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 | F | F(-2) | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 176 | 181 | 377 | 0 | 0 | 882 | 0 | 0 | 0 |
N.S. |
1 | 1.03 | 2.14 | 0.00 | 0.00 | 5.01 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.430 | 0.432 | 0.000 | 0.000 | 0.635 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 25 | 21 | 0 | 27 | 22 | 3 | 23 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 0.00 | 1.17 | 0.96 | 0.13 | 1.00 |
time (sec) |
N/A | 0.372 | 12.186 | 0.184 | 0.000 | 0.266 | 8.833 | 86.050 | 0.962 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F(-2) | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 103 | 104 | 251 | 0 | 0 | 647 | 0 | 0 | 0 |
N.S. |
1 | 1.01 | 2.44 | 0.00 | 0.00 | 6.28 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.288 | 0.354 | 0.000 | 0.000 | 0.329 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 22 | 18 | 0 | 20 | 19 | 3 | 20 |
N.S. |
1 | 1.00 | 1.10 | 0.90 | 0.00 | 1.00 | 0.95 | 0.15 | 1.00 |
time (sec) |
N/A | 0.181 | 2.882 | 0.188 | 0.000 | 0.256 | 2.396 | 52.414 | 0.704 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 25 | 21 | 0 | 31 | 20 | 3 | 23 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 0.00 | 1.35 | 0.87 | 0.13 | 1.00 |
time (sec) |
N/A | 0.361 | 4.670 | 0.198 | 0.000 | 0.252 | 2.920 | 53.421 | 1.079 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F(-2) | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 100 | 108 | 247 | 0 | 0 | 660 | 0 | 0 | 0 |
N.S. |
1 | 1.08 | 2.47 | 0.00 | 0.00 | 6.60 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.333 | 0.335 | 0.000 | 0.000 | 0.342 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 25 | 21 | 0 | 33 | 22 | 3 | 23 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 0.00 | 1.43 | 0.96 | 0.13 | 1.00 |
time (sec) |
N/A | 0.374 | 12.264 | 0.153 | 0.000 | 0.253 | 4.550 | 57.043 | 1.087 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F(-2) | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 179 | 181 | 372 | 0 | 0 | 868 | 0 | 0 | 0 |
N.S. |
1 | 1.01 | 2.08 | 0.00 | 0.00 | 4.85 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.421 | 0.395 | 0.000 | 0.000 | 0.389 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F(-2) | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 137 | 135 | 321 | 0 | 0 | 1291 | 0 | 0 | 0 |
N.S. |
1 | 0.99 | 2.34 | 0.00 | 0.00 | 9.42 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.359 | 0.528 | 0.000 | 0.000 | 0.552 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 25 | 21 | 0 | 47 | 22 | 3 | 23 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 0.00 | 2.04 | 0.96 | 0.13 | 1.00 |
time (sec) |
N/A | 0.388 | 23.461 | 0.508 | 0.000 | 0.268 | 35.224 | 136.836 | 0.795 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F(-2) | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 71 | 71 | 210 | 0 | 0 | 379 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 2.96 | 0.00 | 0.00 | 5.34 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.245 | 0.332 | 0.000 | 0.000 | 0.316 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F(-2) | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 70 | 70 | 202 | 0 | 0 | 388 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 2.89 | 0.00 | 0.00 | 5.54 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.246 | 0.211 | 0.000 | 0.000 | 0.320 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 25 | 21 | 0 | 42 | 20 | 3 | 23 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 0.00 | 1.83 | 0.87 | 0.13 | 1.00 |
time (sec) |
N/A | 0.385 | 10.372 | 0.411 | 0.000 | 0.256 | 32.726 | 42.176 | 1.152 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F(-2) | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 135 | 143 | 306 | 0 | 0 | 1317 | 0 | 0 | 0 |
N.S. |
1 | 1.06 | 2.27 | 0.00 | 0.00 | 9.76 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.373 | 0.482 | 0.000 | 0.000 | 0.425 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 25 | 21 | 0 | 44 | 22 | 3 | 23 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 0.00 | 1.91 | 0.96 | 0.13 | 1.00 |
time (sec) |
N/A | 0.415 | 14.324 | 0.379 | 0.000 | 0.259 | 53.824 | 43.670 | 1.276 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F(-2) | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 249 | 245 | 405 | 0 | 0 | 1920 | 0 | 0 | 0 |
N.S. |
1 | 0.98 | 1.63 | 0.00 | 0.00 | 7.71 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.054 | 0.564 | 0.000 | 0.000 | 0.554 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | N/A | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 25 | 21 | 0 | 58 | 0 | 3 | 23 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 0.00 | 2.52 | 0.00 | 0.13 | 1.00 |
time (sec) |
N/A | 0.432 | 17.784 | 0.587 | 0.000 | 0.264 | 0.000 | 168.206 | 0.985 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F(-2) | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 143 | 138 | 326 | 0 | 0 | 863 | 0 | 0 | 0 |
N.S. |
1 | 0.97 | 2.28 | 0.00 | 0.00 | 6.03 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.366 | 0.488 | 0.000 | 0.000 | 0.600 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | B | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 109 | 113 | 252 | 0 | 0 | 676 | 0 | 0 | 0 |
N.S. |
1 | 1.04 | 2.31 | 0.00 | 0.00 | 6.20 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.339 | 0.771 | 0.000 | 0.000 | 0.417 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F(-2) | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 110 | 110 | 259 | 0 | 0 | 679 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 2.35 | 0.00 | 0.00 | 6.17 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.280 | 0.566 | 0.000 | 0.000 | 0.572 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | B | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 144 | 145 | 317 | 0 | 0 | 864 | 0 | 0 | 0 |
N.S. |
1 | 1.01 | 2.20 | 0.00 | 0.00 | 6.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.327 | 0.424 | 0.000 | 0.000 | 0.630 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 25 | 21 | 0 | 53 | 20 | 3 | 23 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 0.00 | 2.30 | 0.87 | 0.13 | 1.00 |
time (sec) |
N/A | 0.411 | 14.521 | 0.500 | 0.000 | 0.268 | 65.716 | 54.183 | 1.176 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F(-2) | B | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 274 | 263 | 418 | 0 | 0 | 2714 | 0 | 0 | 0 |
N.S. |
1 | 0.96 | 1.53 | 0.00 | 0.00 | 9.91 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.101 | 0.810 | 0.000 | 0.000 | 1.096 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | N/A | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 25 | 21 | 0 | 55 | 0 | 3 | 23 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 0.00 | 2.39 | 0.00 | 0.13 | 1.00 |
time (sec) |
N/A | 0.437 | 18.037 | 0.440 | 0.000 | 0.260 | 0.000 | 55.519 | 1.260 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F(-2) | B | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 423 | 398 | 510 | 0 | 0 | 3460 | 0 | 0 | 0 |
N.S. |
1 | 0.94 | 1.21 | 0.00 | 0.00 | 8.18 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.289 | 1.307 | 0.000 | 0.000 | 1.772 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F(-2) | B | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 208 | 201 | 345 | 0 | 0 | 1280 | 0 | 0 | 0 |
N.S. |
1 | 0.97 | 1.66 | 0.00 | 0.00 | 6.15 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.962 | 0.566 | 0.000 | 0.000 | 0.353 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F(-2) | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 293 | 291 | 450 | 0 | 0 | 1986 | 0 | 0 | 0 |
N.S. |
1 | 0.99 | 1.54 | 0.00 | 0.00 | 6.78 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.163 | 0.915 | 0.000 | 0.000 | 0.634 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 378 | 373 | 264 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.99 | 0.70 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.817 | 0.400 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 230 | 225 | 193 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.98 | 0.84 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.519 | 0.148 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 122 | 120 | 119 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.98 | 0.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.307 | 0.130 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 23 | 21 | 23 | 23 | 19 | 3 | 23 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 1.10 | 1.10 | 0.90 | 0.14 | 1.10 |
time (sec) |
N/A | 0.335 | 2.280 | 0.573 | 0.519 | 0.262 | 160.774 | 154.143 | 0.700 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 23 | 21 | 23 | 34 | 0 | 3 | 23 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 1.10 | 1.62 | 0.00 | 0.14 | 1.10 |
time (sec) |
N/A | 0.330 | 3.992 | 1.636 | 0.507 | 0.267 | 0.000 | 175.282 | 0.703 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 25 | 21 | 23 | 64 | 0 | 23 | 23 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 1.00 | 2.78 | 0.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.408 | 3.168 | 0.692 | 0.670 | 0.274 | 0.000 | 4.328 | 0.814 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 25 | 21 | 23 | 40 | 0 | 23 | 23 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 1.00 | 1.74 | 0.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.398 | 0.096 | 0.562 | 0.516 | 0.268 | 0.000 | 2.874 | 0.776 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 25 | 21 | 23 | 23 | 22 | 23 | 23 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 1.00 | 1.00 | 0.96 | 1.00 | 1.00 |
time (sec) |
N/A | 0.376 | 0.086 | 0.282 | 0.347 | 0.260 | 42.091 | 1.447 | 0.771 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 25 | 21 | 23 | 23 | 22 | 23 | 23 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 1.00 | 1.00 | 0.96 | 1.00 | 1.00 |
time (sec) |
N/A | 0.382 | 3.065 | 0.276 | 0.384 | 0.272 | 22.593 | 0.470 | 0.867 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 25 | 21 | 23 | 43 | 0 | 23 | 23 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 1.00 | 1.87 | 0.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.392 | 4.119 | 0.568 | 0.386 | 0.294 | 0.000 | 0.474 | 0.965 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 25 | 21 | 23 | 54 | 0 | 23 | 23 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 1.00 | 2.35 | 0.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.393 | 5.757 | 0.583 | 0.398 | 0.303 | 0.000 | 0.491 | 0.938 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 23 | 21 | 23 | 23 | 0 | 23 | 23 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 1.10 | 1.10 | 0.00 | 1.10 | 1.10 |
time (sec) |
N/A | 0.342 | 2.525 | 0.740 | 0.725 | 0.284 | 0.000 | 2.946 | 1.204 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 27 | 25 | 27 | 27 | 0 | 27 | 29 |
N.S. |
1 | 1.00 | 1.08 | 1.00 | 1.08 | 1.08 | 0.00 | 1.08 | 1.16 |
time (sec) |
N/A | 0.385 | 2.520 | 0.566 | 0.590 | 0.263 | 0.000 | 3.312 | 0.891 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 129 | 125 | 166 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.97 | 1.29 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.350 | 0.475 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 27 | 25 | 27 | 27 | 0 | 27 | 29 |
N.S. |
1 | 1.00 | 1.08 | 1.00 | 1.08 | 1.08 | 0.00 | 1.08 | 1.16 |
time (sec) |
N/A | 0.400 | 2.869 | 0.632 | 0.606 | 0.278 | 0.000 | 3.395 | 0.865 |
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 | 285 | 270 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.95 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.569 | 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 | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 27 | 25 | 27 | 27 | 0 | 27 | 29 |
N.S. |
1 | 1.00 | 1.08 | 1.00 | 1.08 | 1.08 | 0.00 | 1.08 | 1.16 |
time (sec) |
N/A | 0.390 | 2.968 | 0.607 | 0.605 | 0.300 | 0.000 | 3.320 | 0.818 |
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 | 466 | 432 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.93 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.527 | 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 | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 27 | 25 | 27 | 27 | 0 | 27 | 29 |
N.S. |
1 | 1.00 | 1.08 | 1.00 | 1.08 | 1.08 | 0.00 | 1.08 | 1.16 |
time (sec) |
N/A | 0.392 | 2.499 | 0.862 | 0.607 | 0.285 | 0.000 | 3.329 | 0.866 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 271 | 271 | 240 | 302 | 306 | 289 | 398 | 0 | 338 |
N.S. |
1 | 1.00 | 0.89 | 1.11 | 1.13 | 1.07 | 1.47 | 0.00 | 1.25 |
time (sec) |
N/A | 0.796 | 0.133 | 0.339 | 0.313 | 0.296 | 0.518 | 0.000 | 1.725 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 323 | 323 | 287 | 406 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.89 | 1.26 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.796 | 0.686 | 0.696 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 199 | 199 | 179 | 248 | 247 | 218 | 296 | 0 | 248 |
N.S. |
1 | 1.00 | 0.90 | 1.25 | 1.24 | 1.10 | 1.49 | 0.00 | 1.25 |
time (sec) |
N/A | 0.578 | 0.103 | 0.335 | 0.287 | 0.276 | 0.400 | 0.000 | 1.088 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 231 | 231 | 208 | 321 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.90 | 1.39 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.552 | 0.306 | 0.539 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | F | F | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 217 | 217 | 263 | 1262 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.21 | 5.82 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.637 | 0.249 | 6.619 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | F | F | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 172 | 172 | 204 | 356 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.19 | 2.07 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.513 | 0.221 | 0.677 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | F | F | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 220 | 220 | 273 | 1289 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.24 | 5.86 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.634 | 0.253 | 10.206 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 502 | 502 | 414 | 552 | 516 | 530 | 758 | 0 | 929 |
N.S. |
1 | 1.00 | 0.82 | 1.10 | 1.03 | 1.06 | 1.51 | 0.00 | 1.85 |
time (sec) |
N/A | 1.302 | 0.229 | 0.471 | 0.303 | 0.301 | 0.726 | 0.000 | 7.258 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 580 | 580 | 513 | 634 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.88 | 1.09 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.269 | 1.181 | 0.872 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 380 | 380 | 317 | 492 | 433 | 416 | 575 | 0 | 780 |
N.S. |
1 | 1.00 | 0.83 | 1.29 | 1.14 | 1.09 | 1.51 | 0.00 | 2.05 |
time (sec) |
N/A | 0.945 | 0.173 | 0.434 | 0.309 | 0.280 | 0.544 | 0.000 | 5.643 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 442 | 442 | 391 | 493 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.88 | 1.12 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.924 | 0.693 | 0.615 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | F | F | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 355 | 355 | 389 | 1524 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.10 | 4.29 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.915 | 0.470 | 13.602 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 343 | 343 | 349 | 524 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.02 | 1.53 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.816 | 0.545 | 0.717 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | F | F | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 320 | 320 | 367 | 1500 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.15 | 4.69 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.806 | 0.406 | 15.753 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
size | 590 | 579 | 1520 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.98 | 2.58 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.227 | 13.435 | 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 | F(-1) | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 554 | 568 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.03 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.542 | 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 | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
size | 492 | 492 | 1322 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 2.69 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.541 | 13.376 | 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 | F(-1) | B | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 460 | 460 | 0 | 2344 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.00 | 5.10 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.512 | 0.000 | 225.409 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
size | 637 | 637 | 1264 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.921 | 10.890 | 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 | F(-1) | F | F(-2) | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 553 | 564 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.421 | 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 | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
size | 745 | 724 | 1412 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.97 | 1.90 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.730 | 14.315 | 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 | F | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 943 | 943 | 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 | 1.862 | 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 | F | C | F(-2) | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | N/A | No | TBD | TBD | TBD | TBD | TBD |
size | 1033 | 1033 | 0 | 6565 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.00 | 6.36 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.901 | 0.000 | 157.166 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | B | F(-2) | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 457 | 996 | 836 | 1175 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 2.18 | 1.83 | 2.57 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.457 | 6.928 | 2.576 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | F | C | F(-2) | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | N/A | No | TBD | TBD | TBD | TBD | TBD |
size | 1039 | 1039 | 0 | 6565 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.00 | 6.32 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.534 | 0.000 | 44.793 | 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 | 1087 | 1087 | 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 | 2.111 | 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 | F(-1) | F | F(-2) | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 1141 | 1141 | 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 | 2.062 | 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 | F | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 1181 | 1181 | 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 | 2.256 | 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 | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 111 | 126 | 79 | 91 | 80 | 72 | 107 | 168 | 82 |
N.S. |
1 | 1.14 | 0.71 | 0.82 | 0.72 | 0.65 | 0.96 | 1.51 | 0.74 |
time (sec) |
N/A | 0.571 | 0.020 | 2.105 | 0.265 | 0.256 | 0.873 | 0.274 | 0.525 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 88 | 88 | 56 | 71 | 62 | 49 | 83 | 124 | 69 |
N.S. |
1 | 1.00 | 0.64 | 0.81 | 0.70 | 0.56 | 0.94 | 1.41 | 0.78 |
time (sec) |
N/A | 0.293 | 0.019 | 1.629 | 0.264 | 0.269 | 0.566 | 0.279 | 0.577 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 82 | 97 | 64 | 68 | 65 | 55 | 78 | 135 | 65 |
N.S. |
1 | 1.18 | 0.78 | 0.83 | 0.79 | 0.67 | 0.95 | 1.65 | 0.79 |
time (sec) |
N/A | 0.475 | 0.018 | 1.659 | 0.268 | 0.267 | 0.360 | 0.273 | 0.532 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 49 | 49 | 38 | 48 | 39 | 33 | 56 | 86 | 48 |
N.S. |
1 | 1.00 | 0.78 | 0.98 | 0.80 | 0.67 | 1.14 | 1.76 | 0.98 |
time (sec) |
N/A | 0.227 | 0.014 | 1.247 | 0.346 | 0.261 | 0.237 | 0.277 | 0.495 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 38 | 48 | 38 | 37 | 42 | 33 | 39 | 92 | 39 |
N.S. |
1 | 1.26 | 1.00 | 0.97 | 1.11 | 0.87 | 1.03 | 2.42 | 1.03 |
time (sec) |
N/A | 0.533 | 0.008 | 1.194 | 0.269 | 0.253 | 0.165 | 0.291 | 0.454 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 189 | 165 | 305 | 2965 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.87 | 1.61 | 15.69 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.660 | 0.235 | 2.671 | 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 | A | F | C | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 41 | 44 | 41 | 0 | 58 | 0 | 37 | 0 | 36 |
N.S. |
1 | 1.07 | 1.00 | 0.00 | 1.41 | 0.00 | 0.90 | 0.00 | 0.88 |
time (sec) |
N/A | 0.404 | 0.009 | 0.000 | 0.292 | 0.000 | 37.835 | 0.000 | 0.111 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 69 | 76 | 49 | 0 | 70 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.10 | 0.71 | 0.00 | 1.01 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.249 | 0.023 | 0.000 | 0.298 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | A | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 81 | 100 | 81 | 0 | 95 | 0 | 97 | 0 | 0 |
N.S. |
1 | 1.23 | 1.00 | 0.00 | 1.17 | 0.00 | 1.20 | 0.00 | 0.00 |
time (sec) |
N/A | 0.650 | 0.012 | 0.000 | 0.268 | 0.000 | 12.986 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 102 | 105 | 98 | 0 | 89 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.03 | 0.96 | 0.00 | 0.87 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.311 | 0.029 | 0.000 | 0.298 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | A | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 114 | 157 | 114 | 0 | 115 | 0 | 134 | 0 | 0 |
N.S. |
1 | 1.38 | 1.00 | 0.00 | 1.01 | 0.00 | 1.18 | 0.00 | 0.00 |
time (sec) |
N/A | 0.969 | 0.018 | 0.000 | 0.271 | 0.000 | 17.974 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 278 | 279 | 214 | 289 | 256 | 220 | 338 | 0 | 276 |
N.S. |
1 | 1.00 | 0.77 | 1.04 | 0.92 | 0.79 | 1.22 | 0.00 | 0.99 |
time (sec) |
N/A | 0.859 | 0.127 | 2.691 | 0.269 | 0.257 | 1.628 | 0.000 | 3.721 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 221 | 218 | 164 | 243 | 224 | 178 | 279 | 0 | 297 |
N.S. |
1 | 0.99 | 0.74 | 1.10 | 1.01 | 0.81 | 1.26 | 0.00 | 1.34 |
time (sec) |
N/A | 0.456 | 0.103 | 1.670 | 0.286 | 0.270 | 1.078 | 0.000 | 1.944 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 213 | 217 | 171 | 217 | 212 | 169 | 258 | 0 | 212 |
N.S. |
1 | 1.02 | 0.80 | 1.02 | 1.00 | 0.79 | 1.21 | 0.00 | 1.00 |
time (sec) |
N/A | 0.725 | 0.090 | 1.816 | 0.275 | 0.271 | 0.759 | 0.000 | 2.793 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 137 | 137 | 105 | 168 | 149 | 116 | 202 | 0 | 227 |
N.S. |
1 | 1.00 | 0.77 | 1.23 | 1.09 | 0.85 | 1.47 | 0.00 | 1.66 |
time (sec) |
N/A | 0.327 | 0.067 | 1.244 | 0.267 | 0.266 | 0.528 | 0.000 | 1.424 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 100 | 112 | 138 | 137 | 153 | 105 | 148 | 0 | 134 |
N.S. |
1 | 1.12 | 1.38 | 1.37 | 1.53 | 1.05 | 1.48 | 0.00 | 1.34 |
time (sec) |
N/A | 0.732 | 0.023 | 1.145 | 0.269 | 0.261 | 0.318 | 0.000 | 1.093 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | F | C | F | F | F | F(-1) | F(-1) |
verified |
N/A | Yes | N/A | No | TBD | TBD | TBD | TBD | TBD |
size | 282 | 241 | 0 | 5420 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.85 | 0.00 | 19.22 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.172 | 0.000 | 10.835 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F(-2) | F(-1) | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 100 | 82 | 111 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.82 | 1.11 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.638 | 0.067 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 154 | 147 | 189 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.95 | 1.23 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.349 | 0.096 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F(-2) | F(-1) | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 189 | 175 | 181 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.93 | 0.96 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.329 | 0.121 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 225 | 216 | 260 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.96 | 1.16 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.497 | 0.139 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F(-2) | F(-1) | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 248 | 290 | 278 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.17 | 1.12 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.239 | 0.191 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | C | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 562 | 554 | 1140 | 10102 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.99 | 2.03 | 17.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.894 | 6.752 | 13.535 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 656 | 653 | 1352 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 2.06 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.682 | 3.261 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 26 | 24 | 43 | 37 | 22 | 0 | 26 |
N.S. |
1 | 1.00 | 1.08 | 1.00 | 1.79 | 1.54 | 0.92 | 0.00 | 1.08 |
time (sec) |
N/A | 0.780 | 0.169 | 0.712 | 0.574 | 0.267 | 123.045 | 0.000 | 1.034 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 672 | 649 | 552 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.97 | 0.82 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.292 | 0.806 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |