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 | F | B | F | C | F | F | F(-1) |
verified |
N/A | Yes | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 350 | 372 | 0 | 2734 | 0 | 448 | 0 | 0 | 0 |
N.S. |
1 | 1.06 | 0.00 | 7.81 | 0.00 | 1.28 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.976 | 0.000 | 0.959 | 0.000 | 0.311 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | B | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 390 | 371 | 463 | 0 | 993 | 584 | 0 | 0 | 0 |
N.S. |
1 | 0.95 | 1.19 | 0.00 | 2.55 | 1.50 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.525 | 1.295 | 0.000 | 0.589 | 0.129 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | F | B | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 251 | 244 | 835 | 0 | 503 | 364 | 0 | 0 | 0 |
N.S. |
1 | 0.97 | 3.33 | 0.00 | 2.00 | 1.45 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.354 | 1.925 | 0.000 | 0.351 | 0.121 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 115 | 114 | 166 | 0 | 151 | 152 | 0 | 0 | 0 |
N.S. |
1 | 0.99 | 1.44 | 0.00 | 1.31 | 1.32 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.274 | 0.292 | 0.000 | 0.220 | 0.102 | 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 | 22 | 22 | 24 | 20 | 22 | 59 | 32 | 22 | 22 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 1.00 | 2.68 | 1.45 | 1.00 | 1.00 |
time (sec) |
N/A | 0.176 | 11.035 | 0.180 | 0.899 | 0.264 | 28.566 | 0.601 | 5.879 |
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 | 22 | 22 | 24 | 20 | 22 | 70 | 0 | 22 | 22 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 1.00 | 3.18 | 0.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.180 | 15.252 | 0.178 | 1.161 | 0.284 | 0.000 | 0.758 | 5.952 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 633 | 638 | 256 | 2704 | 2151 | 333 | 0 | 1558 | 0 |
N.S. |
1 | 1.01 | 0.40 | 4.27 | 3.40 | 0.53 | 0.00 | 2.46 | 0.00 |
time (sec) |
N/A | 0.780 | 1.665 | 0.462 | 0.308 | 0.289 | 0.000 | 0.335 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 288 | 293 | 147 | 801 | 681 | 142 | 0 | 453 | 0 |
N.S. |
1 | 1.02 | 0.51 | 2.78 | 2.36 | 0.49 | 0.00 | 1.57 | 0.00 |
time (sec) |
N/A | 0.438 | 0.533 | 0.530 | 0.227 | 0.270 | 0.000 | 0.329 | 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 | 85 | 85 | 65 | 134 | 120 | 58 | 94 | 82 | 69 |
N.S. |
1 | 1.00 | 0.76 | 1.58 | 1.41 | 0.68 | 1.11 | 0.96 | 0.81 |
time (sec) |
N/A | 0.374 | 0.077 | 0.151 | 0.193 | 0.272 | 0.284 | 0.302 | 5.803 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 396 | 424 | 118 | 327 | 0 | 448 | 0 | 0 | 0 |
N.S. |
1 | 1.07 | 0.30 | 0.83 | 0.00 | 1.13 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.407 | 25.223 | 0.283 | 0.000 | 0.293 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 555 | 567 | 180 | 1176 | 0 | 730 | 0 | 0 | 0 |
N.S. |
1 | 1.02 | 0.32 | 2.12 | 0.00 | 1.32 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.637 | 0.872 | 0.356 | 0.000 | 0.383 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | C | A | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 513 | 482 | 432 | 366 | 561 | 308 | 0 | 780 | 0 |
N.S. |
1 | 0.94 | 0.84 | 0.71 | 1.09 | 0.60 | 0.00 | 1.52 | 0.00 |
time (sec) |
N/A | 0.661 | 1.621 | 1.276 | 0.267 | 0.285 | 0.000 | 0.423 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 243 | 228 | 213 | 175 | 248 | 159 | 0 | 409 | 0 |
N.S. |
1 | 0.94 | 0.88 | 0.72 | 1.02 | 0.65 | 0.00 | 1.68 | 0.00 |
time (sec) |
N/A | 0.383 | 0.701 | 0.406 | 0.206 | 0.271 | 0.000 | 0.372 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 130 | 129 | 114 | 86 | 92 | 98 | 0 | 172 | 0 |
N.S. |
1 | 0.99 | 0.88 | 0.66 | 0.71 | 0.75 | 0.00 | 1.32 | 0.00 |
time (sec) |
N/A | 0.349 | 0.110 | 0.103 | 0.205 | 0.283 | 0.000 | 0.329 | 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 | 22 | 22 | 24 | 20 | 22 | 22 | 19 | 22 | 22 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 1.00 | 1.00 | 0.86 | 1.00 | 1.00 |
time (sec) |
N/A | 0.178 | 63.335 | 0.102 | 1.033 | 0.258 | 1.700 | 0.386 | 6.182 |
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 | 22 | 22 | 24 | 20 | 22 | 33 | 20 | 22 | 22 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 1.00 | 1.50 | 0.91 | 1.00 | 1.00 |
time (sec) |
N/A | 0.175 | 58.438 | 0.105 | 1.705 | 0.259 | 10.580 | 0.395 | 6.575 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | C | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 855 | 866 | 929 | 936 | 1003 | 576 | 0 | 11931 | 0 |
N.S. |
1 | 1.01 | 1.09 | 1.09 | 1.17 | 0.67 | 0.00 | 13.95 | 0.00 |
time (sec) |
N/A | 1.125 | 2.980 | 1.894 | 0.668 | 0.300 | 0.000 | 0.952 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 419 | 427 | 540 | 391 | 458 | 258 | 0 | 3727 | 0 |
N.S. |
1 | 1.02 | 1.29 | 0.93 | 1.09 | 0.62 | 0.00 | 8.89 | 0.00 |
time (sec) |
N/A | 0.623 | 0.701 | 1.181 | 0.447 | 0.349 | 0.000 | 0.662 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 136 | 127 | 133 | 108 | 138 | 121 | 0 | 663 | 0 |
N.S. |
1 | 0.93 | 0.98 | 0.79 | 1.01 | 0.89 | 0.00 | 4.88 | 0.00 |
time (sec) |
N/A | 0.635 | 0.072 | 0.898 | 0.425 | 0.266 | 0.000 | 0.510 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 434 | 462 | 170 | 156 | 0 | 548 | 0 | 0 | 0 |
N.S. |
1 | 1.06 | 0.39 | 0.36 | 0.00 | 1.26 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.697 | 25.311 | 0.993 | 0.000 | 0.389 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 566 | 584 | 313 | 1554 | 0 | 798 | 0 | 0 | 0 |
N.S. |
1 | 1.03 | 0.55 | 2.75 | 0.00 | 1.41 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.812 | 0.939 | 1.081 | 0.000 | 0.334 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | C | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 630 | 599 | 613 | 424 | 1260 | 461 | 0 | 0 | 0 |
N.S. |
1 | 0.95 | 0.97 | 0.67 | 2.00 | 0.73 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.830 | 1.950 | 1.921 | 0.778 | 0.306 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 318 | 305 | 378 | 225 | 584 | 247 | 0 | 0 | 0 |
N.S. |
1 | 0.96 | 1.19 | 0.71 | 1.84 | 0.78 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.505 | 0.851 | 0.654 | 0.466 | 0.336 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | F | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 141 | 150 | 146 | 105 | 219 | 143 | 0 | 0 | 0 |
N.S. |
1 | 1.06 | 1.04 | 0.74 | 1.55 | 1.01 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.456 | 0.105 | 0.227 | 0.319 | 0.284 | 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 | 22 | 22 | 24 | 20 | 22 | 36 | 19 | 22 | 22 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 1.00 | 1.64 | 0.86 | 1.00 | 1.00 |
time (sec) |
N/A | 0.177 | 63.411 | 0.191 | 0.825 | 0.305 | 2.925 | 0.458 | 6.430 |
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 | 22 | 22 | 24 | 20 | 22 | 47 | 20 | 22 | 22 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 1.00 | 2.14 | 0.91 | 1.00 | 1.00 |
time (sec) |
N/A | 0.180 | 46.459 | 0.185 | 1.102 | 0.277 | 22.101 | 0.518 | 6.537 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | C | A | F(-1) | A | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 289 | 234 | 226 | 0 | 175 | 234 | 0 | 486 | 0 |
N.S. |
1 | 0.81 | 0.78 | 0.00 | 0.61 | 0.81 | 0.00 | 1.68 | 0.00 |
time (sec) |
N/A | 0.927 | 0.514 | 0.000 | 0.382 | 0.725 | 0.000 | 0.387 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | C | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 202 | 168 | 111 | 0 | 193 | 143 | 0 | 286 | 0 |
N.S. |
1 | 0.83 | 0.55 | 0.00 | 0.96 | 0.71 | 0.00 | 1.42 | 0.00 |
time (sec) |
