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 | A | F(-2) | B | F(-1) | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 144 | 172 | 148 | 152 | 0 | 906 | 0 | 228 | 187 |
| N.S. |
1 | 1.19 | 1.03 | 1.06 | 0.00 | 6.29 | 0.00 | 1.58 | 1.30 |
| time (sec) |
N/A | 0.387 | 0.475 | 0.480 | 0.000 | 0.316 | 0.000 | 0.277 | 12.675 |
| 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 | 214 | 260 | 230 | 230 | 0 | 1539 | 0 | 368 | 310 |
| N.S. |
1 | 1.21 | 1.07 | 1.07 | 0.00 | 7.19 | 0.00 | 1.72 | 1.45 |
| time (sec) |
N/A | 0.503 | 0.907 | 0.538 | 0.000 | 0.343 | 0.000 | 0.275 | 12.682 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F(-2) | A | F | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 147 | 150 | 123 | 306 | 0 | 336 | 0 | 165 | 569 |
| N.S. |
1 | 1.02 | 0.84 | 2.08 | 0.00 | 2.29 | 0.00 | 1.12 | 3.87 |
| time (sec) |
N/A | 0.323 | 0.350 | 0.422 | 0.000 | 0.322 | 0.000 | 0.319 | 32.606 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | C | A | F(-1) | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 16 | 16 | 16 | 13 | 9 | 12 | 0 | 12 | 16 |
| N.S. |
1 | 1.00 | 1.00 | 0.81 | 0.56 | 0.75 | 0.00 | 0.75 | 1.00 |
| time (sec) |
N/A | 0.146 | 0.040 | 0.442 | 0.190 | 0.277 | 0.000 | 0.281 | 12.481 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | F(-1) | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 411 | 409 | 438 | 2385 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.07 | 5.80 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.269 | 1.310 | 0.450 | 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(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 342 | 341 | 363 | 1499 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.06 | 4.38 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.026 | 0.900 | 0.454 | 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 | B | F | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 240 | 240 | 229 | 1387 | 0 | 1921 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.95 | 5.78 | 0.00 | 8.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.473 | 10.305 | 0.405 | 0.000 | 6.811 | 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 | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 351 | 340 | 361 | 5383 | 0 | 5816 | 0 | 0 | 0 |
| N.S. |
1 | 0.97 | 1.03 | 15.34 | 0.00 | 16.57 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.947 | 1.191 | 0.460 | 0.000 | 35.163 | 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 | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 613 | 582 | 422 | 14861 | 0 | 10812 | 0 | 0 | 0 |
| N.S. |
1 | 0.95 | 0.69 | 24.24 | 0.00 | 17.64 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.307 | 1.650 | 0.456 | 0.000 | 160.903 | 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 | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 337 | 337 | 363 | 2336 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.08 | 6.93 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.978 | 1.017 | 0.455 | 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 | B | F | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 240 | 240 | 577 | 1383 | 0 | 1913 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 2.40 | 5.76 | 0.00 | 7.97 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.447 | 6.746 | 0.460 | 0.000 | 8.914 | 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 | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 230 | 230 | 286 | 1415 | 0 | 4325 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.24 | 6.15 | 0.00 | 18.80 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.425 | 0.870 | 0.451 | 0.000 | 15.586 | 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 | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 354 | 354 | 383 | 10977 | 0 | 11846 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.08 | 31.01 | 0.00 | 33.46 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.614 | 0.965 | 0.472 | 0.000 | 56.032 | 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 | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 625 | 574 | 1049 | 8264 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.92 | 1.68 | 13.22 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.303 | 8.148 | 0.480 | 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 | B | F | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 351 | 340 | 361 | 5383 | 0 | 5844 | 0 | 0 | 0 |
| N.S. |
1 | 0.97 | 1.03 | 15.34 | 0.00 | 16.65 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.827 | 1.266 | 0.462 | 0.000 | 46.421 | 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 | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 354 | 354 | 383 | 10977 | 0 | 12028 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.08 | 31.01 | 0.00 | 33.98 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.707 | 0.929 | 0.458 | 0.000 | 90.510 | 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 | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 549 | 543 | 477 | 30648 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.99 | 0.87 | 55.83 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.180 | 1.809 | 0.458 | 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 | B | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 65 | 65 | 59 | 305 | 0 | 129 | 0 | 375 | 1610 |
| N.S. |
1 | 1.00 | 0.91 | 4.69 | 0.00 | 1.98 | 0.00 | 5.77 | 24.77 |
| time (sec) |
N/A | 0.186 | 0.075 | 0.431 | 0.000 | 0.303 | 0.000 | 0.785 | 17.832 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | B | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 80 | 87 | 86 | 82 | 0 | 193 | 0 | 266 | 164 |
| N.S. |
1 | 1.09 | 1.08 | 1.02 | 0.00 | 2.41 | 0.00 | 3.32 | 2.05 |
| time (sec) |
N/A | 0.210 | 0.329 | 0.500 | 0.000 | 0.318 | 0.000 | 0.295 | 0.066 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | A | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 107 | 107 | 130 | 233 | 0 | 318 | 0 | 208 | 148 |
| N.S. |
1 | 1.00 | 1.21 | 2.18 | 0.00 | 2.97 | 0.00 | 1.94 | 1.38 |
| time (sec) |
N/A | 0.300 | 0.542 | 0.561 | 0.000 | 0.392 | 0.000 | 0.300 | 0.298 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F(-2) | A | F | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 107 | 112 | 130 | 233 | 0 | 318 | 0 | 131 | 148 |
| N.S. |
1 | 1.05 | 1.21 | 2.18 | 0.00 | 2.97 | 0.00 | 1.22 | 1.38 |
| time (sec) |
N/A | 0.284 | 0.393 | 0.470 | 0.000 | 0.385 | 0.000 | 0.285 | 0.130 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | C | F | F | F(-1) |
| verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 851 | 1311 | 1045 | 1824 | 0 | 765 | 0 | 0 | 0 |
| N.S. |
1 | 1.54 | 1.23 | 2.14 | 0.00 | 0.90 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 3.638 | 30.019 | 2.815 | 0.000 | 0.108 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | C | F | F | F(-1) |
| verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 635 | 1041 | 809 | 1142 | 0 | 510 | 0 | 0 | 0 |
| N.S. |
1 | 1.64 | 1.27 | 1.80 | 0.00 | 0.80 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.629 | 25.889 | 1.397 | 0.000 | 0.093 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | C | F | F | F(-1) |
| verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 434 | 784 | 610 | 794 | 0 | 343 | 0 | 0 | 0 |
| N.S. |
1 | 1.81 | 1.41 | 1.83 | 0.00 | 0.79 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.067 | 24.391 | 1.444 | 0.000 | 0.107 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 362 | 693 | 521 | 602 | 0 | 229 | 0 | 0 | 0 |
| N.S. |
1 | 1.91 | 1.44 | 1.66 | 0.00 | 0.63 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.809 | 23.158 | 0.927 | 0.000 | 0.089 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | F | C | A | F | F(-1) | F | F | F(-1) |
| verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 683 | 0 | 1216 | 922 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.00 | 1.78 | 1.35 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.000 | 29.085 | 2.612 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | B | C | A | F | F(-1) | F | F | F(-1) |
| verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 650 | 1547 | 1331 | 895 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 2.38 | 2.05 | 1.38 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.971 | 26.771 | 0.516 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | B | C | A | F | F(-1) | F | F | F(-1) |
| verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 1205 | 2763 | 2526 | 1161 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 2.29 | 2.10 | 0.96 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 5.360 | 29.362 | 0.891 | 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 | C | F | F | F(-1) |
| verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 666 | 1085 | 872 | 1156 | 0 | 578 | 0 | 0 | 0 |
| N.S. |
1 | 1.63 | 1.31 | 1.74 | 0.00 | 0.87 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.704 | 27.664 | 2.444 | 0.000 | 0.180 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | C | F | F | F(-1) |
| verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 508 | 878 | 665 | 848 | 0 | 409 | 0 | 0 | 0 |
| N.S. |
1 | 1.73 | 1.31 | 1.67 | 0.00 | 0.81 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.621 | 25.165 | 2.276 | 0.000 | 0.106 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | C | F | F | F(-1) |
| verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 364 | 698 | 545 | 678 | 0 | 268 | 0 | 0 | 0 |
| N.S. |
1 | 1.92 | 1.50 | 1.86 | 0.00 | 0.74 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.889 | 24.317 | 1.075 | 0.000 | 0.104 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 322 | 639 | 456 | 584 | 0 | 208 | 0 | 0 | 0 |
| N.S. |
1 | 1.98 | 1.42 | 1.81 | 0.00 | 0.65 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.668 | 22.495 | 0.977 | 0.000 | 0.097 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | B | C | B | F | F(-1) | F | F | F(-1) |
| verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 473 | 1496 | 1096 | 833 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 3.16 | 2.32 | 1.76 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.519 | 24.768 | 0.784 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | B | C | A | F | F(-1) | F | F | F(-1) |
| verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 694 | 1559 | 1336 | 921 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 2.25 | 1.93 | 1.33 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.732 | 26.289 | 1.467 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | B | C | A | F | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 1241 | 2774 | 2197 | 1196 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 2.24 | 1.77 | 0.96 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 5.308 | 28.723 | 2.721 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | C | F | F | F(-1) |
| verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 531 | 916 | 777 | 882 | 0 | 445 | 0 | 0 | 0 |
| N.S. |
1 | 1.73 | 1.46 | 1.66 | 0.00 | 0.84 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.804 | 25.522 | 3.372 | 0.000 | 0.114 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | C | F | F | F(-1) |
| verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 410 | 764 | 591 | 700 | 0 | 300 | 0 | 0 | 0 |
| N.S. |
