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 | Mupad | |
| grade |
N/A | F | C | B | F | B | F | F(-1) | F(-1) |
| verified |
N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD |
| size | 975 | 0 | 623 | 17768518 | 0 | 5023 | 0 | 0 | 0 |
| N.S. |
1 | 0.00 | 0.64 | 18224.12 | 0.00 | 5.15 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.000 | 6.283 | 3.570 | 0.000 | 1.251 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | F | C | B | F | B | F | F(-1) | F(-1) |
| verified |
N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD |
| size | 889 | 0 | 511 | 17248526 | 0 | 4855 | 0 | 0 | 0 |
| N.S. |
1 | 0.00 | 0.57 | 19402.17 | 0.00 | 5.46 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.000 | 5.621 | 2.219 | 0.000 | 1.130 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | F | C | B | F | B | F | F(-1) | F(-1) |
| verified |
N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD |
| size | 748 | 0 | 386 | 17766953 | 0 | 4793 | 0 | 0 | 0 |
| N.S. |
1 | 0.00 | 0.52 | 23752.61 | 0.00 | 6.41 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.000 | 2.571 | 2.790 | 0.000 | 0.903 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | B | F | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
| size | 676 | 703 | 329 | 17248163 | 0 | 4685 | 0 | 0 | 0 |
| N.S. |
1 | 1.04 | 0.49 | 25515.03 | 0.00 | 6.93 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 28.829 | 1.179 | 2.329 | 0.000 | 0.805 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | B | F | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
| size | 601 | 665 | 252 | 17767879 | 0 | 4660 | 0 | 0 | 0 |
| N.S. |
1 | 1.11 | 0.42 | 29563.86 | 0.00 | 7.75 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 28.428 | 0.426 | 1.919 | 0.000 | 0.738 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F(-2) | B | F | F | F(-1) |
| verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
| size | 574 | 637 | 228 | 17248000 | 0 | 4547 | 0 | 0 | 0 |
| N.S. |
1 | 1.11 | 0.40 | 30048.78 | 0.00 | 7.92 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 28.246 | 0.146 | 1.568 | 0.000 | 0.567 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | F | C | F(-1) | F(-2) | B | F | F | F(-1) |
| verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 571 | 0 | 223 | 0 | 0 | 9103 | 0 | 0 | 0 |
| N.S. |
1 | 0.00 | 0.39 | 0.00 | 0.00 | 15.94 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.000 | 0.464 | 180.000 | 0.000 | 0.827 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | F | C | F(-1) | F | B | F | F | F(-1) |
| verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 612 | 0 | 261 | 0 | 0 | 9221 | 0 | 0 | 0 |
| N.S. |
1 | 0.00 | 0.43 | 0.00 | 0.00 | 15.07 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.000 | 1.217 | 180.000 | 0.000 | 1.049 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | F | C | F(-1) | F | B | F | F | F(-1) |
| verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 690 | 0 | 289 | 0 | 0 | 9425 | 0 | 0 | 0 |
| N.S. |
1 | 0.00 | 0.42 | 0.00 | 0.00 | 13.66 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.000 | 2.003 | 180.000 | 0.000 | 1.153 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | B | F | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
| size | 548 | 531 | 456 | 9581953 | 0 | 10457 | 0 | 0 | 0 |
| N.S. |
1 | 0.97 | 0.83 | 17485.32 | 0.00 | 19.08 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.144 | 6.140 | 1.652 | 0.000 | 1.201 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | B | F | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
| size | 495 | 481 | 283 | 7492392 | 0 | 10089 | 0 | 0 | 0 |
| N.S. |
1 | 0.97 | 0.57 | 15136.15 | 0.00 | 20.38 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.923 | 2.521 | 1.180 | 0.000 | 1.132 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | B | F | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
| size | 383 | 375 | 252 | 9581103 | 0 | 10337 | 0 | 0 | 0 |
| N.S. |
1 | 0.98 | 0.66 | 25015.93 | 0.00 | 26.99 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.843 | 0.906 | 1.566 | 0.000 | 1.046 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | B | F | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
| size | 352 | 347 | 228 | 7491751 | 0 | 9961 | 0 | 0 | 0 |
| N.S. |
1 | 0.99 | 0.65 | 21283.38 | 0.00 | 28.30 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.674 | 0.252 | 1.020 | 0.000 | 0.988 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F(-2) | B | F | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
| size | 294 | 292 | 173 | 9339203 | 0 | 5045 | 0 | 0 | 0 |
| N.S. |
1 | 0.99 | 0.59 | 31766.00 | 0.00 | 17.16 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.522 | 0.108 | 2.298 | 0.000 | 0.810 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F(-2) | B | F | F | F(-1) |
| verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
| size | 298 | 296 | 173 | 7300729 | 0 | 4891 | 0 | 0 | 0 |
| N.S. |
1 | 0.99 | 0.58 | 24499.09 | 0.00 | 16.41 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.471 | 0.195 | 0.710 | 0.000 | 0.762 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | F(-1) | F | B | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 350 | 345 | 223 | 0 | 0 | 20605 | 0 | 0 | 0 |
| N.S. |
1 | 0.99 | 0.64 | 0.00 | 0.00 | 58.87 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.824 | 0.444 | 180.000 | 0.000 | 2.291 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | F(-1) | F | B | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 395 | 387 | 264 | 0 | 0 | 20189 | 0 | 0 | 0 |
| N.S. |
1 | 0.98 | 0.67 | 0.00 | 0.00 | 51.11 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.893 | 1.569 | 180.000 | 0.000 | 2.095 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | F(-1) | F | B | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 500 | 486 | 315 | 0 | 0 | 20910 | 0 | 0 | 0 |
| N.S. |
1 | 0.97 | 0.63 | 0.00 | 0.00 | 41.82 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.964 | 6.014 | 180.000 | 0.000 | 2.397 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F(-1) | B | F | F(-1) | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 1190 | 1158 | 2476 | 13068421 | 0 | 40569 | 0 | 0 | 0 |
| N.S. |
1 | 0.97 | 2.08 | 10981.87 | 0.00 | 34.09 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 5.568 | 11.263 | 2.107 | 0.000 | 9.007 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F(-1) | B | F | F(-1) | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 864 | 847 | 2272 | 13066870 | 0 | 39731 | 0 | 0 | 0 |
| N.S. |
1 | 0.98 | 2.63 | 15123.69 | 0.00 | 45.98 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 4.517 | 7.695 | 2.369 | 0.000 | 4.700 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F(-2) | B | F | F(-1) | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 686 | 678 | 2339 | 13067312 | 0 | 19371 | 0 | 0 | 0 |
| N.S. |
1 | 0.99 | 3.41 | 19048.56 | 0.00 | 28.24 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 4.273 | 7.332 | 1.246 | 0.000 | 2.868 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F(-2) | B | F | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
| size | 638 | 719 | 328 | 11848772 | 0 | 19326 | 0 | 0 | 0 |
| N.S. |
1 | 1.13 | 0.51 | 18571.74 | 0.00 | 30.29 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.258 | 5.299 | 1.134 | 0.000 | 3.086 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F(-2) | B | F | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
| size | 635 | 715 | 318 | 13066372 | 0 | 19368 | 0 | 0 | 0 |
| N.S. |
1 | 1.13 | 0.50 | 20576.96 | 0.00 | 30.50 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.070 | 4.802 | 0.882 | 0.000 | 2.909 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | F(-1) | F(-1) | B | F | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 750 | 739 | 450 | 0 | 0 | 78431 | 0 | 0 | 0 |
| N.S. |
1 | 0.99 | 0.60 | 0.00 | 0.00 | 104.57 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 4.662 | 4.901 | 180.000 | 0.000 | 13.499 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | F(-1) | F(-1) | B | F | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 829 | 815 | 583 | 0 | 0 | 78535 | 0 | 0 | 0 |
| N.S. |
1 | 0.98 | 0.70 | 0.00 | 0.00 | 94.73 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 4.559 | 6.235 | 180.000 | 0.000 | 12.458 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | F(-1) | F(-1) | B | F | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 1007 | 984 | 786 | 0 | 0 | 79389 | 0 | 0 | 0 |
| N.S. |
1 | 0.98 | 0.78 | 0.00 | 0.00 | 78.84 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 4.819 | 6.206 | 180.000 | 0.000 | 13.372 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | A | F | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 270 | 279 | 290 | 455 | 0 | 1405 | 0 | 0 | 0 |
| N.S. |
1 | 1.03 | 1.07 | 1.69 | 0.00 | 5.20 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.623 | 6.061 | 0.290 | 0.000 | 2.886 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | A | F | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 209 | 211 | 208 | 318 | 0 | 1199 | 0 | 0 | 0 |
| N.S. |
1 | 1.01 | 1.00 | 1.52 | 0.00 | 5.74 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.505 | 1.942 | 0.083 | 0.000 | 2.253 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | A | F | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 179 | 173 | 180 | 217 | 0 | 1057 | 0 | 0 | 0 |
| N.S. |
1 | 0.97 | 1.01 | 1.21 | 0.00 | 5.91 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.418 | 0.325 | 0.066 | 0.000 | 1.705 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | A | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 203 | 193 | 192 | 0 | 0 | 2097 | 0 | 0 | 0 |
| N.S. |
1 | 0.95 | 0.95 | 0.00 | 0.00 | 10.33 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.498 | 1.053 | 0.000 | 0.000 | 0.690 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | A | F | F | F(-1) |
| verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 435 | 409 | 187 | 0 | 0 | 1186 | 0 | 0 | 0 |
| N.S. |
1 | 0.94 | 0.43 | 0.00 | 0.00 | 2.73 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.633 | 1.418 | 0.000 | 0.000 | 1.776 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | F(-1) | F | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 1254 | 760 | 633 | 1945 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.61 | 0.50 | 1.55 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.224 | 20.584 | 0.711 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 829 | 694 | 428 | 1497 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.84 | 0.52 | 1.81 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.832 | 12.265 | 0.422 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 861 | 724 | 1258 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.84 | 1.46 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.962 | 20.249 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 943 | 906 | 1590 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.96 | 1.69 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.536 | 22.592 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-1) | A | F | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 182 | 181 | 173 | 232 | 0 | 1226 | 0 | 0 | 0 |
| N.S. |
1 | 0.99 | 0.95 | 1.27 | 0.00 | 6.74 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.471 | 3.270 | 0.113 | 0.000 | 1.317 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | A | F | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 141 | 136 | 136 | 153 | 0 | 993 | 0 | 0 | 0 |
| N.S. |
1 | 0.96 | 0.96 | 1.09 | 0.00 | 7.04 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.401 | 0.278 | 0.075 | 0.000 | 1.094 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | A | F | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 79 | 79 | 79 | 102 | 0 | 299 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.00 | 1.29 | 0.00 | 3.78 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.290 | 0.129 | 0.220 | 0.000 | 0.478 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | A | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 142 | 138 | 139 | 0 | 0 | 1015 | 0 | 0 | 0 |
| N.S. |
1 | 0.97 | 0.98 | 0.00 | 0.00 | 7.15 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.425 | 0.965 | 0.000 | 0.000 | 0.962 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F(-1) | A | F | F | F(-1) |
| verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 249 | 235 | 188 | 0 | 0 | 1350 | 0 | 0 | 0 |
| N.S. |
1 | 0.94 | 0.76 | 0.00 | 0.00 | 5.42 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.477 | 4.422 | 0.000 | 0.000 | 1.291 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | F | F | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 662 | 675 | 533 | 646 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.02 | 0.81 | 0.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.839 | 16.753 | 0.791 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | F | F | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 436 | 447 | 311 | 402 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.03 | 0.71 | 0.92 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.577 | 4.111 | 0.612 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 436 | 446 | 235 | 231 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.02 | 0.54 | 0.53 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.559 | 11.113 | 0.446 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 707 | 725 | 683 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.03 | 0.97 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.053 | 22.211 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F(-2) | B | F | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 235 | 234 | 274 | 684 | 0 | 3773 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.17 | 2.91 | 0.00 | 16.06 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.611 | 7.138 | 0.520 | 0.000 | 2.487 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | B | F | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 159 | 159 | 206 | 509 | 0 | 1095 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.30 | 3.20 | 0.00 | 6.89 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.454 | 4.898 | 0.099 | 0.000 | 0.651 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | B | F | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 154 | 152 | 155 | 456 | 0 | 1077 | 0 | 0 | 0 |
| N.S. |
1 | 0.99 | 1.01 | 2.96 | 0.00 | 6.99 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.420 | 3.167 | 0.089 | 0.000 | 0.627 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | B | F | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 155 | 155 | 156 | 406 | 0 | 1099 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.01 | 2.62 | 0.00 | 7.09 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.367 | 3.203 | 0.061 | 0.000 | 0.656 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F(-2) | B | F | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 280 | 271 | 278 | 0 | 0 | 3951 | 0 | 0 | 0 |
| N.S. |
1 | 0.97 | 0.99 | 0.00 | 0.00 | 14.11 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.558 | 3.888 | 0.000 | 0.000 | 2.617 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F(-1) | B | F | F(-1) | F(-1) |
| verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 477 | 454 | 555 | 0 | 0 | 5189 | 0 | 0 | 0 |
| N.S. |
1 | 0.95 | 1.16 | 0.00 | 0.00 | 10.88 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.682 | 6.096 | 0.000 | 0.000 | 3.268 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | F(-1) | F | F(-1) | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 981 | 824 | 831 | 3598 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.84 | 0.85 | 3.67 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.263 | 19.767 | 0.603 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |