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 | A | C | A | F | A | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 282 | 292 | 219 | 216 | 0 | 179 | 0 | 0 | 0 |
| N.S. |
1 | 1.04 | 0.78 | 0.77 | 0.00 | 0.63 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.355 | 10.252 | 1.308 | 0.000 | 0.081 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | A | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 309 | 318 | 228 | 223 | 0 | 192 | 0 | 0 | 0 |
| N.S. |
1 | 1.03 | 0.74 | 0.72 | 0.00 | 0.62 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.402 | 10.258 | 1.506 | 0.000 | 0.082 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | A | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 326 | 346 | 234 | 228 | 0 | 207 | 0 | 0 | 0 |
| N.S. |
1 | 1.06 | 0.72 | 0.70 | 0.00 | 0.63 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.448 | 10.261 | 2.983 | 0.000 | 0.082 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 297 | 297 | 430 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.45 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.527 | 11.763 | 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 | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 297 | 297 | 386 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.30 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.472 | 11.613 | 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 | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 295 | 295 | 386 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.31 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.484 | 11.561 | 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 | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 295 | 295 | 370 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.25 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.473 | 11.654 | 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 | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 299 | 299 | 567 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.90 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.505 | 12.005 | 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 | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 299 | 299 | 490 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.64 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.482 | 11.936 | 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 | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 297 | 297 | 487 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.64 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.495 | 11.910 | 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 | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 297 | 297 | 447 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.51 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.470 | 11.745 | 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 | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 297 | 297 | 354 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.19 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.463 | 11.500 | 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 | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 297 | 297 | 242 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.81 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.477 | 11.226 | 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 | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 295 | 295 | 241 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.82 