1 | 1.86 | 1.44 | 1.71 | 0.00 | 0.73 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.161 | 25.092 | 2.094 | 0.000 | 0.105 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | B | C | B | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 331 | 667 | 464 | 602 | 0 | 227 | 0 | 0 | 0 |
| N.S. |
1 | 2.02 | 1.40 | 1.82 | 0.00 | 0.69 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.705 | 23.524 | 1.286 | 0.000 | 0.101 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | B | C | B | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 136 | 583 | 294 | 396 | 0 | 173 | 0 | 0 | 0 |
| N.S. |
1 | 4.29 | 2.16 | 2.91 | 0.00 | 1.27 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.588 | 20.378 | 0.440 | 0.000 | 0.104 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | B | C | A | F | F(-1) | F | F | F(-1) |
| verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 319 | 1112 | 300 | 439 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 3.49 | 0.94 | 1.38 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.893 | 21.358 | 1.170 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | B | C | A | F | F(-1) | F | F | F(-1) |
| verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 698 | 1567 | 1330 | 922 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 2.24 | 1.91 | 1.32 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.701 | 25.587 | 2.246 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | B | C | A | F | F(-1) | F | F | F(-1) |
| verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 1246 | 2782 | 2450 | 1224 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 2.23 | 1.97 | 0.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 5.154 | 29.038 | 3.125 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | B | C | A | F | F(-1) | F | F | F(-1) |
| verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 600 | 1848 | 1440 | 948 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 3.08 | 2.40 | 1.58 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 4.034 | 29.463 | 4.530 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | B | C | B | F | F(-1) | F | F | F(-1) |
| verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 469 | 1299 | 927 | 852 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 2.77 | 1.98 | 1.82 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.842 | 10.873 | 1.373 | 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 | C | F | F | F(-1) |
| verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 457 | 831 | 619 | 711 | 0 | 319 | 0 | 0 | 0 |
| N.S. |
1 | 1.82 | 1.35 | 1.56 | 0.00 | 0.70 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.314 | 24.724 | 2.980 | 0.000 | 0.119 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | C | F | F | F(-1) |
| verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 356 | 697 | 473 | 614 | 0 | 246 | 0 | 0 | 0 |
| N.S. |
1 | 1.96 | 1.33 | 1.72 | 0.00 | 0.69 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.894 | 23.650 | 2.535 | 0.000 | 0.133 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | B | C | B | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 288 | 614 | 439 | 520 | 0 | 180 | 0 | 0 | 0 |
| N.S. |
1 | 2.13 | 1.52 | 1.81 | 0.00 | 0.62 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.647 | 22.289 | 1.220 | 0.000 | 0.132 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 136 | 233 | 186 | 200 | 0 | 66 | 0 | 0 | 0 |
| N.S. |
1 | 1.71 | 1.37 | 1.47 | 0.00 | 0.49 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.269 | 21.200 | 0.949 | 0.000 | 0.124 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | B | C | A | F | F(-1) | F | F | F(-1) |
| verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 167 | 867 | 311 | 235 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 5.19 | 1.86 | 1.41 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.560 | 22.363 | 1.845 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | B | C | A | F | F(-1) | F | F | F(-1) |
| verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 746 | 1586 | 1349 | 995 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 2.13 | 1.81 | 1.33 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.760 | 25.970 | 2.599 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | B | C | A | F | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 1257 | 2800 | 2491 | 1192 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 2.23 | 1.98 | 0.95 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 5.120 | 29.749 | 3.459 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | B | C | B | F | F(-1) | F | F | F(-1) |
| verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 387 | 1176 | 468 | 929 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 3.04 | 1.21 | 2.40 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.928 | 23.301 | 2.527 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | B | C | A | F | F(-1) | F | F | F(-1) |
| verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 818 | 1795 | 1917 | 1079 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 2.19 | 2.34 | 1.32 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 3.985 | 27.374 | 3.177 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | B | C | B | F | F(-1) | F | F | F(-1) |
| verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 110 | 826 | 261 | 215 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 7.51 | 2.37 | 1.95 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.643 | 21.998 | 1.809 | 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 | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 454 | 454 | 344 | 401 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.76 | 0.88 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.481 | 24.183 | 5.083 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | A | F | A | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 52 | 52 | 107 | 58 | 0 | 4 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 2.06 | 1.12 | 0.00 | 0.08 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.182 | 34.621 | 1.125 | 0.000 | 0.086 | 0.000 | 0.000 | 0.000 |
| 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 | 269 | 275 | 136 | 170 | 218 | 193 | 0 | 613 | 218 |
| N.S. |
1 | 1.02 | 0.51 | 0.63 | 0.81 | 0.72 | 0.00 | 2.28 | 0.81 |
| time (sec) |
N/A | 0.527 | 0.129 | 0.509 | 0.245 | 0.302 | 0.000 | 0.309 | 12.607 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 200 | 199 | 89 | 98 | 133 | 123 | 0 | 350 | 142 |
| N.S. |
1 | 1.00 | 0.44 | 0.49 | 0.66 | 0.62 | 0.00 | 1.75 | 0.71 |
| time (sec) |
N/A | 0.391 | 0.072 | 0.533 | 0.235 | 0.312 | 0.000 | 0.288 | 12.504 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 125 | 123 | 53 | 49 | 65 | 71 | 0 | 165 | 88 |
| N.S. |
1 | 0.98 | 0.42 | 0.39 | 0.52 | 0.57 | 0.00 | 1.32 | 0.70 |
| time (sec) |
N/A | 0.261 | 0.050 | 0.524 | 0.239 | 0.275 | 0.000 | 0.286 | 12.352 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 46 | 46 | 35 | 32 | 18 | 49 | 0 | 68 | 54 |
| N.S. |
1 | 1.00 | 0.76 | 0.70 | 0.39 | 1.07 | 0.00 | 1.48 | 1.17 |
| time (sec) |
N/A | 0.166 | 0.013 | 0.529 | 0.216 | 0.284 | 0.000 | 0.279 | 12.361 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | A | F | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 80 | 80 | 93 | 77 | 0 | 252 | 0 | 126 | 0 |
| N.S. |
1 | 1.00 | 1.16 | 0.96 | 0.00 | 3.15 | 0.00 | 1.58 | 0.00 |
| time (sec) |
N/A | 0.258 | 0.074 | 0.537 | 0.000 | 0.306 | 0.000 | 0.285 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | B | F | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 140 | 140 | 136 | 158 | 0 | 703 | 0 | 395 | 0 |
| N.S. |
1 | 1.00 | 0.97 | 1.13 | 0.00 | 5.02 | 0.00 | 2.82 | 0.00 |
| time (sec) |
N/A | 0.361 | 0.243 | 0.548 | 0.000 | 0.308 | 0.000 | 0.369 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | B | F | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 213 | 220 | 163 | 275 | 0 | 1283 | 0 | 844 | 0 |
| N.S. |
1 | 1.03 | 0.77 | 1.29 | 0.00 | 6.02 | 0.00 | 3.96 | 0.00 |
| time (sec) |
N/A | 0.464 | 0.293 | 0.526 | 0.000 | 0.352 | 0.000 | 0.454 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | B | F | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 280 | 300 | 191 | 440 | 0 | 2027 | 0 | 1460 | 0 |
| N.S. |
1 | 1.07 | 0.68 | 1.57 | 0.00 | 7.24 | 0.00 | 5.21 | 0.00 |
| time (sec) |
N/A | 0.581 | 0.463 | 0.534 | 0.000 | 0.673 | 0.000 | 0.656 | 0.000 |
| 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 | 257 | 262 | 134 | 179 | 165 | 216 | 0 | 513 | 252 |
| N.S. |
1 | 1.02 | 0.52 | 0.70 | 0.64 | 0.84 | 0.00 | 2.00 | 0.98 |
| time (sec) |
N/A | 0.502 | 0.104 | 0.529 | 0.256 | 0.278 | 0.000 | 0.313 | 12.727 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 181 | 186 | 88 | 108 | 98 | 147 | 0 | 298 | 178 |
| N.S. |
1 | 1.03 | 0.49 | 0.60 | 0.54 | 0.81 | 0.00 | 1.65 | 0.98 |
| time (sec) |
N/A | 0.366 | 0.068 | 0.527 | 0.243 | 0.273 | 0.000 | 0.302 | 12.583 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 150 | 150 | 51 | 58 | 48 | 96 | 0 | 138 | 118 |
| N.S. |
1 | 1.00 | 0.34 | 0.39 | 0.32 | 0.64 | 0.00 | 0.92 | 0.79 |
| time (sec) |
N/A | 0.315 | 0.047 | 0.533 | 0.228 | 0.285 | 0.000 | 0.292 | 12.387 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 46 | 46 | 35 | 42 | 18 | 74 | 0 | 70 | 82 |
| N.S. |
1 | 1.00 | 0.76 | 0.91 | 0.39 | 1.61 | 0.00 | 1.52 | 1.78 |
| time (sec) |
N/A | 0.168 | 0.008 | 0.527 | 0.216 | 0.308 | 0.000 | 0.287 | 12.376 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | B | F(-1) | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 133 | 133 | 109 | 118 | 0 | 553 | 0 | 281 | 0 |
| N.S. |
1 | 1.00 | 0.82 | 0.89 | 0.00 | 4.16 | 0.00 | 2.11 | 0.00 |
| time (sec) |
N/A | 0.343 | 0.101 | 0.545 | 0.000 | 0.294 | 0.000 | 0.385 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | B | F(-1) | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 202 | 215 | 141 | 215 | 0 | 1067 | 0 | 753 | 0 |
| N.S. |
1 | 1.06 | 0.70 | 1.06 | 0.00 | 5.28 | 0.00 | 3.73 | 0.00 |
| time (sec) |
N/A | 0.449 | 0.354 | 0.510 | 0.000 | 0.331 | 0.000 | 0.496 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | B | F(-1) | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 274 | 295 | 185 | 369 | 0 | 1863 | 0 | 1390 | 0 |
| N.S. |
1 | 1.08 | 0.68 | 1.35 | 0.00 | 6.80 | 0.00 | 5.07 | 0.00 |
| time (sec) |
N/A | 0.602 | 0.527 | 0.552 | 0.000 | 0.486 | 0.000 | 0.697 | 0.000 |
| 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 | 239 | 251 | 131 | 179 | 219 | 251 | 0 | 524 | 278 |
| N.S. |
1 | 1.05 | 0.55 | 0.75 | 0.92 | 1.05 | 0.00 | 2.19 | 1.16 |
| time (sec) |
N/A | 0.479 | 0.116 | 0.543 | 0.253 | 0.415 | 0.000 | 0.343 | 12.938 |
| 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 | 211 | 217 | 87 | 108 | 138 | 180 | 0 | 303 | 206 |
| N.S. |
1 | 1.03 | 0.41 | 0.51 | 0.65 | 0.85 | 0.00 | 1.44 | 0.98 |
| time (sec) |
N/A | 0.411 | 0.079 | 0.568 | 0.256 | 0.370 | 0.000 | 0.315 | 12.730 |
| 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 | 154 | 154 | 52 | 58 | 73 | 129 | 0 | 163 | 149 |
| N.S. |
1 | 1.00 | 0.34 | 0.38 | 0.47 | 0.84 | 0.00 | 1.06 | 0.97 |
| time (sec) |
N/A | 0.316 | 0.054 | 0.533 | 0.237 | 0.310 | 0.000 | 0.303 | 12.512 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | B | F(-1) | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 48 | 48 | 37 | 42 | 28 | 107 | 0 | 97 | 110 |
| N.S. |
1 | 1.00 | 0.77 | 0.88 | 0.58 | 2.23 | 0.00 | 2.02 | 2.29 |
| time (sec) |
N/A | 0.172 | 0.018 | 0.536 | 0.209 | 0.270 | 0.000 | 0.294 | 12.472 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | B | F(-1) | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 188 | 203 | 129 | 209 | 0 | 1015 | 0 | 683 | 0 |
| N.S. |
1 | 1.08 | 0.69 | 1.11 | 0.00 | 5.40 | 0.00 | 3.63 | 0.00 |
| time (sec) |
N/A | 0.465 | 0.200 | 0.554 | 0.000 | 0.387 | 0.000 | 0.440 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | B | F(-1) | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 268 | 294 | 180 | 414 | 0 | 1907 | 0 | 1404 | 0 |
| N.S. |
1 | 1.10 | 0.67 | 1.54 | 0.00 | 7.12 | 0.00 | 5.24 | 0.00 |
| time (sec) |
N/A | 0.590 | 0.417 | 0.543 | 0.000 | 0.625 | 0.000 | 0.643 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | B | F(-1) | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 342 | 374 | 240 | 660 | 0 | 2935 | 0 | 2347 | 0 |
| N.S. |
1 | 1.09 | 0.70 | 1.93 | 0.00 | 8.58 | 0.00 | 6.86 | 0.00 |
| time (sec) |
N/A | 0.731 | 0.743 | 0.543 | 0.000 | 1.308 | 0.000 | 1.139 | 0.000 |
| 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 | 336 | 351 | 195 | 273 | 320 | 375 | 0 | 1107 | 347 |
| N.S. |
1 | 1.04 | 0.58 | 0.81 | 0.95 | 1.12 | 0.00 | 3.29 | 1.03 |
| time (sec) |
N/A | 0.672 | 0.158 | 0.536 | 0.251 | 0.277 | 0.000 | 0.324 | 12.361 |
| 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 | 269 | 275 | 136 | 178 | 218 | 264 | 0 | 762 | 242 |
| N.S. |
1 | 1.02 | 0.51 | 0.66 | 0.81 | 0.98 | 0.00 | 2.83 | 0.90 |
| time (sec) |
N/A | 0.533 | 0.113 | 0.541 | 0.246 | 0.308 | 0.000 | 0.304 | 12.292 |
| 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 | 200 | 199 | 90 | 106 | 133 | 173 | 0 | 476 | 157 |
| N.S. |
1 | 1.00 | 0.45 | 0.53 | 0.66 | 0.86 | 0.00 | 2.38 | 0.78 |
| time (sec) |
N/A | 0.394 | 0.070 | 0.534 | 0.233 | 0.369 | 0.000 | 0.300 | 12.085 |
| 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 | 125 | 123 | 54 | 57 | 65 | 102 | 0 | 253 | 93 |
| N.S. |
1 | 0.98 | 0.43 | 0.46 | 0.52 | 0.82 | 0.00 | 2.02 | 0.74 |
| time (sec) |
N/A | 0.268 | 0.043 | 0.529 | 0.221 | 0.371 | 0.000 | 0.281 | 11.983 |
| 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 | 48 | 48 | 37 | 40 | 18 | 57 | 0 | 91 | 49 |
| N.S. |
1 | 1.00 | 0.77 | 0.83 | 0.38 | 1.19 | 0.00 | 1.90 | 1.02 |
| time (sec) |
N/A | 0.173 | 0.016 | 0.484 | 0.215 | 0.366 | 0.000 | 0.279 | 11.983 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | A | F | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 124 | 124 | 114 | 143 | 0 | 318 | 0 | 255 | 0 |
| N.S. |
1 | 1.00 | 0.92 | 1.15 | 0.00 | 2.56 | 0.00 | 2.06 | 0.00 |
| time (sec) |
N/A | 0.349 | 0.105 | 0.549 | 0.000 | 0.380 | 0.000 | 0.364 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | B | F | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 132 | 132 | 110 | 151 | 0 | 562 | 0 | 315 | 0 |
| N.S. |
1 | 1.00 | 0.83 | 1.14 | 0.00 | 4.26 | 0.00 | 2.39 | 0.00 |
| time (sec) |
N/A | 0.332 | 0.242 | 0.553 | 0.000 | 0.439 | 0.000 | 0.355 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | B | F(-1) | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 207 | 202 | 165 | 275 | 0 | 1056 | 0 | 662 | 0 |
| N.S. |
1 | 0.98 | 0.80 | 1.33 | 0.00 | 5.10 | 0.00 | 3.20 | 0.00 |
| time (sec) |
N/A | 0.447 | 0.468 | 0.537 | 0.000 | 0.401 | 0.000 | 0.486 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | B | F(-1) | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 277 | 282 | 202 | 443 | 0 | 1732 | 0 | 1234 | 0 |
| N.S. |
1 | 1.02 | 0.73 | 1.60 | 0.00 | 6.25 | 0.00 | 4.45 | 0.00 |
| time (sec) |
