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 | B | F | B | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 136 | 140 | 153 | 370 | 0 | 684 | 0 | 153 | 410 | 0 |
N.S. |
1 | 1.03 | 1.12 | 2.72 | 0.00 | 5.03 | 0.00 | 1.12 | 3.01 | 0.00 |
time (sec) |
N/A | 0.283 | 2.679 | 1.412 | 0.000 | 0.096 | 0.000 | 0.283 | 0.226 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F(-1) | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 220 | 192 | 253 | 494 | 0 | 588 | 0 | 0 | 492 | 0 |
N.S. |
1 | 0.87 | 1.15 | 2.25 | 0.00 | 2.67 | 0.00 | 0.00 | 2.24 | 0.00 |
time (sec) |
N/A | 0.316 | 1.949 | 1.355 | 0.000 | 0.117 | 0.000 | 0.000 | 0.233 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 172 | 156 | 205 | 350 | 0 | 488 | 0 | 0 | 347 | 0 |
N.S. |
1 | 0.91 | 1.19 | 2.03 | 0.00 | 2.84 | 0.00 | 0.00 | 2.02 | 0.00 |
time (sec) |
N/A | 0.280 | 5.215 | 1.394 | 0.000 | 0.109 | 0.000 | 0.000 | 0.204 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 128 | 124 | 185 | 234 | 0 | 406 | 0 | 117 | 227 | 0 |
N.S. |
1 | 0.97 | 1.45 | 1.83 | 0.00 | 3.17 | 0.00 | 0.91 | 1.77 | 0.00 |
time (sec) |
N/A | 0.260 | 5.095 | 1.310 | 0.000 | 0.109 | 0.000 | 0.415 | 0.234 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 115 | 141 | 171 | 272 | 0 | 454 | 0 | 117 | 117 | 0 |
N.S. |
1 | 1.23 | 1.49 | 2.37 | 0.00 | 3.95 | 0.00 | 1.02 | 1.02 | 0.00 |
time (sec) |
N/A | 0.281 | 10.316 | 1.377 | 0.000 | 0.112 | 0.000 | 0.454 | 0.247 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F(-1) | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 119 | 126 | 165 | 422 | 0 | 631 | 0 | 158 | 241 | 0 |
N.S. |
1 | 1.06 | 1.39 | 3.55 | 0.00 | 5.30 | 0.00 | 1.33 | 2.03 | 0.00 |
time (sec) |
N/A | 0.250 | 10.929 | 1.497 | 0.000 | 0.111 | 0.000 | 0.442 | 0.207 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 97 | 97 | 68 | 58 | 0 | 200 | 0 | 122 | 118 | 172 |
N.S. |
1 | 1.00 | 0.70 | 0.60 | 0.00 | 2.06 | 0.00 | 1.26 | 1.22 | 1.77 |
time (sec) |
N/A | 0.243 | 10.069 | 1.410 | 0.000 | 0.086 | 0.000 | 0.599 | 0.206 | 11.708 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 145 | 140 | 91 | 90 | 0 | 325 | 0 | 218 | 233 | 251 |
N.S. |
1 | 0.97 | 0.63 | 0.62 | 0.00 | 2.24 | 0.00 | 1.50 | 1.61 | 1.73 |
time (sec) |
N/A | 0.265 | 10.101 | 1.522 | 0.000 | 0.094 | 0.000 | 0.728 | 0.238 | 11.875 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 193 | 185 | 120 | 135 | 0 | 476 | 0 | 341 | 383 | 336 |
N.S. |
1 | 0.96 | 0.62 | 0.70 | 0.00 | 2.47 | 0.00 | 1.77 | 1.98 | 1.74 |
time (sec) |
N/A | 0.286 | 7.930 | 1.578 | 0.000 | 0.098 | 0.000 | 0.767 | 0.210 | 11.910 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 241 | 230 | 152 | 191 | 0 | 653 | 0 | 491 | 566 | 436 |
N.S. |
1 | 0.95 | 0.63 | 0.79 | 0.00 | 2.71 | 0.00 | 2.04 | 2.35 | 1.81 |
time (sec) |
N/A | 0.303 | 8.336 | 1.451 | 0.000 | 0.112 | 0.000 | 0.415 | 0.220 | 12.910 |
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 | 145 | 145 | 135 | 0 | 0 | 0 | 0 | 0 | 38 | 0 |
N.S. |
1 | 1.00 | 0.93 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 0.363 | 0.793 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 200.038 | 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 | 143 | 143 | 124 | 0 | 0 | 0 | 0 | 0 | 36 | 0 |
N.S. |
1 | 1.00 | 0.87 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.25 | 0.00 |
time (sec) |
N/A | 0.311 | 0.498 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 200.033 | 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 | 134 | 134 | 123 | 0 | 0 | 0 | 0 | 0 | 31 | 0 |
N.S. |
1 | 1.00 | 0.92 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.23 | 0.00 |
time (sec) |
N/A | 0.265 | 0.317 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 200.033 | 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 | 142 | 142 | 132 | 0 | 0 | 0 | 0 | 0 | 38 | 0 |
N.S. |
1 | 1.00 | 0.93 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.27 | 0.00 |
time (sec) |
N/A | 0.319 | 0.433 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 200.058 | 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 | 143 | 143 | 133 | 0 | 0 | 0 | 0 | 0 | 38 | 0 |
N.S. |
1 | 1.00 | 0.93 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.27 | 0.00 |
time (sec) |
N/A | 0.322 | 0.418 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 200.045 | 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 | 147 | 148 | 138 | 0 | 0 | 0 | 0 | 0 | 38 | 0 |
N.S. |
1 | 1.01 | 0.94 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 0.315 | 0.420 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 200.045 | 0.000 |