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.473 | 11.221 | 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 | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 295 | 295 | 356 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.21 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.488 | 11.537 | 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 | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 303 | 303 | 375 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.24 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.502 | 11.600 | 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 | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 303 | 303 | 397 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.31 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.469 | 11.597 | 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 | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 301 | 301 | 395 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.31 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.477 | 11.573 | 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 | F | F | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 301 | 301 | 460 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.53 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.486 | 11.741 | 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 | A | B | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 243 | 243 | 191 | 1935 | 408 | 1357 | 11266 | 2736 | 769 |
| N.S. |
1 | 1.00 | 0.79 | 7.96 | 1.68 | 5.58 | 46.36 | 11.26 | 3.16 |
| time (sec) |
N/A | 0.433 | 0.815 | 0.354 | 0.251 | 0.261 | 1.529 | 0.357 | 8.067 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | A | B | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 155 | 155 | 117 | 783 | 230 | 573 | 4068 | 1142 | 429 |
| N.S. |
1 | 1.00 | 0.75 | 5.05 | 1.48 | 3.70 | 26.25 | 7.37 | 2.77 |
| time (sec) |
N/A | 0.321 | 0.449 | 0.168 | 0.227 | 0.255 | 0.876 | 0.318 | 7.867 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | B | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 83 | 83 | 59 | 82 | 104 | 171 | 1015 | 338 | 171 |
| N.S. |
1 | 1.00 | 0.71 | 0.99 | 1.25 | 2.06 | 12.23 | 4.07 | 2.06 |
| time (sec) |
N/A | 0.236 | 0.080 | 0.079 | 0.228 | 0.255 | 0.467 | 0.300 | 7.677 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 194 | 194 | 156 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.80 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.389 | 0.346 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | F | C | F | F | F | F(-1) | F | F(-1) |
| verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 392 | 0 | 160 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.00 | 0.41 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.000 | 1.534 | 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 | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 319 | 319 | 466 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.46 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.521 | 2.900 | 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 | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 317 | 317 | 267 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.84 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.486 | 1.983 | 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 | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 317 | 317 | 267 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.84 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.493 | 2.831 | 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 | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 323 | 323 | 307 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.95 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.525 | 11.343 | 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 | A | A | F(-1) | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 134 | 148 | 134 | 103 | 120 | 277 | 0 | 123 | 181 |
