Detailed conclusion table per each integral is given by the table below. The elapsed time is in seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2) if the failure was due to an exception being raised, which could indicate a bug in the system. If the failure was due to integral not being evaluated within the time limit, then it is given as F.
In this table, the column N.S. means normalized size and is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To make the table fit the page, the name Mathematica was abbreviated to MMA
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | B | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 165 | 165 | 139 | 793 | 0 | 767 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.84 | 4.81 | 0.00 | 4.65 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.464 | 1.497 | 5.016 | 0.000 | 3.056 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 89 | 87 | 107 | 303 | 0 | 410 | 0 | 0 | 0 |
N.S. |
1 | 0.98 | 1.20 | 3.40 | 0.00 | 4.61 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.300 | 1.562 | 8.109 | 0.000 | 0.621 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 56 | 59 | 56 | 256 | 0 | 328 | 0 | 0 | 0 |
N.S. |
1 | 1.05 | 1.00 | 4.57 | 0.00 | 5.86 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.276 | 0.604 | 4.970 | 0.000 | 0.371 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 33 | 33 | 33 | 42 | 0 | 261 | 0 | 0 | 27 |
N.S. |
1 | 1.00 | 1.00 | 1.27 | 0.00 | 7.91 | 0.00 | 0.00 | 0.82 |
time (sec) |
N/A | 0.228 | 0.143 | 0.225 | 0.000 | 0.323 | 0.000 | 0.000 | 20.533 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 70 | 72 | 294 | 343 | 0 | 1015 | 0 | 0 | 0 |
N.S. |
1 | 1.03 | 4.20 | 4.90 | 0.00 | 14.50 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.281 | 2.798 | 1.458 | 0.000 | 0.437 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | F | B | F | B | F | F | F(-1) |
verified |
N/A | Yes | N/A | No | TBD | TBD | TBD | TBD | TBD |
size | 116 | 128 | 0 | 1944 | 0 | 1550 | 0 | 0 | 0 |
N.S. |
1 | 1.10 | 0.00 | 16.76 | 0.00 | 13.36 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.327 | 0.000 | 1.378 | 0.000 | 0.618 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | F | B | F | B | F | F | F(-1) |
verified |
N/A | Yes | N/A | No | TBD | TBD | TBD | TBD | TBD |
size | 166 | 194 | 0 | 3596 | 0 | 2257 | 0 | 0 | 0 |
N.S. |
1 | 1.17 | 0.00 | 21.66 | 0.00 | 13.60 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.384 | 0.000 | 1.546 | 0.000 | 1.378 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 173 | 181 | 230 | 1930 | 0 | 1673 | 0 | 0 | 0 |
N.S. |
1 | 1.05 | 1.33 | 11.16 | 0.00 | 9.67 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.462 | 3.645 | 17.678 | 0.000 | 1.390 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 120 | 122 | 196 | 1334 | 0 | 1507 | 0 | 0 | 0 |
N.S. |
1 | 1.02 | 1.63 | 11.12 | 0.00 | 12.56 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.363 | 2.542 | 12.662 | 0.000 | 0.665 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 80 | 78 | 296 | 344 | 0 | 1259 | 0 | 0 | 0 |
N.S. |
1 | 0.98 | 3.70 | 4.30 | 0.00 | 15.74 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.331 | 2.479 | 8.970 | 0.000 | 0.503 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 39 | 39 | 87 | 138 | 992 | 408 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 2.23 | 3.54 | 25.44 | 10.46 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.195 | 0.117 | 3.317 | 0.415 | 0.372 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 74 | 72 | 127 | 507 | 0 | 525 | 0 | 0 | 0 |
N.S. |
1 | 0.97 | 1.72 | 6.85 | 0.00 | 7.09 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.333 | 0.252 | 4.121 | 0.000 | 0.442 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 119 | 126 | 168 | 891 | 0 | 723 | 0 | 0 | 0 |
N.S. |
1 | 1.06 | 1.41 | 7.49 | 0.00 | 6.08 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.393 | 1.494 | 5.279 | 0.000 | 0.677 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 172 | 187 | 199 | 1279 | 0 | 987 | 0 | 0 | 0 |
N.S. |
1 | 1.09 | 1.16 | 7.44 | 0.00 | 5.74 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.455 | 3.337 | 6.782 | 0.000 | 1.910 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 88 | 88 | 121 | 562 | 0 | 458 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.38 | 6.39 | 0.00 | 5.20 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.317 | 5.465 | 5.375 | 0.000 | 0.828 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 63 | 65 | 62 | 2293 | 2532 | 417 | 0 | 0 | 0 |
N.S. |
1 | 1.03 | 0.98 | 36.40 | 40.19 | 6.62 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.286 | 0.829 | 1.587 | 0.629 | 0.385 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | B | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 57 | 59 | 382 | 62 | 0 | 392 | 75 | 0 | 49 |
N.S. |
1 | 1.04 | 6.70 | 1.09 | 0.00 | 6.88 | 1.32 | 0.00 | 0.86 |
time (sec) |
N/A | 0.248 | 6.657 | 0.155 | 0.000 | 0.370 | 5.886 | 0.000 | 21.308 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | F | B | F | B | F | F | F(-1) |
verified |
N/A | Yes | N/A | No | TBD | TBD | TBD | TBD | TBD |
size | 100 | 113 | 0 | 9462 | 0 | 1569 | 0 | 0 | 0 |
N.S. |
1 | 1.13 | 0.00 | 94.62 | 0.00 | 15.69 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.326 | 0.000 | 1.806 | 0.000 | 0.610 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | F | B | F(-1) | B | F | F | F(-1) |
verified |
N/A | Yes | N/A | No | TBD | TBD | TBD | TBD | TBD |
size | 153 | 173 | 0 | 13610 | 0 | 2347 | 0 | 0 | 0 |
N.S. |
1 | 1.13 | 0.00 | 88.95 | 0.00 | 15.34 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.385 | 0.000 | 1.157 | 0.000 | 1.485 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | F | B | F(-1) | B | F | F | F(-1) |
verified |
N/A | Yes | N/A | No | TBD | TBD | TBD | TBD | TBD |
size | 213 | 247 | 0 | 17868 | 0 | 3501 | 0 | 0 | 0 |
N.S. |
1 | 1.16 | 0.00 | 83.89 | 0.00 | 16.44 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.449 | 0.000 | 2.335 | 0.000 | 4.800 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-1) | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 172 | 178 | 247 | 2792 | 0 | 1895 | 0 | 0 | 0 |
N.S. |
1 | 1.03 | 1.44 | 16.23 | 0.00 | 11.02 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.474 | 9.405 | 13.013 | 0.000 | 1.765 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 116 | 121 | 201 | 1186 | 0 | 1655 | 0 | 0 | 0 |
N.S. |
1 | 1.04 | 1.73 | 10.22 | 0.00 | 14.27 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.371 | 4.615 | 10.586 | 0.000 | 0.715 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 71 | 69 | 169 | 282 | 2005 | 548 | 0 | 0 | 0 |
N.S. |
1 | 0.97 | 2.38 | 3.97 | 28.24 | 7.72 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.338 | 2.612 | 4.092 | 0.497 | 0.434 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 77 | 75 | 168 | 515 | 2055 | 601 | 0 | 0 | 0 |
N.S. |
1 | 0.97 | 2.18 | 6.69 | 26.69 | 7.81 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.221 | 1.452 | 4.431 | 0.540 | 0.432 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 119 | 124 | 182 | 1228 | 0 | 741 | 0 | 0 | 0 |
N.S. |
1 | 1.04 | 1.53 | 10.32 | 0.00 | 6.23 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.395 | 4.462 | 5.738 | 0.000 | 0.731 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-1) | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 174 | 184 | 224 | 1779 | 0 | 1061 | 0 | 0 | 0 |
N.S. |
1 | 1.06 | 1.29 | 10.22 | 0.00 | 6.10 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.458 | 4.241 | 6.691 | 0.000 | 2.113 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-1) | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 241 | 254 | 237 | 2449 | 0 | 1517 | 0 | 0 | 0 |
N.S. |
1 | 1.05 | 0.98 | 10.16 | 0.00 | 6.29 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.543 | 6.093 | 8.818 | 0.000 | 7.207 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F(-1) | B | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
size | 97 | 96 | 187 | 6373 | 0 | 564 | 0 | 0 | 0 |
N.S. |
1 | 0.99 | 1.93 | 65.70 | 0.00 | 5.81 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.323 | 8.911 | 2.938 | 0.000 | 0.973 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F(-1) | B | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
size | 89 | 93 | 613 | 6313 | 0 | 522 | 0 | 0 | 0 |
N.S. |
1 | 1.04 | 6.89 | 70.93 | 0.00 | 5.87 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.298 | 10.448 | 2.750 | 0.000 | 0.838 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | B | A | F | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
size | 83 | 87 | 613 | 86 | 0 | 494 | 100 | 0 | 68 |
N.S. |
1 | 1.05 | 7.39 | 1.04 | 0.00 | 5.95 | 1.20 | 0.00 | 0.82 |
time (sec) |
N/A | 0.260 | 7.123 | 0.165 | 0.000 | 0.714 | 9.786 | 0.000 | 24.035 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | F | B | F | B | F | F | F(-1) |
verified |
N/A | Yes | N/A | No | TBD | TBD | TBD | TBD | TBD |
size | 137 | 161 | 0 | 43855 | 0 | 2279 | 0 | 0 | 0 |
N.S. |
1 | 1.18 | 0.00 | 320.11 | 0.00 | 16.64 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.369 | 0.000 | 4.924 | 0.000 | 1.483 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | F | B | F(-1) | B | F | F | F(-1) |
verified |
N/A | Yes | N/A | No | TBD | TBD | TBD | TBD | TBD |
size | 200 | 227 | 0 | 73511 | 0 | 3507 | 0 | 0 | 0 |
N.S. |
1 | 1.14 | 0.00 | 367.56 | 0.00 | 17.54 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.438 | 0.000 | 8.714 | 0.000 | 4.923 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | F | B | F(-1) | B | F | F | F(-1) |
verified |
N/A | Yes | N/A | No | TBD | TBD | TBD | TBD | TBD |
size | 268 | 311 | 0 | 77709 | 0 | 4751 | 0 | 0 | 0 |
N.S. |
1 | 1.16 | 0.00 | 289.96 | 0.00 | 17.73 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.524 | 0.000 | 10.432 | 0.000 | 18.704 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 157 | 178 | 316 | 1500 | 0 | 2035 | 0 | 0 | 0 |
N.S. |
1 | 1.13 | 2.01 | 9.55 | 0.00 | 12.96 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.468 | 11.147 | 9.863 | 0.000 | 2.147 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | F(-1) | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 120 | 122 | 409 | 657 | 0 | 661 | 0 | 0 | 0 |
N.S. |
1 | 1.02 | 3.41 | 5.48 | 0.00 | 5.51 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.377 | 6.554 | 4.586 | 0.000 | 0.952 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | F(-1) | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 119 | 120 | 410 | 1003 | 0 | 773 | 0 | 0 | 0 |
N.S. |
1 | 1.01 | 3.45 | 8.43 | 0.00 | 6.50 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.378 | 4.692 | 5.600 | 0.000 | 0.825 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F(-1) | B | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
size | 125 | 135 | 1927 | 1263 | 0 | 881 | 0 | 0 | 0 |
N.S. |
1 | 1.08 | 15.42 | 10.10 | 0.00 | 7.05 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.271 | 6.484 | 6.398 | 0.000 | 0.733 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 174 | 187 | 247 | 1862 | 0 | 1097 | 0 | 0 | 0 |
N.S. |
1 | 1.07 | 1.42 | 10.70 | 0.00 | 6.30 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.481 | 7.765 | 7.589 | 0.000 | 2.145 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-1) | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 236 | 253 | 234 | 2612 | 0 | 1579 | 0 | 0 | 0 |
