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 | C | F(-2) | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 251 | 244 | 389 | 1082 | 0 | 0 | 0 | 0 | 210 | 0 |
N.S. |
1 | 0.97 | 1.55 | 4.31 | 0.00 | 0.00 | 0.00 | 0.00 | 0.84 | 0.00 |
time (sec) |
N/A | 0.464 | 0.221 | 102.766 | 0.000 | 0.000 | 0.000 | 0.000 | 0.176 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F(-2) | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 194 | 188 | 332 | 841 | 0 | 0 | 0 | 0 | 151 | 0 |
N.S. |
1 | 0.97 | 1.71 | 4.34 | 0.00 | 0.00 | 0.00 | 0.00 | 0.78 | 0.00 |
time (sec) |
N/A | 0.363 | 0.153 | 19.626 | 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 | A | A | C | F(-2) | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 179 | 175 | 305 | 733 | 0 | 0 | 0 | 0 | 153 | 0 |
N.S. |
1 | 0.98 | 1.70 | 4.09 | 0.00 | 0.00 | 0.00 | 0.00 | 0.85 | 0.00 |
time (sec) |
N/A | 0.366 | 0.167 | 19.204 | 0.000 | 0.000 | 0.000 | 0.000 | 0.182 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F(-2) | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 227 | 222 | 362 | 965 | 0 | 0 | 0 | 0 | 191 | 0 |
N.S. |
1 | 0.98 | 1.59 | 4.25 | 0.00 | 0.00 | 0.00 | 0.00 | 0.84 | 0.00 |
time (sec) |
N/A | 0.400 | 0.197 | 41.109 | 0.000 | 0.000 | 0.000 | 0.000 | 0.171 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F(-2) | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 267 | 260 | 399 | 1146 | 0 | 0 | 0 | 0 | 222 | 0 |
N.S. |
1 | 0.97 | 1.49 | 4.29 | 0.00 | 0.00 | 0.00 | 0.00 | 0.83 | 0.00 |
time (sec) |
N/A | 0.462 | 0.276 | 189.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.174 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 310 | 318 | 814 | 4839 | 0 | 0 | 0 | 0 | 453 | 0 |
N.S. |
1 | 1.03 | 2.63 | 15.61 | 0.00 | 0.00 | 0.00 | 0.00 | 1.46 | 0.00 |
time (sec) |
N/A | 0.782 | 0.334 | 214.750 | 0.000 | 0.000 | 0.000 | 0.000 | 0.166 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 147 | 161 | 736 | 1930 | 0 | 0 | 0 | 0 | 118 | 0 |
N.S. |
1 | 1.10 | 5.01 | 13.13 | 0.00 | 0.00 | 0.00 | 0.00 | 0.80 | 0.00 |
time (sec) |
N/A | 0.635 | 0.287 | 96.776 | 0.000 | 0.000 | 0.000 | 0.000 | 0.159 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 276 | 267 | 946 | 5175 | 0 | 0 | 0 | 0 | 407 | 0 |
N.S. |
1 | 0.97 | 3.43 | 18.75 | 0.00 | 0.00 | 0.00 | 0.00 | 1.47 | 0.00 |
time (sec) |
N/A | 0.611 | 0.498 | 93.622 | 0.000 | 0.000 | 0.000 | 0.000 | 0.172 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 356 | 334 | 1111 | 6432 | 0 | 0 | 0 | 0 | 476 | 0 |
N.S. |
1 | 0.94 | 3.12 | 18.07 | 0.00 | 0.00 | 0.00 | 0.00 | 1.34 | 0.00 |
time (sec) |
N/A | 0.878 | 0.550 | 93.825 | 0.000 | 0.000 | 0.000 | 0.000 | 0.167 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | C | F | F(-2) | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 576 | 627 | 1128 | 0 | 0 | 0 | 0 | 0 | 497 | 0 |
N.S. |
1 | 1.09 | 1.96 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.86 | 0.00 |
time (sec) |
N/A | 1.240 | 0.542 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.171 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | C | F | F(-2) | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 495 | 553 | 993 | 0 | 0 | 0 | 0 | 0 | 360 | 0 |
N.S. |
1 | 1.12 | 2.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.73 | 0.00 |
time (sec) |
N/A | 1.071 | 0.471 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.175 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | C | F | F(-2) | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 427 | 476 | 917 | 0 | 0 | 0 | 0 | 0 | 367 | 0 |
N.S. |
1 | 1.11 | 2.15 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.86 | 0.00 |
time (sec) |
N/A | 0.805 | 0.478 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.194 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | C | F | F(-2) | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 517 | 560 | 1083 | 0 | 0 | 0 | 0 | 0 | 441 | 0 |
N.S. |
1 | 1.08 | 2.09 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.85 | 0.00 |
time (sec) |
N/A | 1.177 | 0.500 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.179 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 514 | 517 | 1911 | 21242 | 0 | 0 | 0 | 0 | 834 | 0 |
N.S. |
1 | 1.01 | 3.72 | 41.33 | 0.00 | 0.00 | 0.00 | 0.00 | 1.62 | 0.00 |
time (sec) |
N/A | 1.253 | 0.592 | 0.102 | 0.000 | 0.000 | 0.000 | 0.000 | 0.177 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 181 | 194 | 1348 | 5812 | 0 | 0 | 0 | 0 | 153 | 0 |
N.S. |
1 | 1.07 | 7.45 | 32.11 | 0.00 | 0.00 | 0.00 | 0.00 | 0.85 | 0.00 |
time (sec) |
N/A | 0.785 | 0.432 | 0.030 | 0.000 | 0.000 | 0.000 | 0.000 | 0.165 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 451 | 434 | 2248 | 22905 | 0 | 0 | 0 | 0 | 738 | 0 |
N.S. |
1 | 0.96 | 4.98 | 50.79 | 0.00 | 0.00 | 0.00 | 0.00 | 1.64 | 0.00 |
time (sec) |
N/A | 0.936 | 1.045 | 0.109 | 0.000 | 0.000 | 0.000 | 0.000 | 0.171 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | C | F | F(-2) | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 983 | 1085 | 2544 | 0 | 0 | 0 | 0 | 0 | 906 | 0 |
N.S. |
1 | 1.10 | 2.59 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.92 | 0.00 |
time (sec) |
N/A | 1.996 | 1.047 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.179 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | C | F | F(-2) | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 873 | 988 | 2302 | 0 | 0 | 0 | 0 | 0 | 658 | 0 |
N.S. |
1 | 1.13 | 2.64 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.75 | 0.00 |
time (sec) |
N/A | 1.782 | 0.856 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.163 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | C | F | F(-2) | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 775 | 879 | 2166 | 0 | 0 | 0 | 0 | 0 | 676 | 0 |
N.S. |
1 | 1.13 | 2.79 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.87 | 0.00 |
time (sec) |
N/A | 1.389 | 0.844 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.171 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | C | F | F(-2) | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 898 | 989 | 2488 | 0 | 0 | 0 | 0 | 0 | 792 | 0 |
N.S. |
1 | 1.10 | 2.77 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.88 | 0.00 |
time (sec) |
N/A | 1.889 | 1.002 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.184 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 403 | 388 | 434 | 0 | 0 | 0 | 0 | 0 | 523 | 0 |
N.S. |
1 | 0.96 | 1.08 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.30 | 0.00 |
time (sec) |
N/A | 0.702 | 0.620 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.237 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 313 | 304 | 336 | 0 | 0 | 0 | 0 | 0 | 413 | 0 |
N.S. |
1 | 0.97 | 1.07 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.32 | 0.00 |
time (sec) |
N/A | 0.581 | 0.484 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.179 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 209 | 203 | 218 | 0 | 0 | 0 | 0 | 0 | 303 | 0 |
N.S. |
1 | 0.97 | 1.04 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.45 | 0.00 |
time (sec) |
N/A | 0.445 | 0.351 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.174 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 117 | 130 | 186 | 0 | 0 | 0 | 0 | 0 | 120 | 0 |
N.S. |
1 | 1.11 | 1.59 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.03 | 0.00 |
time (sec) |
N/A | 0.554 | 0.299 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.170 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 248 | 239 | 250 | 0 | 0 | 0 | 0 | 0 | 385 | 0 |
N.S. |
1 | 0.96 | 1.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.55 | 0.00 |
time (sec) |
N/A | 0.500 | 0.434 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.162 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 346 | 331 | 359 | 0 | 0 | 0 | 0 | 0 | 513 | 0 |
N.S. |
1 | 0.96 | 1.04 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.48 | 0.00 |
time (sec) |
N/A | 0.635 | 0.580 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.173 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 434 | 417 | 457 | 0 | 0 | 0 | 0 | 0 | 631 | 0 |
N.S. |
1 | 0.96 | 1.05 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.45 | 0.00 |
time (sec) |
N/A | 0.701 | 0.669 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.169 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 750 | 764 | 1319 | 0 | 0 | 0 | 0 | 0 | 1128 | 0 |
N.S. |
1 | 1.02 | 1.76 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.50 | 0.00 |
time (sec) |
N/A | 1.287 | 1.038 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.308 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 598 | 627 | 960 | 0 | 0 | 0 | 0 | 0 | 888 | 0 |
N.S. |
1 | 1.05 | 1.61 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.48 | 0.00 |
time (sec) |
N/A | 1.083 | 0.593 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.207 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 405 | 452 | 718 | 0 | 0 | 0 | 0 | 0 | 648 | 0 |
N.S. |
1 | 1.12 | 1.77 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.60 | 0.00 |
time (sec) |
N/A | 0.810 | 0.469 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.193 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 145 | 159 | 263 | 0 | 0 | 0 | 0 | 0 | 145 | 0 |
N.S. |
1 | 1.10 | 1.81 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | 0.00 |
time (sec) |
N/A | 0.661 | 0.305 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.170 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 441 | 536 | 821 | 0 | 0 | 0 | 0 | 0 | 560 | 0 |
N.S. |
1 | 1.22 | 1.86 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.27 | 0.00 |
time (sec) |
N/A | 1.059 | 0.639 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.187 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 608 | 693 | 1078 | 0 | 0 | 0 | 0 | 0 | 669 | 0 |
N.S. |
1 | 1.14 | 1.77 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.10 | 0.00 |
time (sec) |
N/A | 1.261 | 0.759 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.195 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 907 | 935 | 1968 | 0 | 0 | 0 | 0 | 0 | 26 | 0 |
N.S. |
1 | 1.03 | 2.17 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.03 | 0.00 |
time (sec) |
N/A | 1.666 | 1.081 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 200.018 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 639 | 678 | 1522 | 0 | 0 | 0 | 0 | 0 | 1230 | 0 |
N.S. |
1 | 1.06 | 2.38 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.92 | 0.00 |
time (sec) |
N/A | 1.234 | 0.972 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.252 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 178 | 191 | 403 | 0 | 0 | 0 | 0 | 0 | 177 | 0 |
N.S. |
1 | 1.07 | 2.26 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.99 | 0.00 |
time (sec) |
N/A | 0.766 | 0.509 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.168 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 673 | 779 | 976 | 0 | 0 | 0 | 0 | 0 | 1043 | 0 |
N.S. |
1 | 1.16 | 1.45 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.55 | 0.00 |
time (sec) |
N/A | 1.577 | 1.358 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.208 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 914 | 1011 | 1549 | 0 | 0 | 0 | 0 | 0 | 1206 | 0 |
N.S. |
1 | 1.11 | 1.69 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.32 | 0.00 |
time (sec) |
N/A | 1.896 | 2.385 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.229 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 367 | 354 | 394 | 0 | 0 | 0 | 0 | 0 | 477 | 0 |
N.S. |
1 | 0.96 | 1.07 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.30 | 0.00 |
time (sec) |
N/A | 0.614 | 0.519 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.165 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 283 | 274 | 296 | 0 | 0 | 0 | 0 | 0 | 361 | 0 |
N.S. |
1 | 0.97 | 1.05 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.28 | 0.00 |
time (sec) |
N/A | 0.516 | 0.382 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.174 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 199 | 192 | 145 | 0 | 0 | 0 | 0 | 0 | 294 | 0 |
N.S. |
1 | 0.96 | 0.73 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.48 | 0.00 |
time (sec) |
N/A | 0.441 | 0.504 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.164 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 310 | 299 | 326 | 0 | 0 | 0 | 0 | 0 | 461 | 0 |
N.S. |
1 | 0.96 | 1.05 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.49 | 0.00 |
time (sec) |
N/A | 0.553 | 0.484 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.159 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 394 | 379 | 422 | 0 | 0 | 0 | 0 | 0 | 595 | 0 |
N.S. |
1 | 0.96 | 1.07 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.51 | 0.00 |
time (sec) |
N/A | 0.634 | 0.568 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.166 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | B | N/A | N/A | N/A | F(-1) | N/A | N/A | N/A |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 304 | 28 | 276 | 36 | 0 | 30 | 944 | 30 |
N.S. |
1 | 1.00 | 10.86 | 1.00 | 9.86 | 1.29 | 0.00 | 1.07 | 33.71 | 1.07 |
time (sec) |
N/A | 0.202 | 0.594 | 0.148 | 0.165 | 0.085 | 0.000 | 0.687 | 0.160 | 25.976 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | B | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 185 | 204 | 1395 | 0 | 0 | 765 | 0 | 0 | 161 | 0 |
N.S. |
1 | 1.10 | 7.54 | 0.00 | 0.00 | 4.14 | 0.00 | 0.00 | 0.87 | 0.00 |
time (sec) |
N/A | 0.849 | 0.771 | 0.000 | 0.000 | 0.089 | 0.000 | 0.000 | 0.176 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | B | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 150 | 169 | 741 | 0 | 0 | 406 | 0 | 0 | 125 | 0 |
N.S. |
1 | 1.13 | 4.94 | 0.00 | 0.00 | 2.71 | 0.00 | 0.00 | 0.83 | 0.00 |
time (sec) |
N/A | 0.707 | 0.380 | 0.000 | 0.000 | 0.104 | 0.000 | 0.000 | 0.156 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | A | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 114 | 133 | 277 | 0 | 0 | 173 | 0 | 0 | 87 | 0 |
N.S. |
1 | 1.17 | 2.43 | 0.00 | 0.00 | 1.52 | 0.00 | 0.00 | 0.76 | 0.00 |
time (sec) |
N/A | 0.549 | 0.223 | 0.000 | 0.000 | 0.091 | 0.000 | 0.000 | 0.156 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 30 | 28 | 30 | 30 | 0 | 30 | 30 | 30 |
N.S. |
1 | 1.00 | 1.07 | 1.00 | 1.07 | 1.07 | 0.00 | 1.07 | 1.07 | 1.07 |
time (sec) |
N/A | 0.203 | 0.429 | 0.049 | 0.199 | 0.070 | 0.000 | 0.131 | 0.155 | 25.673 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 30 | 28 | 110 | 47 | 0 | 30 | 224 | 30 |
N.S. |
1 | 1.00 | 1.07 | 1.00 | 3.93 | 1.68 | 0.00 | 1.07 | 8.00 | 1.07 |
time (sec) |
N/A | 0.217 | 8.735 | 0.050 | 0.156 | 0.079 | 0.000 | 0.149 | 0.170 | 25.367 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | B | N/A | N/A | N/A | F(-1) | N/A | N/A | N/A |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 292 | 26 | 151 | 32 | 0 | 28 | 163 | 28 |
N.S. |
1 | 1.00 | 11.23 | 1.00 | 5.81 | 1.23 | 0.00 | 1.08 | 6.27 | 1.08 |
time (sec) |
N/A | 0.203 | 0.298 | 0.053 | 0.190 | 0.095 | 0.000 | 0.177 | 0.171 | 25.664 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | B | N/A | N/A | N/A | F(-1) | N/A | N/A | N/A |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 292 | 24 | 143 | 28 | 0 | 26 | 157 | 26 |
N.S. |
1 | 1.00 | 12.17 | 1.00 | 5.96 | 1.17 | 0.00 | 1.08 | 6.54 | 1.08 |
time (sec) |
N/A | 0.197 | 0.271 | 0.053 | 0.168 | 0.078 | 0.000 | 0.172 | 0.174 | 25.897 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | B | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 165 | 23 | 129 | 25 | 22 | 25 | 136 | 25 |
N.S. |
1 | 1.00 | 7.17 | 1.00 | 5.61 | 1.09 | 0.96 | 1.09 | 5.91 | 1.09 |
time (sec) |
N/A | 0.192 | 0.432 | 0.052 | 0.171 | 0.077 | 75.260 | 0.155 | 0.174 | 25.997 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | A | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 114 | 133 | 277 | 0 | 0 | 173 | 0 | 0 | 87 | 0 |
N.S. |
1 | 1.17 | 2.43 | 0.00 | 0.00 | 1.52 | 0.00 | 0.00 | 0.76 | 0.00 |
time (sec) |
N/A | 0.660 | 0.255 | 0.000 | 0.000 | 0.080 | 0.000 | 0.000 | 0.161 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | B | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 282 | 26 | 123 | 28 | 26 | 28 | 162 | 28 |
N.S. |
1 | 1.00 | 10.85 | 1.00 | 4.73 | 1.08 | 1.00 | 1.08 | 6.23 | 1.08 |
time (sec) |
N/A | 0.197 | 0.220 | 0.053 | 0.183 | 0.076 | 93.238 | 0.146 | 0.176 | 26.093 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | B | N/A | N/A | N/A | F(-1) | N/A | N/A | N/A |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 292 | 26 | 138 | 28 | 0 | 28 | 169 | 28 |
N.S. |
1 | 1.00 | 11.23 | 1.00 | 5.31 | 1.08 | 0.00 | 1.08 | 6.50 | 1.08 |
time (sec) |
N/A | 0.196 | 0.237 | 0.053 | 0.179 | 0.079 | 0.000 | 0.154 | 0.159 | 26.261 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 433 | 424 | 410 | 0 | 0 | 368 | 0 | 0 | 303 | 0 |
N.S. |
1 | 0.98 | 0.95 | 0.00 | 0.00 | 0.85 | 0.00 | 0.00 | 0.70 | 0.00 |
time (sec) |
N/A | 0.864 | 0.706 | 0.000 | 0.000 | 0.133 | 0.000 | 0.000 | 0.165 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 363 | 356 | 352 | 0 | 0 | 301 | 0 | 0 | 247 | 0 |
N.S. |
1 | 0.98 | 0.97 | 0.00 | 0.00 | 0.83 | 0.00 | 0.00 | 0.68 | 0.00 |
time (sec) |
N/A | 0.695 | 0.699 | 0.000 | 0.000 | 0.092 | 0.000 | 0.000 | 0.166 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 255 | 246 | 268 | 0 | 0 | 196 | 0 | 0 | 176 | 0 |
N.S. |
1 | 0.96 | 1.05 | 0.00 | 0.00 | 0.77 | 0.00 | 0.00 | 0.69 | 0.00 |
time (sec) |
N/A | 0.530 | 0.505 | 0.000 | 0.000 | 0.091 | 0.000 | 0.000 | 0.167 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 304 | 298 | 162 | 0 | 0 | 239 | 0 | 0 | 192 | 0 |
N.S. |
1 | 0.98 | 0.53 | 0.00 | 0.00 | 0.79 | 0.00 | 0.00 | 0.63 | 0.00 |
time (sec) |
N/A | 0.584 | 0.626 | 0.000 | 0.000 | 0.088 | 0.000 | 0.000 | 0.167 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 414 | 405 | 302 | 0 | 0 | 338 | 0 | 0 | 249 | 0 |
N.S. |
1 | 0.98 | 0.73 | 0.00 | 0.00 | 0.82 | 0.00 | 0.00 | 0.60 | 0.00 |
time (sec) |
N/A | 0.764 | 0.688 | 0.000 | 0.000 | 0.103 | 0.000 | 0.000 | 0.178 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 484 | 473 | 358 | 0 | 0 | 403 | 0 | 0 | 281 | 0 |
N.S. |
1 | 0.98 | 0.74 | 0.00 | 0.00 | 0.83 | 0.00 | 0.00 | 0.58 | 0.00 |
time (sec) |
N/A | 0.911 | 0.750 | 0.000 | 0.000 | 0.094 | 0.000 | 0.000 | 0.165 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 84 | 87 | 71 | 136 | 104 | 134 | 128 | 150 | 84 | 82 |
N.S. |
1 | 1.04 | 0.85 | 1.62 | 1.24 | 1.60 | 1.52 | 1.79 | 1.00 | 0.98 |
time (sec) |
N/A | 0.290 | 0.097 | 4.796 | 0.037 | 0.071 | 1.855 | 0.122 | 0.161 | 25.456 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 84 | 87 | 68 | 132 | 102 | 128 | 126 | 150 | 83 | 82 |
N.S. |
1 | 1.04 | 0.81 | 1.57 | 1.21 | 1.52 | 1.50 | 1.79 | 0.99 | 0.98 |
time (sec) |
N/A | 0.278 | 0.077 | 1.964 | 0.037 | 0.071 | 0.828 | 0.121 | 0.155 | 25.440 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 75 | 58 | 114 | 82 | 110 | 97 | 111 | 77 | 66 |
N.S. |
1 | 0.97 | 0.75 | 1.48 | 1.06 | 1.43 | 1.26 | 1.44 | 1.00 | 0.86 |
time (sec) |
N/A | 0.251 | 0.059 | 0.868 | 0.036 | 0.074 | 0.380 | 0.120 | 0.159 | 25.437 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 57 | 57 | 72 | 103 | 73 | 62 | 0 | 79 | 65 | 73 |
N.S. |
1 | 1.00 | 1.26 | 1.81 | 1.28 | 1.09 | 0.00 | 1.39 | 1.14 | 1.28 |
time (sec) |
N/A | 0.277 | 0.095 | 1.004 | 0.034 | 0.072 | 0.000 | 0.112 | 0.167 | 25.724 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 72 | 72 | 57 | 104 | 94 | 91 | 99 | 100 | 83 | 75 |
N.S. |
1 | 1.00 | 0.79 | 1.44 | 1.31 | 1.26 | 1.38 | 1.39 | 1.15 | 1.04 |
time (sec) |
N/A | 0.287 | 0.103 | 0.893 | 0.039 | 0.075 | 0.387 | 0.113 | 0.156 | 25.730 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 83 | 86 | 64 | 107 | 93 | 95 | 128 | 102 | 84 | 83 |
N.S. |
1 | 1.04 | 0.77 | 1.29 | 1.12 | 1.14 | 1.54 | 1.23 | 1.01 | 1.00 |
time (sec) |
N/A | 0.293 | 0.094 | 0.874 | 0.037 | 0.070 | 0.937 | 0.114 | 0.156 | 25.784 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 83 | 86 | 69 | 85 | 99 | 105 | 129 | 112 | 84 | 83 |
N.S. |
1 | 1.04 | 0.83 | 1.02 | 1.19 | 1.27 | 1.55 | 1.35 | 1.01 | 1.00 |
time (sec) |
N/A | 0.294 | 0.099 | 0.898 | 0.041 | 0.097 | 1.878 | 0.120 | 0.155 | 25.512 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 207 | 196 | 157 | 319 | 250 | 388 | 340 | 480 | 225 | 189 |
N.S. |
1 | 0.95 | 0.76 | 1.54 | 1.21 | 1.87 | 1.64 | 2.32 | 1.09 | 0.91 |
time (sec) |
N/A | 0.491 | 0.169 | 28.770 | 0.047 | 0.071 | 4.019 | 0.119 | 0.175 | 25.658 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 206 | 193 | 154 | 319 | 247 | 386 | 318 | 471 | 225 | 187 |
N.S. |
1 | 0.94 | 0.75 | 1.55 | 1.20 | 1.87 | 1.54 | 2.29 | 1.09 | 0.91 |
time (sec) |
N/A | 0.443 | 0.144 | 12.546 | 0.046 | 0.077 | 1.851 | 0.124 | 0.164 | 25.827 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 147 | 141 | 141 | 281 | 213 | 345 | 279 | 399 | 218 | 165 |
N.S. |
1 | 0.96 | 0.96 | 1.91 | 1.45 | 2.35 | 1.90 | 2.71 | 1.48 | 1.12 |
time (sec) |
N/A | 0.339 | 0.125 | 5.064 | 0.047 | 0.071 | 0.879 | 0.111 | 0.161 | 25.656 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | F | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 57 | 57 | 129 | 170 | 163 | 170 | 0 | 211 | 116 | 124 |
N.S. |
1 | 1.00 | 2.26 | 2.98 | 2.86 | 2.98 | 0.00 | 3.70 | 2.04 | 2.18 |
time (sec) |
N/A | 0.321 | 0.165 | 5.595 | 0.036 | 0.108 | 0.000 | 0.114 | 0.157 | 25.294 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 181 | 173 | 138 | 262 | 221 | 311 | 280 | 345 | 224 | 181 |
N.S. |
1 | 0.96 | 0.76 | 1.45 | 1.22 | 1.72 | 1.55 | 1.91 | 1.24 | 1.00 |
time (sec) |
N/A | 0.505 | 0.173 | 5.109 | 0.045 | 0.075 | 0.835 | 0.118 | 0.169 | 25.522 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 204 | 193 | 151 | 268 | 224 | 326 | 320 | 355 | 225 | 186 |
N.S. |
1 | 0.95 | 0.74 | 1.31 | 1.10 | 1.60 | 1.57 | 1.74 | 1.10 | 0.91 |
time (sec) |
N/A | 0.498 | 0.194 | 5.182 | 0.046 | 0.079 | 0.910 | 0.134 | 0.202 | 25.523 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 205 | 194 | 155 | 268 | 230 | 329 | 342 | 352 | 225 | 190 |
N.S. |
1 | 0.95 | 0.76 | 1.31 | 1.12 | 1.60 | 1.67 | 1.72 | 1.10 | 0.93 |
time (sec) |
N/A | 0.513 | 0.198 | 5.026 | 0.045 | 0.084 | 1.860 | 0.119 | 0.173 | 25.661 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | A | F | A | F | F(-1) |
verified |
N/A | No | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 141 | 150 | 93 | 2350 | 0 | 92 | 0 | 219 | 47 | 0 |
N.S. |
1 | 1.06 | 0.66 | 16.67 | 0.00 | 0.65 | 0.00 | 1.55 | 0.33 | 0.00 |
time (sec) |
N/A | 0.639 | 0.225 | 2.704 | 0.000 | 0.069 | 0.000 | 0.130 | 0.159 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | A | F | A | F | F(-1) |
verified |
N/A | No | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 141 | 150 | 93 | 2350 | 0 | 92 | 0 | 219 | 43 | 0 |
N.S. |
1 | 1.06 | 0.66 | 16.67 | 0.00 | 0.65 | 0.00 | 1.55 | 0.30 | 0.00 |
time (sec) |
N/A | 0.613 | 0.206 | 1.480 | 0.000 | 0.077 | 0.000 | 0.131 | 0.168 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | A | F | A | F | F(-1) |
verified |
N/A | No | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 130 | 139 | 86 | 2329 | 0 | 84 | 0 | 192 | 40 | 0 |
N.S. |
1 | 1.07 | 0.66 | 17.92 | 0.00 | 0.65 | 0.00 | 1.48 | 0.31 | 0.00 |
time (sec) |
N/A | 0.586 | 0.147 | 1.046 | 0.000 | 0.091 | 0.000 | 0.132 | 0.159 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 71 | 74 | 58 | 1239 | 118 | 51 | 0 | 80 | 49 | 0 |
N.S. |
1 | 1.04 | 0.82 | 17.45 | 1.66 | 0.72 | 0.00 | 1.13 | 0.69 | 0.00 |
time (sec) |
N/A | 0.370 | 0.174 | 0.962 | 0.040 | 0.071 | 0.000 | 0.117 | 0.156 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | A | F | F | F | F(-1) |
verified |
N/A | No | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 133 | 141 | 87 | 2296 | 0 | 81 | 0 | 0 | 54 | 0 |
N.S. |
1 | 1.06 | 0.65 | 17.26 | 0.00 | 0.61 | 0.00 | 0.00 | 0.41 | 0.00 |
time (sec) |
N/A | 0.645 | 0.149 | 2.639 | 0.000 | 0.072 | 0.000 | 0.000 | 0.176 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | A | F | F | F | F(-1) |
verified |
N/A | No | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 141 | 150 | 94 | 2341 | 0 | 88 | 0 | 0 | 54 | 0 |
N.S. |
1 | 1.06 | 0.67 | 16.60 | 0.00 | 0.62 | 0.00 | 0.00 | 0.38 | 0.00 |
time (sec) |
N/A | 0.655 | 0.152 | 5.829 | 0.000 | 0.077 | 0.000 | 0.000 | 0.165 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 89 | 135 | 87 | 370 | 0 | 154 | 0 | 712 | 878 | 0 |
N.S. |
1 | 1.52 | 0.98 | 4.16 | 0.00 | 1.73 | 0.00 | 8.00 | 9.87 | 0.00 |
time (sec) |
N/A | 0.373 | 0.173 | 0.874 | 0.000 | 0.070 | 0.000 | 0.137 | 0.157 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | A | A | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 30 | 28 | 117 | 32 | 16 | 32 | 17 | 24 | 0 |
N.S. |
1 | 1.03 | 0.97 | 4.03 | 1.10 | 0.55 | 1.10 | 0.59 | 0.83 | 0.00 |
time (sec) |
N/A | 0.254 | 0.067 | 0.164 | 0.028 | 0.068 | 3.742 | 0.112 | 0.159 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F(-2) | F | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 355 | 293 | 179 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.83 | 0.50 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.117 | 0.884 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.202 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F(-2) | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 298 | 244 | 156 | 0 | 0 | 0 | 0 | 0 | 570 | 0 |
N.S. |
1 | 0.82 | 0.52 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.91 | 0.00 |
time (sec) |
N/A | 0.918 | 0.447 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.178 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F(-2) | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 298 | 244 | 156 | 0 | 0 | 0 | 0 | 0 | 556 | 0 |
N.S. |
1 | 0.82 | 0.52 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.87 | 0.00 |
time (sec) |
N/A | 0.951 | 0.464 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.186 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F(-2) | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 271 | 226 | 146 | 0 | 0 | 131 | 0 | 0 | 512 | 0 |
N.S. |
1 | 0.83 | 0.54 | 0.00 | 0.00 | 0.48 | 0.00 | 0.00 | 1.89 | 0.00 |
time (sec) |
N/A | 0.878 | 0.398 | 0.000 | 0.000 | 0.080 | 0.000 | 0.000 | 0.172 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 71 | 71 | 71 | 323 | 95 | 222 | 0 | 244 | 164 | 0 |
N.S. |
1 | 1.00 | 1.00 | 4.55 | 1.34 | 3.13 | 0.00 | 3.44 | 2.31 | 0.00 |
time (sec) |
N/A | 0.374 | 0.165 | 17.405 | 0.034 | 0.081 | 0.000 | 0.120 | 0.162 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F(-2) | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 260 | 216 | 141 | 0 | 0 | 0 | 0 | 0 | 626 | 0 |
N.S. |
1 | 0.83 | 0.54 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 2.41 | 0.00 |
time (sec) |
N/A | 0.885 | 0.414 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.176 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F(-2) | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 295 | 243 | 154 | 0 | 0 | 0 | 0 | 0 | 660 | 0 |
N.S. |
1 | 0.82 | 0.52 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 2.24 | 0.00 |
time (sec) |
N/A | 0.921 | 0.431 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.177 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F(-2) | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 295 | 243 | 154 | 0 | 0 | 0 | 0 | 0 | 660 | 0 |
N.S. |
1 | 0.82 | 0.52 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 2.24 | 0.00 |
time (sec) |
N/A | 0.925 | 0.446 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.184 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | A | A | B | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 246 | 241 | 248 | 6894 | 0 | 221 | 435 | 5306 | 34 | 0 |
N.S. |
1 | 0.98 | 1.01 | 28.02 | 0.00 | 0.90 | 1.77 | 21.57 | 0.14 | 0.00 |
time (sec) |
N/A | 0.540 | 0.229 | 7.069 | 0.000 | 0.242 | 52.723 | 0.263 | 0.177 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | A | A | B | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 245 | 242 | 248 | 5619 | 0 | 308 | 445 | 11159 | 34 | 0 |
N.S. |
1 | 0.99 | 1.01 | 22.93 | 0.00 | 1.26 | 1.82 | 45.55 | 0.14 | 0.00 |
time (sec) |
N/A | 0.513 | 0.232 | 5.961 | 0.000 | 0.245 | 47.914 | 0.526 | 0.181 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 182 | 179 | 165 | 1490 | 0 | 0 | 221 | 0 | 216 | 0 |
N.S. |
1 | 0.98 | 0.91 | 8.19 | 0.00 | 0.00 | 1.21 | 0.00 | 1.19 | 0.00 |
time (sec) |
N/A | 0.427 | 0.205 | 66.759 | 0.000 | 0.000 | 44.265 | 0.000 | 0.152 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 182 | 179 | 178 | 1633 | 0 | 0 | 231 | 0 | 216 | 0 |
N.S. |
1 | 0.98 | 0.98 | 8.97 | 0.00 | 0.00 | 1.27 | 0.00 | 1.19 | 0.00 |
time (sec) |
N/A | 0.403 | 0.176 | 63.136 | 0.000 | 0.000 | 39.585 | 0.000 | 0.161 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | A | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 244 | 241 | 240 | 4121 | 0 | 307 | 0 | 0 | 34 | 0 |
N.S. |
1 | 0.99 | 0.98 | 16.89 | 0.00 | 1.26 | 0.00 | 0.00 | 0.14 | 0.00 |
time (sec) |
N/A | 0.527 | 0.205 | 4.688 | 0.000 | 0.184 | 0.000 | 0.000 | 0.167 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | A | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 312 | 308 | 145 | 4757 | 0 | 275 | 0 | 0 | 34 | 0 |
N.S. |
1 | 0.99 | 0.46 | 15.25 | 0.00 | 0.88 | 0.00 | 0.00 | 0.11 | 0.00 |
time (sec) |
N/A | 0.518 | 0.298 | 6.557 | 0.000 | 0.194 | 0.000 | 0.000 | 0.261 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | C | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 180 | 177 | 167 | 726 | 354 | 0 | 0 | 0 | 243 | 0 |
N.S. |
1 | 0.98 | 0.93 | 4.03 | 1.97 | 0.00 | 0.00 | 0.00 | 1.35 | 0.00 |
time (sec) |
N/A | 0.424 | 0.210 | 58.352 | 0.079 | 0.000 | 0.000 | 0.000 | 0.157 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 180 | 177 | 178 | 715 | 319 | 0 | 0 | 0 | 243 | 0 |
N.S. |
1 | 0.98 | 0.99 | 3.97 | 1.77 | 0.00 | 0.00 | 0.00 | 1.35 | 0.00 |
time (sec) |
N/A | 0.424 | 0.189 | 61.007 | 0.077 | 0.000 | 0.000 | 0.000 | 0.165 | 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 | 482 | 471 | 456 | 0 | 0 | 0 | 0 | 0 | 38 | 0 |
N.S. |
1 | 0.98 | 0.95 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 1.105 | 1.293 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.195 | 0.000 |