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 | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 538 | 553 | 718 | 904 | 0 | 892 | 0 | 0 | 31 | 0 |
N.S. |
1 | 1.03 | 1.33 | 1.68 | 0.00 | 1.66 | 0.00 | 0.00 | 0.06 | 0.00 |
time (sec) |
N/A | 2.048 | 29.033 | 5.375 | 0.000 | 0.115 | 0.000 | 0.000 | 200.018 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 495 | 509 | 632 | 854 | 0 | 779 | 0 | 0 | 30 | 0 |
N.S. |
1 | 1.03 | 1.28 | 1.73 | 0.00 | 1.57 | 0.00 | 0.00 | 0.06 | 0.00 |
time (sec) |
N/A | 1.576 | 27.119 | 5.367 | 0.000 | 0.107 | 0.000 | 0.000 | 200.015 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 619 | 1037 | 1728 | 1102 | 0 | 0 | 0 | 0 | 281 | 0 |
N.S. |
1 | 1.68 | 2.79 | 1.78 | 0.00 | 0.00 | 0.00 | 0.00 | 0.45 | 0.00 |
time (sec) |
N/A | 3.100 | 31.242 | 5.636 | 0.000 | 0.000 | 0.000 | 0.000 | 75.314 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | C | A | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 681 | 2117 | 2682 | 1145 | 0 | 0 | 0 | 0 | 33 | 0 |
N.S. |
1 | 3.11 | 3.94 | 1.68 | 0.00 | 0.00 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 9.903 | 33.273 | 9.635 | 0.000 | 0.000 | 0.000 | 0.000 | 200.019 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | C | A | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 786 | 2545 | 3781 | 1263 | 0 | 0 | 0 | 0 | 33 | 0 |
N.S. |
1 | 3.24 | 4.81 | 1.61 | 0.00 | 0.00 | 0.00 | 0.00 | 0.04 | 0.00 |
time (sec) |
N/A | 15.074 | 35.406 | 10.809 | 0.000 | 0.000 | 0.000 | 0.000 | 200.033 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 270 | 268 | 405 | 498 | 0 | 182 | 0 | 0 | 90 | 0 |
N.S. |
1 | 0.99 | 1.50 | 1.84 | 0.00 | 0.67 | 0.00 | 0.00 | 0.33 | 0.00 |
time (sec) |
N/A | 0.671 | 22.838 | 2.845 | 0.000 | 0.092 | 0.000 | 0.000 | 22.089 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 615 | 700 | 818 | 1079 | 0 | 981 | 0 | 0 | 33 | 0 |
N.S. |
1 | 1.14 | 1.33 | 1.75 | 0.00 | 1.60 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 4.455 | 30.209 | 10.734 | 0.000 | 0.110 | 0.000 | 0.000 | 200.028 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 520 | 579 | 729 | 908 | 0 | 736 | 0 | 0 | 33 | 0 |
N.S. |
1 | 1.11 | 1.40 | 1.75 | 0.00 | 1.42 | 0.00 | 0.00 | 0.06 | 0.00 |
time (sec) |
N/A | 2.971 | 28.854 | 10.260 | 0.000 | 0.103 | 0.000 | 0.000 | 200.022 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 450 | 489 | 643 | 801 | 0 | 581 | 0 | 0 | 33 | 0 |
N.S. |
1 | 1.09 | 1.43 | 1.78 | 0.00 | 1.29 | 0.00 | 0.00 | 0.07 | 0.00 |
time (sec) |
N/A | 2.131 | 27.123 | 8.476 | 0.000 | 0.099 | 0.000 | 0.000 | 200.045 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 383 | 401 | 567 | 750 | 0 | 441 | 0 | 0 | 31 | 0 |
N.S. |
1 | 1.05 | 1.48 | 1.96 | 0.00 | 1.15 | 0.00 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 1.247 | 26.057 | 4.910 | 0.000 | 0.094 | 0.000 | 0.000 | 200.021 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 363 | 385 | 520 | 762 | 0 | 451 | 0 | 0 | 30 | 0 |
