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 | F | F(-2) | F(-1) | F | F | F | F(-1) |
| verified |
N/A | No | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 618 | 798 | 377 | 0 | 0 | 0 | 0 | 0 | 25 | 0 |
| N.S. |
1 | 1.29 | 0.61 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.04 | 0.00 |
| time (sec) |
N/A | 1.472 | 14.275 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 200.027 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | B | F | F(-2) | F(-1) | F(-1) | F | F | F(-1) |
| verified |
N/A | N/A | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 1133 | 0 | 3485 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.00 | 3.08 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.000 | 23.987 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 1.738 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | C | F | F(-2) | F(-1) | F(-1) | F | F | F(-1) |
| verified |
N/A | N/A | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 1 | 0 | 5962 | 0 | 0 | 0 | 0 | 0 | 25 | 0 |
| N.S. |
1 | 0.00 | 5962.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 25.00 | 0.00 |
| time (sec) |
N/A | 0.000 | 24.668 | 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 | C | F | F | F | F(-2) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 646 | 371 | 356 | 1396 | 0 | 0 | 0 | 0 | 341 | 0 |
| N.S. |
1 | 0.57 | 0.55 | 2.16 | 0.00 | 0.00 | 0.00 | 0.00 | 0.53 | 0.00 |
| time (sec) |
N/A | 1.069 | 0.261 | 1.120 | 0.000 | 0.000 | 0.000 | 0.000 | 0.263 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | C | F | F | F | F(-2) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 443 | 263 | 237 | 973 | 0 | 0 | 0 | 0 | 223 | 0 |
| N.S. |
1 | 0.59 | 0.53 | 2.20 | 0.00 | 0.00 | 0.00 | 0.00 | 0.50 | 0.00 |
| time (sec) |
N/A | 0.842 | 0.307 | 0.770 | 0.000 | 0.000 | 0.000 | 0.000 | 0.237 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | C | F | F | F | F(-2) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 231 | 140 | 132 | 628 | 0 | 0 | 0 | 0 | 127 | 0 |
| N.S. |
1 | 0.61 | 0.57 | 2.72 | 0.00 | 0.00 | 0.00 | 0.00 | 0.55 | 0.00 |
| time (sec) |
N/A | 0.513 | 0.146 | 0.889 | 0.000 | 0.000 | 0.000 | 0.000 | 0.277 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F(-2) | F | F | F(-2) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 736 | 517 | 368 | 823 | 0 | 0 | 0 | 0 | 110 | 0 |
| N.S. |
1 | 0.70 | 0.50 | 1.12 | 0.00 | 0.00 | 0.00 | 0.00 | 0.15 | 0.00 |
| time (sec) |
N/A | 2.365 | 0.620 | 1.029 | 0.000 | 0.000 | 0.000 | 0.000 | 0.240 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F(-2) | F | F | F(-2) | F | F(-1) |
| verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 860 | 632 | 600 | 1352 | 0 | 0 | 0 | 0 | 412 | 0 |
| N.S. |
1 | 0.73 | 0.70 | 1.57 | 0.00 | 0.00 | 0.00 | 0.00 | 0.48 | 0.00 |
| time (sec) |
N/A | 2.911 | 1.839 | 1.201 | 0.000 | 0.000 | 0.000 | 0.000 | 0.234 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | C | F | F | F(-1) | F(-2) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 904 | 498 | 463 | 2074 | 0 | 0 | 0 | 0 | 558 | 0 |
| N.S. |
1 | 0.55 | 0.51 | 2.29 | 0.00 | 0.00 | 0.00 | 0.00 | 0.62 | 0.00 |
| time (sec) |
N/A | 1.269 | 0.677 | 1.612 | 0.000 | 0.000 | 0.000 | 0.000 | 0.279 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | C | F | F | F(-1) | F(-2) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 645 | 367 | 332 | 1535 | 0 | 0 | 0 | 0 | 381 | 0 |
| N.S. |
1 | 0.57 | 0.51 | 2.38 | 0.00 | 0.00 | 0.00 | 0.00 | 0.59 | 0.00 |
| time (sec) |
N/A | 1.037 | 0.287 | 1.029 | 0.000 | 0.000 | 0.000 | 0.000 | 0.294 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | C | F | F | F | F(-2) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 346 | 193 | 216 | 1014 | 0 | 0 | 0 | 0 | 226 | 0 |
| N.S. |
1 | 0.56 | 0.62 | 2.93 | 0.00 | 0.00 | 0.00 | 0.00 | 0.65 | 0.00 |
| time (sec) |
N/A | 0.609 | 0.174 | 1.052 | 0.000 | 0.000 | 0.000 | 0.000 | 0.247 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F(-2) | F | F | F(-2) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 1062 | 709 | 507 | 1546 | 0 | 0 | 0 | 0 | 298 | 0 |
| N.S. |
1 | 0.67 | 0.48 | 1.46 | 0.00 | 0.00 | 0.00 | 0.00 | 0.28 | 0.00 |
| time (sec) |
N/A | 2.892 | 0.940 | 1.029 | 0.000 | 0.000 | 0.000 | 0.000 | 0.232 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | C | F | F | F(-1) | F(-2) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 1188 | 630 | 587 | 2903 | 0 | 0 | 0 | 0 | 776 | 0 |
| N.S. |
1 | 0.53 | 0.49 | 2.44 | 0.00 | 0.00 | 0.00 | 0.00 | 0.65 | 0.00 |
| time (sec) |
N/A | 1.653 | 0.592 | 2.135 | 0.000 | 0.000 | 0.000 | 0.000 | 0.358 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | C | F | F | F(-1) | F(-2) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 871 | 481 | 390 | 2090 | 0 | 0 | 0 | 0 | 540 | 0 |
| N.S. |
1 | 0.55 | 0.45 | 2.40 | 0.00 | 0.00 | 0.00 | 0.00 | 0.62 | 0.00 |
| time (sec) |
N/A | 1.268 | 0.409 | 1.559 | 0.000 | 0.000 | 0.000 | 0.000 | 0.318 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | C | F | F | F(-1) | F(-2) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 475 | 256 | 251 | 1423 | 0 | 0 | 0 | 0 | 326 | 0 |
| N.S. |
1 | 0.54 | 0.53 | 3.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.69 | 0.00 |
| time (sec) |
N/A | 0.704 | 0.244 | 1.302 | 0.000 | 0.000 | 0.000 | 0.000 | 0.260 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F(-2) | F | F | F(-2) | F | F(-1) |
| verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 1609 | 1019 | 787 | 2580 | 0 | 0 | 0 | 0 | 547 | 0 |
| N.S. |
1 | 0.63 | 0.49 | 1.60 | 0.00 | 0.00 | 0.00 | 0.00 | 0.34 | 0.00 |
| time (sec) |
N/A | 3.166 | 1.690 | 1.332 | 0.000 | 0.000 | 0.000 | 0.000 | 0.276 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | C | F | F | F(-2) | F(-2) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 422 | 262 | 343 | 856 | 0 | 0 | 0 | 0 | 234 | 0 |
| N.S. |
1 | 0.62 | 0.81 | 2.03 | 0.00 | 0.00 | 0.00 | 0.00 | 0.55 | 0.00 |
| time (sec) |
N/A | 0.868 | 0.820 | 0.863 | 0.000 | 0.000 | 0.000 | 0.000 | 0.249 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | C | F | F | F(-2) | F(-2) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 256 | 162 | 266 | 505 | 0 | 0 | 0 | 0 | 150 | 0 |
| N.S. |
1 | 0.63 | 1.04 | 1.97 | 0.00 | 0.00 | 0.00 | 0.00 | 0.59 | 0.00 |
| time (sec) |
N/A | 0.763 | 0.525 | 0.685 | 0.000 | 0.000 | 0.000 | 0.000 | 0.223 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | C | A | F | F(-2) | F(-2) | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 119 | 87 | 172 | 247 | 90 | 0 | 0 | 0 | 70 | 0 |
| N.S. |
1 | 0.73 | 1.45 | 2.08 | 0.76 | 0.00 | 0.00 | 0.00 | 0.59 | 0.00 |
| time (sec) |
N/A | 0.530 | 0.225 | 0.734 | 0.139 | 0.000 | 0.000 | 0.000 | 0.238 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | F | F | F(-2) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 380 | 288 | 232 | 508 | 0 | 0 | 0 | 0 | 156 | 0 |
| N.S. |
1 | 0.76 | 0.61 | 1.34 | 0.00 | 0.00 | 0.00 | 0.00 | 0.41 | 0.00 |
| time (sec) |
N/A | 1.143 | 0.136 | 0.853 | 0.000 | 0.000 | 0.000 | 0.000 | 0.233 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | F | F | F(-2) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 500 | 384 | 295 | 931 | 0 | 0 | 0 | 0 | 610 | 0 |
| N.S. |
1 | 0.77 | 0.59 | 1.86 | 0.00 | 0.00 | 0.00 | 0.00 | 1.22 | 0.00 |
| time (sec) |
N/A | 1.469 | 0.298 | 0.898 | 0.000 | 0.000 | 0.000 | 0.000 | 0.260 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | C | F | F | F | F(-2) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 305 | 213 | 185 | 724 | 0 | 0 | 0 | 0 | 373 | 0 |
| N.S. |
1 | 0.70 | 0.61 | 2.37 | 0.00 | 0.00 | 0.00 | 0.00 | 1.22 | 0.00 |
| time (sec) |
N/A | 0.796 | 0.700 | 1.293 | 0.000 | 0.000 | 0.000 | 0.000 | 0.253 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | C | F | F | F | F(-2) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 213 | 143 | 147 | 488 | 0 | 0 | 0 | 0 | 275 | 0 |
| N.S. |
1 | 0.67 | 0.69 | 2.29 | 0.00 | 0.00 | 0.00 | 0.00 | 1.29 | 0.00 |
| time (sec) |
N/A | 0.651 | 0.466 | 1.039 | 0.000 | 0.000 | 0.000 | 0.000 | 0.234 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | C | F | F | F | F(-2) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 144 | 100 | 126 | 305 | 0 | 0 | 0 | 0 | 154 | 0 |
| N.S. |
1 | 0.69 | 0.88 | 2.12 | 0.00 | 0.00 | 0.00 | 0.00 | 1.07 | 0.00 |
| time (sec) |
N/A | 0.407 | 0.374 | 1.484 | 0.000 | 0.000 | 0.000 | 0.000 | 0.211 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | F | F | F(-2) | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 654 | 431 | 351 | 1101 | 0 | 0 | 0 | 0 | 470 | 0 |
| N.S. |
1 | 0.66 | 0.54 | 1.68 | 0.00 | 0.00 | 0.00 | 0.00 | 0.72 | 0.00 |
| time (sec) |
N/A | 1.450 | 1.293 | 2.250 | 0.000 | 0.000 | 0.000 | 0.000 | 0.225 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | C | F | F | F | F(-2) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 570 | 452 | 868 | 6743 | 0 | 0 | 0 | 0 | 1086 | 0 |
| N.S. |
1 | 0.79 | 1.52 | 11.83 | 0.00 | 0.00 | 0.00 | 0.00 | 1.91 | 0.00 |
| time (sec) |
N/A | 0.925 | 2.058 | 1.972 | 0.000 | 0.000 | 0.000 | 0.000 | 0.272 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | C | F | F | F | F(-2) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 330 | 277 | 366 | 5114 | 0 | 0 | 0 | 0 | 839 | 0 |
| N.S. |
1 | 0.84 | 1.11 | 15.50 | 0.00 | 0.00 | 0.00 | 0.00 | 2.54 | 0.00 |
| time (sec) |
N/A | 0.738 | 0.795 | 1.440 | 0.000 | 0.000 | 0.000 | 0.000 | 0.232 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | C | F | F | F | F(-2) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 259 | 192 | 285 | 3783 | 0 | 0 | 0 | 0 | 597 | 0 |
| N.S. |
1 | 0.74 | 1.10 | 14.61 | 0.00 | 0.00 | 0.00 | 0.00 | 2.31 | 0.00 |
| time (sec) |
N/A | 0.582 | 0.621 | 1.213 | 0.000 | 0.000 | 0.000 | 0.000 | 0.235 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | C | F | F | F | F(-2) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 216 | 159 | 208 | 2237 | 0 | 0 | 0 | 0 | 371 | 0 |
| N.S. |
1 | 0.74 | 0.96 | 10.36 | 0.00 | 0.00 | 0.00 | 0.00 | 1.72 | 0.00 |
| time (sec) |
N/A | 0.466 | 0.471 | 1.783 | 0.000 | 0.000 | 0.000 | 0.000 | 0.258 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F | F | F | F(-2) | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 1300 | 821 | 2078 | 8599 | 0 | 0 | 0 | 0 | 1557 | 0 |
| N.S. |
1 | 0.63 | 1.60 | 6.61 | 0.00 | 0.00 | 0.00 | 0.00 | 1.20 | 0.00 |
| time (sec) |
N/A | 2.238 | 12.705 | 2.129 | 0.000 | 0.000 | 0.000 | 0.000 | 0.256 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | C | F | F | F | F(-2) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 1084 | 750 | 708 | 2728 | 0 | 0 | 0 | 0 | 502 | 0 |
| N.S. |
1 | 0.69 | 0.65 | 2.52 | 0.00 | 0.00 | 0.00 | 0.00 | 0.46 | 0.00 |
| time (sec) |
N/A | 1.899 | 0.659 | 1.085 | 0.000 | 0.000 | 0.000 | 0.000 | 0.296 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | C | F | F | F | F(-2) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 723 | 477 | 441 | 1852 | 0 | 0 | 0 | 0 | 338 | 0 |
| N.S. |
1 | 0.66 | 0.61 | 2.56 | 0.00 | 0.00 | 0.00 | 0.00 | 0.47 | 0.00 |
| time (sec) |
N/A | 1.247 | 0.529 | 0.785 | 0.000 | 0.000 | 0.000 | 0.000 | 0.294 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | C | F | F | F | F(-2) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 382 | 256 | 225 | 1236 | 0 | 0 | 0 | 0 | 198 | 0 |
| N.S. |
1 | 0.67 | 0.59 | 3.24 | 0.00 | 0.00 | 0.00 | 0.00 | 0.52 | 0.00 |
| time (sec) |
N/A | 0.772 | 0.154 | 0.649 | 0.000 | 0.000 | 0.000 | 0.000 | 0.230 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F(-2) | F | F | F(-2) | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 1442 | 1018 | 516 | 0 | 0 | 0 | 0 | 0 | 154 | 0 |
| N.S. |
1 | 0.71 | 0.36 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.11 | 0.00 |
| time (sec) |
N/A | 3.577 | 0.864 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.235 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | C | F | F | F(-1) | F(-2) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 1538 | 1066 | 872 | 4176 | 0 | 0 | 0 | 0 | 869 | 0 |
| N.S. |
1 | 0.69 | 0.57 | 2.72 | 0.00 | 0.00 | 0.00 | 0.00 | 0.57 | 0.00 |
| time (sec) |
N/A | 2.477 | 1.349 | 1.514 | 0.000 | 0.000 | 0.000 | 0.000 | 0.374 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | C | F | F | F(-1) | F(-2) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 1044 | 699 | 616 | 3032 | 0 | 0 | 0 | 0 | 606 | 0 |
| N.S. |
1 | 0.67 | 0.59 | 2.90 | 0.00 | 0.00 | 0.00 | 0.00 | 0.58 | 0.00 |
| time (sec) |
N/A | 1.721 | 0.601 | 1.110 | 0.000 | 0.000 | 0.000 | 0.000 | 0.291 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | C | F | F | F | F(-2) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 568 | 384 | 395 | 2021 | 0 | 0 | 0 | 0 | 367 | 0 |
| N.S. |
1 | 0.68 | 0.70 | 3.56 | 0.00 | 0.00 | 0.00 | 0.00 | 0.65 | 0.00 |
| time (sec) |
N/A | 0.958 | 0.374 | 0.984 | 0.000 | 0.000 | 0.000 | 0.000 | 0.287 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F(-2) | F | F | F(-2) | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 1970 | 1369 | 740 | 0 | 0 | 0 | 0 | 0 | 394 | 0 |
| N.S. |
1 | 0.69 | 0.38 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.20 | 0.00 |
| time (sec) |
N/A | 4.068 | 1.550 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.307 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | C | F | F | F(-1) | F(-2) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 2037 | 1379 | 1114 | 5977 | 0 | 0 | 0 | 0 | 1237 | 0 |
| N.S. |
1 | 0.68 | 0.55 | 2.93 | 0.00 | 0.00 | 0.00 | 0.00 | 0.61 | 0.00 |
| time (sec) |
N/A | 3.522 | 1.070 | 2.094 | 0.000 | 0.000 | 0.000 | 0.000 | 0.444 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | C | F | F | F(-1) | F(-2) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 1401 | 922 | 742 | 4170 | 0 | 0 | 0 | 0 | 875 | 0 |
| N.S. |
1 | 0.66 | 0.53 | 2.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.62 | 0.00 |
| time (sec) |
N/A | 2.295 | 0.779 | 1.709 | 0.000 | 0.000 | 0.000 | 0.000 | 0.370 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | C | F | F | F(-1) | F(-2) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 773 | 513 | 470 | 2852 | 0 | 0 | 0 | 0 | 537 | 0 |
| N.S. |
1 | 0.66 | 0.61 | 3.69 | 0.00 | 0.00 | 0.00 | 0.00 | 0.69 | 0.00 |
| time (sec) |
N/A | 1.214 | 0.506 | 1.231 | 0.000 | 0.000 | 0.000 | 0.000 | 0.322 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F(-2) | F | F(-1) | F(-2) | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 2897 | 1986 | 1275 | 0 | 0 | 0 | 0 | 0 | 703 | 0 |
| N.S. |
1 | 0.69 | 0.44 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.24 | 0.00 |
| time (sec) |
N/A | 4.971 | 3.054 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 20.338 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | C | F | F | F(-2) | F(-2) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 634 | 417 | 582 | 1636 | 0 | 0 | 0 | 0 | 410 | 0 |
| N.S. |
1 | 0.66 | 0.92 | 2.58 | 0.00 | 0.00 | 0.00 | 0.00 | 0.65 | 0.00 |
| time (sec) |
N/A | 0.917 | 1.255 | 0.991 | 0.000 | 0.000 | 0.000 | 0.000 | 0.240 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | C | F | F | F(-2) | F(-2) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 382 | 240 | 400 | 928 | 0 | 0 | 0 | 0 | 278 | 0 |
| N.S. |
1 | 0.63 | 1.05 | 2.43 | 0.00 | 0.00 | 0.00 | 0.00 | 0.73 | 0.00 |
| time (sec) |
N/A | 0.780 | 1.081 | 0.706 | 0.000 | 0.000 | 0.000 | 0.000 | 0.266 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | C | A | F | F(-2) | F(-2) | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 157 | 128 | 118 | 460 | 184 | 0 | 0 | 0 | 142 | 0 |
| N.S. |
1 | 0.82 | 0.75 | 2.93 | 1.17 | 0.00 | 0.00 | 0.00 | 0.90 | 0.00 |
| time (sec) |
N/A | 0.585 | 0.528 | 0.738 | 0.157 | 0.000 | 0.000 | 0.000 | 0.246 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | F | F(-2) | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 589 | 402 | 357 | 0 | 0 | 0 | 0 | 0 | 257 | 0 |
| N.S. |
1 | 0.68 | 0.61 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.44 | 0.00 |
| time (sec) |
N/A | 1.711 | 0.238 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.224 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | F | F(-2) | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 1106 | 721 | 651 | 0 | 0 | 0 | 0 | 0 | 1061 | 0 |
| N.S. |
1 | 0.65 | 0.59 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.96 | 0.00 |
| time (sec) |
N/A | 3.254 | 0.483 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.268 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F | F | F | F(-2) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 677 | 447 | 325 | 1528 | 0 | 0 | 0 | 0 | 681 | 0 |
| N.S. |
1 | 0.66 | 0.48 | 2.26 | 0.00 | 0.00 | 0.00 | 0.00 | 1.01 | 0.00 |
| time (sec) |
N/A | 1.432 | 2.117 | 1.545 | 0.000 | 0.000 | 0.000 | 0.000 | 0.247 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | F | F | F(-2) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 513 | 314 | 259 | 974 | 0 | 0 | 0 | 0 | 505 | 0 |
| N.S. |
1 | 0.61 | 0.50 | 1.90 | 0.00 | 0.00 | 0.00 | 0.00 | 0.98 | 0.00 |
| time (sec) |
N/A | 1.259 | 1.365 | 0.955 | 0.000 | 0.000 | 0.000 | 0.000 | 0.241 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | F | F | F(-2) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 410 | 243 | 237 | 612 | 0 | 0 | 0 | 0 | 287 | 0 |
| N.S. |
1 | 0.59 | 0.58 | 1.49 | 0.00 | 0.00 | 0.00 | 0.00 | 0.70 | 0.00 |
| time (sec) |
N/A | 0.982 | 0.890 | 0.958 | 0.000 | 0.000 | 0.000 | 0.000 | 0.264 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | F | F(-2) | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 1137 | 722 | 597 | 0 | 0 | 0 | 0 | 0 | 790 | 0 |
| N.S. |
1 | 0.64 | 0.53 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.69 | 0.00 |
| time (sec) |
N/A | 2.684 | 3.241 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.275 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F | F | F | F(-2) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 1589 | 918 | 715 | 13140 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.58 | 0.45 | 8.27 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.512 | 6.154 | 1.664 | 0.000 | 0.000 | 0.000 | 0.000 | 0.261 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F | F | F | F(-2) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 989 | 614 | 618 | 9720 | 0 | 0 | 0 | 0 | 1122 | 0 |
| N.S. |
1 | 0.62 | 0.62 | 9.83 | 0.00 | 0.00 | 0.00 | 0.00 | 1.13 | 0.00 |
| time (sec) |
N/A | 1.741 | 4.994 | 1.404 | 0.000 | 0.000 | 0.000 | 0.000 | 0.257 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F | F | F | F(-2) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 617 | 398 | 591 | 5894 | 0 | 0 | 0 | 0 | 709 | 0 |
| N.S. |
1 | 0.65 | 0.96 | 9.55 | 0.00 | 0.00 | 0.00 | 0.00 | 1.15 | 0.00 |
| time (sec) |
N/A | 1.156 | 4.878 | 1.055 | 0.000 | 0.000 | 0.000 | 0.000 | 0.246 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A | N/A |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 35 | 35 | 37 | 33 | 35 | 47 | 0 | 35 | 36 | 35 |
| N.S. |
1 | 1.00 | 1.06 | 0.94 | 1.00 | 1.34 | 0.00 | 1.00 | 1.03 | 1.00 |
| time (sec) |
N/A | 0.384 | 0.100 | 3.766 | 1.918 | 0.118 | 0.000 | 0.272 | 0.284 | 0.337 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | F | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 634 | 628 | 0 | 0 | 0 | 0 | 0 | 0 | 141 | 0 |
| N.S. |
1 | 0.99 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.22 | 0.00 |
| time (sec) |
N/A | 2.323 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.339 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | B | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 514 | 506 | 7541 | 0 | 0 | 0 | 0 | 0 | 101 | 0 |
| N.S. |
1 | 0.98 | 14.67 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.20 | 0.00 |
| time (sec) |
N/A | 1.815 | 85.057 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.253 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | B | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 390 | 386 | 2724 | 0 | 0 | 0 | 0 | 0 | 61 | 0 |
| N.S. |
1 | 0.99 | 6.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.16 | 0.00 |
| time (sec) |
N/A | 1.312 | 8.367 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.250 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 237 | 238 | 246 | 0 | 0 | 0 | 0 | 0 | 26 | 0 |
| N.S. |
1 | 1.00 | 1.04 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.11 | 0.00 |
| time (sec) |
N/A | 0.723 | 0.015 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.236 | 0.000 |
| 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 | 35 | 35 | 37 | 33 | 35 | 57 | 34 | 35 | 46 | 35 |
| N.S. |
1 | 1.00 | 1.06 | 0.94 | 1.00 | 1.63 | 0.97 | 1.00 | 1.31 | 1.00 |
| time (sec) |
N/A | 0.350 | 0.211 | 1.573 | 0.890 | 0.093 | 8.687 | 0.296 | 0.243 | 0.297 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | B | B | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 523 | 556 | 463 | 609 | 859 | 676 | 1263 | 1337 | 1010 | 0 |
| N.S. |
1 | 1.06 | 0.89 | 1.16 | 1.64 | 1.29 | 2.41 | 2.56 | 1.93 | 0.00 |
| time (sec) |
N/A | 2.432 | 0.308 | 0.344 | 0.143 | 0.129 | 0.646 | 0.160 | 0.252 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | B | B | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 369 | 389 | 307 | 434 | 581 | 449 | 821 | 847 | 669 | 0 |
| N.S. |
1 | 1.05 | 0.83 | 1.18 | 1.57 | 1.22 | 2.22 | 2.30 | 1.81 | 0.00 |
| time (sec) |
N/A | 1.423 | 0.301 | 0.247 | 0.128 | 0.129 | 0.474 | 0.147 | 0.268 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | B | B | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 235 | 249 | 186 | 267 | 334 | 245 | 449 | 448 | 368 | 0 |
| N.S. |
1 | 1.06 | 0.79 | 1.14 | 1.42 | 1.04 | 1.91 | 1.91 | 1.57 | 0.00 |
| time (sec) |
N/A | 0.799 | 0.177 | 0.217 | 0.130 | 0.116 | 0.350 | 0.136 | 0.298 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F | F | F | F(-2) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 476 | 476 | 457 | 2438 | 0 | 0 | 0 | 0 | 178 | 0 |
| N.S. |
1 | 1.00 | 0.96 | 5.12 | 0.00 | 0.00 | 0.00 | 0.00 | 0.37 | 0.00 |
| time (sec) |
N/A | 1.250 | 0.539 | 1.924 | 0.000 | 0.000 | 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(-2) | F | F | F(-2) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 460 | 457 | 432 | 1883 | 0 | 0 | 0 | 0 | 467 | 0 |
| N.S. |
1 | 0.99 | 0.94 | 4.09 | 0.00 | 0.00 | 0.00 | 0.00 | 1.02 | 0.00 |
| time (sec) |
N/A | 1.261 | 0.570 | 2.830 | 0.000 | 0.000 | 0.000 | 0.000 | 0.268 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F(-2) | F | F | F(-2) | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 488 | 478 | 940 | 2027 | 0 | 0 | 0 | 0 | 538 | 0 |
| N.S. |
1 | 0.98 | 1.93 | 4.15 | 0.00 | 0.00 | 0.00 | 0.00 | 1.10 | 0.00 |
| time (sec) |
N/A | 1.589 | 4.589 | 3.494 | 0.000 | 0.000 | 0.000 | 0.000 | 4.259 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F | B | F | F(-2) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 349 | 357 | 442 | 1177 | 0 | 3003 | 0 | 0 | 783 | 0 |
| N.S. |
1 | 1.02 | 1.27 | 3.37 | 0.00 | 8.60 | 0.00 | 0.00 | 2.24 | 0.00 |
| time (sec) |
N/A | 0.798 | 1.246 | 0.278 | 0.000 | 76.830 | 0.000 | 0.000 | 1.377 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F | F(-1) | F | F(-2) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 470 | 494 | 575 | 1924 | 0 | 0 | 0 | 0 | 28 | 0 |
| N.S. |
1 | 1.05 | 1.22 | 4.09 | 0.00 | 0.00 | 0.00 | 0.00 | 0.06 | 0.00 |
| time (sec) |
N/A | 1.071 | 1.750 | 0.285 | 0.000 | 0.000 | 0.000 | 0.000 | 200.017 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F | F(-1) | F | F(-2) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 593 | 630 | 682 | 3208 | 0 | 0 | 0 | 0 | 28 | 0 |
| N.S. |
1 | 1.06 | 1.15 | 5.41 | 0.00 | 0.00 | 0.00 | 0.00 | 0.05 | 0.00 |
| time (sec) |
N/A | 1.315 | 1.645 | 0.279 | 0.000 | 0.000 | 0.000 | 0.000 | 200.019 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | B | B | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 689 | 729 | 619 | 802 | 1231 | 936 | 1809 | 2010 | 1449 | 0 |
| N.S. |
1 | 1.06 | 0.90 | 1.16 | 1.79 | 1.36 | 2.63 | 2.92 | 2.10 | 0.00 |
| time (sec) |
N/A | 4.182 | 0.553 | 0.293 | 0.147 | 0.225 | 0.887 | 0.183 | 0.296 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | B | B | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 495 | 528 | 380 | 580 | 840 | 621 | 1197 | 1287 | 965 | 0 |
| N.S. |
1 | 1.07 | 0.77 | 1.17 | 1.70 | 1.25 | 2.42 | 2.60 | 1.95 | 0.00 |
| time (sec) |
N/A | 2.679 | 0.531 | 0.266 | 0.164 | 0.225 | 0.658 | 0.148 | 0.286 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | B | B | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 316 | 336 | 253 | 370 | 490 | 341 | 658 | 692 | 539 | 0 |
| N.S. |
1 | 1.06 | 0.80 | 1.17 | 1.55 | 1.08 | 2.08 | 2.19 | 1.71 | 0.00 |
| time (sec) |
N/A | 1.403 | 0.274 | 0.185 | 0.127 | 0.196 | 0.443 | 0.136 | 0.253 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F | F | F | F(-2) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 639 | 636 | 610 | 3403 | 0 | 0 | 0 | 0 | 256 | 0 |
| N.S. |
1 | 1.00 | 0.95 | 5.33 | 0.00 | 0.00 | 0.00 | 0.00 | 0.40 | 0.00 |
| time (sec) |
N/A | 1.738 | 0.502 | 2.262 | 0.000 | 0.000 | 0.000 | 0.000 | 0.242 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F(-2) | F | F | F(-2) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 617 | 613 | 593 | 2873 | 0 | 0 | 0 | 0 | 635 | 0 |
| N.S. |
1 | 0.99 | 0.96 | 4.66 | 0.00 | 0.00 | 0.00 | 0.00 | 1.03 | 0.00 |
| time (sec) |
N/A | 1.961 | 0.885 | 3.843 | 0.000 | 0.000 | 0.000 | 0.000 | 0.272 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F(-2) | F | F | F(-2) | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 1016 | 965 | 1556 | 3617 | 0 | 0 | 0 | 0 | 1201 | 0 |
| N.S. |
1 | 0.95 | 1.53 | 3.56 | 0.00 | 0.00 | 0.00 | 0.00 | 1.18 | 0.00 |
| time (sec) |
N/A | 2.902 | 9.975 | 4.129 | 0.000 | 0.000 | 0.000 | 0.000 | 6.403 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F | F | F | F(-2) | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 1278 | 1244 | 1921 | 3757 | 0 | 0 | 0 | 0 | 1126 | 0 |
| N.S. |
1 | 0.97 | 1.50 | 2.94 | 0.00 | 0.00 | 0.00 | 0.00 | 0.88 | 0.00 |
| time (sec) |
N/A | 3.325 | 7.666 | 5.416 | 0.000 | 0.000 | 0.000 | 0.000 | 1.955 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | A | B | B | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 1016 | 1016 | 734 | 1706 | 0 | 1537 | 2992 | 3444 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.72 | 1.68 | 0.00 | 1.51 | 2.94 | 3.39 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.083 | 0.599 | 1.306 | 0.000 | 0.275 | 1.076 | 0.214 | 0.399 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | A | B | B | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 701 | 701 | 534 | 1176 | 0 | 1029 | 1935 | 2166 | 1077 | 0 |
| N.S. |
1 | 1.00 | 0.76 | 1.68 | 0.00 | 1.47 | 2.76 | 3.09 | 1.54 | 0.00 |
| time (sec) |
N/A | 1.467 | 0.303 | 0.819 | 0.000 | 0.182 | 0.739 | 0.195 | 0.324 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | A | B | B | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 425 | 425 | 364 | 673 | 0 | 579 | 1059 | 1145 | 665 | 0 |
| N.S. |
1 | 1.00 | 0.86 | 1.58 | 0.00 | 1.36 | 2.49 | 2.69 | 1.56 | 0.00 |
| time (sec) |
N/A | 1.013 | 0.207 | 0.655 | 0.000 | 0.168 | 0.505 | 0.158 | 0.258 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | F | F(-2) | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 1085 | 1085 | 556 | 0 | 0 | 0 | 0 | 0 | 329 | 0 |
| N.S. |
1 | 1.00 | 0.51 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.30 | 0.00 |
| time (sec) |
N/A | 2.561 | 0.442 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.279 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F(-2) | F | F | F(-2) | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 1323 | 1323 | 688 | 0 | 0 | 0 | 0 | 0 | 742 | 0 |
| N.S. |
1 | 1.00 | 0.52 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.56 | 0.00 |
| time (sec) |
N/A | 3.093 | 0.793 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 5.933 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F(-2) | F | F | F(-2) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 520 | 507 | 307 | 1251 | 0 | 0 | 0 | 0 | 506 | 0 |
| N.S. |
1 | 0.98 | 0.59 | 2.41 | 0.00 | 0.00 | 0.00 | 0.00 | 0.97 | 0.00 |
| time (sec) |
N/A | 2.005 | 0.274 | 1.431 | 0.000 | 0.000 | 0.000 | 0.000 | 11.108 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F(-2) | F | F | F(-2) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 907 | 888 | 526 | 2192 | 0 | 0 | 0 | 0 | 37 | 0 |
| N.S. |
1 | 0.98 | 0.58 | 2.42 | 0.00 | 0.00 | 0.00 | 0.00 | 0.04 | 0.00 |
| time (sec) |
N/A | 4.552 | 0.526 | 1.980 | 0.000 | 0.000 | 0.000 | 0.000 | 200.027 | 0.000 |