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 | C | F | A | C | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 453 | 878 | 217 | 327 | 0 | 283 | 364 | 0 | 0 |
| N.S. |
1 | 1.94 | 0.48 | 0.72 | 0.00 | 0.62 | 0.80 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.902 | 10.207 | 5.690 | 0.000 | 0.088 | 3.491 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | C | F | A | C | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 367 | 706 | 159 | 258 | 0 | 206 | 262 | 0 | 0 |
| N.S. |
1 | 1.92 | 0.43 | 0.70 | 0.00 | 0.56 | 0.71 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.713 | 10.120 | 3.023 | 0.000 | 0.092 | 2.590 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | C | F | A | C | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 277 | 432 | 121 | 203 | 0 | 127 | 167 | 0 | 0 |
| N.S. |
1 | 1.56 | 0.44 | 0.73 | 0.00 | 0.46 | 0.60 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.493 | 10.074 | 1.205 | 0.000 | 0.090 | 1.767 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | C | F | A | C | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 226 | 228 | 77 | 169 | 0 | 90 | 78 | 0 | 0 |
| N.S. |
1 | 1.01 | 0.34 | 0.75 | 0.00 | 0.40 | 0.35 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.294 | 10.029 | 0.530 | 0.000 | 0.091 | 0.856 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | C | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 369 | 382 | 138 | 192 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.04 | 0.37 | 0.52 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.594 | 10.274 | 0.815 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | C | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 641 | 600 | 297 | 679 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.94 | 0.46 | 1.06 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.293 | 10.785 | 1.418 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | C | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 875 | 788 | 453 | 1591 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.90 | 0.52 | 1.82 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.191 | 11.327 | 3.007 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | C | F | A | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 912 | 912 | 222 | 426 | 0 | 448 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.24 | 0.47 | 0.00 | 0.49 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.016 | 10.188 | 8.289 | 0.000 | 0.117 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | C | F | A | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 694 | 694 | 166 | 323 | 0 | 332 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.24 | 0.47 | 0.00 | 0.48 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.785 | 10.138 | 1.549 | 0.000 | 0.101 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | C | F | A | C | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 395 | 395 | 126 | 253 | 0 | 188 | 167 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.32 | 0.64 | 0.00 | 0.48 | 0.42 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.523 | 10.083 | 0.690 | 0.000 | 0.102 | 4.471 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | C | F | A | C | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 262 | 262 | 99 | 212 | 0 | 115 | 78 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.38 | 0.81 | 0.00 | 0.44 | 0.30 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.325 | 10.041 | 0.559 | 0.000 | 0.085 | 2.465 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | C | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 732 | 732 | 432 | 564 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.59 | 0.77 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.031 | 10.660 | 0.865 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | C | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 1494 | 1494 | 427 | 1384 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.29 | 0.93 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.224 | 11.135 | 1.503 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | C | F | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 2452 | 2452 | 630 | 2326 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.26 | 0.95 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 3.990 | 11.740 | 3.429 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | F | F | F | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 169 | 169 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.382 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | C | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 48 | 48 | 94 | 80 | 0 | 59 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.96 | 1.67 | 0.00 | 1.23 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.174 | 10.169 | 1.564 | 0.000 | 0.136 | 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 | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 755 | 690 | 901 | 673 | 0 | 1041 | 0 | 0 | 0 |
| N.S. |
1 | 0.91 | 1.19 | 0.89 | 0.00 | 1.38 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.447 | 14.513 | 10.893 | 0.000 | 0.148 | 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 | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 528 | 498 | 674 | 508 | 0 | 681 | 0 | 0 | 0 |
| N.S. |
1 | 0.94 | 1.28 | 0.96 | 0.00 | 1.29 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.887 | 12.807 | 4.278 | 0.000 | 0.114 | 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 | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 368 | 358 | 521 | 409 | 0 | 435 | 0 | 0 | 0 |
| N.S. |
1 | 0.97 | 1.42 | 1.11 | 0.00 | 1.18 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.507 | 11.347 | 3.066 | 0.000 | 0.123 | 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 | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 283 | 285 | 302 | 362 | 0 | 300 | 0 | 0 | 0 |
| N.S. |
1 | 1.01 | 1.07 | 1.28 | 0.00 | 1.06 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.333 | 0.117 | 0.931 | 0.000 | 0.113 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 436 | 449 | 298 | 359 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.03 | 0.68 | 0.82 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.664 | 10.428 | 1.734 | 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 | 782 | 727 | 1853 | 1495 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.93 | 2.37 | 1.91 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.590 | 12.375 | 3.167 | 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 | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 1125 | 985 | 781 | 4476 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.88 | 0.69 | 3.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 3.514 | 13.909 | 4.712 | 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 | B | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 859 | 765 | 1058 | 1141 | 0 | 2623 | 0 | 0 | 0 |
| N.S. |
1 | 0.89 | 1.23 | 1.33 | 0.00 | 3.05 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.716 | 15.269 | 12.568 | 0.000 | 0.134 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | B | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 628 | 576 | 766 | 799 | 0 | 1669 | 0 | 0 | 0 |
| N.S. |
1 | 0.92 | 1.22 | 1.27 | 0.00 | 2.66 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.918 | 12.987 | 2.938 | 0.000 | 0.108 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | B | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 481 | 446 | 597 | 593 | 0 | 1031 | 0 | 0 | 0 |
| N.S. |
1 | 0.93 | 1.24 | 1.23 | 0.00 | 2.14 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.660 | 11.657 | 1.671 | 0.000 | 0.100 | 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 | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 398 | 382 | 497 | 509 | 0 | 656 | 0 | 0 | 0 |
| N.S. |
1 | 0.96 | 1.25 | 1.28 | 0.00 | 1.65 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.462 | 10.911 | 1.035 | 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 | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 867 | 1045 | 1736 | 3241 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.21 | 2.00 | 3.74 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.574 | 13.305 | 1.759 | 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 | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 1301 | 2112 | 1116 | 8276 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.62 | 0.86 | 6.36 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 3.431 | 15.222 | 3.607 | 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(-2) | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 273 | 273 | 310 | 365 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.14 | 1.34 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.373 | 10.417 | 1.798 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 271 | 271 | 312 | 369 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.15 | 1.36 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.423 | 10.408 | 4.428 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | C | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 106 | 106 | 74 | 93 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.70 | 0.88 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.305 | 10.251 | 1.544 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | F | F | F | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 218 | 218 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.482 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | B | F | A | B |
| verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 106 | 114 | 81 | 81 | 0 | 286 | 0 | 80 | 397 |
| N.S. |
1 | 1.08 | 0.76 | 0.76 | 0.00 | 2.70 | 0.00 | 0.75 | 3.75 |
| time (sec) |
N/A | 0.378 | 0.024 | 1.168 | 0.000 | 0.331 | 0.000 | 0.309 | 8.632 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | B | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 145 | 191 | 139 | 126 | 0 | 603 | 0 | 0 | 0 |
| N.S. |
1 | 1.32 | 0.96 | 0.87 | 0.00 | 4.16 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.366 | 0.908 | 1.668 | 0.000 | 1.782 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | B | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 239 | 239 | 151 | 351 | 0 | 669 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.63 | 1.47 | 0.00 | 2.80 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.394 | 0.643 | 2.488 | 0.000 | 1.677 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | F | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 309 | 215 | 212 | 245 | 0 | 469 | 0 | 358 | 0 |
| N.S. |
1 | 0.70 | 0.69 | 0.79 | 0.00 | 1.52 | 0.00 | 1.16 | 0.00 |
| time (sec) |
N/A | 0.438 | 0.689 | 0.726 | 0.000 | 0.325 | 0.000 | 0.310 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | F | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 283 | 189 | 214 | 191 | 0 | 361 | 0 | 262 | 0 |
| N.S. |
1 | 0.67 | 0.76 | 0.67 | 0.00 | 1.28 | 0.00 | 0.93 | 0.00 |
| time (sec) |
N/A | 0.376 | 1.190 | 0.581 | 0.000 | 0.301 | 0.000 | 0.333 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 286 | 210 | 174 | 251 | 0 | 743 | 0 | 0 | 0 |
| N.S. |
1 | 0.73 | 0.61 | 0.88 | 0.00 | 2.60 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.525 | 0.537 | 0.574 | 0.000 | 0.733 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | F | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 294 | 212 | 171 | 229 | 0 | 731 | 0 | 238 | 0 |
| N.S. |
1 | 0.72 | 0.58 | 0.78 | 0.00 | 2.49 | 0.00 | 0.81 | 0.00 |
| time (sec) |
N/A | 0.543 | 0.607 | 0.590 | 0.000 | 0.659 | 0.000 | 0.327 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 288 | 200 | 173 | 214 | 0 | 749 | 0 | 360 | 0 |
| N.S. |
1 | 0.69 | 0.60 | 0.74 | 0.00 | 2.60 | 0.00 | 1.25 | 0.00 |
| time (sec) |
N/A | 0.518 | 0.641 | 0.607 | 0.000 | 0.585 | 0.000 | 0.343 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | F(-1) | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 294 | 220 | 186 | 194 | 0 | 791 | 0 | 683 | 0 |
| N.S. |
1 | 0.75 | 0.63 | 0.66 | 0.00 | 2.69 | 0.00 | 2.32 | 0.00 |
| time (sec) |
N/A | 0.541 | 0.877 | 0.614 | 0.000 | 0.595 | 0.000 | 0.351 | 0.000 |