| N.S. |
1 | 1.10 | 1.00 | 0.77 | 0.90 | 2.07 | 0.00 | 0.92 | 1.35 |
| time (sec) |
N/A | 0.454 | 0.070 | 0.412 | 0.281 | 2.891 | 0.000 | 0.292 | 8.010 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F(-1) | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 118 | 127 | 99 | 92 | 107 | 212 | 0 | 108 | 166 |
| N.S. |
1 | 1.08 | 0.84 | 0.78 | 0.91 | 1.80 | 0.00 | 0.92 | 1.41 |
| time (sec) |
N/A | 0.384 | 0.074 | 0.410 | 0.305 | 1.185 | 0.000 | 0.281 | 7.882 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F(-1) | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 105 | 104 | 77 | 80 | 89 | 170 | 0 | 90 | 138 |
| N.S. |
1 | 0.99 | 0.73 | 0.76 | 0.85 | 1.62 | 0.00 | 0.86 | 1.31 |
| time (sec) |
N/A | 0.268 | 0.031 | 0.398 | 0.292 | 0.730 | 0.000 | 0.280 | 8.061 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F(-1) | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 96 | 84 | 66 | 72 | 82 | 145 | 0 | 85 | 944 |
| N.S. |
1 | 0.88 | 0.69 | 0.75 | 0.85 | 1.51 | 0.00 | 0.89 | 9.83 |
| time (sec) |
N/A | 0.224 | 0.033 | 0.389 | 0.285 | 0.365 | 0.000 | 0.274 | 8.743 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F(-1) | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 96 | 87 | 67 | 75 | 82 | 146 | 0 | 86 | 328 |
| N.S. |
1 | 0.91 | 0.70 | 0.78 | 0.85 | 1.52 | 0.00 | 0.90 | 3.42 |
| time (sec) |
N/A | 0.221 | 0.031 | 0.381 | 0.285 | 0.428 | 0.000 | 0.284 | 8.309 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F(-1) | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 114 | 116 | 134 | 90 | 101 | 201 | 0 | 103 | 527 |
| N.S. |
1 | 1.02 | 1.18 | 0.79 | 0.89 | 1.76 | 0.00 | 0.90 | 4.62 |
| time (sec) |
N/A | 0.289 | 0.061 | 0.399 | 0.276 | 4.431 | 0.000 | 0.279 | 8.043 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F(-1) | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 129 | 128 | 169 | 107 | 120 | 265 | 0 | 131 | 820 |
| N.S. |
1 | 0.99 | 1.31 | 0.83 | 0.93 | 2.05 | 0.00 | 1.02 | 6.36 |
| time (sec) |
N/A | 0.306 | 0.075 | 0.386 | 0.279 | 22.700 | 0.000 | 0.280 | 8.290 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F(-1) | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 156 | 154 | 209 | 127 | 145 | 338 | 0 | 170 | 1017 |
| N.S. |
1 | 0.99 | 1.34 | 0.81 | 0.93 | 2.17 | 0.00 | 1.09 | 6.52 |
| time (sec) |
N/A | 0.342 | 0.069 | 0.425 | 0.282 | 49.460 | 0.000 | 0.269 | 8.597 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 359 | 359 | 344 | 279 | 0 | 4414 | 0 | 370 | 6097 |
| N.S. |
1 | 1.00 | 0.96 | 0.78 | 0.00 | 12.30 | 0.00 | 1.03 | 16.98 |
| time (sec) |
N/A | 0.516 | 0.261 | 0.408 | 0.000 | 5.530 | 0.000 | 0.288 | 8.484 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 345 | 345 | 373 | 263 | 0 | 4354 | 0 | 338 | 5908 |
| N.S. |
1 | 1.00 | 1.08 | 0.76 | 0.00 | 12.62 | 0.00 | 0.98 | 17.12 |
| time (sec) |
N/A | 0.469 | 0.166 | 0.409 | 0.000 | 1.084 | 0.000 | 0.282 | 8.439 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 336 | 336 | 233 | 254 | 0 | 4040 | 0 | 332 | 5111 |
| N.S. |
1 | 1.00 | 0.69 | 0.76 | 0.00 | 12.02 | 0.00 | 0.99 | 15.21 |
| time (sec) |
N/A | 0.453 | 0.108 | 0.406 | 0.000 | 0.474 | 0.000 | 0.290 | 8.647 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 337 | 337 | 232 | 246 | 0 | 3892 | 0 | 340 | 4720 |
| N.S. |
1 | 1.00 | 0.69 | 0.73 | 0.00 | 11.55 | 0.00 | 1.01 | 14.01 |
| time (sec) |
N/A | 0.445 | 0.097 | 0.390 | 0.000 | 0.364 | 0.000 | 0.283 | 8.459 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 336 | 336 | 234 | 253 | 0 | 4084 | 0 | 344 | 4802 |
| N.S. |
1 | 1.00 | 0.70 | 0.75 | 0.00 | 12.15 | 0.00 | 1.02 | 14.29 |
| time (sec) |
N/A | 0.451 | 0.102 | 0.332 | 0.000 | 0.683 | 0.000 | 0.313 | 8.516 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 348 | 348 | 389 | 266 | 0 | 4362 | 0 | 353 | 5761 |
| N.S. |
1 | 1.00 | 1.12 | 0.76 | 0.00 | 12.53 | 0.00 | 1.01 | 16.55 |
| time (sec) |
N/A | 0.482 | 0.176 | 0.404 | 0.000 | 1.807 | 0.000 | 0.284 | 8.682 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 360 | 360 | 367 | 284 | 0 | 4442 | 0 | 368 | 5972 |
| N.S. |
1 | 1.00 | 1.02 | 0.79 | 0.00 | 12.34 | 0.00 | 1.02 | 16.59 |
| time (sec) |
N/A | 0.494 | 0.304 | 0.398 | 0.000 | 5.978 | 0.000 | 0.299 | 8.707 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F(-1) | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 169 | 177 | 159 | 160 | 220 | 555 | 0 | 258 | 305 |
| N.S. |
1 | 1.05 | 0.94 | 0.95 | 1.30 | 3.28 | 0.00 | 1.53 | 1.80 |
| time (sec) |
N/A | 0.575 | 0.088 | 0.431 | 0.278 | 8.772 | 0.000 | 0.275 | 8.247 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F(-1) | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 150 | 169 | 142 | 146 | 197 | 457 | 0 | 229 | 647 |
| N.S. |
1 | 1.13 | 0.95 | 0.97 | 1.31 | 3.05 | 0.00 | 1.53 | 4.31 |
| time (sec) |
N/A | 0.381 | 0.076 | 0.495 | 0.286 | 4.234 | 0.000 | 0.286 | 8.263 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F(-1) | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 155 | 164 | 149 | 136 | 192 | 487 | 0 | 228 | 528 |
| N.S. |
1 | 1.06 | 0.96 | 0.88 | 1.24 | 3.14 | 0.00 | 1.47 | 3.41 |
| time (sec) |
N/A | 0.354 | 0.072 | 0.415 | 0.280 | 1.787 | 0.000 | 0.279 | 8.276 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F(-1) | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 149 | 159 | 114 | 132 | 186 | 492 | 0 | 196 | 527 |
| N.S. |
1 | 1.07 | 0.77 | 0.89 | 1.25 | 3.30 | 0.00 | 1.32 | 3.54 |
| time (sec) |
N/A | 0.317 | 0.100 | 0.423 | 0.297 | 1.745 | 0.000 | 0.274 | 8.241 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F(-1) | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 151 | 171 | 144 | 146 | 196 | 458 | 0 | 208 | 649 |
| N.S. |
1 | 1.13 | 0.95 | 0.97 | 1.30 | 3.03 | 0.00 | 1.38 | 4.30 |
| time (sec) |
N/A | 0.350 | 0.068 | 0.421 | 0.313 | 4.215 | 0.000 | 0.291 | 8.410 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F(-1) | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 209 | 211 | 241 | 171 | 228 | 686 | 0 | 289 | 1082 |
| N.S. |
1 | 1.01 | 1.15 | 0.82 | 1.09 | 3.28 | 0.00 | 1.38 | 5.18 |
| time (sec) |
N/A | 0.397 | 0.128 | 0.457 | 0.279 | 74.982 | 0.000 | 0.283 | 9.055 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F(-1) | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 236 | 235 | 248 | 181 | 278 | 852 | 0 | 357 | 1337 |
| N.S. |
1 | 1.00 | 1.05 | 0.77 | 1.18 | 3.61 | 0.00 | 1.51 | 5.67 |
| time (sec) |
N/A | 0.430 | 0.312 | 0.494 | 0.283 | 224.195 | 0.000 | 0.268 | 9.143 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | F(-1) | F(-1) | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 265 | 263 | 278 | 209 | 332 | 0 | 0 | 361 | 1545 |
| N.S. |
1 | 0.99 | 1.05 | 0.79 | 1.25 | 0.00 | 0.00 | 1.36 | 5.83 |
| time (sec) |
N/A | 0.489 | 0.303 | 0.481 | 0.293 | 0.000 | 0.000 | 0.295 | 9.492 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 712 | 652 | 431 | 334 | 0 | 9856 | 0 | 599 | 18343 |
| N.S. |
1 | 0.92 | 0.61 | 0.47 | 0.00 | 13.84 | 0.00 | 0.84 | 25.76 |
| time (sec) |
N/A | 1.141 | 0.212 | 0.457 | 0.000 | 9.624 | 0.000 | 0.293 | 9.057 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 687 | 641 | 428 | 339 | 0 | 9822 | 0 | 614 | 17909 |
| N.S. |
1 | 0.93 | 0.62 | 0.49 | 0.00 | 14.30 | 0.00 | 0.89 | 26.07 |
| time (sec) |
N/A | 1.029 | 0.257 | 0.460 | 0.000 | 6.610 | 0.000 | 0.294 | 9.022 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 685 | 635 | 423 | 327 | 0 | 9678 | 0 | 607 | 17180 |
| N.S. |
1 | 0.93 | 0.62 | 0.48 | 0.00 | 14.13 | 0.00 | 0.89 | 25.08 |
| time (sec) |
N/A | 0.925 | 0.183 | 0.477 | 0.000 | 5.778 | 0.000 | 0.292 | 10.458 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 685 | 633 | 428 | 339 | 0 | 9774 | 0 | 622 | 17812 |
| N.S. |
1 | 0.92 | 0.62 | 0.49 | 0.00 | 14.27 | 0.00 | 0.91 | 26.00 |
| time (sec) |
N/A | 0.916 | 0.182 | 0.438 | 0.000 | 6.449 | 0.000 | 0.297 | 9.657 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 689 | 689 | 429 | 334 | 0 | 9892 | 0 | 621 | 17945 |
| N.S. |
1 | 1.00 | 0.62 | 0.48 | 0.00 | 14.36 | 0.00 | 0.90 | 26.04 |
| time (sec) |
N/A | 0.814 | 0.198 | 0.368 | 0.000 | 11.957 | 0.000 | 0.299 | 9.257 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 745 | 745 | 499 | 355 | 0 | 10188 | 0 | 659 | 24015 |
| N.S. |
1 | 1.00 | 0.67 | 0.48 | 0.00 | 13.68 | 0.00 | 0.88 | 32.23 |
| time (sec) |
N/A | 0.949 | 0.242 | 0.502 | 0.000 | 29.014 | 0.000 | 0.285 | 10.732 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 751 | 751 | 513 | 355 | 0 | 10352 | 0 | 645 | 20828 |
| N.S. |
1 | 1.00 | 0.68 | 0.47 | 0.00 | 13.78 | 0.00 | 0.86 | 27.73 |
| time (sec) |
N/A | 0.913 | 0.266 | 0.488 | 0.000 | 65.773 | 0.000 | 0.277 | 11.043 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | C | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 70 | 70 | 40 | 110 | 0 | 32 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.57 | 1.57 | 0.00 | 0.46 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.261 | 10.186 | 1.065 | 0.000 | 0.120 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | C | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 70 | 70 | 36 | 112 | 0 | 56 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.51 | 1.60 | 0.00 | 0.80 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.258 | 10.173 | 1.303 | 0.000 | 0.113 | 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 | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 99 | 43 | 46 | 88 | 0 | 42 | 0 | 0 | 0 |
| N.S. |
1 | 0.43 | 0.46 | 0.89 | 0.00 | 0.42 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.209 | 10.125 | 1.408 | 0.000 | 0.082 | 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 | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 61 | 34 | 37 | 88 | 0 | 31 | 0 | 0 | 0 |
| N.S. |
1 | 0.56 | 0.61 | 1.44 | 0.00 | 0.51 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.188 | 10.152 | 0.963 | 0.000 | 0.085 | 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 | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 113 | 67 | 54 | 93 | 0 | 44 | 0 | 0 | 0 |
| N.S. |
1 | 0.59 | 0.48 | 0.82 | 0.00 | 0.39 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.174 | 10.100 | 1.581 | 0.000 | 0.086 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | A | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 57 | 99 | 35 | 93 | 0 | 31 | 0 | 0 | 0 |
| N.S. |
1 | 1.74 | 0.61 | 1.63 | 0.00 | 0.54 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.192 | 10.142 | 1.154 | 0.000 | 0.084 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | C | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 74 | 74 | 60 | 168 | 0 | 75 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.81 | 2.27 | 0.00 | 1.01 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.277 | 10.118 | 1.399 | 0.000 | 0.103 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | C | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 74 | 74 | 56 | 115 | 0 | 74 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.76 | 1.55 | 0.00 | 1.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.270 | 10.166 | 1.474 | 0.000 | 0.116 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 243 | 143 | 128 | 128 | 124 | 206 | 0 | 156 | 0 |
| N.S. |
1 | 0.59 | 0.53 | 0.53 | 0.51 | 0.85 | 0.00 | 0.64 | 0.00 |
| time (sec) |
N/A | 0.293 | 0.477 | 0.345 | 0.205 | 0.318 | 0.000 | 0.276 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 108 | 81 | 56 | 51 | 50 | 50 | 0 | 68 | 0 |
| N.S. |
1 | 0.75 | 0.52 | 0.47 | 0.46 | 0.46 | 0.00 | 0.63 | 0.00 |
| time (sec) |
N/A | 0.247 | 0.037 | 0.305 | 0.207 | 0.280 | 0.000 | 0.272 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 178 | 114 | 96 | 103 | 81 | 155 | 0 | 109 | 0 |
| N.S. |
1 | 0.64 | 0.54 | 0.58 | 0.46 | 0.87 | 0.00 | 0.61 | 0.00 |
| time (sec) |
N/A | 0.238 | 0.123 | 0.324 | 0.199 | 0.271 | 0.000 | 0.277 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 152 | 96 | 83 | 80 | 45 | 123 | 0 | 84 | 0 |
| N.S. |
1 | 0.63 | 0.55 | 0.53 | 0.30 | 0.81 | 0.00 | 0.55 | 0.00 |
| time (sec) |
N/A | 0.247 | 0.089 | 0.327 | 0.201 | 0.293 | 0.000 | 0.272 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 177 | 111 | 101 | 94 | 59 | 134 | 0 | 111 | 0 |
| N.S. |
1 | 0.63 | 0.57 | 0.53 | 0.33 | 0.76 | 0.00 | 0.63 | 0.00 |
| time (sec) |
N/A | 0.255 | 0.173 | 0.330 | 0.194 | 0.269 | 0.000 | 0.282 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 177 | 110 | 90 | 106 | 83 | 141 | 0 | 100 | 0 |
| N.S. |
1 | 0.62 | 0.51 | 0.60 | 0.47 | 0.80 | 0.00 | 0.56 | 0.00 |
| time (sec) |
N/A | 0.264 | 0.129 | 0.340 | 0.190 | 0.277 | 0.000 | 0.280 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | A | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 78 | 82 | 72 | 73 | 72 | 72 | 76 | 79 | 73 |
| N.S. |
1 | 1.05 | 0.92 | 0.94 | 0.92 | 0.92 | 0.97 | 1.01 | 0.94 |
| time (sec) |
N/A | 0.277 | 0.024 | 0.362 | 0.205 | 0.263 | 0.024 | 0.259 | 0.023 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | A | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 78 | 78 | 78 | 73 | 72 | 72 | 82 | 79 | 73 |
| N.S. |
1 | 1.00 | 1.00 | 0.94 | 0.92 | 0.92 | 1.05 | 1.01 | 0.94 |
| time (sec) |
N/A | 0.242 | 0.016 | 0.351 | 0.191 | 0.258 | 0.024 | 0.260 | 0.017 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | A | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 75 | 79 | 72 | 73 | 72 | 72 | 76 | 79 | 73 |
| N.S. |
1 | 1.05 | 0.96 | 0.97 | 0.96 | 0.96 | 1.01 | 1.05 | 0.97 |
| time (sec) |
N/A | 0.256 | 0.019 | 0.350 | 0.189 | 0.251 | 0.025 | 0.288 | 0.016 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | A | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 73 | 73 | 73 | 70 | 69 | 69 | 78 | 76 | 70 |
| N.S. |
1 | 1.00 | 1.00 | 0.96 | 0.95 | 0.95 | 1.07 | 1.04 | 0.96 |
| time (sec) |
N/A | 0.230 | 0.014 | 0.289 | 0.183 | 0.269 | 0.023 | 0.285 | 0.016 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | A | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 74 | 77 | 74 | 71 | 73 | 70 | 73 | 79 | 70 |
| N.S. |
1 | 1.04 | 1.00 | 0.96 | 0.99 | 0.95 | 0.99 | 1.07 | 0.95 |
| time (sec) |
N/A | 0.245 | 0.018 | 0.311 | 0.251 | 0.242 | 0.085 | 0.266 | 0.019 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | A | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 71 | 71 | 71 | 74 | 69 | 74 | 73 | 74 | 70 |
| N.S. |
1 | 1.00 | 1.00 | 1.04 | 0.97 | 1.04 | 1.03 | 1.04 | 0.99 |
| time (sec) |
N/A | 0.226 | 0.026 | 0.302 | 0.255 | 0.250 | 0.080 | 0.269 | 0.019 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | A | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 74 | 75 | 71 | 73 | 73 | 76 | 71 | 96 | 70 |
| N.S. |
1 | 1.01 | 0.96 | 0.99 | 0.99 | 1.03 | 0.96 | 1.30 | 0.95 |
| time (sec) |
N/A | 0.249 | 0.032 | 0.284 | 0.191 | 0.247 | 0.130 | 0.269 | 0.021 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 168 | 168 | 165 | 159 | 0 | 426 | 320 | 174 | 251 |
| N.S. |
1 | 1.00 | 0.98 | 0.95 | 0.00 | 2.54 | 1.90 | 1.04 | 1.49 |
| time (sec) |
N/A | 0.504 | 0.105 | 0.346 | 0.000 | 0.335 | 0.650 | 0.422 | 7.700 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | A | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 135 | 136 | 133 | 122 | 0 | 350 | 189 | 136 | 179 |
| N.S. |
1 | 1.01 | 0.99 | 0.90 | 0.00 | 2.59 | 1.40 | 1.01 | 1.33 |
| time (sec) |
N/A | 0.409 | 0.056 | 0.346 | 0.000 | 0.269 | 0.621 | 0.390 | 7.680 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | A | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 106 | 106 | 102 | 90 | 0 | 302 | 162 | 99 | 95 |
| N.S. |
1 | 1.00 | 0.96 | 0.85 | 0.00 | 2.85 | 1.53 | 0.93 | 0.90 |
| time (sec) |
N/A | 0.301 | 0.056 | 0.371 | 0.000 | 0.272 | 0.526 | 0.359 | 7.788 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 83 | 94 | 88 | 79 | 0 | 268 | 153 | 83 | 77 |
| N.S. |
1 | 1.13 | 1.06 | 0.95 | 0.00 | 3.23 | 1.84 | 1.00 | 0.93 |
| time (sec) |
N/A | 0.253 | 0.048 | 0.304 | 0.000 | 0.267 | 0.418 | 0.329 | 7.720 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | A | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 89 | 92 | 89 | 85 | 0 | 267 | 155 | 89 | 81 |
| N.S. |
1 | 1.03 | 1.00 | 0.96 | 0.00 | 3.00 | 1.74 | 1.00 | 0.91 |
| time (sec) |
N/A | 0.274 | 0.048 | 0.329 | 0.000 | 0.271 | 0.595 | 0.359 | 7.630 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | A | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 106 | 115 | 105 | 94 | 0 | 316 | 167 | 96 | 98 |
| N.S. |
1 | 1.08 | 0.99 | 0.89 | 0.00 | 2.98 | 1.58 | 0.91 | 0.92 |
| time (sec) |
N/A | 0.323 | 0.048 | 0.343 | 0.000 | 0.354 | 0.771 | 0.325 | 7.638 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 136 | 149 | 135 | 122 | 0 | 360 | 284 | 135 | 128 |
| N.S. |
1 | 1.10 | 0.99 | 0.90 | 0.00 | 2.65 | 2.09 | 0.99 | 0.94 |
| time (sec) |
N/A | 0.528 | 0.066 | 0.340 | 0.000 | 0.266 | 1.045 | 0.294 | 7.696 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 167 | 182 | 166 | 149 | 0 | 436 | 328 | 173 | 156 |
| N.S. |
1 | 1.09 | 0.99 | 0.89 | 0.00 | 2.61 | 1.96 | 1.04 | 0.93 |
| time (sec) |
N/A | 0.596 | 0.078 | 0.347 | 0.000 | 0.340 | 1.248 | 0.287 | 7.797 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | A | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 173 | 182 | 170 | 151 | 0 | 504 | 235 | 172 | 223 |
| N.S. |
1 | 1.05 | 0.98 | 0.87 | 0.00 | 2.91 | 1.36 | 0.99 | 1.29 |
| time (sec) |
N/A | 0.676 | 0.083 | 0.333 | 0.000 | 0.276 | 1.919 | 0.307 | 7.751 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | A | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 143 | 150 | 141 | 120 | 0 | 462 | 212 | 134 | 137 |
| N.S. |
1 | 1.05 | 0.99 | 0.84 | 0.00 | 3.23 | 1.48 | 0.94 | 0.96 |
| time (sec) |
N/A | 0.466 | 0.063 | 0.327 | 0.000 | 0.256 | 1.719 | 0.283 | 7.710 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | A | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 124 | 133 | 122 | 106 | 0 | 421 | 201 | 116 | 118 |
| N.S. |
1 | 1.07 | 0.98 | 0.85 | 0.00 | 3.40 | 1.62 | 0.94 | 0.95 |
| time (sec) |
N/A | 0.320 | 0.073 | 0.319 | 0.000 | 0.279 | 1.294 | 0.285 | 7.759 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | A | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 115 | 125 | 110 | 107 | 0 | 391 | 196 | 109 | 112 |
| N.S. |
1 | 1.09 | 0.96 | 0.93 | 0.00 | 3.40 | 1.70 | 0.95 | 0.97 |
| time (sec) |
N/A | 0.270 | 0.068 | 0.290 | 0.000 | 0.319 | 0.770 | 0.286 | 7.713 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | A | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 127 | 135 | 124 | 111 | 0 | 421 | 202 | 118 | 118 |
| N.S. |
1 | 1.06 | 0.98 | 0.87 | 0.00 | 3.31 | 1.59 | 0.93 | 0.93 |
| time (sec) |
N/A | 0.347 | 0.099 | 0.365 | 0.000 | 0.268 | 1.026 | 0.276 | 7.700 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | A | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 142 | 170 | 141 | 124 | 0 | 476 | 214 | 131 | 138 |
| N.S. |
1 | 1.20 | 0.99 | 0.87 | 0.00 | 3.35 | 1.51 | 0.92 | 0.97 |
| time (sec) |
N/A | 0.438 | 0.062 | 0.365 | 0.000 | 0.266 | 1.351 | 0.266 | 7.740 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 171 | 194 | 173 | 151 | 0 | 514 | 330 | 171 | 168 |
| N.S. |
1 | 1.13 | 1.01 | 0.88 | 0.00 | 3.01 | 1.93 | 1.00 | 0.98 |
| time (sec) |
N/A | 0.791 | 0.080 | 0.378 | 0.000 | 0.260 | 1.788 | 0.272 | 7.728 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | F(-1) | F(-1) | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 230 | 227 | 228 | 216 | 0 | 0 | 0 | 233 | 7024 |
| N.S. |
1 | 0.99 | 0.99 | 0.94 | 0.00 | 0.00 | 0.00 | 1.01 | 30.54 |
| time (sec) |
N/A | 0.560 | 0.180 | 0.507 | 0.000 | 0.000 | 0.000 | 0.596 | 73.398 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 189 | 185 | 186 | 172 | 0 | 616 | 0 | 194 | 2304 |
| N.S. |
1 | 0.98 | 0.98 | 0.91 | 0.00 | 3.26 | 0.00 | 1.03 | 12.19 |
| time (sec) |
N/A | 0.434 | 0.121 | 0.565 | 0.000 | 113.048 | 0.000 | 0.587 | 18.413 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 158 | 157 | 139 | 137 | 0 | 421 | 0 | 155 | 1853 |
| N.S. |
1 | 0.99 | 0.88 | 0.87 | 0.00 | 2.66 | 0.00 | 0.98 | 11.73 |
| time (sec) |
N/A | 0.380 | 0.068 | 0.439 | 0.000 | 32.438 | 0.000 | 0.577 | 15.421 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 132 | 131 | 114 | 112 | 0 | 321 | 0 | 131 | 3704 |
| N.S. |
1 | 0.99 | 0.86 | 0.85 | 0.00 | 2.43 | 0.00 | 0.99 | 28.06 |
| time (sec) |
N/A | 0.330 | 0.049 | 0.459 | 0.000 | 11.072 | 0.000 | 0.563 | 14.133 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 133 | 116 | 112 | 113 | 0 | 321 | 0 | 133 | 2434 |
| N.S. |
1 | 0.87 | 0.84 | 0.85 | 0.00 | 2.41 | 0.00 | 1.00 | 18.30 |
| time (sec) |
N/A | 0.311 | 0.048 | 0.362 | 0.000 | 7.675 | 0.000 | 0.593 | 13.230 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | F(-1) | F(-1) | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 167 | 168 | 242 | 166 | 0 | 0 | 0 | 170 | 6285 |
| N.S. |
1 | 1.01 | 1.45 | 0.99 | 0.00 | 0.00 | 0.00 | 1.02 | 37.63 |
| time (sec) |
N/A | 0.441 | 0.214 | 0.419 | 0.000 | 0.000 | 0.000 | 0.559 | 19.843 |