N.S. |
1 | 1.06 | 1.43 | 2.10 | 0.00 | 1.24 | 0.00 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 1.088 | 26.638 | 4.448 | 0.000 | 0.093 | 0.000 | 0.000 | 200.018 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | B | F | F | F | F | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 476 | 0 | 1223 | 985 | 0 | 0 | 0 | 0 | 33 | 0 |
N.S. |
1 | 0.00 | 2.57 | 2.07 | 0.00 | 0.00 | 0.00 | 0.00 | 0.07 | 0.00 |
time (sec) |
N/A | 0.000 | 27.477 | 5.144 | 0.000 | 0.000 | 0.000 | 0.000 | 200.024 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | B | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 545 | 0 | 1739 | 1045 | 0 | 0 | 0 | 0 | 33 | 0 |
N.S. |
1 | 0.00 | 3.19 | 1.92 | 0.00 | 0.00 | 0.00 | 0.00 | 0.06 | 0.00 |
time (sec) |
N/A | 0.000 | 30.392 | 8.596 | 0.000 | 0.000 | 0.000 | 0.000 | 200.027 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | B | F | F(-1) | F(-1) | F | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 623 | 0 | 2670 | 1123 | 0 | 0 | 0 | 0 | 33 | 0 |
N.S. |
1 | 0.00 | 4.29 | 1.80 | 0.00 | 0.00 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 0.000 | 32.356 | 8.641 | 0.000 | 0.000 | 0.000 | 0.000 | 200.014 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 713 | 777 | 935 | 1483 | 0 | 1822 | 0 | 0 | 33 | 0 |
N.S. |
1 | 1.09 | 1.31 | 2.08 | 0.00 | 2.56 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 4.958 | 31.994 | 12.898 | 0.000 | 0.169 | 0.000 | 0.000 | 200.018 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 625 | 669 | 834 | 1287 | 0 | 1548 | 0 | 0 | 33 | 0 |
N.S. |
1 | 1.07 | 1.33 | 2.06 | 0.00 | 2.48 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 3.509 | 29.947 | 12.392 | 0.000 | 0.125 | 0.000 | 0.000 | 200.020 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 556 | 586 | 733 | 1058 | 0 | 1220 | 0 | 0 | 33 | 0 |
N.S. |
1 | 1.05 | 1.32 | 1.90 | 0.00 | 2.19 | 0.00 | 0.00 | 0.06 | 0.00 |
time (sec) |
N/A | 2.385 | 28.771 | 6.026 | 0.000 | 0.126 | 0.000 | 0.000 | 200.035 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 498 | 516 | 660 | 968 | 0 | 1067 | 0 | 0 | 31 | 0 |
N.S. |
1 | 1.04 | 1.33 | 1.94 | 0.00 | 2.14 | 0.00 | 0.00 | 0.06 | 0.00 |
time (sec) |
N/A | 1.704 | 27.404 | 6.211 | 0.000 | 0.114 | 0.000 | 0.000 | 200.021 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 487 | 506 | 665 | 952 | 0 | 1006 | 0 | 0 | 1552 | 0 |
N.S. |
1 | 1.04 | 1.37 | 1.95 | 0.00 | 2.07 | 0.00 | 0.00 | 3.19 | 0.00 |
time (sec) |
N/A | 1.650 | 27.020 | 6.133 | 0.000 | 0.112 | 0.000 | 0.000 | 22.653 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | B | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 611 | 0 | 1424 | 1281 | 0 | 0 | 0 | 0 | 33 | 0 |
N.S. |
1 | 0.00 | 2.33 | 2.10 | 0.00 | 0.00 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 0.000 | 30.152 | 6.268 | 0.000 | 0.000 | 0.000 | 0.000 | 200.050 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | B | F | F(-1) | F(-1) | F | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 719 | 0 | 2824 | 1436 | 0 | 0 | 0 | 0 | 33 | 0 |
N.S. |
1 | 0.00 | 3.93 | 2.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 0.000 | 33.775 | 11.002 | 0.000 | 0.000 | 0.000 | 0.000 | 200.029 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | B | F | F(-1) | F(-1) | F | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 803 | 0 | 3770 | 1562 | 0 | 0 | 0 | 0 | 33 | 0 |
N.S. |
1 | 0.00 | 4.69 | 1.95 | 0.00 | 0.00 | 0.00 | 0.00 | 0.04 | 0.00 |
time (sec) |
N/A | 0.000 | 35.099 | 12.059 | 0.000 | 0.000 | 0.000 | 0.000 | 200.027 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | B | F(-1) | F | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 854 | 912 | 1232 | 1470 | 0 | 2719 | 0 | 0 | 33 | 0 |
N.S. |
1 | 1.07 | 1.44 | 1.72 | 0.00 | 3.18 | 0.00 | 0.00 | 0.04 | 0.00 |
time (sec) |
N/A | 5.557 | 33.548 | 15.461 | 0.000 | 0.342 | 0.000 | 0.000 | 200.021 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | B | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 767 | 810 | 1167 | 1376 | 0 | 2290 | 0 | 0 | 33 | 0 |
N.S. |
1 | 1.06 | 1.52 | 1.79 | 0.00 | 2.99 | 0.00 | 0.00 | 0.04 | 0.00 |
time (sec) |
N/A | 3.704 | 33.062 | 9.098 | 0.000 | 0.241 | 0.000 | 0.000 | 200.031 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 714 | 749 | 891 | 1358 | 0 | 2078 | 0 | 0 | 33 | 0 |
N.S. |
1 | 1.05 | 1.25 | 1.90 | 0.00 | 2.91 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 2.810 | 31.210 | 7.773 | 0.000 | 0.257 | 0.000 | 0.000 | 200.019 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 642 | 671 | 866 | 1318 | 0 | 1759 | 0 | 0 | 31 | 0 |
N.S. |
1 | 1.05 | 1.35 | 2.05 | 0.00 | 2.74 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 2.176 | 30.059 | 8.003 | 0.000 | 0.308 | 0.000 | 0.000 | 200.018 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 627 | 655 | 832 | 1295 | 0 | 1804 | 0 | 0 | 30 | 0 |
N.S. |
1 | 1.04 | 1.33 | 2.07 | 0.00 | 2.88 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 2.052 | 30.013 | 7.873 | 0.000 | 0.208 | 0.000 | 0.000 | 200.024 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | B | F | F(-1) | F(-1) | F | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 782 | 0 | 2384 | 1552 | 0 | 0 | 0 | 0 | 33 | 0 |
N.S. |
1 | 0.00 | 3.05 | 1.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.04 | 0.00 |
time (sec) |
N/A | 0.000 | 33.506 | 8.191 | 0.000 | 0.000 | 0.000 | 0.000 | 200.031 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | A | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 919 | 0 | 9484 | 1621 | 0 | 0 | 0 | 0 | 33 | 0 |
N.S. |
1 | 0.00 | 10.32 | 1.76 | 0.00 | 0.00 | 0.00 | 0.00 | 0.04 | 0.00 |
time (sec) |
N/A | 0.000 | 35.830 | 13.644 | 0.000 | 0.000 | 0.000 | 0.000 | 200.034 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | A | F | F(-1) | F(-1) | F | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 1012 | 0 | 12354 | 1732 | 0 | 0 | 0 | 0 | 33 | 0 |
N.S. |
1 | 0.00 | 12.21 | 1.71 | 0.00 | 0.00 | 0.00 | 0.00 | 0.03 | 0.00 |
time (sec) |
N/A | 0.000 | 36.556 | 16.141 | 0.000 | 0.000 | 0.000 | 0.000 | 200.026 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | B | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 748 | 819 | 1155 | 1273 | 0 | 1621 | 0 | 0 | 33 | 0 |
N.S. |
1 | 1.09 | 1.54 | 1.70 | 0.00 | 2.17 | 0.00 | 0.00 | 0.04 | 0.00 |
time (sec) |
N/A | 4.952 | 33.284 | 15.644 | 0.000 | 0.148 | 0.000 | 0.000 | 200.017 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | B | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 681 | 727 | 1061 | 1187 | 0 | 1357 | 0 | 0 | 33 | 0 |
N.S. |
1 | 1.07 | 1.56 | 1.74 | 0.00 | 1.99 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 3.719 | 32.211 | 14.947 | 0.000 | 0.132 | 0.000 | 0.000 | 200.018 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 608 | 629 | 813 | 1110 | 0 | 1116 | 0 | 0 | 33 | 0 |
N.S. |
1 | 1.03 | 1.34 | 1.83 | 0.00 | 1.84 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 2.500 | 30.586 | 7.510 | 0.000 | 0.124 | 0.000 | 0.000 | 200.029 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 601 | 617 | 821 | 1126 | 0 | 1093 | 0 | 0 | 33 | 0 |
N.S. |
1 | 1.03 | 1.37 | 1.87 | 0.00 | 1.82 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 2.470 | 29.657 | 6.512 | 0.000 | 0.126 | 0.000 | 0.000 | 200.015 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 571 | 595 | 782 | 1069 | 0 | 1006 | 0 | 0 | 31 | 0 |
N.S. |
1 | 1.04 | 1.37 | 1.87 | 0.00 | 1.76 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 1.821 | 29.236 | 6.520 | 0.000 | 0.116 | 0.000 | 0.000 | 200.025 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 593 | 620 | 802 | 1104 | 0 | 1079 | 0 | 0 | 30 | 0 |
N.S. |
1 | 1.05 | 1.35 | 1.86 | 0.00 | 1.82 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 1.851 | 29.250 | 6.314 | 0.000 | 0.116 | 0.000 | 0.000 | 200.016 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | B | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 685 | 0 | 1968 | 1319 | 0 | 0 | 0 | 0 | 33 | 0 |
N.S. |
1 | 0.00 | 2.87 | 1.93 | 0.00 | 0.00 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 0.000 | 32.397 | 7.661 | 0.000 | 0.000 | 0.000 | 0.000 | 200.022 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | B | F | F(-1) | F(-1) | F | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 783 | 0 | 2943 | 1412 | 0 | 0 | 0 | 0 | 33 | 0 |
N.S. |
1 | 0.00 | 3.76 | 1.80 | 0.00 | 0.00 | 0.00 | 0.00 | 0.04 | 0.00 |
time (sec) |
N/A | 0.000 | 34.450 | 13.260 | 0.000 | 0.000 | 0.000 | 0.000 | 200.031 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | A | F | F(-1) | F(-1) | F | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 845 | 0 | 9327 | 1478 | 0 | 0 | 0 | 0 | 33 | 0 |
N.S. |
1 | 0.00 | 11.04 | 1.75 | 0.00 | 0.00 | 0.00 | 0.00 | 0.04 | 0.00 |
time (sec) |
N/A | 0.000 | 35.743 | 14.023 | 0.000 | 0.000 | 0.000 | 0.000 | 200.019 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 800 | 834 | 949 | 1324 | 0 | 687 | 0 | 0 | 1354 | 0 |
N.S. |
1 | 1.04 | 1.19 | 1.66 | 0.00 | 0.86 | 0.00 | 0.00 | 1.69 | 0.00 |
time (sec) |
N/A | 5.286 | 32.867 | 8.099 | 0.000 | 0.122 | 0.000 | 0.000 | 37.011 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 644 | 669 | 797 | 978 | 0 | 514 | 0 | 0 | 970 | 0 |
N.S. |
1 | 1.04 | 1.24 | 1.52 | 0.00 | 0.80 | 0.00 | 0.00 | 1.51 | 0.00 |
time (sec) |
N/A | 3.460 | 30.314 | 6.132 | 0.000 | 0.101 | 0.000 | 0.000 | 5.135 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 517 | 532 | 645 | 780 | 0 | 404 | 0 | 0 | 723 | 0 |
N.S. |
1 | 1.03 | 1.25 | 1.51 | 0.00 | 0.78 | 0.00 | 0.00 | 1.40 | 0.00 |
time (sec) |
N/A | 2.390 | 28.844 | 3.888 | 0.000 | 0.099 | 0.000 | 0.000 | 3.931 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 529 | 591 | 792 | 894 | 0 | 0 | 0 | 0 | 487 | 0 |
N.S. |
1 | 1.12 | 1.50 | 1.69 | 0.00 | 0.00 | 0.00 | 0.00 | 0.92 | 0.00 |
time (sec) |
N/A | 2.372 | 25.430 | 3.137 | 0.000 | 0.000 | 0.000 | 0.000 | 75.107 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 522 | 592 | 784 | 871 | 0 | 0 | 0 | 0 | 43 | 0 |
N.S. |
1 | 1.13 | 1.50 | 1.67 | 0.00 | 0.00 | 0.00 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 2.572 | 26.263 | 3.587 | 0.000 | 0.000 | 0.000 | 0.000 | 200.031 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 548 | 603 | 1598 | 911 | 0 | 0 | 0 | 0 | 43 | 0 |
N.S. |
1 | 1.10 | 2.92 | 1.66 | 0.00 | 0.00 | 0.00 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 3.001 | 29.753 | 4.331 | 0.000 | 0.000 | 0.000 | 0.000 | 200.026 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 642 | 707 | 2328 | 1015 | 0 | 0 | 0 | 0 | 43 | 0 |
N.S. |
1 | 1.10 | 3.63 | 1.58 | 0.00 | 0.00 | 0.00 | 0.00 | 0.07 | 0.00 |
time (sec) |
N/A | 4.051 | 32.431 | 6.056 | 0.000 | 0.000 | 0.000 | 0.000 | 200.032 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 782 | 856 | 3260 | 1171 | 0 | 0 | 0 | 0 | 43 | 0 |
N.S. |
1 | 1.09 | 4.17 | 1.50 | 0.00 | 0.00 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 5.488 | 34.374 | 7.034 | 0.000 | 0.000 | 0.000 | 0.000 | 200.032 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 329 | 347 | 333 | 521 | 0 | 0 | 0 | 0 | 208 | 0 |
N.S. |
1 | 1.05 | 1.01 | 1.58 | 0.00 | 0.00 | 0.00 | 0.00 | 0.63 | 0.00 |
time (sec) |
N/A | 2.405 | 24.512 | 3.073 | 0.000 | 0.000 | 0.000 | 0.000 | 2.835 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 269 | 271 | 199 | 413 | 0 | 0 | 0 | 0 | 85 | 0 |
N.S. |
1 | 1.01 | 0.74 | 1.54 | 0.00 | 0.00 | 0.00 | 0.00 | 0.32 | 0.00 |
time (sec) |
N/A | 1.717 | 22.122 | 1.285 | 0.000 | 0.000 | 0.000 | 0.000 | 0.469 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 177 | 179 | 152 | 248 | 0 | 0 | 0 | 0 | 90 | 0 |
N.S. |
1 | 1.01 | 0.86 | 1.40 | 0.00 | 0.00 | 0.00 | 0.00 | 0.51 | 0.00 |
