |
time (sec) |
N/A | 0.335 | 0.157 | 0.000 | 0.000 | 0.190 | 0.000 | 0.000 | 0.320 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | B | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 226 | 242 | 189 | 0 | 0 | 1324 | 0 | 0 | 461 | 0 |
N.S. |
1 | 1.07 | 0.84 | 0.00 | 0.00 | 5.86 | 0.00 | 0.00 | 2.04 | 0.00 |
time (sec) |
N/A | 1.110 | 0.266 | 0.000 | 0.000 | 0.289 | 0.000 | 0.000 | 0.347 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 24 | 20 | 0 | 34 | 20 | 22 | 89 | 22 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 0.00 | 1.55 | 0.91 | 1.00 | 4.05 | 1.00 |
time (sec) |
N/A | 0.213 | 16.112 | 1.287 | 0.000 | 0.122 | 8.998 | 0.369 | 0.321 | 0.387 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | F(-2) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 24 | 20 | 0 | 34 | 20 | 0 | 76 | 22 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 0.00 | 1.55 | 0.91 | 0.00 | 3.45 | 1.00 |
time (sec) |
N/A | 0.213 | 8.327 | 1.145 | 0.000 | 0.105 | 5.154 | 0.000 | 0.325 | 0.399 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | F(-2) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 24 | 20 | 0 | 54 | 20 | 0 | 222 | 22 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 0.00 | 2.45 | 0.91 | 0.00 | 10.09 | 1.00 |
time (sec) |
N/A | 0.217 | 3.074 | 2.135 | 0.000 | 0.134 | 5.033 | 0.000 | 0.340 | 0.366 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 24 | 20 | 130 | 65 | 20 | 0 | 488 | 22 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 5.91 | 2.95 | 0.91 | 0.00 | 22.18 | 1.00 |
time (sec) |
N/A | 0.221 | 7.822 | 2.062 | 0.384 | 0.153 | 58.250 | 0.000 | 0.371 | 0.401 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 24 | 20 | 22 | 22 | 19 | 22 | 22 | 22 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 1.00 | 1.00 | 0.86 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.221 | 0.973 | 1.921 | 0.206 | 0.110 | 0.363 | 0.265 | 200.042 | 0.300 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 24 | 20 | 22 | 39 | 20 | 22 | 29 | 22 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 1.00 | 1.77 | 0.91 | 1.00 | 1.32 | 1.00 |
time (sec) |
N/A | 0.232 | 0.873 | 1.407 | 0.205 | 0.125 | 0.636 | 0.207 | 0.642 | 0.313 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 24 | 20 | 22 | 63 | 20 | 22 | 63 | 22 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 1.00 | 2.86 | 0.91 | 1.00 | 2.86 | 1.00 |
time (sec) |
N/A | 0.227 | 1.543 | 1.949 | 0.243 | 0.097 | 1.732 | 0.248 | 0.679 | 0.300 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 24 | 20 | 22 | 87 | 20 | 22 | 107 | 22 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 1.00 | 3.95 | 0.91 | 1.00 | 4.86 | 1.00 |
time (sec) |
N/A | 0.244 | 3.519 | 1.971 | 0.257 | 0.118 | 7.646 | 0.286 | 0.883 | 0.300 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 24 | 20 | 237 | 36 | 20 | 22 | 22 | 22 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 10.77 | 1.64 | 0.91 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.216 | 6.535 | 1.877 | 1.480 | 0.114 | 0.655 | 0.383 | 200.019 | 0.327 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 24 | 20 | 365 | 67 | 22 | 22 | 22 | 22 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 16.59 | 3.05 | 1.00 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.218 | 12.519 | 1.379 | 1.610 | 0.116 | 1.227 | 0.277 | 200.027 | 0.340 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 24 | 20 | 456 | 108 | 22 | 22 | 22 | 22 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 20.73 | 4.91 | 1.00 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.219 | 26.706 | 1.930 | 3.282 | 0.125 | 4.679 | 0.366 | 200.023 | 0.335 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 24 | 20 | 578 | 149 | 22 | 22 | 187 | 22 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 26.27 | 6.77 | 1.00 | 1.00 | 8.50 | 1.00 |
time (sec) |
N/A | 0.220 | 53.527 | 2.057 | 4.439 | 0.129 | 26.584 | 0.415 | 0.782 | 0.325 |