N/A | 0.579 | 0.717 | 0.534 | 0.000 | 0.803 | 0.000 | 0.663 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | B | F(-1) | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 347 | 362 | 234 | 686 | 0 | 2610 | 0 | 1955 | 0 |
| N.S. |
1 | 1.04 | 0.67 | 1.98 | 0.00 | 7.52 | 0.00 | 5.63 | 0.00 |
| time (sec) |
N/A | 0.731 | 1.059 | 0.538 | 0.000 | 1.346 | 0.000 | 1.733 | 0.000 |
| 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 | 336 | 351 | 195 | 275 | 413 | 472 | 0 | 2535 | 445 |
| N.S. |
1 | 1.04 | 0.58 | 0.82 | 1.23 | 1.40 | 0.00 | 7.54 | 1.32 |
| time (sec) |
N/A | 0.690 | 0.201 | 0.545 | 0.261 | 0.349 | 0.000 | 0.384 | 12.561 |
| 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 | 269 | 275 | 137 | 180 | 294 | 340 | 0 | 1778 | 310 |
| N.S. |
1 | 1.02 | 0.51 | 0.67 | 1.09 | 1.26 | 0.00 | 6.61 | 1.15 |
| time (sec) |
N/A | 0.528 | 0.153 | 0.515 | 0.246 | 0.316 | 0.000 | 0.358 | 12.428 |
| 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 | 200 | 199 | 90 | 108 | 192 | 230 | 0 | 1145 | 206 |
| N.S. |
1 | 1.00 | 0.45 | 0.54 | 0.96 | 1.15 | 0.00 | 5.72 | 1.03 |
| time (sec) |
N/A | 0.396 | 0.101 | 0.543 | 0.234 | 0.302 | 0.000 | 0.325 | 12.126 |
| 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 | 125 | 123 | 54 | 59 | 107 | 137 | 0 | 632 | 109 |
| N.S. |
1 | 0.98 | 0.43 | 0.47 | 0.86 | 1.10 | 0.00 | 5.06 | 0.87 |
| time (sec) |
N/A | 0.271 | 0.064 | 0.575 | 0.225 | 0.296 | 0.000 | 0.298 | 11.946 |
| 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 | 48 | 48 | 37 | 42 | 43 | 74 | 0 | 254 | 62 |
| N.S. |
1 | 1.00 | 0.77 | 0.88 | 0.90 | 1.54 | 0.00 | 5.29 | 1.29 |
| time (sec) |
N/A | 0.172 | 0.023 | 0.559 | 0.214 | 0.286 | 0.000 | 0.287 | 12.110 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | A | F | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 179 | 185 | 132 | 253 | 0 | 408 | 0 | 506 | 0 |
| N.S. |
1 | 1.03 | 0.74 | 1.41 | 0.00 | 2.28 | 0.00 | 2.83 | 0.00 |
| time (sec) |
N/A | 0.476 | 0.186 | 0.562 | 0.000 | 0.351 | 0.000 | 0.469 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | A | F(-1) | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 178 | 184 | 144 | 296 | 0 | 444 | 0 | 605 | 0 |
| N.S. |
1 | 1.03 | 0.81 | 1.66 | 0.00 | 2.49 | 0.00 | 3.40 | 0.00 |
| time (sec) |
N/A | 0.448 | 0.333 | 0.553 | 0.000 | 0.331 | 0.000 | 0.424 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | B | F(-1) | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 195 | 194 | 135 | 266 | 0 | 840 | 0 | 581 | 0 |
| N.S. |
1 | 0.99 | 0.69 | 1.36 | 0.00 | 4.31 | 0.00 | 2.98 | 0.00 |
| time (sec) |
N/A | 0.437 | 0.462 | 0.550 | 0.000 | 0.343 | 0.000 | 0.476 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | B | F(-1) | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 265 | 264 | 201 | 443 | 0 | 1434 | 0 | 1087 | 0 |
| N.S. |
1 | 1.00 | 0.76 | 1.67 | 0.00 | 5.41 | 0.00 | 4.10 | 0.00 |
| time (sec) |
N/A | 0.573 | 0.731 | 0.565 | 0.000 | 0.437 | 0.000 | 0.688 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | B | F(-1) | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 335 | 344 | 240 | 655 | 0 | 2238 | 0 | 1785 | 0 |
| N.S. |
1 | 1.03 | 0.72 | 1.96 | 0.00 | 6.68 | 0.00 | 5.33 | 0.00 |
| time (sec) |
N/A | 0.705 | 1.103 | 0.573 | 0.000 | 0.800 | 0.000 | 1.208 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | B | F(-1) | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 405 | 424 | 302 | 945 | 0 | 3204 | 0 | 2659 | 0 |
| N.S. |
1 | 1.05 | 0.75 | 2.33 | 0.00 | 7.91 | 0.00 | 6.57 | 0.00 |
| time (sec) |
N/A | 0.828 | 2.194 | 0.582 | 0.000 | 2.278 | 0.000 | 2.799 | 0.000 |
| 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 | 336 | 351 | 205 | 275 | 498 | 567 | 0 | 4287 | 523 |
| N.S. |
1 | 1.04 | 0.61 | 0.82 | 1.48 | 1.69 | 0.00 | 12.76 | 1.56 |
| time (sec) |
N/A | 0.682 | 0.206 | 0.585 | 0.258 | 0.320 | 0.000 | 0.483 | 12.826 |