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 | A | C | F | C | F(-1) | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 316 | 323 | 276 | 1384 | 0 | 377 | 0 | 0 | 378 |
| N.S. |
1 | 1.02 | 0.87 | 4.38 | 0.00 | 1.19 | 0.00 | 0.00 | 1.20 |
| time (sec) |
N/A | 2.227 | 6.177 | 34.102 | 0.000 | 0.180 | 0.000 | 0.000 | 5.744 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 325 | 335 | 268 | 1424 | 0 | 410 | 0 | 0 | 658 |
| N.S. |
1 | 1.03 | 0.82 | 4.38 | 0.00 | 1.26 | 0.00 | 0.00 | 2.02 |
| time (sec) |
N/A | 2.280 | 10.004 | 42.929 | 0.000 | 0.165 | 0.000 | 0.000 | 7.997 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 377 | 369 | 284 | 1494 | 0 | 451 | 0 | 0 | 685 |
| N.S. |
1 | 0.98 | 0.75 | 3.96 | 0.00 | 1.20 | 0.00 | 0.00 | 1.82 |
| time (sec) |
N/A | 2.453 | 10.191 | 49.337 | 0.000 | 0.153 | 0.000 | 0.000 | 9.767 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 299 | 329 | 360 | 1554 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.10 | 1.20 | 5.20 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.666 | 4.353 | 20.898 | 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 | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 239 | 265 | 291 | 1244 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.11 | 1.22 | 5.21 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.042 | 3.619 | 19.688 | 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 | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 181 | 199 | 244 | 948 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.10 | 1.35 | 5.24 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.495 | 3.346 | 7.714 | 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 | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 130 | 141 | 198 | 722 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.08 | 1.52 | 5.55 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.065 | 2.641 | 7.013 | 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 | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 85 | 90 | 127 | 259 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.06 | 1.49 | 3.05 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.712 | 1.151 | 6.470 | 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 | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 112 | 112 | 205 | 380 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.83 | 3.39 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.023 | 3.129 | 7.296 | 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 | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 140 | 151 | 219 | 436 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.08 | 1.56 | 3.11 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.447 | 6.144 | 10.591 | 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 | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 206 | 224 | 295 | 759 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.09 | 1.43 | 3.68 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.983 | 4.753 | 14.987 | 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 | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 270 | 293 | 338 | 955 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.09 | 1.25 | 3.54 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.684 | 4.704 | 20.079 | 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 | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 344 | 372 | 427 | 1293 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.08 | 1.24 | 3.76 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 3.340 | 5.062 | 26.480 | 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 | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 370 | 356 | 354 | 1337 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.96 | 0.96 | 3.61 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.594 | 4.622 | 24.353 | 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 | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 292 | 283 | 301 | 1102 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.97 | 1.03 | 3.77 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.941 | 3.272 | 12.904 | 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 | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 217 | 214 | 280 | 834 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.99 | 1.29 | 3.84 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.370 | 3.656 | 11.964 | 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 | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 214 | 204 | 271 | 804 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.95 | 1.27 | 3.76 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.353 | 2.946 | 10.490 | 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(-1) | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 270 | 249 | 306 | 872 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.92 | 1.13 | 3.23 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.885 | 4.665 | 12.414 | 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(-1) | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 336 | 316 | 332 | 992 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.94 | 0.99 | 2.95 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.602 | 5.887 | 18.737 | 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(-1) | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 427 | 403 | 492 | 1326 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.94 | 1.15 | 3.11 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 3.313 | 7.432 | 25.263 | 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 | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
| size | 433 | 436 | 428 | 2240 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.01 | 0.99 | 5.17 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.996 | 5.423 | 101.911 | 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 | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 345 | 351 | 368 | 1966 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.02 | 1.07 | 5.70 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.264 | 5.543 | 19.790 | 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 | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 348 | 345 | 364 | 1934 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.99 | 1.05 | 5.56 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.226 | 4.348 | 19.014 | 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(-1) | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 345 | 342 | 366 | 1846 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.99 | 1.06 | 5.35 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.240 | 5.267 | 18.353 | 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) | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 417 | 401 | 425 | 1996 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.96 | 1.02 | 4.79 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.945 | 6.090 | 21.916 | 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(-1) | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 494 | 483 | 543 | 2113 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.98 | 1.10 | 4.28 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 3.933 | 7.754 | 33.890 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 553 | 557 | 1220 | 3397 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.01 | 2.21 | 6.14 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.709 | 7.777 | 20.001 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 455 | 453 | 1169 | 1871 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 2.57 | 4.11 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.056 | 19.252 | 21.453 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
| size | 439 | 449 | 1166 | 1857 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.02 | 2.66 | 4.23 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.984 | 20.782 | 21.526 | 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 | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 394 | 395 | 315 | 1362 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.80 | 3.46 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.547 | 9.736 | 26.747 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
| size | 345 | 354 | 1288 | 2877 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.03 | 3.73 | 8.34 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.449 | 6.905 | 26.691 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 415 | 432 | 1373 | 3682 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.04 | 3.31 | 8.87 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.947 | 6.945 | 36.971 | 0.000 | 0.000 | 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(-1) | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 638 | 641 | 1270 | 5169 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.99 | 8.10 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 3.493 | 7.726 | 24.903 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 553 | 556 | 1221 | 3676 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.01 | 2.21 | 6.65 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.688 | 10.958 | 25.635 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
| size | 509 | 514 | 1209 | 2964 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.01 | 2.38 | 5.82 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.564 | 11.376 | 26.915 | 0.000 | 0.000 | 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(-1) | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 500 | 511 | 1219 | 2815 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.02 | 2.44 | 5.63 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.604 | 6.910 | 27.141 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 465 | 464 | 1296 | 3122 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 2.79 | 6.71 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.078 | 7.074 | 31.069 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 418 | 432 | 1371 | 3950 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.03 | 3.28 | 9.45 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.930 | 7.101 | 35.824 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 502 | 520 | 1485 | 5558 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.04 | 2.96 | 11.07 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.634 | 7.340 | 41.197 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 746 | 754 | 1341 | 6457 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.01 | 1.80 | 8.66 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 4.379 | 8.797 | 27.789 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 635 | 643 | 1275 | 5455 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.01 | 2.01 | 8.59 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 3.489 | 14.159 | 29.038 | 0.000 | 0.000 | 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(-1) | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 609 | 618 | 1262 | 4796 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.01 | 2.07 | 7.88 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 3.393 | 14.374 | 30.458 | 0.000 | 0.000 | 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(-1) | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 567 | 579 | 1256 | 4332 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.02 | 2.22 | 7.64 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 3.389 | 7.194 | 32.737 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 606 | 620 | 1309 | 4690 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.02 | 2.16 | 7.74 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 3.333 | 7.218 | 32.184 | 0.000 | 0.000 | 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(-1) | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 540 | 544 | 1378 | 4586 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.01 | 2.55 | 8.49 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.654 | 7.353 | 35.228 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 504 | 519 | 1485 | 5829 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.03 | 2.95 | 11.57 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.675 | 7.635 | 39.444 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 587 | 606 | 1591 | 6392 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.03 | 2.71 | 10.89 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 3.317 | 7.979 | 45.417 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 554 | 564 | 1216 | 3147 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.02 | 2.19 | 5.68 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.686 | 14.631 | 24.142 | 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 | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 455 | 457 | 497 | 1835 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.09 | 4.03 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.982 | 13.197 | 18.783 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 393 | 397 | 741 | 946 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.01 | 1.89 | 2.41 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.523 | 18.961 | 19.045 | 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 | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
| size | 343 | 344 | 351 | 805 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.02 | 2.35 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.128 | 14.576 | 19.919 | 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 | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 283 | 287 | 349 | 1297 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.01 | 1.23 | 4.58 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.019 | 12.478 | 27.547 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
| size | 354 | 366 | 1298 | 2764 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.03 | 3.67 | 7.81 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.420 | 6.987 | 30.230 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 429 | 449 | 1376 | 3685 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.05 | 3.21 | 8.59 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.984 | 6.941 | 31.707 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 604 | 620 | 1276 | 4220 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.03 | 2.11 | 6.99 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 3.127 | 7.575 | 22.250 | 0.000 | 0.000 | 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 | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 503 | 532 | 1234 | 3309 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.06 | 2.45 | 6.58 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.399 | 7.373 | 19.361 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | F | F | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 421 | 440 | 1225 | 1786 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.05 | 2.91 | 4.24 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.727 | 6.970 | 22.448 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
| size | 308 | 335 | 1269 | 2011 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.09 | 4.12 | 6.53 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.171 | 7.075 | 21.744 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 392 | 412 | 1327 | 3368 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.05 | 3.39 | 8.59 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.657 | 7.109 | 26.721 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 494 | 507 | 1418 | 4604 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.03 | 2.87 | 9.32 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.323 | 7.362 | 33.158 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 650 | 674 | 1366 | 8101 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.04 | 2.10 | 12.46 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 3.355 | 7.713 | 21.974 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 563 | 581 | 1388 | 7059 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.03 | 2.47 | 12.54 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.560 | 7.543 | 21.896 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 417 | 431 | 1364 | 4970 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.03 | 3.27 | 11.92 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.662 | 7.050 | 25.761 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 449 | 467 | 1421 | 6289 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.04 | 3.16 | 14.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.919 | 7.362 | 10.678 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 549 | 560 | 1471 | 8065 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.02 | 2.68 | 14.69 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.550 | 7.358 | 8.049 | 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 | 318 | 318 | 250 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.79 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.379 | 2.240 | 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 | 217 | 222 | 194 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.02 | 0.89 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.735 | 1.017 | 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 | B | F | F | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 353 | 338 | 10459 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.96 | 29.63 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.918 | 37.226 | 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 | B | F | F | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 514 | 467 | 14082 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.91 | 27.40 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.499 | 51.727 | 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 | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 105 | 97 | 91 | 86 | 101 | 81 | 255 | 89 | 117 |
| N.S. |
1 | 0.92 | 0.87 | 0.82 | 0.96 | 0.77 | 2.43 | 0.85 | 1.11 |
| time (sec) |
N/A | 0.636 | 0.223 | 3.694 | 0.215 | 0.279 | 0.177 | 0.314 | 1.814 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 84 | 108 | 75 | 65 | 79 | 60 | 170 | 68 | 84 |
| N.S. |
1 | 1.29 | 0.89 | 0.77 | 0.94 | 0.71 | 2.02 | 0.81 | 1.00 |
| time (sec) |
N/A | 0.342 | 0.159 | 0.806 | 0.251 | 0.296 | 0.124 | 0.320 | 1.762 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 52 | 52 | 51 | 51 | 55 | 42 | 0 | 121 | 50 |
| N.S. |
1 | 1.00 | 0.98 | 0.98 | 1.06 | 0.81 | 0.00 | 2.33 | 0.96 |
| time (sec) |
N/A | 0.288 | 0.080 | 1.355 | 0.228 | 0.290 | 0.000 | 0.313 | 1.830 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 35 | 35 | 46 | 48 | 58 | 54 | 0 | 79 | 100 |
| N.S. |
1 | 1.00 | 1.31 | 1.37 | 1.66 | 1.54 | 0.00 | 2.26 | 2.86 |
| time (sec) |
N/A | 0.522 | 0.026 | 1.818 | 0.218 | 0.291 | 0.000 | 0.340 | 1.827 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | B | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 35 | 35 | 43 | 50 | 73 | 85 | 0 | 84 | 114 |
| N.S. |
1 | 1.00 | 1.23 | 1.43 | 2.09 | 2.43 | 0.00 | 2.40 | 3.26 |
| time (sec) |
N/A | 0.545 | 0.140 | 3.143 | 0.226 | 0.280 | 0.000 | 0.341 | 2.074 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 61 | 64 | 75 | 75 | 95 | 96 | 0 | 151 | 104 |
| N.S. |
1 | 1.05 | 1.23 | 1.23 | 1.56 | 1.57 | 0.00 | 2.48 | 1.70 |
| time (sec) |
N/A | 0.638 | 0.015 | 3.511 | 0.232 | 0.281 | 0.000 | 0.343 | 2.698 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F(-1) | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 93 | 91 | 67 | 81 | 127 | 115 | 0 | 210 | 145 |
| N.S. |
1 | 0.98 | 0.72 | 0.87 | 1.37 | 1.24 | 0.00 | 2.26 | 1.56 |
| time (sec) |
N/A | 0.748 | 0.285 | 4.565 | 0.226 | 0.290 | 0.000 | 0.356 | 4.125 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F(-1) | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 114 | 106 | 85 | 119 | 163 | 136 | 0 | 304 | 194 |
| N.S. |
1 | 0.93 | 0.75 | 1.04 | 1.43 | 1.19 | 0.00 | 2.67 | 1.70 |
| time (sec) |
N/A | 0.768 | 0.618 | 3.202 | 0.221 | 0.294 | 0.000 | 0.355 | 6.271 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 189 | 164 | 146 | 147 | 176 | 142 | 462 | 156 | 307 |
| N.S. |
1 | 0.87 | 0.77 | 0.78 | 0.93 | 0.75 | 2.44 | 0.83 | 1.62 |
| time (sec) |
N/A | 0.893 | 1.801 | 3.327 | 0.229 | 0.288 | 0.300 | 0.326 | 5.670 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 170 | 177 | 118 | 118 | 142 | 114 | 340 | 124 | 169 |
| N.S. |
1 | 1.04 | 0.69 | 0.69 | 0.84 | 0.67 | 2.00 | 0.73 | 0.99 |
| time (sec) |
N/A | 0.542 | 2.503 | 1.003 | 0.214 | 0.292 | 0.194 | 0.347 | 1.850 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 107 | 110 | 90 | 88 | 108 | 85 | 0 | 254 | 115 |
| N.S. |
1 | 1.03 | 0.84 | 0.82 | 1.01 | 0.79 | 0.00 | 2.37 | 1.07 |
| time (sec) |
N/A | 0.469 | 0.894 | 1.550 | 0.214 | 0.271 | 0.000 | 0.332 | 1.868 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 86 | 86 | 120 | 94 | 99 | 87 | 0 | 178 | 169 |
| N.S. |
1 | 1.00 | 1.40 | 1.09 | 1.15 | 1.01 | 0.00 | 2.07 | 1.97 |
| time (sec) |
N/A | 0.728 | 1.418 | 1.576 | 0.222 | 0.296 | 0.000 | 0.340 | 2.155 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 60 | 60 | 109 | 79 | 103 | 117 | 0 | 152 | 169 |
| N.S. |
1 | 1.00 | 1.82 | 1.32 | 1.72 | 1.95 | 0.00 | 2.53 | 2.82 |
| time (sec) |
N/A | 0.692 | 1.844 | 1.257 | 0.218 | 0.291 | 0.000 | 0.362 | 2.298 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F(-1) | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 80 | 84 | 67 | 104 | 140 | 136 | 0 | 190 | 176 |
| N.S. |
1 | 1.05 | 0.84 | 1.30 | 1.75 | 1.70 | 0.00 | 2.38 | 2.20 |
| time (sec) |
N/A | 0.757 | 0.287 | 1.080 | 0.221 | 0.303 | 0.000 | 0.357 | 2.528 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F(-1) | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 116 | 122 | 92 | 118 | 172 | 150 | 0 | 294 | 227 |
| N.S. |
1 | 1.05 | 0.79 | 1.02 | 1.48 | 1.29 | 0.00 | 2.53 | 1.96 |
| time (sec) |
N/A | 0.921 | 0.497 | 1.296 | 0.240 | 0.287 | 0.000 | 0.373 | 6.019 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F(-1) | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 156 | 149 | 120 | 148 | 228 | 180 | 0 | 478 | 314 |
| N.S. |
1 | 0.96 | 0.77 | 0.95 | 1.46 | 1.15 | 0.00 | 3.06 | 2.01 |
| time (sec) |
N/A | 1.059 | 0.755 | 1.345 | 0.218 | 0.281 | 0.000 | 0.345 | 5.355 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 243 | 252 | 176 | 176 | 217 | 174 | 552 | 188 | 277 |
| N.S. |
1 | 1.04 | 0.72 | 0.72 | 0.89 | 0.72 | 2.27 | 0.77 | 1.14 |
| time (sec) |
N/A | 0.787 | 3.104 | 1.076 | 0.230 | 0.275 | 0.301 | 0.315 | 2.159 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 171 | 179 | 140 | 142 | 171 | 136 | 0 | 536 | 202 |
| N.S. |
1 | 1.05 | 0.82 | 0.83 | 1.00 | 0.80 | 0.00 | 3.13 | 1.18 |
| time (sec) |
N/A | 0.679 | 1.505 | 1.319 | 0.208 | 0.274 | 0.000 | 0.328 | 2.141 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 137 | 146 | 159 | 135 | 152 | 131 | 0 | 314 | 1924 |
| N.S. |
1 | 1.07 | 1.16 | 0.99 | 1.11 | 0.96 | 0.00 | 2.29 | 14.04 |
| time (sec) |
N/A | 1.079 | 1.982 | 1.186 | 0.219 | 0.292 | 0.000 | 0.344 | 3.402 |
| 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 | 131 | 134 | 217 | 124 | 144 | 152 | 0 | 234 | 236 |
| N.S. |
1 | 1.02 | 1.66 | 0.95 | 1.10 | 1.16 | 0.00 | 1.79 | 1.80 |
| time (sec) |
N/A | 1.075 | 2.460 | 1.082 | 0.219 | 0.286 | 0.000 | 0.374 | 3.352 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | A | A | A | F(-1) | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 124 | 126 | 277 | 133 | 169 | 167 | 0 | 239 | 249 |
| N.S. |
1 | 1.02 | 2.23 | 1.07 | 1.36 | 1.35 | 0.00 | 1.93 | 2.01 |
| time (sec) |
N/A | 1.088 | 4.521 | 1.345 | 0.236 | 0.290 | 0.000 | 0.363 | 2.998 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F(-1) | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 145 | 154 | 108 | 146 | 216 | 189 | 0 | 336 | 526 |
| N.S. |
1 | 1.06 | 0.74 | 1.01 | 1.49 | 1.30 | 0.00 | 2.32 | 3.63 |
| time (sec) |
N/A | 1.141 | 0.630 | 1.339 | 0.248 | 0.287 | 0.000 | 0.374 | 3.461 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F(-1) | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 188 | 199 | 140 | 185 | 273 | 211 | 0 | 586 | 395 |
| N.S. |
1 | 1.06 | 0.74 | 0.98 | 1.45 | 1.12 | 0.00 | 3.12 | 2.10 |
| time (sec) |
N/A | 1.339 | 0.860 | 1.457 | 0.237 | 0.283 | 0.000 | 0.374 | 5.515 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F(-1) | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 236 | 225 | 181 | 200 | 341 | 249 | 0 | 722 | 470 |
| N.S. |
1 | 0.95 | 0.77 | 0.85 | 1.44 | 1.06 | 0.00 | 3.06 | 1.99 |
| time (sec) |
N/A | 1.493 | 3.397 | 4.957 | 0.220 | 0.301 | 0.000 | 0.397 | 5.554 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | F(-1) | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 178 | 195 | 152 | 240 | 0 | 541 | 0 | 360 | 4568 |
| N.S. |
1 | 1.10 | 0.85 | 1.35 | 0.00 | 3.04 | 0.00 | 2.02 | 25.66 |
| time (sec) |
N/A | 1.170 | 1.478 | 1.398 | 0.000 | 0.299 | 0.000 | 0.320 | 7.027 |
| 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 | 134 | 146 | 121 | 169 | 0 | 426 | 0 | 227 | 3761 |
| N.S. |
1 | 1.09 | 0.90 | 1.26 | 0.00 | 3.18 | 0.00 | 1.69 | 28.07 |
| time (sec) |
N/A | 0.783 | 1.077 | 0.944 | 0.000 | 0.304 | 0.000 | 0.328 | 5.739 |
| 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 | 89 | 86 | 85 | 110 | 0 | 322 | 3235 | 142 | 541 |
| N.S. |
1 | 0.97 | 0.96 | 1.24 | 0.00 | 3.62 | 36.35 | 1.60 | 6.08 |
| time (sec) |
N/A | 0.413 | 0.746 | 0.696 | 0.000 | 0.301 | 164.767 | 0.346 | 2.480 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 67 | 67 | 68 | 73 | 0 | 242 | 0 | 296 | 344 |
| N.S. |
1 | 1.00 | 1.01 | 1.09 | 0.00 | 3.61 | 0.00 | 4.42 | 5.13 |
| time (sec) |
N/A | 0.416 | 0.207 | 1.005 | 0.000 | 0.296 | 0.000 | 0.329 | 3.425 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | F | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 76 | 76 | 112 | 92 | 0 | 304 | 0 | 128 | 342 |
| N.S. |
1 | 1.00 | 1.47 | 1.21 | 0.00 | 4.00 | 0.00 | 1.68 | 4.50 |
| time (sec) |
N/A | 0.535 | 0.533 | 1.162 | 0.000 | 0.640 | 0.000 | 0.338 | 3.047 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | B | F | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 99 | 96 | 129 | 144 | 0 | 460 | 0 | 175 | 675 |
| N.S. |
1 | 0.97 | 1.30 | 1.45 | 0.00 | 4.65 | 0.00 | 1.77 | 6.82 |
| time (sec) |
N/A | 0.637 | 1.122 | 1.500 | 0.000 | 0.391 | 0.000 | 0.351 | 3.592 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | A | F(-2) | B | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 143 | 154 | 300 | 229 | 0 | 589 | 0 | 269 | 4051 |
| N.S. |
1 | 1.08 | 2.10 | 1.60 | 0.00 | 4.12 | 0.00 | 1.88 | 28.33 |
| time (sec) |
N/A | 1.089 | 2.730 | 1.755 | 0.000 | 2.997 | 0.000 | 0.349 | 5.840 |