N.S. |
1 | 1.07 | 0.99 | 11.07 | 0.00 | 6.69 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.564 | 11.188 | 9.646 | 0.000 | 7.358 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-1) | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 315 | 337 | 272 | 3418 | 0 | 2059 | 0 | 0 | 0 |
N.S. |
1 | 1.07 | 0.86 | 10.85 | 0.00 | 6.54 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.662 | 16.993 | 11.213 | 0.000 | 24.643 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
size | 105 | 105 | 259 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 2.47 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.330 | 5.254 | 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(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 122 | 113 | 94 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.93 | 0.77 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.309 | 0.903 | 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 | 86 | 83 | 61 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.97 | 0.71 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.260 | 0.204 | 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 | 54 | 54 | 54 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.227 | 0.060 | 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 | 114 | 110 | 115 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.96 | 1.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.286 | 1.903 | 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(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 157 | 163 | 139 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.04 | 0.89 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.318 | 3.958 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
size | 88 | 88 | 2777 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 31.56 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.308 | 18.567 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
size | 88 | 88 | 2465 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 28.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.305 | 17.515 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
size | 83 | 83 | 2137 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 25.75 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.220 | 6.254 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
size | 84 | 84 | 2469 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 29.39 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.298 | 17.480 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
size | 88 | 88 | 3033 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 34.47 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.305 | 18.978 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 92 | 77 | 87 | 70 | 73 | 81 | 119 | 340 | 227 |
N.S. |
1 | 0.84 | 0.95 | 0.76 | 0.79 | 0.88 | 1.29 | 3.70 | 2.47 |
time (sec) |
N/A | 0.292 | 0.584 | 3.185 | 0.181 | 0.266 | 0.794 | 1.627 | 24.339 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 61 | 55 | 59 | 49 | 51 | 59 | 82 | 271 | 167 |
N.S. |
1 | 0.90 | 0.97 | 0.80 | 0.84 | 0.97 | 1.34 | 4.44 | 2.74 |
time (sec) |
N/A | 0.267 | 0.327 | 1.561 | 0.199 | 0.257 | 0.380 | 0.694 | 24.518 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 28 | 30 | 26 | 28 | 37 | 42 | 181 | 83 |
N.S. |
1 | 0.93 | 1.00 | 0.87 | 0.93 | 1.23 | 1.40 | 6.03 | 2.77 |
time (sec) |
N/A | 0.213 | 0.015 | 0.722 | 0.190 | 0.261 | 0.174 | 0.352 | 20.762 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 54 | 51 | 69 | 42 | 45 | 61 | 0 | 87 | 72 |
N.S. |
1 | 0.94 | 1.28 | 0.78 | 0.83 | 1.13 | 0.00 | 1.61 | 1.33 |
time (sec) |
N/A | 0.279 | 0.017 | 0.636 | 0.188 | 0.249 | 0.000 | 0.284 | 20.052 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 72 | 63 | 114 | 63 | 62 | 99 | 0 | 172 | 86 |
N.S. |
1 | 0.88 | 1.58 | 0.88 | 0.86 | 1.38 | 0.00 | 2.39 | 1.19 |
time (sec) |
N/A | 0.263 | 1.176 | 1.473 | 0.183 | 0.253 | 0.000 | 0.298 | 20.234 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | A | C | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 219 | 209 | 251 | 233 | 218 | 4427 | 0 | 0 | 7402 |
N.S. |
1 | 0.95 | 1.15 | 1.06 | 1.00 | 20.21 | 0.00 | 0.00 | 33.80 |
time (sec) |
N/A | 0.500 | 0.892 | 4.023 | 0.282 | 0.995 | 0.000 | 0.000 | 22.955 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | A | C | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 166 | 156 | 242 | 113 | 159 | 1052 | 0 | 0 | 1620 |
N.S. |
1 | 0.94 | 1.46 | 0.68 | 0.96 | 6.34 | 0.00 | 0.00 | 9.76 |
time (sec) |
N/A | 0.413 | 0.644 | 4.378 | 0.275 | 0.893 | 0.000 | 0.000 | 24.316 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 23 | 35 | 21 | 21 | 139 | 0 | 114 |
N.S. |
1 | 1.00 | 1.00 | 1.52 | 0.91 | 0.91 | 6.04 | 0.00 | 4.96 |
time (sec) |
N/A | 0.208 | 0.020 | 1.704 | 0.197 | 0.258 | 18.047 | 0.000 | 20.761 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | A | C | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 295 | 281 | 215 | 288 | 306 | 6482 | 0 | 0 | 11182 |
N.S. |
1 | 0.95 | 0.73 | 0.98 | 1.04 | 21.97 | 0.00 | 0.00 | 37.91 |
time (sec) |
N/A | 0.674 | 0.690 | 3.434 | 0.298 | 1.063 | 0.000 | 0.000 | 23.775 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | C | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 393 | 375 | 336 | 374 | 488 | 10746 | 0 | 0 | 58699 |
N.S. |
1 | 0.95 | 0.85 | 0.95 | 1.24 | 27.34 | 0.00 | 0.00 | 149.36 |
time (sec) |
N/A | 0.805 | 2.653 | 8.548 | 0.277 | 2.208 | 0.000 | 0.000 | 35.830 |
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 | 27 | 27 | 29 | 27 | 29 | 29 | 26 | 29 | 31 |
N.S. |
1 | 1.00 | 1.07 | 1.00 | 1.07 | 1.07 | 0.96 | 1.07 | 1.15 |
time (sec) |
N/A | 0.234 | 5.725 | 0.832 | 5.460 | 0.257 | 104.479 | 0.827 | 21.065 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
size | 226 | 221 | 245 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.98 | 1.08 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.736 | 13.762 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
size | 143 | 141 | 162 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.99 | 1.13 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.554 | 6.427 | 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 | 59 | 59 | 59 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.254 | 0.114 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 25 | 23 | 25 | 25 | 22 | 25 | 27 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 1.09 | 1.09 | 0.96 | 1.09 | 1.17 |
time (sec) |
N/A | 0.218 | 4.534 | 0.602 | 3.783 | 0.260 | 12.664 | 0.795 | 20.712 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 27 | 25 | 27 | 27 | 0 | 27 | 29 |
N.S. |
1 | 1.00 | 1.08 | 1.00 | 1.08 | 1.08 | 0.00 | 1.08 | 1.16 |
time (sec) |
N/A | 0.225 | 31.508 | 0.622 | 9.322 | 0.257 | 0.000 | 1.040 | 21.969 |
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 | 25 | 25 | 27 | 25 | 27 | 27 | 24 | 27 | 29 |
N.S. |
1 | 1.00 | 1.08 | 1.00 | 1.08 | 1.08 | 0.96 | 1.08 | 1.16 |
time (sec) |
N/A | 0.228 | 3.319 | 0.459 | 5.858 | 0.258 | 19.172 | 1.015 | 21.034 |
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 | 20 |
N.S. |
1 | 1.00 | 1.12 | 1.00 | 1.12 | 1.12 | 0.94 | 1.12 | 1.25 |
time (sec) |
N/A | 0.185 | 1.738 | 0.479 | 3.951 | 0.258 | 1.725 | 0.520 | 20.775 |
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 | 25 | 25 | 27 | 25 | 27 | 27 | 24 | 27 | 29 |
N.S. |
1 | 1.00 | 1.08 | 1.00 | 1.08 | 1.08 | 0.96 | 1.08 | 1.16 |
time (sec) |
N/A | 0.229 | 2.788 | 0.602 | 6.345 | 0.263 | 73.546 | 0.975 | 21.323 |