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 | F | F | A | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 569 | 335 | 292 | 0 | 0 | 755 | 0 | 0 | 0 |
N.S. |
1 | 0.59 | 0.51 | 0.00 | 0.00 | 1.33 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.976 | 0.335 | 0.000 | 0.000 | 0.269 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 569 | 0 | 238 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.00 | 0.42 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 1.036 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | N/A | N/A | F(-1) | N/A | F(-1) | N/A |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 586 | 587 | 604 | 239 | 38 | 0 | 32 | 0 | 38 |
N.S. |
1 | 1.00 | 1.03 | 0.41 | 0.06 | 0.00 | 0.05 | 0.00 | 0.06 |
time (sec) |
N/A | 1.686 | 0.510 | 0.371 | 0.256 | 0.000 | 2.270 | 0.000 | 8.887 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | N/A | N/A | C | N/A | N/A | N/A |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 590 | 0 | 551 | 30 | 32 | 1162 | 54 | 31 | 31 |
N.S. |
1 | 0.00 | 0.93 | 0.05 | 0.05 | 1.97 | 0.09 | 0.05 | 0.05 |
time (sec) |
N/A | 0.000 | 0.768 | 0.016 | 0.892 | 0.356 | 19.269 | 1.592 | 8.738 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | N/A | N/A | C | N/A | N/A | N/A |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 590 | 0 | 551 | 30 | 32 | 1162 | 54 | 31 | 31 |
N.S. |
1 | 0.00 | 0.93 | 0.05 | 0.05 | 1.97 | 0.09 | 0.05 | 0.05 |
time (sec) |
N/A | 0.000 | 0.001 | 0.001 | 0.871 | 0.351 | 19.435 | 1.630 | 0.003 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | N/A | N/A | C | F(-1) | F(-1) | N/A |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 603 | 0 | 852 | 32 | 32 | 6743 | 0 | 0 | 32 |
N.S. |
1 | 0.00 | 1.41 | 0.05 | 0.05 | 11.18 | 0.00 | 0.00 | 0.05 |
time (sec) |
N/A | 0.000 | 1.185 | 0.019 | 0.604 | 1.190 | 0.000 | 0.000 | 8.273 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | N/A | N/A | C | F(-1) | F(-1) | N/A |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 603 | 0 | 852 | 32 | 32 | 6743 | 0 | 0 | 32 |
N.S. |
1 | 0.00 | 1.41 | 0.05 | 0.05 | 11.18 | 0.00 | 0.00 | 0.05 |
time (sec) |
N/A | 0.000 | 0.009 | 0.001 | 0.598 | 1.165 | 0.000 | 0.000 | 0.002 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | F | F | A | F | F | F(-1) |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 604 | 0 | 546 | 0 | 0 | 686 | 0 | 0 | 0 |
N.S. |
1 | 0.00 | 0.90 | 0.00 | 0.00 | 1.14 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 7.271 | 0.000 | 0.000 | 5.070 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | A | F | F(-1) | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 617 | 980 | 329 | 0 | 0 | 391 | 0 | 0 | 0 |
N.S. |
1 | 1.59 | 0.53 | 0.00 | 0.00 | 0.63 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.440 | 2.225 | 0.000 | 0.000 | 0.261 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | F | F | F | F(-1) | F(-1) | F | F(-1) |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 622 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 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 | F | A | N/A | N/A | C | F(-1) | F(-1) | N/A |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 639 | 0 | 636 | 43 | 43 | 6983 | 0 | 0 | 43 |
N.S. |
1 | 0.00 | 1.00 | 0.07 | 0.07 | 10.93 | 0.00 | 0.00 | 0.07 |
time (sec) |
N/A | 0.000 | 1.160 | 0.019 | 0.872 | 1.269 | 0.000 | 0.000 | 8.321 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | N/A | N/A | C | F(-1) | F(-1) | N/A |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 639 | 0 | 636 | 43 | 43 | 6983 | 0 | 0 | 43 |
N.S. |
1 | 0.00 | 1.00 | 0.07 | 0.07 | 10.93 | 0.00 | 0.00 | 0.07 |
time (sec) |
N/A | 0.000 | 0.008 | 0.000 | 0.877 | 1.284 | 0.000 | 0.000 | 0.004 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | N/A | N/A | C | F(-1) | F(-1) | N/A |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 639 | 0 | 849 | 43 | 43 | 7099 | 0 | 0 | 43 |
N.S. |
1 | 0.00 | 1.33 | 0.07 | 0.07 | 11.11 | 0.00 | 0.00 | 0.07 |
time (sec) |
N/A | 0.000 | 1.142 | 0.016 | 0.910 | 1.271 | 0.000 | 0.000 | 7.687 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | N/A | N/A | C | F(-1) | F(-1) | N/A |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 639 | 0 | 849 | 43 | 43 | 7099 | 0 | 0 | 43 |
N.S. |
1 | 0.00 | 1.33 | 0.07 | 0.07 | 11.11 | 0.00 | 0.00 | 0.07 |
time (sec) |
N/A | 0.000 | 0.007 | 0.000 | 0.900 | 1.242 | 0.000 | 0.000 | 0.003 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | F | F | A | F | F(-1) | F(-1) |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 650 | 0 | 514 | 0 | 0 | 317 | 0 | 0 | 0 |
N.S. |
1 | 0.00 | 0.79 | 0.00 | 0.00 | 0.49 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 2.159 | 0.000 | 0.000 | 0.334 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 669 | 254 | 464 | 0 | 0 | 3267 | 0 | 0 | 0 |
N.S. |
1 | 0.38 | 0.69 | 0.00 | 0.00 | 4.88 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.480 | 3.292 | 0.000 | 0.000 | 0.350 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | F | F | C | F | F(-1) | F(-1) |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 674 | 0 | 637 | 0 | 0 | 560 | 0 | 0 | 0 |
N.S. |
1 | 0.00 | 0.95 | 0.00 | 0.00 | 0.83 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 1.983 | 0.000 | 0.000 | 0.425 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | C | F | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 678 | 749 | 606 | 0 | 0 | 1065 | 0 | 0 | 0 |
N.S. |
1 | 1.10 | 0.89 | 0.00 | 0.00 | 1.57 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.904 | 2.411 | 0.000 | 0.000 | 0.972 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | F | N/A | N/A | F(-1) | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 685 | 0 | 0 | 83 | 85 | 0 | 0 | 85 | 85 |
N.S. |
1 | 0.00 | 0.00 | 0.12 | 0.12 | 0.00 | 0.00 | 0.12 | 0.12 |
time (sec) |
N/A | 0.000 | 0.000 | 0.063 | 0.383 | 0.000 | 0.000 | 0.696 | 9.437 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | F | F | A | F | F(-1) | F(-1) |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 697 | 0 | 438 | 0 | 0 | 1036 | 0 | 0 | 0 |
N.S. |
1 | 0.00 | 0.63 | 0.00 | 0.00 | 1.49 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 2.340 | 0.000 | 0.000 | 0.409 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | F | F | A | F | F | F(-1) |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 699 | 0 | 436 | 0 | 0 | 1039 | 0 | 0 | 0 |
N.S. |
1 | 0.00 | 0.62 | 0.00 | 0.00 | 1.49 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 1.384 | 0.000 | 0.000 | 0.410 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | C | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 708 | 325 | 171 | 0 | 0 | 3408 | 0 | 0 | 0 |
N.S. |
1 | 0.46 | 0.24 | 0.00 | 0.00 | 4.81 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.584 | 10.169 | 0.000 | 0.000 | 0.355 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | F | F | A | F | F | F(-1) |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 719 | 0 | 443 | 0 | 0 | 396 | 0 | 0 | 0 |
N.S. |
1 | 0.00 | 0.62 | 0.00 | 0.00 | 0.55 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 1.497 | 0.000 | 0.000 | 0.383 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | C | F | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 725 | 763 | 624 | 0 | 0 | 979 | 0 | 0 | 0 |
N.S. |
1 | 1.05 | 0.86 | 0.00 | 0.00 | 1.35 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.826 | 2.353 | 0.000 | 0.000 | 0.313 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | F | N/A | N/A | F(-1) | F(-1) | F(-2) | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 726 | 0 | 0 | 80 | 82 | 0 | 0 | 0 | 81 |
N.S. |
1 | 0.00 | 0.00 | 0.11 | 0.11 | 0.00 | 0.00 | 0.00 | 0.11 |
time (sec) |
N/A | 0.000 | 0.000 | 0.023 | 0.361 | 0.000 | 0.000 | 0.000 | 9.519 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 747 | 279 | 363 | 0 | 0 | 511 | 0 | 0 | 0 |
N.S. |
1 | 0.37 | 0.49 | 0.00 | 0.00 | 0.68 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.989 | 1.799 | 0.000 | 0.000 | 0.291 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 752 | 318 | 568 | 0 | 0 | 3627 | 0 | 0 | 0 |
N.S. |
1 | 0.42 | 0.76 | 0.00 | 0.00 | 4.82 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.742 | 4.364 | 0.000 | 0.000 | 0.326 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | F(-1) | N/A | F(-1) | N/A | N/A | N/A |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 757 | 0 | 734 | 0 | 31 | 0 | 71 | 3 | 33 |
N.S. |
1 | 0.00 | 0.97 | 0.00 | 0.04 | 0.00 | 0.09 | 0.00 | 0.04 |
time (sec) |
N/A | 0.000 | 5.167 | 180.000 | 0.234 | 0.000 | 2.879 | 3.686 | 10.617 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | C | F | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 757 | 863 | 679 | 0 | 0 | 1190 | 0 | 0 | 0 |
N.S. |
1 | 1.14 | 0.90 | 0.00 | 0.00 | 1.57 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.000 | 3.885 | 0.000 | 0.000 | 0.317 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | N/A | N/A | F(-1) | F(-1) | F(-2) | N/A |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 773 | 0 | 656 | 34 | 36 | 0 | 0 | 0 | 36 |
N.S. |
1 | 0.00 | 0.85 | 0.04 | 0.05 | 0.00 | 0.00 | 0.00 | 0.05 |
time (sec) |
N/A | 0.000 | 6.457 | 0.063 | 0.914 | 0.000 | 0.000 | 0.000 | 8.034 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | F | F | C | F | F(-1) | F(-1) |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 787 | 0 | 721 | 0 | 0 | 948 | 0 | 0 | 0 |
N.S. |
1 | 0.00 | 0.92 | 0.00 | 0.00 | 1.20 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 1.830 | 0.000 | 0.000 | 0.415 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | F | F | C | F | F(-1) | F(-1) |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 803 | 0 | 803 | 0 | 0 | 1010 | 0 | 0 | 0 |
N.S. |
1 | 0.00 | 1.00 | 0.00 | 0.00 | 1.26 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 2.624 | 0.000 | 0.000 | 0.364 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 827 | 908 | 72 | 64 | 0 | 246 | 0 | 0 | 0 |
N.S. |
1 | 1.10 | 0.09 | 0.08 | 0.00 | 0.30 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 4.150 | 0.637 | 2.217 | 0.000 | 0.302 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 849 | 203 | 235 | 0 | 0 | 389 | 0 | 0 | 0 |
N.S. |
1 | 0.24 | 0.28 | 0.00 | 0.00 | 0.46 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.842 | 0.334 | 0.000 | 0.000 | 0.252 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 857 | 205 | 282 | 0 | 0 | 976 | 0 | 0 | 0 |
N.S. |
1 | 0.24 | 0.33 | 0.00 | 0.00 | 1.14 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.404 | 0.301 | 0.000 | 0.000 | 0.263 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | F | F | C | F | F(-1) | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
size | 876 | 1407 | 12230 | 0 | 0 | 3342 | 0 | 0 | 0 |
N.S. |
1 | 1.61 | 13.96 | 0.00 | 0.00 | 3.82 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 3.490 | 51.843 | 0.000 | 0.000 | 13.025 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F(-2) | B | F(-1) | F(-2) | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 884 | 732 | 821 | 0 | 0 | 56059 | 0 | 0 | 0 |
N.S. |
1 | 0.83 | 0.93 | 0.00 | 0.00 | 63.42 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.441 | 1.659 | 0.000 | 0.000 | 45.158 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F(-2) | F(-1) | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 887 | 1738 | 322 | 0 | 0 | 0 | 0 | 2528 | 0 |
N.S. |
1 | 1.96 | 0.36 | 0.00 | 0.00 | 0.00 | 0.00 | 2.85 | 0.00 |
time (sec) |
N/A | 4.532 | 10.353 | 0.000 | 0.000 | 0.000 | 0.000 | 113.160 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | F | F | A | F | F(-1) | F(-1) |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 963 | 0 | 922 | 0 | 0 | 617 | 0 | 0 | 0 |
N.S. |
1 | 0.00 | 0.96 | 0.00 | 0.00 | 0.64 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 4.102 | 0.000 | 0.000 | 0.392 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F(-1) | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 1178 | 856 | 1140 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.73 | 0.97 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.536 | 6.256 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | F | F | A | F | F(-1) | F(-1) |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 1186 | 0 | 1096 | 0 | 0 | 644 | 0 | 0 | 0 |
N.S. |
1 | 0.00 | 0.92 | 0.00 | 0.00 | 0.54 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 3.160 | 0.000 | 0.000 | 0.392 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | F | F | A | F | F(-2) | F(-1) |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 1202 | 0 | 1202 | 0 | 0 | 1193 | 0 | 0 | 0 |
N.S. |
1 | 0.00 | 1.00 | 0.00 | 0.00 | 0.99 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 5.412 | 0.000 | 0.000 | 0.355 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | F | F | A | F | F(-1) | F(-1) |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 1225 | 0 | 1219 | 0 | 0 | 719 | 0 | 0 | 0 |
N.S. |
1 | 0.00 | 1.00 | 0.00 | 0.00 | 0.59 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 4.348 | 0.000 | 0.000 | 0.362 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | N/A | N/A | F(-1) | N/A | F(-1) | N/A |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 1196 | 1707 | 1991 | 1250 | 42 | 0 | 39 | 0 | 42 |
N.S. |
1 | 1.43 | 1.66 | 1.05 | 0.04 | 0.00 | 0.03 | 0.00 | 0.04 |
time (sec) |
N/A | 33.852 | 3.397 | 0.455 | 0.274 | 0.000 | 24.321 | 0.000 | 8.652 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 1310 | 0 | 235 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.00 | 0.18 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 1.106 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | N/A | N/A | F(-1) | N/A | N/A | N/A |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 1356 | 0 | 2003 | 38 | 40 | 0 | 39 | 40 | 40 |
N.S. |
1 | 0.00 | 1.48 | 0.03 | 0.03 | 0.00 | 0.03 | 0.03 | 0.03 |
time (sec) |
N/A | 0.000 | 7.077 | 0.028 | 0.255 | 0.000 | 1.003 | 40.493 | 7.592 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 1387 | 202 | 305 | 0 | 0 | 473 | 0 | 0 | 0 |
N.S. |
1 | 0.15 | 0.22 | 0.00 | 0.00 | 0.34 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.394 | 0.344 | 0.000 | 0.000 | 0.263 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | B | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 1655 | 382 | 501 | 0 | 0 | 5102 | 0 | 0 | 0 |
N.S. |
1 | 0.23 | 0.30 | 0.00 | 0.00 | 3.08 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.179 | 0.443 | 0.000 | 0.000 | 0.465 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | B | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 1707 | 382 | 495 | 0 | 0 | 5190 | 0 | 0 | 0 |
N.S. |
1 | 0.22 | 0.29 | 0.00 | 0.00 | 3.04 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.157 | 0.449 | 0.000 | 0.000 | 0.441 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F(-1) | F | F(-2) | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 1716 | 1077 | 1337 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.63 | 0.78 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 21.371 | 10.868 | 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 | B | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 1835 | 382 | 495 | 0 | 0 | 3720 | 0 | 0 | 0 |
N.S. |
1 | 0.21 | 0.27 | 0.00 | 0.00 | 2.03 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.505 | 0.495 | 0.000 | 0.000 | 0.354 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | B | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 1886 | 382 | 501 | 0 | 0 | 3644 | 0 | 0 | 0 |
N.S. |
1 | 0.20 | 0.27 | 0.00 | 0.00 | 1.93 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.429 | 0.454 | 0.000 | 0.000 | 0.348 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | A | F(-1) | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 1916 | 1116 | 1590 | 168215 | 2606 | 4048 | 0 | 0 | 0 |
N.S. |
1 | 0.58 | 0.83 | 87.79 | 1.36 | 2.11 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 4.953 | 8.252 | 0.351 | 0.357 | 131.383 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | F | F | F(-1) | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 3329 | 1936 | 8468 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.58 | 2.54 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 3.702 | 16.654 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |