Detailed conclusion table per each integral is given by the table below. The elapsed time is in seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2) if the failure was due to an exception being raised, which could indicate a bug in the system. If the failure was due to integral not being evaluated within the time limit, then it is given as F.
In this table, the column N.S.
means normalized size and is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To make the table
fit the page, the name Mathematica
was abbreviated to MMA
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | F | F | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 332 | 376 | 608 | 347 | 420 | 4816 | 0 | 0 | 62 | 17912 |
N.S. |
1 | 1.13 | 1.83 | 1.05 | 1.27 | 14.51 | 0.00 | 0.00 | 0.19 | 53.95 |
time (sec) |
N/A | 1.671 | 9.018 | 0.358 | 0.156 | 0.959 | 0.000 | 0.000 | 0.301 | 7.467 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | B | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 328 | 365 | 426 | 339 | 408 | 4747 | 0 | 0 | 62 | 12531 |
N.S. |
1 | 1.11 | 1.30 | 1.03 | 1.24 | 14.47 | 0.00 | 0.00 | 0.19 | 38.20 |
time (sec) |
N/A | 1.711 | 7.623 | 0.356 | 0.153 | 0.617 | 0.000 | 0.000 | 0.296 | 18.969 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | B | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 322 | 360 | 326 | 339 | 402 | 4822 | 0 | 0 | 60 | 17010 |
N.S. |
1 | 1.12 | 1.01 | 1.05 | 1.25 | 14.98 | 0.00 | 0.00 | 0.19 | 52.83 |
time (sec) |
N/A | 1.584 | 2.458 | 0.141 | 0.132 | 0.453 | 0.000 | 0.000 | 0.308 | 6.799 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | B | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 328 | 364 | 259 | 343 | 411 | 4751 | 0 | 0 | 54 | 12659 |
N.S. |
1 | 1.11 | 0.79 | 1.05 | 1.25 | 14.48 | 0.00 | 0.00 | 0.16 | 38.59 |
time (sec) |
N/A | 1.596 | 3.662 | 0.146 | 0.140 | 0.654 | 0.000 | 0.000 | 0.345 | 14.783 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | B | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 332 | 375 | 235 | 347 | 419 | 4811 | 0 | 0 | 63 | 17833 |
N.S. |
1 | 1.13 | 0.71 | 1.05 | 1.26 | 14.49 | 0.00 | 0.00 | 0.19 | 53.71 |
time (sec) |
N/A | 1.724 | 1.869 | 0.147 | 0.133 | 1.062 | 0.000 | 0.000 | 0.278 | 7.353 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | B | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 382 | 418 | 358 | 356 | 464 | 4995 | 0 | 0 | 65 | 16740 |
N.S. |
1 | 1.09 | 0.94 | 0.93 | 1.21 | 13.08 | 0.00 | 0.00 | 0.17 | 43.82 |
time (sec) |
N/A | 2.173 | 2.697 | 0.146 | 0.125 | 1.878 | 0.000 | 0.000 | 0.240 | 11.541 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | B | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 430 | 463 | 495 | 372 | 502 | 5133 | 0 | 0 | 65 | 20088 |
N.S. |
1 | 1.08 | 1.15 | 0.87 | 1.17 | 11.94 | 0.00 | 0.00 | 0.15 | 46.72 |
time (sec) |
N/A | 2.688 | 6.150 | 0.151 | 0.174 | 3.154 | 0.000 | 0.000 | 0.231 | 17.073 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 231 | 229 | 282 | 1092020 | 0 | 5600 | 0 | 0 | 29 | 0 |
N.S. |
1 | 0.99 | 1.22 | 4727.36 | 0.00 | 24.24 | 0.00 | 0.00 | 0.13 | 0.00 |
time (sec) |
N/A | 1.117 | 1.235 | 1.902 | 0.000 | 0.789 | 0.000 | 0.000 | 0.211 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 184 | 182 | 217 | 1091181 | 0 | 5584 | 0 | 0 | 27 | 0 |
N.S. |
1 | 0.99 | 1.18 | 5930.33 | 0.00 | 30.35 | 0.00 | 0.00 | 0.15 | 0.00 |
time (sec) |
N/A | 0.754 | 0.990 | 0.576 | 0.000 | 0.675 | 0.000 | 0.000 | 0.205 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | F(-1) | F | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 151 | 154 | 189 | 1088397 | 0 | 5450 | 0 | 0 | 21 | 289 |
N.S. |
1 | 1.02 | 1.25 | 7207.93 | 0.00 | 36.09 | 0.00 | 0.00 | 0.14 | 1.91 |
time (sec) |
N/A | 0.559 | 0.388 | 1.078 | 0.000 | 0.414 | 0.000 | 0.000 | 0.207 | 4.329 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | F(-1) | F | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 115 | 113 | 123 | 1085174 | 0 | 2625 | 0 | 0 | 159 | 224 |
N.S. |
1 | 0.98 | 1.07 | 9436.30 | 0.00 | 22.83 | 0.00 | 0.00 | 1.38 | 1.95 |
time (sec) |
N/A | 0.336 | 0.062 | 0.610 | 0.000 | 0.417 | 0.000 | 0.000 | 0.308 | 3.459 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 139 | 139 | 154 | 1089777 | 0 | 2696 | 0 | 0 | 29 | 0 |
N.S. |
1 | 1.00 | 1.11 | 7840.12 | 0.00 | 19.40 | 0.00 | 0.00 | 0.21 | 0.00 |
time (sec) |
N/A | 0.763 | 0.273 | 0.582 | 0.000 | 0.309 | 0.000 | 0.000 | 0.288 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 181 | 184 | 161 | 1089917 | 0 | 2743 | 0 | 0 | 29 | 0 |
N.S. |
1 | 1.02 | 0.89 | 6021.64 | 0.00 | 15.15 | 0.00 | 0.00 | 0.16 | 0.00 |
time (sec) |
N/A | 0.758 | 0.422 | 0.615 | 0.000 | 0.307 | 0.000 | 0.000 | 0.236 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 221 | 244 | 197 | 1090929 | 0 | 2779 | 0 | 0 | 29 | 0 |
N.S. |
1 | 1.10 | 0.89 | 4936.33 | 0.00 | 12.57 | 0.00 | 0.00 | 0.13 | 0.00 |
time (sec) |
N/A | 1.403 | 1.017 | 0.586 | 0.000 | 0.310 | 0.000 | 0.000 | 0.201 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 280 | 279 | 313 | 1346642 | 0 | 7354 | 0 | 0 | 63 | 0 |
N.S. |
1 | 1.00 | 1.12 | 4809.44 | 0.00 | 26.26 | 0.00 | 0.00 | 0.22 | 0.00 |
time (sec) |
N/A | 1.564 | 2.569 | 0.691 | 0.000 | 1.025 | 0.000 | 0.000 | 0.235 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 226 | 226 | 268 | 1345246 | 0 | 7326 | 0 | 0 | 61 | 0 |
N.S. |
1 | 1.00 | 1.19 | 5952.42 | 0.00 | 32.42 | 0.00 | 0.00 | 0.27 | 0.00 |
time (sec) |
N/A | 1.147 | 4.156 | 0.695 | 0.000 | 0.916 | 0.000 | 0.000 | 0.241 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 186 | 183 | 219 | 1345539 | 0 | 7202 | 0 | 0 | 53 | 0 |
N.S. |
1 | 0.98 | 1.18 | 7234.08 | 0.00 | 38.72 | 0.00 | 0.00 | 0.28 | 0.00 |
time (sec) |
N/A | 0.873 | 1.612 | 0.694 | 0.000 | 0.904 | 0.000 | 0.000 | 0.220 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 152 | 147 | 203 | 1342398 | 0 | 7203 | 0 | 0 | 190 | 0 |
N.S. |
1 | 0.97 | 1.34 | 8831.57 | 0.00 | 47.39 | 0.00 | 0.00 | 1.25 | 0.00 |
time (sec) |
N/A | 0.521 | 0.507 | 0.707 | 0.000 | 0.496 | 0.000 | 0.000 | 0.300 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 145 | 163 | 175 | 1344185 | 0 | 3461 | 0 | 0 | 206 | 0 |
N.S. |
1 | 1.12 | 1.21 | 9270.24 | 0.00 | 23.87 | 0.00 | 0.00 | 1.42 | 0.00 |
time (sec) |
N/A | 0.797 | 0.194 | 0.706 | 0.000 | 0.406 | 0.000 | 0.000 | 0.337 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 173 | 202 | 176 | 1343875 | 0 | 3507 | 0 | 0 | 231 | 0 |
N.S. |
1 | 1.17 | 1.02 | 7768.06 | 0.00 | 20.27 | 0.00 | 0.00 | 1.34 | 0.00 |
time (sec) |
N/A | 1.117 | 0.590 | 0.684 | 0.000 | 0.364 | 0.000 | 0.000 | 0.257 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 224 | 258 | 197 | 1345372 | 0 | 3526 | 0 | 0 | 273 | 0 |
N.S. |
1 | 1.15 | 0.88 | 6006.12 | 0.00 | 15.74 | 0.00 | 0.00 | 1.22 | 0.00 |
time (sec) |
N/A | 1.489 | 1.159 | 0.868 | 0.000 | 0.409 | 0.000 | 0.000 | 0.300 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 266 | 307 | 229 | 1347641 | 0 | 3585 | 0 | 0 | 370 | 0 |
N.S. |
1 | 1.15 | 0.86 | 5066.32 | 0.00 | 13.48 | 0.00 | 0.00 | 1.39 | 0.00 |
time (sec) |
N/A | 1.934 | 1.980 | 0.716 | 0.000 | 0.449 | 0.000 | 0.000 | 0.325 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 332 | 334 | 349 | 1348388 | 0 | 9486 | 0 | 0 | 100 | 0 |
N.S. |
1 | 1.01 | 1.05 | 4061.41 | 0.00 | 28.57 | 0.00 | 0.00 | 0.30 | 0.00 |
time (sec) |
N/A | 2.071 | 2.195 | 0.735 | 0.000 | 1.504 | 0.000 | 0.000 | 0.269 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 277 | 292 | 300 | 1311074 | 0 | 9482 | 0 | 0 | 98 | 0 |
N.S. |
1 | 1.05 | 1.08 | 4733.12 | 0.00 | 34.23 | 0.00 | 0.00 | 0.35 | 0.00 |
time (sec) |
N/A | 1.847 | 2.099 | 0.592 | 0.000 | 1.183 | 0.000 | 0.000 | 0.302 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 231 | 235 | 264 | 1345969 | 0 | 9318 | 0 | 0 | 90 | 0 |
N.S. |
1 | 1.02 | 1.14 | 5826.71 | 0.00 | 40.34 | 0.00 | 0.00 | 0.39 | 0.00 |
time (sec) |
N/A | 1.352 | 1.275 | 0.548 | 0.000 | 1.235 | 0.000 | 0.000 | 0.241 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 188 | 184 | 221 | 2579 | 0 | 9367 | 0 | 0 | 228 | 0 |
N.S. |
1 | 0.98 | 1.18 | 13.72 | 0.00 | 49.82 | 0.00 | 0.00 | 1.21 | 0.00 |
time (sec) |
N/A | 0.956 | 0.523 | 8.695 | 0.000 | 1.117 | 0.000 | 0.000 | 0.248 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 183 | 184 | 244 | 2433 | 0 | 9395 | 0 | 0 | 229 | 0 |
N.S. |
1 | 1.01 | 1.33 | 13.30 | 0.00 | 51.34 | 0.00 | 0.00 | 1.25 | 0.00 |
time (sec) |
N/A | 0.904 | 1.430 | 2.639 | 0.000 | 1.142 | 0.000 | 0.000 | 0.257 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 182 | 205 | 170 | 2631 | 0 | 5026 | 0 | 0 | 332 | 0 |
N.S. |
1 | 1.13 | 0.93 | 14.46 | 0.00 | 27.62 | 0.00 | 0.00 | 1.82 | 0.00 |
time (sec) |
N/A | 1.215 | 0.591 | 1.619 | 0.000 | 0.664 | 0.000 | 0.000 | 0.286 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 219 | 243 | 194 | 1346017 | 0 | 5025 | 0 | 0 | 326 | 0 |
N.S. |
1 | 1.11 | 0.89 | 6146.20 | 0.00 | 22.95 | 0.00 | 0.00 | 1.49 | 0.00 |
time (sec) |
N/A | 1.601 | 1.082 | 2.475 | 0.000 | 0.666 | 0.000 | 0.000 | 0.311 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 270 | 308 | 249 | 1309621 | 0 | 5085 | 0 | 0 | 429 | 0 |
N.S. |
1 | 1.14 | 0.92 | 4850.45 | 0.00 | 18.83 | 0.00 | 0.00 | 1.59 | 0.00 |
time (sec) |
N/A | 2.058 | 2.385 | 1.209 | 0.000 | 0.658 | 0.000 | 0.000 | 0.319 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 318 | 354 | 300 | 1348361 | 0 | 5108 | 0 | 0 | 499 | 0 |
N.S. |
1 | 1.11 | 0.94 | 4240.13 | 0.00 | 16.06 | 0.00 | 0.00 | 1.57 | 0.00 |
time (sec) |
N/A | 2.598 | 2.783 | 0.748 | 0.000 | 0.676 | 0.000 | 0.000 | 0.329 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 232 | 243 | 270 | 946881 | 0 | 8244 | 0 | 0 | 41 | 0 |
N.S. |
1 | 1.05 | 1.16 | 4081.38 | 0.00 | 35.53 | 0.00 | 0.00 | 0.18 | 0.00 |
time (sec) |
N/A | 1.058 | 2.703 | 0.619 | 0.000 | 0.973 | 0.000 | 0.000 | 0.219 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 188 | 189 | 221 | 946041 | 0 | 8120 | 0 | 0 | 41 | 0 |
N.S. |
1 | 1.01 | 1.18 | 5032.13 | 0.00 | 43.19 | 0.00 | 0.00 | 0.22 | 0.00 |
time (sec) |
N/A | 0.745 | 1.210 | 0.715 | 0.000 | 0.822 | 0.000 | 0.000 | 0.221 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 152 | 147 | 189 | 944369 | 0 | 8112 | 0 | 0 | 39 | 0 |
N.S. |
1 | 0.97 | 1.24 | 6212.95 | 0.00 | 53.37 | 0.00 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 0.367 | 0.501 | 0.628 | 0.000 | 0.710 | 0.000 | 0.000 | 0.219 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | F(-1) | F | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 115 | 113 | 123 | 940498 | 0 | 3933 | 0 | 0 | 163 | 4102 |
N.S. |
1 | 0.98 | 1.07 | 8178.24 | 0.00 | 34.20 | 0.00 | 0.00 | 1.42 | 35.67 |
time (sec) |
N/A | 0.307 | 0.063 | 0.654 | 0.000 | 0.478 | 0.000 | 0.000 | 0.218 | 42.429 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | F(-1) | F | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 109 | 107 | 124 | 940259 | 0 | 3949 | 0 | 0 | 42 | 1716 |
N.S. |
1 | 0.98 | 1.14 | 8626.23 | 0.00 | 36.23 | 0.00 | 0.00 | 0.39 | 15.74 |
time (sec) |
N/A | 0.328 | 0.053 | 0.605 | 0.000 | 0.516 | 0.000 | 0.000 | 0.203 | 10.659 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 147 | 147 | 157 | 943928 | 0 | 4031 | 0 | 0 | 44 | 0 |
N.S. |
1 | 1.00 | 1.07 | 6421.28 | 0.00 | 27.42 | 0.00 | 0.00 | 0.30 | 0.00 |
time (sec) |
N/A | 0.438 | 0.267 | 0.676 | 0.000 | 0.492 | 0.000 | 0.000 | 0.194 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 180 | 185 | 172 | 944677 | 0 | 4096 | 0 | 0 | 121 | 0 |
N.S. |
1 | 1.03 | 0.96 | 5248.21 | 0.00 | 22.76 | 0.00 | 0.00 | 0.67 | 0.00 |
time (sec) |
N/A | 0.715 | 1.118 | 0.721 | 0.000 | 0.518 | 0.000 | 0.000 | 0.260 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 229 | 246 | 197 | 947049 | 0 | 4103 | 0 | 0 | 157 | 0 |
N.S. |
1 | 1.07 | 0.86 | 4135.59 | 0.00 | 17.92 | 0.00 | 0.00 | 0.69 | 0.00 |
time (sec) |
N/A | 0.982 | 1.858 | 0.761 | 0.000 | 0.490 | 0.000 | 0.000 | 0.259 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 250 | 278 | 270 | 764550 | 0 | 15640 | 0 | 0 | 57 | 0 |
N.S. |
1 | 1.11 | 1.08 | 3058.20 | 0.00 | 62.56 | 0.00 | 0.00 | 0.23 | 0.00 |
time (sec) |
N/A | 1.340 | 2.016 | 1.141 | 0.000 | 2.102 | 0.000 | 0.000 | 0.221 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 195 | 233 | 321 | 799742 | 0 | 15380 | 0 | 0 | 57 | 0 |
N.S. |
1 | 1.19 | 1.65 | 4101.24 | 0.00 | 78.87 | 0.00 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 0.900 | 0.878 | 1.034 | 0.000 | 2.043 | 0.000 | 0.000 | 0.198 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 154 | 174 | 182 | 761722 | 0 | 7525 | 0 | 0 | 173 | 0 |
N.S. |
1 | 1.13 | 1.18 | 4946.25 | 0.00 | 48.86 | 0.00 | 0.00 | 1.12 | 0.00 |
time (sec) |
N/A | 0.812 | 0.827 | 1.108 | 0.000 | 1.225 | 0.000 | 0.000 | 0.219 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 149 | 176 | 163 | 798609 | 0 | 7445 | 0 | 0 | 49 | 0 |
N.S. |
1 | 1.18 | 1.09 | 5359.79 | 0.00 | 49.97 | 0.00 | 0.00 | 0.33 | 0.00 |
time (sec) |
N/A | 0.803 | 0.851 | 1.063 | 0.000 | 1.223 | 0.000 | 0.000 | 0.207 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 159 | 183 | 183 | 762494 | 0 | 7563 | 0 | 0 | 58 | 0 |
N.S. |
1 | 1.15 | 1.15 | 4795.56 | 0.00 | 47.57 | 0.00 | 0.00 | 0.36 | 0.00 |
time (sec) |
N/A | 0.851 | 0.633 | 1.039 | 0.000 | 1.377 | 0.000 | 0.000 | 0.242 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 193 | 235 | 202 | 799509 | 0 | 7597 | 0 | 0 | 201 | 0 |
N.S. |
1 | 1.22 | 1.05 | 4142.53 | 0.00 | 39.36 | 0.00 | 0.00 | 1.04 | 0.00 |
time (sec) |
N/A | 1.146 | 2.920 | 1.029 | 0.000 | 1.233 | 0.000 | 0.000 | 0.227 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 241 | 279 | 223 | 763546 | 0 | 7726 | 0 | 0 | 256 | 0 |
N.S. |
1 | 1.16 | 0.93 | 3168.24 | 0.00 | 32.06 | 0.00 | 0.00 | 1.06 | 0.00 |
time (sec) |
N/A | 1.472 | 3.959 | 1.094 | 0.000 | 1.232 | 0.000 | 0.000 | 0.219 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 317 | 371 | 260 | 1493684 | 0 | 23240 | 0 | 0 | 73 | 0 |
N.S. |
1 | 1.17 | 0.82 | 4711.94 | 0.00 | 73.31 | 0.00 | 0.00 | 0.23 | 0.00 |
time (sec) |
N/A | 1.983 | 4.485 | 1.493 | 0.000 | 3.856 | 0.000 | 0.000 | 0.205 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 251 | 310 | 396 | 1490358 | 0 | 23066 | 0 | 0 | 73 | 0 |
N.S. |
1 | 1.24 | 1.58 | 5937.68 | 0.00 | 91.90 | 0.00 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 1.390 | 4.236 | 1.533 | 0.000 | 3.899 | 0.000 | 0.000 | 0.226 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 214 | 263 | 189 | 1487710 | 0 | 11334 | 0 | 0 | 292 | 0 |
N.S. |
1 | 1.23 | 0.88 | 6951.92 | 0.00 | 52.96 | 0.00 | 0.00 | 1.36 | 0.00 |
time (sec) |
N/A | 1.282 | 1.851 | 1.375 | 0.000 | 2.184 | 0.000 | 0.000 | 0.226 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 199 | 246 | 198 | 1488901 | 0 | 11381 | 0 | 0 | 71 | 0 |
N.S. |
1 | 1.24 | 0.99 | 7481.91 | 0.00 | 57.19 | 0.00 | 0.00 | 0.36 | 0.00 |
time (sec) |
N/A | 1.219 | 1.863 | 1.360 | 0.000 | 2.438 | 0.000 | 0.000 | 0.263 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 211 | 258 | 194 | 1487734 | 0 | 11374 | 0 | 0 | 65 | 0 |
N.S. |
1 | 1.22 | 0.92 | 7050.87 | 0.00 | 53.91 | 0.00 | 0.00 | 0.31 | 0.00 |
time (sec) |
N/A | 1.222 | 2.511 | 1.532 | 0.000 | 2.182 | 0.000 | 0.000 | 0.223 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 212 | 264 | 235 | 1487449 | 0 | 11439 | 0 | 0 | 74 | 0 |
N.S. |
1 | 1.25 | 1.11 | 7016.27 | 0.00 | 53.96 | 0.00 | 0.00 | 0.35 | 0.00 |
time (sec) |
N/A | 1.325 | 0.978 | 1.418 | 0.000 | 2.428 | 0.000 | 0.000 | 0.229 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 265 | 325 | 294 | 1489246 | 0 | 11517 | 0 | 0 | 366 | 0 |
N.S. |
1 | 1.23 | 1.11 | 5619.80 | 0.00 | 43.46 | 0.00 | 0.00 | 1.38 | 0.00 |
time (sec) |
N/A | 1.671 | 1.921 | 1.188 | 0.000 | 2.242 | 0.000 | 0.000 | 0.218 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 298 | 363 | 270 | 1489930 | 0 | 11607 | 0 | 0 | 483 | 0 |
N.S. |
1 | 1.22 | 0.91 | 4999.77 | 0.00 | 38.95 | 0.00 | 0.00 | 1.62 | 0.00 |
time (sec) |
N/A | 2.081 | 4.404 | 1.273 | 0.000 | 2.473 | 0.000 | 0.000 | 0.242 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 89 | 87 | 89 | 480 | 0 | 1477 | 0 | 663 | 42 | 207 |
N.S. |
1 | 0.98 | 1.00 | 5.39 | 0.00 | 16.60 | 0.00 | 7.45 | 0.47 | 2.33 |
time (sec) |
N/A | 0.304 | 0.114 | 20.664 | 0.000 | 0.157 | 0.000 | 0.219 | 0.202 | 3.426 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 89 | 87 | 89 | 480 | 0 | 1477 | 0 | 663 | 42 | 89 |
N.S. |
1 | 0.98 | 1.00 | 5.39 | 0.00 | 16.60 | 0.00 | 7.45 | 0.47 | 1.00 |
time (sec) |
N/A | 0.300 | 0.088 | 3.540 | 0.000 | 0.154 | 0.000 | 0.220 | 0.255 | 3.382 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 89 | 87 | 101 | 427 | 0 | 1477 | 0 | 1061 | 44 | 205 |
N.S. |
1 | 0.98 | 1.13 | 4.80 | 0.00 | 16.60 | 0.00 | 11.92 | 0.49 | 2.30 |
time (sec) |
N/A | 0.302 | 0.115 | 0.554 | 0.000 | 0.170 | 0.000 | 0.379 | 0.216 | 3.480 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 89 | 87 | 101 | 427 | 0 | 1477 | 0 | 269 | 44 | 129 |
N.S. |
1 | 0.98 | 1.13 | 4.80 | 0.00 | 16.60 | 0.00 | 3.02 | 0.49 | 1.45 |
time (sec) |
N/A | 0.301 | 0.095 | 0.576 | 0.000 | 0.161 | 0.000 | 0.197 | 0.216 | 3.262 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 89 | 87 | 89 | 480 | 0 | 1485 | 0 | 470 | 42 | 204 |
N.S. |
1 | 0.98 | 1.00 | 5.39 | 0.00 | 16.69 | 0.00 | 5.28 | 0.47 | 2.29 |
time (sec) |
N/A | 0.303 | 0.115 | 2.211 | 0.000 | 0.211 | 0.000 | 0.191 | 0.219 | 3.628 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 89 | 87 | 101 | 427 | 0 | 1485 | 0 | 1061 | 44 | 201 |
N.S. |
1 | 0.98 | 1.13 | 4.80 | 0.00 | 16.69 | 0.00 | 11.92 | 0.49 | 2.26 |
time (sec) |
N/A | 0.302 | 0.111 | 2.250 | 0.000 | 0.163 | 0.000 | 0.387 | 0.221 | 3.541 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 89 | 87 | 89 | 480 | 0 | 1485 | 0 | 470 | 42 | 89 |
N.S. |
1 | 0.98 | 1.00 | 5.39 | 0.00 | 16.69 | 0.00 | 5.28 | 0.47 | 1.00 |
time (sec) |
N/A | 0.291 | 0.090 | 1.020 | 0.000 | 0.241 | 0.000 | 0.192 | 0.223 | 3.257 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 89 | 87 | 101 | 427 | 0 | 1485 | 0 | 413 | 44 | 219 |
N.S. |
1 | 0.98 | 1.13 | 4.80 | 0.00 | 16.69 | 0.00 | 4.64 | 0.49 | 2.46 |
time (sec) |
N/A | 0.291 | 0.097 | 0.405 | 0.000 | 0.161 | 0.000 | 0.186 | 0.236 | 3.693 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 95 | 93 | 95 | 479 | 0 | 1477 | 0 | 0 | 156 | 207 |
N.S. |
1 | 0.98 | 1.00 | 5.04 | 0.00 | 15.55 | 0.00 | 0.00 | 1.64 | 2.18 |
time (sec) |
N/A | 0.259 | 0.054 | 0.297 | 0.000 | 0.158 | 0.000 | 0.000 | 0.226 | 2.742 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 95 | 93 | 95 | 479 | 0 | 1477 | 0 | 0 | 154 | 191 |
N.S. |
1 | 0.98 | 1.00 | 5.04 | 0.00 | 15.55 | 0.00 | 0.00 | 1.62 | 2.01 |
time (sec) |
N/A | 0.259 | 0.047 | 0.452 | 0.000 | 0.160 | 0.000 | 0.000 | 0.233 | 2.942 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 95 | 93 | 103 | 426 | 0 | 1477 | 0 | 641 | 157 | 205 |
N.S. |
1 | 0.98 | 1.08 | 4.48 | 0.00 | 15.55 | 0.00 | 6.75 | 1.65 | 2.16 |
time (sec) |
N/A | 0.264 | 0.042 | 0.161 | 0.000 | 0.158 | 0.000 | 0.414 | 0.239 | 2.712 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 95 | 93 | 103 | 426 | 0 | 1477 | 0 | 0 | 155 | 189 |
N.S. |
1 | 0.98 | 1.08 | 4.48 | 0.00 | 15.55 | 0.00 | 0.00 | 1.63 | 1.99 |
time (sec) |
N/A | 0.263 | 0.064 | 0.115 | 0.000 | 0.156 | 0.000 | 0.000 | 0.242 | 2.883 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 95 | 93 | 95 | 479 | 0 | 1485 | 0 | 498 | 157 | 207 |
N.S. |
1 | 0.98 | 1.00 | 5.04 | 0.00 | 15.63 | 0.00 | 5.24 | 1.65 | 2.18 |
time (sec) |
N/A | 0.263 | 0.047 | 0.131 | 0.000 | 0.161 | 0.000 | 0.687 | 0.237 | 2.657 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 95 | 93 | 103 | 426 | 0 | 1485 | 0 | 641 | 157 | 205 |
N.S. |
1 | 0.98 | 1.08 | 4.48 | 0.00 | 15.63 | 0.00 | 6.75 | 1.65 | 2.16 |
time (sec) |
N/A | 0.260 | 0.056 | 0.328 | 0.000 | 0.213 | 0.000 | 0.393 | 0.253 | 2.771 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 95 | 93 | 95 | 479 | 0 | 1485 | 0 | 498 | 157 | 191 |
N.S. |
1 | 0.98 | 1.00 | 5.04 | 0.00 | 15.63 | 0.00 | 5.24 | 1.65 | 2.01 |
time (sec) |
N/A | 0.263 | 0.052 | 0.174 | 0.000 | 0.161 | 0.000 | 0.661 | 0.220 | 2.884 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 95 | 93 | 103 | 426 | 0 | 1485 | 0 | 209 | 157 | 189 |
N.S. |
1 | 0.98 | 1.08 | 4.48 | 0.00 | 15.63 | 0.00 | 2.20 | 1.65 | 1.99 |
time (sec) |
N/A | 0.264 | 0.051 | 0.114 | 0.000 | 0.199 | 0.000 | 0.396 | 0.237 | 2.880 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-1) | C | F | A | F | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 466 | 425 | 153 | 341 | 0 | 73878 | 0 | 435 | 23 | 2137 |
N.S. |
1 | 0.91 | 0.33 | 0.73 | 0.00 | 158.54 | 0.00 | 0.93 | 0.05 | 4.59 |
time (sec) |
N/A | 1.544 | 0.243 | 0.195 | 0.000 | 2.081 | 0.000 | 0.280 | 0.213 | 10.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-1) | C | F | A | F | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 465 | 379 | 204 | 328 | 0 | 74435 | 0 | 424 | 108 | 2111 |
N.S. |
1 | 0.82 | 0.44 | 0.71 | 0.00 | 160.08 | 0.00 | 0.91 | 0.23 | 4.54 |
time (sec) |
N/A | 1.333 | 0.262 | 0.092 | 0.000 | 1.838 | 0.000 | 0.262 | 0.314 | 8.917 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-1) | C | F | A | F | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 467 | 341 | 162 | 340 | 0 | 73744 | 0 | 430 | 25 | 2050 |
N.S. |
1 | 0.73 | 0.35 | 0.73 | 0.00 | 157.91 | 0.00 | 0.92 | 0.05 | 4.39 |
time (sec) |
N/A | 1.112 | 0.179 | 0.143 | 0.000 | 1.915 | 0.000 | 0.276 | 0.216 | 9.452 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-1) | C | F | A | F | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 525 | 383 | 104 | 350 | 0 | 74494 | 0 | 457 | 25 | 3159 |
N.S. |
1 | 0.73 | 0.20 | 0.67 | 0.00 | 141.89 | 0.00 | 0.87 | 0.05 | 6.02 |
time (sec) |
N/A | 1.392 | 0.157 | 0.093 | 0.000 | 2.186 | 0.000 | 0.301 | 0.212 | 2.906 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F(-1) | F | F(-1) | F | F(-1) |
verified |
N/A | No | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 165 | 161 | 0 | 0 | 0 | 0 | 0 | 0 | 34 | 0 |
N.S. |
1 | 0.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.21 | 0.00 |
time (sec) |
N/A | 0.437 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.204 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | F | F | F(-1) | F | F(-1) | F | F(-1) |
verified |
N/A | N/A | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 165 | 0 | 7362 | 0 | 0 | 0 | 0 | 0 | 153 | 0 |
N.S. |
1 | 0.00 | 44.62 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.93 | 0.00 |
time (sec) |
N/A | 0.000 | 102.498 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.296 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | F | F | F(-1) | F | F(-1) | F | F(-1) |
verified |
N/A | N/A | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 165 | 0 | 6076 | 0 | 0 | 0 | 0 | 0 | 153 | 0 |
N.S. |
1 | 0.00 | 36.82 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.93 | 0.00 |
time (sec) |
N/A | 0.000 | 54.966 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.383 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | F | F | F(-1) | F | F(-1) | F | F(-1) |
verified |
N/A | N/A | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 165 | 0 | 39974 | 0 | 0 | 0 | 0 | 0 | 37 | 0 |
N.S. |
1 | 0.00 | 242.27 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.22 | 0.00 |
time (sec) |
N/A | 0.000 | 177.560 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.216 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | F | F | F(-1) | F | F(-1) | F | F(-1) |
verified |
N/A | N/A | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 165 | 0 | 6066 | 0 | 0 | 0 | 0 | 0 | 43 | 0 |
N.S. |
1 | 0.00 | 36.76 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 0.000 | 162.482 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.231 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F(-1) | F | F | F(-1) | F | F(-1) | F | F(-1) |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 165 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 37 | 0 |
N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.22 | 0.00 |
time (sec) |
N/A | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.226 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | F | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 525 | 497 | 371 | 130 | 0 | 663 | 0 | 0 | 23 | 1015 |
N.S. |
1 | 0.95 | 0.71 | 0.25 | 0.00 | 1.26 | 0.00 | 0.00 | 0.04 | 1.93 |
time (sec) |
N/A | 1.363 | 14.735 | 1.162 | 0.000 | 0.109 | 0.000 | 0.000 | 0.214 | 17.155 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | A | F | F(-1) | F | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 373 | 321 | 442 | 120 | 0 | 544 | 0 | 0 | 23 | 890 |
N.S. |
1 | 0.86 | 1.18 | 0.32 | 0.00 | 1.46 | 0.00 | 0.00 | 0.06 | 2.39 |
time (sec) |
N/A | 0.991 | 0.707 | 0.674 | 0.000 | 0.127 | 0.000 | 0.000 | 0.223 | 9.107 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 439 | 405 | 313 | 79 | 0 | 582 | 0 | 0 | 23 | 881 |
N.S. |
1 | 0.92 | 0.71 | 0.18 | 0.00 | 1.33 | 0.00 | 0.00 | 0.05 | 2.01 |
time (sec) |
N/A | 0.598 | 0.532 | 0.147 | 0.000 | 0.109 | 0.000 | 0.000 | 0.219 | 5.980 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | B | F | A | F | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 318 | 254 | 346 | 88 | 0 | 476 | 0 | 17 | 21 | 830 |
N.S. |
1 | 0.80 | 1.09 | 0.28 | 0.00 | 1.50 | 0.00 | 0.05 | 0.07 | 2.61 |
time (sec) |
N/A | 0.645 | 0.165 | 0.163 | 0.000 | 0.109 | 0.000 | 1.497 | 0.215 | 5.135 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 415 | 379 | 294 | 60 | 0 | 536 | 0 | 0 | 14 | 863 |
N.S. |
1 | 0.91 | 0.71 | 0.14 | 0.00 | 1.29 | 0.00 | 0.00 | 0.03 | 2.08 |
time (sec) |
N/A | 0.519 | 0.140 | 0.562 | 0.000 | 0.105 | 0.000 | 0.000 | 0.231 | 4.193 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | F | F | F | B |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 402 | 368 | 744 | 0 | 0 | 562 | 0 | 0 | 21 | 2133 |
N.S. |
1 | 0.92 | 1.85 | 0.00 | 0.00 | 1.40 | 0.00 | 0.00 | 0.05 | 5.31 |
time (sec) |
N/A | 1.333 | 0.557 | 0.000 | 0.000 | 0.103 | 0.000 | 0.000 | 0.622 | 13.028 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | F | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 546 | 507 | 941 | 0 | 0 | 801 | 0 | 0 | 23 | 3239 |
N.S. |
1 | 0.93 | 1.72 | 0.00 | 0.00 | 1.47 | 0.00 | 0.00 | 0.04 | 5.93 |
time (sec) |
N/A | 1.329 | 25.149 | 0.000 | 0.000 | 0.118 | 0.000 | 0.000 | 1.667 | 18.992 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | B | F | F | F | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 329 | 259 | 300 | 89 | 0 | 2071 | 0 | 0 | 40 | 1540 |
N.S. |
1 | 0.79 | 0.91 | 0.27 | 0.00 | 6.29 | 0.00 | 0.00 | 0.12 | 4.68 |
time (sec) |
N/A | 0.691 | 0.640 | 0.702 | 0.000 | 0.214 | 0.000 | 0.000 | 0.218 | 7.521 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | B | F | F | F | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 327 | 257 | 365 | 90 | 0 | 1567 | 0 | 0 | 40 | 924 |
N.S. |
1 | 0.79 | 1.12 | 0.28 | 0.00 | 4.79 | 0.00 | 0.00 | 0.12 | 2.83 |
time (sec) |
N/A | 0.654 | 0.493 | 0.096 | 0.000 | 0.113 | 0.000 | 0.000 | 0.208 | 4.562 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | B | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 415 | 379 | 224 | 60 | 0 | 1011 | 0 | 0 | 14 | 1229 |
N.S. |
1 | 0.91 | 0.54 | 0.14 | 0.00 | 2.44 | 0.00 | 0.00 | 0.03 | 2.96 |
time (sec) |
N/A | 0.570 | 0.198 | 0.321 | 0.000 | 0.122 | 0.000 | 0.000 | 0.199 | 5.440 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 415 | 379 | 294 | 60 | 0 | 536 | 0 | 0 | 14 | 863 |
N.S. |
1 | 0.91 | 0.71 | 0.14 | 0.00 | 1.29 | 0.00 | 0.00 | 0.03 | 2.08 |
time (sec) |
N/A | 0.508 | 0.154 | 0.417 | 0.000 | 0.115 | 0.000 | 0.000 | 0.202 | 4.316 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | B | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 415 | 379 | 251 | 58 | 0 | 1225 | 0 | 0 | 14 | 817 |
N.S. |
1 | 0.91 | 0.60 | 0.14 | 0.00 | 2.95 | 0.00 | 0.00 | 0.03 | 1.97 |
time (sec) |
N/A | 0.493 | 0.147 | 0.155 | 0.000 | 0.127 | 0.000 | 0.000 | 0.239 | 4.547 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | B | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 415 | 379 | 313 | 57 | 0 | 2139 | 0 | 0 | 14 | 1048 |
N.S. |
1 | 0.91 | 0.75 | 0.14 | 0.00 | 5.15 | 0.00 | 0.00 | 0.03 | 2.53 |
time (sec) |
N/A | 0.481 | 0.234 | 0.141 | 0.000 | 0.136 | 0.000 | 0.000 | 0.197 | 5.590 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | B | F | F | F | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 336 | 273 | 106 | 101 | 0 | 4277 | 0 | 0 | 39 | 3130 |
N.S. |
1 | 0.81 | 0.32 | 0.30 | 0.00 | 12.73 | 0.00 | 0.00 | 0.12 | 9.32 |
time (sec) |
N/A | 0.693 | 0.174 | 0.090 | 0.000 | 0.212 | 0.000 | 0.000 | 0.213 | 3.862 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | B | F | F | F | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 338 | 275 | 106 | 100 | 0 | 4842 | 0 | 0 | 39 | 4348 |
N.S. |
1 | 0.81 | 0.31 | 0.30 | 0.00 | 14.33 | 0.00 | 0.00 | 0.12 | 12.86 |
time (sec) |
N/A | 0.674 | 0.097 | 0.085 | 0.000 | 0.225 | 0.000 | 0.000 | 0.210 | 3.878 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 261 | 269 | 191 | 0 | 0 | 0 | 0 | 0 | 357 | 0 |
N.S. |
1 | 1.03 | 0.73 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.37 | 0.00 |
time (sec) |
N/A | 1.421 | 1.164 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.231 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 198 | 199 | 141 | 0 | 0 | 0 | 0 | 0 | 293 | 0 |
N.S. |
1 | 1.01 | 0.71 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.48 | 0.00 |
time (sec) |
N/A | 0.858 | 0.551 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.239 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 140 | 140 | 116 | 0 | 0 | 0 | 0 | 0 | 89 | 0 |
N.S. |
1 | 1.00 | 0.83 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.64 | 0.00 |
time (sec) |
N/A | 0.500 | 0.331 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.245 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 103 | 103 | 99 | 0 | 0 | 0 | 0 | 0 | 59 | 0 |
N.S. |
1 | 1.00 | 0.96 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.57 | 0.00 |
time (sec) |
N/A | 0.327 | 0.203 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.198 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 181 | 174 | 142 | 0 | 0 | 0 | 0 | 0 | 129 | 0 |
N.S. |
1 | 0.96 | 0.78 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.71 | 0.00 |
time (sec) |
N/A | 0.794 | 0.352 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.214 | 0.000 |