Detailed conclusion table per each integral is given by 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 just an F.
In this table,the column N.S. in the table below, which stands for normalized size is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To help make the table fit, Mathematica was abbreviated to MMA.
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | C | F | B | B | F(-1) | F | B |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 384 | 384 | 899 | 0 | 936 | 791 | 0 | 0 | 1110 |
| N.S. |
1 | 1.00 | 2.34 | 0.00 | 2.44 | 2.06 | 0.00 | 0.00 | 2.89 |
| time (sec) |
N/A | 0.607 | 6.685 | 1.339 | 0.590 | 0.427 | 0.000 | 0.000 | 23.158 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | F | B | A | F(-2) | F | B |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 285 | 285 | 264 | 0 | 684 | 473 | 0 | 0 | 714 |
| N.S. |
1 | 1.00 | 0.93 | 0.00 | 2.40 | 1.66 | 0.00 | 0.00 | 2.51 |
| time (sec) |
N/A | 0.473 | 2.367 | 1.348 | 0.569 | 0.408 | 0.000 | 0.000 | 20.659 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | F | B | A | F | F | B |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 180 | 180 | 160 | 0 | 469 | 271 | 0 | 0 | 185 |
| N.S. | 1 | 1.00 | 0.89 | 0.00 | 2.61 | 1.51 | 0.00 | 0.00 | 1.03 |
| time (sec) |
N/A | 0.377 | 0.535 | 1.173 | 0.557 | 0.421 | 0.000 | 0.000 | 17.164 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | C | F | F | F | F | F(-1) | F |
| verified |
N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 123 | 123 | 19244 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 156.46 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
| time (sec) |
N/A | 0.187 | 75.012 | 0.646 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | C | F | F | F | F | F(-2) | F |
| verified |
N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 202 | 202 | 4061 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 20.10 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.389 | 6.974 | 0.623 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | C | F | F | F | F(-1) | F(-2) | F |
| verified |
N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 207 | 207 | 8316 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 40.17 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.416 | 6.742 | 0.596 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | B | F | F | F | A | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 167 | 167 | 190 | 345 | 0 | 0 | 0 | 220 | -1 |
| N.S. | 1 | 1.00 | 1.14 | 2.07 | 0.00 | 0.00 | 0.00 | 1.32 | -0.01 |
| time (sec) |
N/A | 0.410 | 0.448 | 21.878 | 0.000 | 0.000 | 0.000 | 0.572 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | C | F | F | F | F | F | F |
| verified |
N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 257 | 257 | 4861 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. | 1 | 1.00 | 18.91 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.445 | 15.680 | 0.704 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | B | F | F | F | F(-1) | F | F |
| verified |
N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 366 | 365 | 1873 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 5.12 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.548 | 8.098 | 1.429 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | B | F | F | F | F(-2) | F | F |
| verified |
N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 392 | 392 | 7530 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 19.21 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.674 | 50.475 | 5.803 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | B | F | F | F | F(-2) | F | F |
| verified |
N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 385 | 384 | 4492 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 11.67 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.654 | 29.238 | 0.642 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | B | F | F | F | F | F | F |
| verified |
N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 375 | 374 | 1874 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. | 1 | 1.00 | 5.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.606 | 7.265 | 0.601 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | B | F | F | F | F | F | F |
| verified |
N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 365 | 365 | 9629 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. | 1 | 1.00 | 26.38 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.601 | 55.879 | 0.576 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | B | F | F | F | F | F | F |
| verified |
N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 413 | 413 | 19634 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. | 1 | 1.00 | 47.54 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.651 | 57.911 | 0.541 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | B | F | F | F | F(-1) | F | F |
| verified |
N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 424 | 424 | 25065 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 59.12 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.693 | 63.895 | 0.542 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | B | F | F | F | A | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 174 | 174 | 196 | 476 | 0 | 0 | 0 | 252 | -1 |
| N.S. | 1 | 1.00 | 1.13 | 2.74 | 0.00 | 0.00 | 0.00 | 1.45 | -0.01 |
| time (sec) |
N/A | 0.411 | 0.505 | 25.378 | 0.000 | 0.000 | 0.000 | 0.558 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | C | F | F | F | F | F | F |
| verified |
N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 269 | 269 | 6226 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. | 1 | 1.00 | 23.14 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.477 | 17.751 | 1.652 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | C | F | B | B | F(-1) | F | B |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 435 | 435 | 1029 | 0 | 1390 | 951 | 0 | 0 | 1253 |
| N.S. |
1 | 1.00 | 2.37 | 0.00 | 3.20 | 2.19 | 0.00 | 0.00 | 2.88 |
| time (sec) |
N/A | 0.576 | 6.899 | 1.642 | 0.651 | 0.484 | 0.000 | 0.000 | 22.847 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | F | B | A | F(-2) | F | B |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 322 | 322 | 306 | 0 | 1004 | 575 | 0 | 0 | 790 |
| N.S. |
1 | 1.00 | 0.95 | 0.00 | 3.12 | 1.79 | 0.00 | 0.00 | 2.45 |
| time (sec) |
N/A | 0.465 | 3.426 | 1.736 | 0.604 | 0.452 | 0.000 | 0.000 | 23.159 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | F | B | A | F | F | B |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 197 | 197 | 177 | 0 | 686 | 320 | 0 | 0 | 510 |
| N.S. | 1 | 1.00 | 0.90 | 0.00 | 3.48 | 1.62 | 0.00 | 0.00 | 2.59 |
| time (sec) |
N/A | 0.407 | 0.710 | 1.637 | 0.598 | 0.411 | 0.000 | 0.000 | 19.422 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | C | F | F | F | F | F(-1) | F |
| verified |
N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 170 | 170 | 21299 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 125.29 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
| time (sec) |
N/A | 0.294 | 36.635 | 1.548 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | C | F | F | F | F | F(-2) | F |
| verified |
N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 216 | 216 | 4066 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 18.82 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.428 | 6.873 | 1.470 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | C | F | F | F | F(-1) | F(-2) | F |
| verified |
N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 230 | 230 | 8321 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 36.18 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.449 | 6.984 | 1.479 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | C | F | F | F | F(-2) | F | F |
| verified |
N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 232 | 232 | 1087 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 4.69 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.470 | 24.560 | 4.656 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | B | F | F | F | F(-1) | F | F |
| verified |
N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 383 | 381 | 2572 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 0.99 | 6.72 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.617 | 7.974 | 1.642 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | B | F | F | F | F(-2) | F | F |
| verified |
N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 410 | 410 | 5175 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 12.62 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.706 | 40.222 | 5.910 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | B | F | F | F | F(-2) | F | F |
| verified |
N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 406 | 403 | 6591 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 0.99 | 16.23 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.678 | 8.481 | 1.608 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | B | F | F | F | F | F | F |
| verified |
N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 396 | 393 | 2574 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. | 1 | 0.99 | 6.50 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.652 | 7.724 | 1.615 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | B | F | F | F | F | F | F |
| verified |
N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 389 | 386 | 9760 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. | 1 | 0.99 | 25.09 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.648 | 57.648 | 1.537 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | B | F | F | F | F | F | F |
| verified |
N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 433 | 433 | 31369 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. | 1 | 1.00 | 72.45 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.703 | 60.567 | 1.439 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | B | F | F | F | F(-1) | F | F |
| verified |
N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 451 | 451 | 20654 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 45.80 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.780 | 64.501 | 1.414 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | A | A | A | B | A | B |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 81 | 113 | 92 | 104 | 102 | 71 | 189 | 76 | 93 |
| N.S. | 1 | 1.40 | 1.14 | 1.28 | 1.26 | 0.88 | 2.33 | 0.94 | 1.15 |
| time (sec) |
N/A | 0.067 | 0.141 | 0.224 | 0.283 | 0.390 | 0.136 | 0.445 | 13.758 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | B | F | C | F | F | B |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 117 | 117 | 97 | 516 | 0 | 249 | 0 | 0 | 169 |
| N.S. | 1 | 1.00 | 0.83 | 4.41 | 0.00 | 2.13 | 0.00 | 0.00 | 1.44 |
| time (sec) |
N/A | 0.142 | 0.537 | 6.129 | 0.000 | 0.123 | 0.000 | 0.000 | 14.847 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-1) | A | F(-2) | F(-1) | A |
| verified |
N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 48 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.02 |
| time (sec) |
N/A | 0.071 | 39.977 | 1.677 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |