Detailed conclusion table per each integral is given by the table below. The elapsed time is in seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2) if the failure was due to an exception being raised, which could indicate a bug in the system. If the failure was due to integral not being evaluated within the time limit, then it is given as F.
In this table, the column N.S. means normalized size and is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To make the table fit the page, the name Mathematica was abbreviated to MMA
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 102 | 102 | 111 | 90 | 154 | 98 | 0 | 0 | 190 |
N.S. |
1 | 1.00 | 1.09 | 0.88 | 1.51 | 0.96 | 0.00 | 0.00 | 1.86 |
time (sec) |
N/A | 0.254 | 7.024 | 0.343 | 0.406 | 0.253 | 0.000 | 0.000 | 9.817 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 155 | 155 | 130 | 113 | 186 | 117 | 0 | 0 | 215 |
N.S. |
1 | 1.00 | 0.84 | 0.73 | 1.20 | 0.75 | 0.00 | 0.00 | 1.39 |
time (sec) |
N/A | 0.291 | 6.887 | 0.405 | 0.415 | 0.245 | 0.000 | 0.000 | 10.302 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 208 | 208 | 131 | 136 | 260 | 136 | 0 | 0 | 290 |
N.S. |
1 | 1.00 | 0.63 | 0.65 | 1.25 | 0.65 | 0.00 | 0.00 | 1.39 |
time (sec) |
N/A | 0.331 | 7.063 | 0.392 | 0.429 | 0.250 | 0.000 | 0.000 | 11.046 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 261 | 261 | 153 | 158 | 312 | 155 | 0 | 0 | 315 |
N.S. |
1 | 1.00 | 0.59 | 0.61 | 1.20 | 0.59 | 0.00 | 0.00 | 1.21 |
time (sec) |
N/A | 0.353 | 7.699 | 0.362 | 0.432 | 0.251 | 0.000 | 0.000 | 12.508 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | F(-1) | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 288 | 288 | 231 | 478 | 2033 | 756 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.80 | 1.66 | 7.06 | 2.62 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.397 | 11.105 | 0.475 | 4.577 | 0.278 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | F(-1) | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 213 | 213 | 148 | 221 | 1445 | 585 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.69 | 1.04 | 6.78 | 2.75 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.325 | 8.533 | 0.395 | 0.942 | 0.276 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 222 | 222 | 222 | 350 | 1375 | 614 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.00 | 1.58 | 6.19 | 2.77 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.362 | 7.934 | 0.375 | 1.098 | 0.289 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 217 | 217 | 198 | 285 | 1087 | 547 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.91 | 1.31 | 5.01 | 2.52 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.332 | 5.744 | 0.343 | 0.583 | 0.279 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 227 | 227 | 170 | 565 | 993 | 530 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.75 | 2.49 | 4.37 | 2.33 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.331 | 7.328 | 0.423 | 0.506 | 0.278 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 226 | 226 | 179 | 667 | 795 | 493 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.79 | 2.95 | 3.52 | 2.18 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.339 | 7.633 | 0.351 | 0.485 | 0.265 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 203 | 203 | 203 | 507 | 214 | 418 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.00 | 2.50 | 1.05 | 2.06 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.324 | 17.953 | 0.351 | 0.429 | 0.270 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 102 | 102 | 113 | 106 | 166 | 104 | 0 | 0 | 192 |
N.S. |
1 | 1.00 | 1.11 | 1.04 | 1.63 | 1.02 | 0.00 | 0.00 | 1.88 |
time (sec) |
N/A | 0.251 | 6.898 | 0.384 | 0.430 | 0.245 | 0.000 | 0.000 | 9.961 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 155 | 155 | 130 | 119 | 198 | 125 | 0 | 0 | 217 |
N.S. |
1 | 1.00 | 0.84 | 0.77 | 1.28 | 0.81 | 0.00 | 0.00 | 1.40 |
time (sec) |
N/A | 0.285 | 7.025 | 0.353 | 0.432 | 0.240 | 0.000 | 0.000 | 10.562 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 208 | 208 | 156 | 156 | 276 | 146 | 0 | 0 | 292 |
N.S. |
1 | 1.00 | 0.75 | 0.75 | 1.33 | 0.70 | 0.00 | 0.00 | 1.40 |
time (sec) |
N/A | 0.338 | 16.384 | 0.417 | 0.610 | 0.247 | 0.000 | 0.000 | 12.413 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | A | A | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 261 | 261 | 577 | 169 | 332 | 167 | 0 | 0 | 191 |
N.S. |
1 | 1.00 | 2.21 | 0.65 | 1.27 | 0.64 | 0.00 | 0.00 | 0.73 |
time (sec) |
N/A | 0.369 | 19.166 | 0.378 | 0.604 | 0.245 | 0.000 | 0.000 | 13.404 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 350 | 350 | 241 | 604 | 2603 | 882 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.69 | 1.73 | 7.44 | 2.52 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.442 | 9.429 | 0.495 | 19.778 | 0.288 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 267 | 267 | 159 | 269 | 1901 | 693 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.60 | 1.01 | 7.12 | 2.60 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.326 | 8.561 | 0.405 | 2.745 | 0.275 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 284 | 284 | 510 | 478 | 2033 | 756 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.80 | 1.68 | 7.16 | 2.66 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.393 | 11.712 | 0.492 | 5.957 | 0.286 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 279 | 279 | 458 | 412 | 1657 | 682 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.64 | 1.48 | 5.94 | 2.44 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.368 | 11.533 | 0.319 | 2.784 | 0.287 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | F(-1) | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 272 | 272 | 221 | 349 | 1345 | 604 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.81 | 1.28 | 4.94 | 2.22 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.373 | 7.961 | 0.354 | 1.058 | 0.274 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 283 | 283 | 183 | 627 | 1329 | 590 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.65 | 2.22 | 4.70 | 2.08 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.376 | 8.512 | 0.403 | 0.710 | 0.270 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 285 | 285 | 196 | 731 | 1176 | 571 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.69 | 2.56 | 4.13 | 2.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.387 | 9.274 | 0.378 | 0.555 | 0.284 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | F(-1) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
size | 283 | 283 | 528 | 833 | 936 | 515 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.87 | 2.94 | 3.31 | 1.82 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.405 | 19.930 | 0.368 | 0.496 | 0.274 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | A | B | F(-1) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
size | 251 | 251 | 570 | 598 | 246 | 434 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 2.27 | 2.38 | 0.98 | 1.73 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.368 | 19.877 | 0.343 | 0.442 | 0.278 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 102 | 102 | 111 | 106 | 166 | 104 | 0 | 0 | 192 |
N.S. |
1 | 1.00 | 1.09 | 1.04 | 1.63 | 1.02 | 0.00 | 0.00 | 1.88 |
time (sec) |
N/A | 0.324 | 6.957 | 0.359 | 0.444 | 0.260 | 0.000 | 0.000 | 10.600 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | A | A | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 155 | 155 | 417 | 119 | 198 | 125 | 0 | 0 | 217 |
N.S. |
1 | 1.00 | 2.69 | 0.77 | 1.28 | 0.81 | 0.00 | 0.00 | 1.40 |
time (sec) |
N/A | 0.424 | 18.824 | 0.369 | 0.635 | 0.248 | 0.000 | 0.000 | 10.820 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | A | A | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 208 | 208 | 495 | 156 | 276 | 146 | 0 | 0 | 167 |
N.S. |
1 | 1.00 | 2.38 | 0.75 | 1.33 | 0.70 | 0.00 | 0.00 | 0.80 |
time (sec) |
N/A | 0.480 | 19.123 | 0.341 | 0.666 | 0.250 | 0.000 | 0.000 | 13.008 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | A | A | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 261 | 261 | 577 | 169 | 332 | 167 | 0 | 0 | 191 |
N.S. |
1 | 1.00 | 2.21 | 0.65 | 1.27 | 0.64 | 0.00 | 0.00 | 0.73 |
time (sec) |
N/A | 0.530 | 19.377 | 0.377 | 1.087 | 0.254 | 0.000 | 0.000 | 12.602 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | A | A | F(-1) | F | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
size | 314 | 314 | 655 | 206 | 412 | 188 | 0 | 0 | 229 |
N.S. |
1 | 1.00 | 2.09 | 0.66 | 1.31 | 0.60 | 0.00 | 0.00 | 0.73 |
time (sec) |
N/A | 0.470 | 19.832 | 0.374 | 0.556 | 0.245 | 0.000 | 0.000 | 13.227 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 228 | 228 | 162 | 566 | 1319 | 548 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.71 | 2.48 | 5.79 | 2.40 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.348 | 7.738 | 0.393 | 0.656 | 0.284 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 169 | 169 | 136 | 499 | 898 | 456 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.80 | 2.95 | 5.31 | 2.70 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.330 | 4.597 | 0.382 | 0.473 | 0.272 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | B | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 110 | 110 | 119 | 323 | 138 | 348 | 0 | 0 | 250 |
N.S. |
1 | 1.00 | 1.08 | 2.94 | 1.25 | 3.16 | 0.00 | 0.00 | 2.27 |
time (sec) |
N/A | 0.247 | 3.018 | 0.413 | 0.395 | 0.266 | 0.000 | 0.000 | 11.562 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 92 | 92 | 50 | 92 | 124 | 114 | 0 | 0 | 143 |
N.S. |
1 | 1.00 | 0.54 | 1.00 | 1.35 | 1.24 | 0.00 | 0.00 | 1.55 |
time (sec) |
N/A | 0.222 | 2.489 | 0.474 | 0.391 | 0.248 | 0.000 | 0.000 | 0.804 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 157 | 157 | 97 | 110 | 0 | 147 | 0 | 0 | 146 |
N.S. |
1 | 1.00 | 0.62 | 0.70 | 0.00 | 0.94 | 0.00 | 0.00 | 0.93 |
time (sec) |
N/A | 0.279 | 4.824 | 0.407 | 0.000 | 0.254 | 0.000 | 0.000 | 0.728 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 213 | 213 | 116 | 148 | 0 | 161 | 0 | 0 | 186 |
N.S. |
1 | 1.00 | 0.54 | 0.69 | 0.00 | 0.76 | 0.00 | 0.00 | 0.87 |
time (sec) |
N/A | 0.324 | 6.241 | 0.467 | 0.000 | 0.257 | 0.000 | 0.000 | 9.339 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | B | B | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 287 | 287 | 160 | 733 | 1373 | 589 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.56 | 2.55 | 4.78 | 2.05 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.415 | 8.382 | 0.382 | 0.828 | 0.273 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F(-2) | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 229 | 229 | 141 | 669 | 0 | 511 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.62 | 2.92 | 0.00 | 2.23 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.351 | 6.781 | 0.407 | 0.000 | 0.268 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 157 | 157 | 137 | 408 | 168 | 400 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.87 | 2.60 | 1.07 | 2.55 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.298 | 5.233 | 0.340 | 0.414 | 0.275 | 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 | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 104 | 104 | 81 | 103 | 0 | 92 | 0 | 0 | 195 |
N.S. |
1 | 1.00 | 0.78 | 0.99 | 0.00 | 0.88 | 0.00 | 0.00 | 1.88 |
time (sec) |
N/A | 0.234 | 3.021 | 0.438 | 0.000 | 0.257 | 0.000 | 0.000 | 9.691 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 152 | 152 | 97 | 152 | 0 | 145 | 0 | 0 | 170 |
N.S. |
1 | 1.00 | 0.64 | 1.00 | 0.00 | 0.95 | 0.00 | 0.00 | 1.12 |
time (sec) |
N/A | 0.286 | 3.167 | 0.398 | 0.000 | 0.284 | 0.000 | 0.000 | 9.356 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 152 | 150 | 79 | 113 | 200 | 150 | 0 | 0 | 198 |
N.S. |
1 | 0.99 | 0.52 | 0.74 | 1.32 | 0.99 | 0.00 | 0.00 | 1.30 |
time (sec) |
N/A | 0.274 | 5.922 | 0.399 | 0.420 | 0.244 | 0.000 | 0.000 | 9.377 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 269 | 269 | 152 | 199 | 0 | 181 | 0 | 0 | 196 |
N.S. |
1 | 1.00 | 0.57 | 0.74 | 0.00 | 0.67 | 0.00 | 0.00 | 0.73 |
time (sec) |
N/A | 0.362 | 6.749 | 0.386 | 0.000 | 0.264 | 0.000 | 0.000 | 9.536 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F(-2) | B | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 343 | 343 | 228 | 899 | 0 | 610 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.66 | 2.62 | 0.00 | 1.78 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.437 | 9.772 | 0.444 | 0.000 | 0.276 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | B | B | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 284 | 284 | 191 | 835 | 1025 | 533 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.67 | 2.94 | 3.61 | 1.88 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.377 | 7.674 | 0.383 | 0.571 | 0.274 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | A | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 205 | 205 | 167 | 509 | 216 | 436 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.81 | 2.48 | 1.05 | 2.13 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.332 | 7.654 | 0.410 | 0.422 | 0.285 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 104 | 104 | 92 | 92 | 153 | 98 | 0 | 0 | 240 |
N.S. |
1 | 1.00 | 0.88 | 0.88 | 1.47 | 0.94 | 0.00 | 0.00 | 2.31 |
time (sec) |
N/A | 0.264 | 5.365 | 0.408 | 0.427 | 0.250 | 0.000 | 0.000 | 10.101 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 157 | 157 | 99 | 127 | 0 | 112 | 0 | 0 | 246 |
N.S. |
1 | 1.00 | 0.63 | 0.81 | 0.00 | 0.71 | 0.00 | 0.00 | 1.57 |
time (sec) |
N/A | 0.284 | 3.526 | 0.427 | 0.000 | 0.249 | 0.000 | 0.000 | 10.323 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 212 | 212 | 115 | 186 | 0 | 161 | 0 | 0 | 246 |
N.S. |
1 | 1.00 | 0.54 | 0.88 | 0.00 | 0.76 | 0.00 | 0.00 | 1.16 |
time (sec) |
N/A | 0.352 | 4.514 | 0.388 | 0.000 | 0.279 | 0.000 | 0.000 | 9.877 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 218 | 216 | 152 | 199 | 0 | 181 | 0 | 0 | 249 |
N.S. |
1 | 0.99 | 0.70 | 0.91 | 0.00 | 0.83 | 0.00 | 0.00 | 1.14 |
time (sec) |
N/A | 0.351 | 6.656 | 0.391 | 0.000 | 0.251 | 0.000 | 0.000 | 9.971 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 206 | 204 | 90 | 124 | 334 | 185 | 0 | 0 | 249 |
N.S. |
1 | 0.99 | 0.44 | 0.60 | 1.62 | 0.90 | 0.00 | 0.00 | 1.21 |
time (sec) |
N/A | 0.327 | 7.038 | 0.396 | 0.591 | 0.255 | 0.000 | 0.000 | 10.478 |
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 | 150 | 150 | 122 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.81 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.270 | 1.133 | 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 | 147 | 147 | 133 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.90 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.272 | 5.836 | 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 | B | F(-2) | A | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 33 | 33 | 31 | 92 | 0 | 54 | 66 | 0 | 90 |
N.S. |
1 | 1.00 | 0.94 | 2.79 | 0.00 | 1.64 | 2.00 | 0.00 | 2.73 |
time (sec) |
N/A | 0.119 | 5.453 | 0.738 | 0.000 | 0.241 | 0.638 | 0.000 | 8.459 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 104 | 104 | 93 | 154 | 0 | 84 | 296 | 185 | 159 |
N.S. |
1 | 1.00 | 0.89 | 1.48 | 0.00 | 0.81 | 2.85 | 1.78 | 1.53 |
time (sec) |
N/A | 0.284 | 2.060 | 0.235 | 0.000 | 0.244 | 0.261 | 0.491 | 8.727 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 147 | 147 | 141 | 131 | 142 | 619 | 0 | 0 | 245 |
N.S. |
1 | 1.00 | 0.96 | 0.89 | 0.97 | 4.21 | 0.00 | 0.00 | 1.67 |
time (sec) |
N/A | 0.357 | 2.517 | 0.314 | 0.330 | 0.250 | 0.000 | 0.000 | 1.588 |