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 | A | B | F(-2) | F(-1) | F | F(-2) | B |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 271 | 271 | 266 | 2291 | 0 | 0 | 0 | 0 | 2500 |
| N.S. |
1 | 1.00 | 0.98 | 8.45 | 0.00 | 0.00 | 0.00 | 0.00 | 9.23 |
| time (sec) |
N/A | 1.205 | 1.650 | 0.635 | 0.000 | 0.000 | 0.000 | 0.000 | 58.881 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | B | B | F(-2) | F(-1) | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 372 | 372 | 1732 | 3605 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 4.66 | 9.69 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 1.676 | 4.137 | 0.680 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | B | B | F(-2) | F(-1) | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 532 | 532 | 7678 | 4969 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 14.43 | 9.34 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 2.850 | 6.349 | 0.654 | 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(-1) | F(-1) | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 503 | 503 | 564 | 5353 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 1.12 | 10.64 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 1.546 | 6.321 | 0.577 | 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(-1) | F(-1) | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 353 | 351 | 324 | 3368 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 0.99 | 0.92 | 9.54 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.833 | 3.498 | 0.526 | 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(-1) | F | F(-2) | B |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 229 | 229 | 262 | 1787 | 0 | 0 | 0 | 0 | 2500 |
| N.S. |
1 | 1.00 | 1.14 | 7.80 | 0.00 | 0.00 | 0.00 | 0.00 | 10.92 |
| time (sec) |
N/A | 0.416 | 1.391 | 0.482 | 0.000 | 0.000 | 0.000 | 0.000 | 117.306 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | B | F(-2) | F(-1) | F(-1) | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 336 | 336 | 322 | 3356 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 0.96 | 9.99 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 1.852 | 3.444 | 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 | B | F(-2) | F(-1) | F(-1) | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 473 | 473 | 6112 | 5214 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 12.92 | 11.02 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 2.642 | 6.349 | 0.686 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | B | B | F(-2) | F(-1) | F(-1) | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 643 | 643 | 18214 | 7283 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 28.33 | 11.33 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 4.322 | 6.604 | 0.784 | 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(-1) | F(-1) | F | F(-2) | B |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 407 | 407 | 392 | 8228 | 0 | 0 | 0 | 0 | 2500 |
| N.S. |
1 | 1.00 | 0.96 | 20.22 | 0.00 | 0.00 | 0.00 | 0.00 | 6.14 |
| time (sec) |
N/A | 1.105 | 5.772 | 0.456 | 0.000 | 0.000 | 0.000 | 0.000 | 122.079 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | B | F(-1) | F(-1) | F | F(-2) | B |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 287 | 287 | 275 | 5860 | 0 | 0 | 0 | 0 | 2500 |
| N.S. |
1 | 1.00 | 0.96 | 20.42 | 0.00 | 0.00 | 0.00 | 0.00 | 8.71 |
| time (sec) |
N/A | 0.647 | 3.920 | 0.458 | 0.000 | 0.000 | 0.000 | 0.000 | 47.981 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | B | F | F(-1) | F | F(-2) | B |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 194 | 194 | 192 | 1349 | 0 | 0 | 0 | 0 | 2500 |
| N.S. |
1 | 1.00 | 0.99 | 6.95 | 0.00 | 0.00 | 0.00 | 0.00 | 12.89 |
| time (sec) |
N/A | 0.326 | 0.985 | 0.437 | 0.000 | 0.000 | 0.000 | 0.000 | 23.482 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | B | F | F(-1) | F | F(-2) | B |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 133 | 133 | 129 | 1894 | 0 | 0 | 0 | 0 | 2500 |
| N.S. |
1 | 1.00 | 0.97 | 14.24 | 0.00 | 0.00 | 0.00 | 0.00 | 18.80 |
| time (sec) |
N/A | 0.151 | 0.150 | 0.432 | 0.000 | 0.000 | 0.000 | 0.000 | 14.206 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | B | F(-2) | F(-1) | F | F(-2) | B |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 210 | 210 | 194 | 3761 | 0 | 0 | 0 | 0 | 2500 |
| N.S. |
1 | 1.00 | 0.92 | 17.91 | 0.00 | 0.00 | 0.00 | 0.00 | 11.90 |
| time (sec) |
N/A | 0.414 | 0.290 | 0.531 | 0.000 | 0.000 | 0.000 | 0.000 | 69.145 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | B | F(-2) | F(-1) | F | F(-2) | B |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 327 | 327 | 338 | 5887 | 0 | 0 | 0 | 0 | 2500 |
| N.S. |
1 | 1.00 | 1.03 | 18.00 | 0.00 | 0.00 | 0.00 | 0.00 | 7.65 |
| time (sec) |
N/A | 0.943 | 4.717 | 0.580 | 0.000 | 0.000 | 0.000 | 0.000 | 57.653 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | C | B | F(-1) | F(-1) | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 511 | 511 | 920 | 13578 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 1.80 | 26.57 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 1.656 | 6.503 | 0.655 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | C | B | F(-1) | F(-1) | F | F(-2) | B |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 343 | 343 | 476 | 9979 | 0 | 0 | 0 | 0 | 2500 |
| N.S. |
1 | 1.00 | 1.39 | 29.09 | 0.00 | 0.00 | 0.00 | 0.00 | 7.29 |
| time (sec) |
N/A | 0.901 | 6.354 | 0.527 | 0.000 | 0.000 | 0.000 | 0.000 | 66.251 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | C | B | F(-1) | F(-1) | F | F(-2) | B |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 201 | 201 | 290 | 6237 | 0 | 0 | 0 | 0 | 2500 |
| N.S. |
1 | 1.00 | 1.44 | 31.03 | 0.00 | 0.00 | 0.00 | 0.00 | 12.44 |
| time (sec) |
N/A | 0.372 | 1.710 | 0.481 | 0.000 | 0.000 | 0.000 | 0.000 | 41.071 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | C | B | F(-1) | F(-1) | F | F(-2) | B |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 157 | 157 | 218 | 3124 | 0 | 0 | 0 | 0 | 2500 |
| N.S. |
1 | 1.00 | 1.39 | 19.90 | 0.00 | 0.00 | 0.00 | 0.00 | 15.92 |
| time (sec) |
N/A | 0.201 | 0.697 | 0.454 | 0.000 | 0.000 | 0.000 | 0.000 | 19.614 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | B | F(-2) | F(-1) | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 262 | 262 | 296 | 6344 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 1.13 | 24.21 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.872 | 3.275 | 0.634 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | B | B | F(-2) | F(-1) | F(-1) | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 447 | 446 | 2078 | 10088 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 4.65 | 22.57 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 1.923 | 6.216 | 0.650 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | C | B | F(-1) | F(-1) | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 585 | 585 | 670 | 21768 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 1.15 | 37.21 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 2.006 | 6.590 | 0.649 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | C | B | F(-1) | F(-1) | F | F(-2) | B |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 358 | 358 | 414 | 15609 | 0 | 0 | 0 | 0 | 2500 |
| N.S. |
1 | 1.00 | 1.16 | 43.60 | 0.00 | 0.00 | 0.00 | 0.00 | 6.98 |
| time (sec) |
N/A | 1.038 | 4.681 | 0.704 | 0.000 | 0.000 | 0.000 | 0.000 | 116.899 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | C | B | F(-1) | F(-1) | F | F(-2) | B |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 273 | 271 | 300 | 9672 | 0 | 0 | 0 | 0 | 2500 |
| N.S. |
1 | 0.99 | 1.10 | 35.43 | 0.00 | 0.00 | 0.00 | 0.00 | 9.16 |
| time (sec) |
N/A | 0.540 | 1.965 | 0.554 | 0.000 | 0.000 | 0.000 | 0.000 | 88.469 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | C | B | F(-1) | F(-1) | F | F(-2) | B |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 209 | 209 | 223 | 4918 | 0 | 0 | 0 | 0 | 2500 |
| N.S. |
1 | 1.00 | 1.07 | 23.53 | 0.00 | 0.00 | 0.00 | 0.00 | 11.96 |
| time (sec) |
N/A | 0.323 | 0.650 | 0.464 | 0.000 | 0.000 | 0.000 | 0.000 | 37.590 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | B | B | F(-2) | F(-1) | F(-1) | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 365 | 365 | 1948 | 10189 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 5.34 | 27.92 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 1.691 | 6.189 | 0.614 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | B | B | F(-2) | F(-1) | F(-1) | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 679 | 678 | 6052 | 15715 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 8.91 | 23.14 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 3.471 | 6.283 | 0.747 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | F | F | F(-1) | F | F(-2) | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 679 | 679 | 1202 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 1.77 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 7.307 | 8.579 | 180.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | F | F | F(-1) | F | F(-2) | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 505 | 505 | 835 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 1.65 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 5.431 | 7.887 | 180.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | F | F | F(-1) | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 381 | 383 | 619 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.01 | 1.62 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 3.560 | 7.189 | 180.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | F | F | F(-1) | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 287 | 287 | 441 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 1.54 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 1.924 | 2.738 | 180.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | C | F(-1) | F(-1) | F(-1) | F | F(-2) | F(-1) |
| verified |
N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 300 | 300 | 621058 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 2070.19 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 2.876 | 33.566 | 180.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | F | F(-2) | F(-1) | F | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 370 | 370 | 424 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 1.15 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 1.341 | 6.146 | 180.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | F | F(-1) | F(-1) | F | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 597 | 597 | 1109 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 1.86 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 2.381 | 6.886 | 180.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | F | F | F(-1) | F | F(-2) | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 682 | 682 | 1304 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 1.91 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 8.725 | 8.081 | 180.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | F | F | F(-1) | F | F(-2) | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 508 | 508 | 867 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 1.71 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 5.339 | 7.978 | 180.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | F | F | F(-1) | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 384 | 384 | 580 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 1.51 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 3.104 | 6.546 | 180.000 | 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(-1) | F(-1) | F | F(-2) | F(-1) |
| verified |
N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 382 | 382 | 1073629 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 2810.55 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 4.280 | 36.188 | 180.000 | 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(-1) | F | F(-2) | F(-1) |
| verified |
N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 402 | 402 | 1347065 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 3350.91 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 5.144 | 36.897 | 180.000 | 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(-2) | F(-1) | F | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 586 | 586 | 3134 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 5.35 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 2.465 | 7.957 | 180.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | F | F | F(-1) | F | F(-2) | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 697 | 697 | 1261 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 1.81 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 7.539 | 8.415 | 180.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | F | F(-1) | F(-1) | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 505 | 505 | 780 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 1.54 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 4.480 | 7.969 | 180.000 | 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(-1) | F(-1) | F | F(-2) | F(-1) |
| verified |
N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 535 | 535 | 1654245 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 3092.05 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 6.184 | 39.156 | 180.000 | 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(-1) | F(-1) | F | F(-2) | F(-1) |
| verified |
N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 545 | 545 | 2018669 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 3703.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 8.262 | 40.815 | 180.000 | 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(-1) | F(-1) | F(-1) | F(-2) | F(-1) |
| verified |
N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 590 | 590 | 2345519 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 3975.46 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 10.903 | 41.820 | 180.000 | 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(-2) | F(-1) | F(-2) | F(-1) | F(-1) |
| verified |