N/A | 0.652 | 0.290 | 0.000 | 0.373 | 0.698 | 0.000 | 0.340 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | C | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 160 | 135 | 97 | 0 | 156 | 128 | 0 | 192 | 0 |
N.S. |
1 | 0.84 | 0.61 | 0.00 | 0.98 | 0.80 | 0.00 | 1.20 | 0.00 |
time (sec) |
N/A | 0.525 | 0.235 | 0.000 | 0.379 | 0.662 | 0.000 | 0.337 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | C | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 85 | 72 | 70 | 0 | 129 | 84 | 0 | 90 | 0 |
N.S. |
1 | 0.85 | 0.82 | 0.00 | 1.52 | 0.99 | 0.00 | 1.06 | 0.00 |
time (sec) |
N/A | 0.318 | 0.097 | 0.000 | 0.363 | 0.679 | 0.000 | 0.303 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | A | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 42 | 42 | 42 | 0 | 23 | 46 | 0 | 37 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.55 | 1.10 | 0.00 | 0.88 | 0.00 |
time (sec) |
N/A | 0.248 | 0.111 | 0.000 | 0.217 | 0.269 | 0.000 | 0.310 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 120 | 88 | 85 | 0 | 126 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.73 | 0.71 | 0.00 | 1.05 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.500 | 0.184 | 0.000 | 0.374 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 175 | 121 | 115 | 0 | 129 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.69 | 0.66 | 0.00 | 0.74 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.607 | 0.227 | 0.000 | 0.386 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | C | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 267 | 185 | 184 | 0 | 129 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.69 | 0.69 | 0.00 | 0.48 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.859 | 0.337 | 0.000 | 0.376 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | C | F | F(-1) | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 267 | 222 | 175 | 0 | 386 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.83 | 0.66 | 0.00 | 1.45 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.643 | 0.609 | 0.000 | 0.520 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | C | F | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 227 | 182 | 160 | 0 | 424 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.80 | 0.70 | 0.00 | 1.87 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.556 | 0.382 | 0.000 | 0.505 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | C | A | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 89 | 74 | 72 | 0 | 129 | 89 | 0 | 0 | 0 |
N.S. |
1 | 0.83 | 0.81 | 0.00 | 1.45 | 1.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.399 | 0.045 | 0.000 | 0.371 | 0.667 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | A | A | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 44 | 44 | 44 | 0 | 23 | 46 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.52 | 1.05 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.317 | 0.105 | 0.000 | 0.218 | 0.262 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | C | F | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 133 | 110 | 96 | 0 | 487 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.83 | 0.72 | 0.00 | 3.66 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.403 | 0.153 | 0.000 | 0.482 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | C | F | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 168 | 143 | 133 | 0 | 380 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.85 | 0.79 | 0.00 | 2.26 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.465 | 0.229 | 0.000 | 0.501 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | C | F | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 126 | 90 | 87 | 0 | 126 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.71 | 0.69 | 0.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.580 | 0.197 | 0.000 | 0.379 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 247 | 180 | 208 | 0 | 129 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.73 | 0.84 | 0.00 | 0.52 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.817 | 0.316 | 0.000 | 0.381 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 168 | 118 | 131 | 0 | 172 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.70 | 0.78 | 0.00 | 1.02 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.599 | 0.194 | 0.000 | 0.372 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 116 | 85 | 88 | 0 | 155 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.73 | 0.76 | 0.00 | 1.34 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.488 | 0.204 | 0.000 | 0.378 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 45 | 45 | 42 | 0 | 31 | 64 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.93 | 0.00 | 0.69 | 1.42 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.246 | 0.112 | 0.000 | 0.197 | 0.256 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | C | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 91 | 75 | 72 | 0 | 171 | 116 | 0 | 0 | 0 |
N.S. |
1 | 0.82 | 0.79 | 0.00 | 1.88 | 1.27 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.318 | 0.068 | 0.000 | 0.377 | 0.681 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | C | A | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 172 | 140 | 113 | 0 | 1389 | 160 | 0 | 0 | 0 |
N.S. |
1 | 0.81 | 0.66 | 0.00 | 8.08 | 0.93 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.537 | 0.167 | 0.000 | 1.173 | 0.777 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | C | A | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 217 | 173 | 112 | 0 | 1943 | 181 | 0 | 0 | 0 |
N.S. |
1 | 0.80 | 0.52 | 0.00 | 8.95 | 0.83 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.661 | 0.262 | 0.000 | 1.667 | 0.780 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | C | F | F(-1) | F(-2) | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 299 | 237 | 237 | 0 | 1120 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.79 | 0.79 | 0.00 | 3.75 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.747 | 0.701 | 0.000 | 1.021 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | C | F | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 262 | 204 | 228 | 0 | 749 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.78 | 0.87 | 0.00 | 2.86 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.679 | 0.312 | 0.000 | 0.770 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 168 | 120 | 113 | 0 | 129 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.71 | 0.67 | 0.00 | 0.77 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.696 | 0.294 | 0.000 | 0.399 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 122 | 87 | 90 | 0 | 126 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.71 | 0.74 | 0.00 | 1.03 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.580 | 0.232 | 0.000 | 0.375 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | C | F | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 164 | 140 | 136 | 0 | 383 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.85 | 0.83 | 0.00 | 2.34 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.523 | 0.273 | 0.000 | 0.487 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 141 | 113 | 96 | 0 | 487 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.80 | 0.68 | 0.00 | 3.45 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.423 | 0.185 | 0.000 | 0.499 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 47 | 47 | 44 | 0 | 31 | 64 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.94 | 0.00 | 0.66 | 1.36 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.327 | 0.119 | 0.000 | 0.210 | 0.270 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | C | A | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 95 | 77 | 72 | 0 | 129 | 133 | 0 | 0 | 0 |
N.S. |
1 | 0.81 | 0.76 | 0.00 | 1.36 | 1.40 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.410 | 0.072 | 0.000 | 0.382 | 0.719 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | C | F | F(-1) | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 237 | 185 | 165 | 0 | 408 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.78 | 0.70 | 0.00 | 1.72 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.604 | 0.768 | 0.000 | 0.498 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | C | F | F(-1) | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 277 | 224 | 192 | 0 | 405 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.81 | 0.69 | 0.00 | 1.46 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.716 | 0.944 | 0.000 | 0.505 | 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 | 18 | 18 | 20 | 18 | 20 | 20 | 17 | 20 | 20 |
N.S. |
1 | 1.00 | 1.11 | 1.00 | 1.11 | 1.11 | 0.94 | 1.11 | 1.11 |
time (sec) |
N/A | 0.171 | 10.993 | 0.054 | 0.438 | 0.276 | 8.020 | 0.320 | 6.135 |
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 | 503 | 483 | 384 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.96 | 0.76 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.599 | 0.550 | 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 | 369 | 355 | 288 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.96 | 0.78 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.446 | 0.365 | 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 | 243 | 235 | 192 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.97 | 0.79 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.313 | 0.330 | 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 | 117 | 117 | 121 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.03 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.241 | 0.078 | 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 | 16 | 16 | 18 | 16 | 18 | 18 | 14 | 18 | 18 |
N.S. |
1 | 1.00 | 1.12 | 1.00 | 1.12 | 1.12 | 0.88 | 1.12 | 1.12 |
time (sec) |
N/A | 0.168 | 1.027 | 0.049 | 0.502 | 0.265 | 1.878 | 0.338 | 6.331 |
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 | 16 | 16 | 18 | 16 | 18 | 18 | 15 | 18 | 18 |
N.S. |
1 | 1.00 | 1.12 | 1.00 | 1.12 | 1.12 | 0.94 | 1.12 | 1.12 |
time (sec) |
N/A | 0.170 | 0.905 | 0.049 | 0.508 | 0.274 | 7.610 | 0.325 | 6.314 |
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 | 519 | 519 | 411 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.79 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.797 | 0.621 | 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 | 383 | 383 | 313 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.82 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.590 | 0.402 | 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 | 255 | 255 | 215 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.84 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.423 | 0.388 | 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 | 122 | 126 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.03 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.224 | 0.196 | 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 | 20 | 20 | 22 | 20 | 25 | 22 | 17 | 22 | 22 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 1.25 | 1.10 | 0.85 | 1.10 | 1.10 |
time (sec) |
N/A | 0.182 | 2.165 | 0.048 | 0.482 | 0.286 | 4.458 | 0.328 | 6.146 |
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 | 20 | 20 | 22 | 20 | 27 | 22 | 19 | 22 | 22 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 1.35 | 1.10 | 0.95 | 1.10 | 1.10 |
time (sec) |
N/A | 0.182 | 1.835 | 0.043 | 0.489 | 0.275 | 19.634 | 0.319 | 6.073 |
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 | 856 | 819 | 648 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.96 | 0.76 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.017 | 1.114 | 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 | 556 | 534 | 434 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.96 | 0.78 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.598 | 1.075 | 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 | 261 | 261 | 247 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.95 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.392 | 0.479 | 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 | 22 | 22 | 24 | 22 | 62 | 52 | 19 | 24 | 24 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 2.82 | 2.36 | 0.86 | 1.09 | 1.09 |
time (sec) |
N/A | 0.179 | 3.245 | 0.326 | 1.041 | 0.301 | 18.645 | 0.384 | 6.223 |
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 | 22 | 22 | 24 | 22 | 67 | 52 | 20 | 24 | 24 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 3.05 | 2.36 | 0.91 | 1.09 | 1.09 |
time (sec) |
N/A | 0.183 | 2.811 | 0.371 | 1.035 | 0.283 | 51.056 | 0.382 | 6.065 |
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 | 22 | 22 | 24 | 22 | 24 | 24 | 0 | 24 | 24 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 1.09 | 1.09 | 0.00 | 1.09 | 1.09 |
time (sec) |
N/A | 0.186 | 2.040 | 0.066 | 0.982 | 0.255 | 0.000 | 0.347 | 6.107 |
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 | 20 | 20 | 22 | 20 | 22 | 22 | 17 | 22 | 22 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 1.10 | 1.10 | 0.85 | 1.10 | 1.10 |
time (sec) |
N/A | 0.176 | 1.782 | 0.098 | 0.861 | 0.290 | 103.165 | 0.353 | 5.884 |
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 | 18 | 18 | 20 | 18 | 20 | 20 | 17 | 20 | 20 |
N.S. |
1 | 1.00 | 1.11 | 1.00 | 1.11 | 1.11 | 0.94 | 1.11 | 1.11 |
time (sec) |
N/A | 0.169 | 0.189 | 0.084 | 0.560 | 0.261 | 41.919 | 0.322 | 6.071 |
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 | 22 | 22 | 24 | 22 | 24 | 23 | 19 | 24 | 24 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 1.09 | 1.05 | 0.86 | 1.09 | 1.09 |
time (sec) |
N/A | 0.182 | 1.508 | 0.092 | 0.524 | 0.259 | 106.656 | 0.326 | 5.842 |
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 | 22 | 22 | 24 | 22 | 24 | 27 | 0 | 24 | 24 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 1.09 | 1.23 | 0.00 | 1.09 | 1.09 |
time (sec) |
N/A | 0.188 | 1.328 | 0.066 | 0.527 | 0.275 | 0.000 | 0.332 | 5.948 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | F(-1) | 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 | 22 | 22 | 0 | 22 | 1509 | 54 | 0 | 24 | 24 |
N.S. |
1 | 1.00 | 0.00 | 1.00 | 68.59 | 2.45 | 0.00 | 1.09 | 1.09 |
time (sec) |
N/A | 0.181 | 0.000 | 0.304 | 4.797 | 0.272 | 0.000 | 0.403 | 5.915 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | F(-1) | 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 | 20 | 20 | 0 | 20 | 1476 | 52 | 0 | 22 | 22 |
N.S. |
1 | 1.00 | 0.00 | 1.00 | 73.80 | 2.60 | 0.00 | 1.10 | 1.10 |
time (sec) |
N/A | 0.176 | 0.000 | 0.273 | 4.587 | 0.276 | 0.000 | 0.425 | 6.055 |
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 | 18 | 18 | 20 | 18 | 1403 | 51 | 0 | 20 | 20 |
N.S. |
1 | 1.00 | 1.11 | 1.00 | 77.94 | 2.83 | 0.00 | 1.11 | 1.11 |
time (sec) |
N/A | 0.163 | 7.925 | 0.296 | 1.468 | 0.279 | 0.000 | 0.347 | 6.012 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | F(-1) | 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 | 22 | 22 | 0 | 22 | 5041 | 53 | 0 | 24 | 24 |
N.S. |
1 | 1.00 | 0.00 | 1.00 | 229.14 | 2.41 | 0.00 | 1.09 | 1.09 |
time (sec) |
N/A | 0.185 | 0.000 | 0.369 | 24.272 | 0.288 | 0.000 | 0.366 | 5.969 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | F(-1) | 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 | 22 | 22 | 0 | 22 | 5369 | 59 | 0 | 24 | 24 |
N.S. |
1 | 1.00 | 0.00 | 1.00 | 244.05 | 2.68 | 0.00 | 1.09 | 1.09 |
time (sec) |
N/A | 0.185 | 0.000 | 0.280 | 33.204 | 0.286 | 0.000 | 0.363 | 5.859 |
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 | 24 | 24 | 26 | 24 | 26 | 26 | 0 | 26 | 26 |
N.S. |
1 | 1.00 | 1.08 | 1.00 | 1.08 | 1.08 | 0.00 | 1.08 | 1.08 |
time (sec) |
N/A | 0.186 | 1.843 | 0.113 | 1.935 | 0.271 | 0.000 | 171.343 | 5.808 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 224 | 224 | 150 | 188 | 258 | 185 | 0 | 1263 | 0 |
N.S. |
1 | 1.00 | 0.67 | 0.84 | 1.15 | 0.83 | 0.00 | 5.64 | 0.00 |
time (sec) |
N/A | 0.623 | 0.421 | 0.558 | 0.292 | 0.287 | 0.000 | 0.375 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 118 | 118 | 79 | 109 | 153 | 108 | 0 | 520 | 0 |
N.S. |
1 | 1.00 | 0.67 | 0.92 | 1.30 | 0.92 | 0.00 | 4.41 | 0.00 |
time (sec) |
N/A | 0.396 | 0.183 | 0.404 | 0.258 | 0.283 | 0.000 | 0.317 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 38 | 38 | 50 | 43 | 65 | 40 | 0 | 137 | 0 |
N.S. |
1 | 1.00 | 1.32 | 1.13 | 1.71 | 1.05 | 0.00 | 3.61 | 0.00 |
time (sec) |
N/A | 0.229 | 0.034 | 0.317 | 0.233 | 0.296 | 0.000 | 0.382 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 103 | 108 | 83 | 129 | 0 | 100 | 0 | 169 | 0 |
N.S. |
1 | 1.05 | 0.81 | 1.25 | 0.00 | 0.97 | 0.00 | 1.64 | 0.00 |
time (sec) |
N/A | 0.448 | 0.157 | 0.468 | 0.000 | 0.264 | 0.000 | 0.295 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 94 | 96 | 85 | 131 | 0 | 129 | 0 | 339 | 0 |
N.S. |
1 | 1.02 | 0.90 | 1.39 | 0.00 | 1.37 | 0.00 | 3.61 | 0.00 |
time (sec) |
N/A | 0.432 | 0.538 | 0.547 | 0.000 | 0.270 | 0.000 | 0.312 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 233 | 237 | 151 | 423 | 0 | 328 | 0 | 1501 | 0 |
N.S. |
1 | 1.02 | 0.65 | 1.82 | 0.00 | 1.41 | 0.00 | 6.44 | 0.00 |
time (sec) |
N/A | 0.655 | 1.290 | 0.652 | 0.000 | 0.297 | 0.000 | 0.377 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 254 | 254 | 252 | 249 | 321 | 240 | 0 | 1125 | 0 |
N.S. |
1 | 1.00 | 0.99 | 0.98 | 1.26 | 0.94 | 0.00 | 4.43 | 0.00 |
time (sec) |
N/A | 0.779 | 0.342 | 0.599 | 0.305 | 0.303 | 0.000 | 0.317 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 94 | 94 | 105 | 100 | 137 | 103 | 0 | 305 | 0 |
N.S. |
1 | 1.00 | 1.12 | 1.06 | 1.46 | 1.10 | 0.00 | 3.24 | 0.00 |
time (sec) |
N/A | 0.444 | 0.094 | 0.424 | 0.250 | 0.267 | 0.000 | 0.385 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 255 | 266 | 195 | 302 | 0 | 217 | 0 | 362 | 0 |
N.S. |
1 | 1.04 | 0.76 | 1.18 | 0.00 | 0.85 | 0.00 | 1.42 | 0.00 |
time (sec) |
N/A | 0.822 | 0.303 | 0.622 | 0.000 | 0.271 | 0.000 | 0.343 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 195 | 201 | 263 | 292 | 0 | 271 | 0 | 686 | 0 |
N.S. |
1 | 1.03 | 1.35 | 1.50 | 0.00 | 1.39 | 0.00 | 3.52 | 0.00 |
time (sec) |
N/A | 0.653 | 1.003 | 0.675 | 0.000 | 0.315 | 0.000 | 0.306 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | A | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 470 | 482 | 740 | 866 | 0 | 710 | 0 | 3078 | 0 |
N.S. |
1 | 1.03 | 1.57 | 1.84 | 0.00 | 1.51 | 0.00 | 6.55 | 0.00 |
time (sec) |
N/A | 1.184 | 2.341 | 0.962 | 0.000 | 0.331 | 0.000 | 0.587 | 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 | 22 | 22 | 24 | 22 | 24 | 35 | 0 | 24 | 24 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 1.09 | 1.59 | 0.00 | 1.09 | 1.09 |
time (sec) |
N/A | 0.199 | 0.833 | 0.247 | 2.614 | 0.275 | 0.000 | 1.219 | 6.304 |
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 | 20 | 20 | 22 | 20 | 22 | 24 | 0 | 22 | 22 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 1.10 | 1.20 | 0.00 | 1.10 | 1.10 |
time (sec) |
N/A | 0.190 | 0.407 | 0.232 | 0.615 | 0.260 | 0.000 | 1.125 | 6.077 |