time (sec) |
N/A | 1.121 | 22.902 | 1.299 | 0.000 | 0.000 | 0.000 | 0.000 | 2.152 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 280 | 277 | 221 | 375 | 0 | 0 | 0 | 0 | 222 | 0 |
N.S. |
1 | 0.99 | 0.79 | 1.34 | 0.00 | 0.00 | 0.00 | 0.00 | 0.79 | 0.00 |
time (sec) |
N/A | 1.416 | 23.763 | 2.230 | 0.000 | 0.000 | 0.000 | 0.000 | 0.338 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 356 | 409 | 366 | 539 | 0 | 0 | 0 | 0 | 30 | 0 |
N.S. |
1 | 1.15 | 1.03 | 1.51 | 0.00 | 0.00 | 0.00 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 1.686 | 25.175 | 2.831 | 0.000 | 0.000 | 0.000 | 0.000 | 200.019 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 626 | 707 | 336 | 546 | 0 | 0 | 0 | 0 | 197 | 0 |
N.S. |
1 | 1.13 | 0.54 | 0.87 | 0.00 | 0.00 | 0.00 | 0.00 | 0.31 | 0.00 |
time (sec) |
N/A | 3.312 | 24.795 | 3.184 | 0.000 | 0.000 | 0.000 | 0.000 | 3.275 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 562 | 643 | 212 | 443 | 0 | 0 | 0 | 0 | 79 | 0 |
N.S. |
1 | 1.14 | 0.38 | 0.79 | 0.00 | 0.00 | 0.00 | 0.00 | 0.14 | 0.00 |
time (sec) |
N/A | 2.352 | 22.160 | 1.240 | 0.000 | 0.000 | 0.000 | 0.000 | 0.736 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 407 | 453 | 158 | 267 | 0 | 0 | 0 | 0 | 84 | 0 |
N.S. |
1 | 1.11 | 0.39 | 0.66 | 0.00 | 0.00 | 0.00 | 0.00 | 0.21 | 0.00 |
time (sec) |
N/A | 1.519 | 22.891 | 1.284 | 0.000 | 0.000 | 0.000 | 0.000 | 2.503 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 598 | 740 | 235 | 393 | 0 | 0 | 0 | 0 | 207 | 0 |
N.S. |
1 | 1.24 | 0.39 | 0.66 | 0.00 | 0.00 | 0.00 | 0.00 | 0.35 | 0.00 |
time (sec) |
N/A | 2.287 | 23.568 | 2.188 | 0.000 | 0.000 | 0.000 | 0.000 | 0.536 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 682 | 922 | 384 | 563 | 0 | 0 | 0 | 0 | 29 | 0 |
N.S. |
1 | 1.35 | 0.56 | 0.83 | 0.00 | 0.00 | 0.00 | 0.00 | 0.04 | 0.00 |
time (sec) |
N/A | 2.531 | 24.658 | 2.795 | 0.000 | 0.000 | 0.000 | 0.000 | 200.018 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | A | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | N/A | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 1090 | 0 | 1004 | 1215 | 0 | 0 | 0 | 0 | 34 | 0 |
N.S. |
1 | 0.00 | 0.92 | 1.11 | 0.00 | 0.00 | 0.00 | 0.00 | 0.03 | 0.00 |
time (sec) |
N/A | 0.000 | 24.036 | 8.520 | 0.000 | 0.000 | 0.000 | 0.000 | 200.016 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | C | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 139 | 95 | 37 | 33 | 40 | 54 | 76 | 169 | 36 |
N.S. |
1 | 3.66 | 2.50 | 0.97 | 0.87 | 1.05 | 1.42 | 2.00 | 4.45 | 0.95 |
time (sec) |
N/A | 1.773 | 0.407 | 17.318 | 0.093 | 0.079 | 92.643 | 0.171 | 0.195 | 17.361 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 248 | 176 | 102 | 0 | 0 | 0 | 0 | 0 | 122 | 0 |
N.S. |
1 | 0.71 | 0.41 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.49 | 0.00 |
time (sec) |
N/A | 0.879 | 6.071 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.487 | 0.000 |