N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 946 | 946 | 2719441 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 2874.67 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 4.317 | 46.370 | 180.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | F | F(-1) | F(-1) | F | F(-1) | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 505 | 505 | 785 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 1.55 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 4.374 | 7.643 | 180.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | F | F | F(-1) | F | F(-1) | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 383 | 383 | 582 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 1.52 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 3.034 | 4.582 | 180.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | F | F | F(-1) | F | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 290 | 290 | 450 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 1.55 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 1.945 | 4.340 | 180.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | F(-1) | F | F(-1) | F | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 239 | 239 | 362 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 1.51 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 1.094 | 1.534 | 180.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | F | F | F(-1) | F | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 251 | 251 | 264 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 1.05 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.652 | 1.716 | 180.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | F | F(-1) | F(-1) | F | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 375 | 375 | 388 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 1.03 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 1.209 | 4.107 | 180.000 | 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(-1) | F(-1) | F | F(-1) | F |
| verified |
N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 528 | 528 | 1653959 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 3132.50 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 5.902 | 39.127 | 180.000 | 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(-1) | F(-1) | F | F(-1) | F |
| verified |
N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 380 | 380 | 1073499 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 2825.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 4.118 | 36.186 | 180.000 | 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(-1) | F(-1) | F | F(-1) | F |
| verified |
N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 299 | 299 | 621084 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 2077.20 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 2.476 | 33.565 | 180.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | F | F | F(-1) | F | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 251 | 251 | 275 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 1.10 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.642 | 2.198 | 180.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | F | F(-1) | F(-1) | F | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 383 | 382 | 484 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 1.26 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 1.277 | 6.498 | 180.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | F | F(-1) | F(-1) | F | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 598 | 598 | 902 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 1.51 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 2.357 | 6.618 | 180.000 | 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(-1) | F(-1) | F | F(-1) | F |
| verified |
N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 549 | 549 | 2018643 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 3676.95 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 7.959 | 40.927 | 180.000 | 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(-1) | F | F(-1) | F |
| verified |
N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 407 | 407 | 1347117 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 3309.87 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 5.473 | 37.116 | 180.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | F | F(-2) | F(-1) | F | F(-1) | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 373 | 373 | 434 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 1.16 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 1.296 | 6.105 | 180.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | F | F(-1) | F(-1) | F | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 379 | 379 | 403 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 1.06 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 1.236 | 3.720 | 180.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | F(-1) | F(-1) | F(-1) | F | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 651 | 650 | 903 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 1.39 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 2.397 | 6.648 | 180.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | F | F | F | F | F(-2) | F | F |
| verified |
N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 376 | 376 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.616 | 16.614 | 0.370 | 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(-1) | F | F | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 560 | 551 | 1390 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 0.98 | 2.48 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 1.550 | 6.298 | 0.618 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | F | F | F | F | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 363 | 360 | 308 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. | 1 | 0.99 | 0.85 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.771 | 4.836 | 0.324 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | F | F | F | F | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 247 | 247 | 202 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. | 1 | 1.00 | 0.82 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.355 | 1.995 | 0.250 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | F | F | F | F | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 178 | 178 | 135 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. | 1 | 1.00 | 0.76 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
| time (sec) |
N/A | 0.127 | 0.180 | 0.160 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | F | F | F | F | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 258 | 258 | 204 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. | 1 | 1.00 | 0.79 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.336 | 0.753 | 0.342 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | F | F | F | F(-2) | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 403 | 402 | 360 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 0.89 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.842 | 5.702 | 0.398 | 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 | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 702 | 702 | 2238 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. | 1 | 1.00 | 3.19 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 2.106 | 6.169 | 0.601 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |