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 | C | A | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 437 | 461 | 382 | 2901 | 0 | 0 | 0 | 0 | 429 | 0 |
N.S. |
1 | 1.05 | 0.87 | 6.64 | 0.00 | 0.00 | 0.00 | 0.00 | 0.98 | 0.00 |
time (sec) |
N/A | 2.827 | 1.854 | 0.793 | 0.000 | 0.000 | 0.000 | 0.000 | 0.282 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 324 | 330 | 356 | 635 | 0 | 0 | 0 | 0 | 381 | 0 |
N.S. |
1 | 1.02 | 1.10 | 1.96 | 0.00 | 0.00 | 0.00 | 0.00 | 1.18 | 0.00 |
time (sec) |
N/A | 3.805 | 3.635 | 0.608 | 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 | C | A | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 344 | 249 | 264 | 2657 | 0 | 0 | 0 | 0 | 364 | 0 |
N.S. |
1 | 0.72 | 0.77 | 7.72 | 0.00 | 0.00 | 0.00 | 0.00 | 1.06 | 0.00 |
time (sec) |
N/A | 1.403 | 1.777 | 0.701 | 0.000 | 0.000 | 0.000 | 0.000 | 0.246 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 286 | 189 | 388 | 582 | 0 | 0 | 0 | 0 | 362 | 0 |
N.S. |
1 | 0.66 | 1.36 | 2.03 | 0.00 | 0.00 | 0.00 | 0.00 | 1.27 | 0.00 |
time (sec) |
N/A | 0.946 | 2.377 | 0.622 | 0.000 | 0.000 | 0.000 | 0.000 | 0.244 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 319 | 278 | 289 | 2435 | 0 | 0 | 0 | 0 | 361 | 0 |
N.S. |
1 | 0.87 | 0.91 | 7.63 | 0.00 | 0.00 | 0.00 | 0.00 | 1.13 | 0.00 |
time (sec) |
N/A | 2.201 | 0.935 | 0.593 | 0.000 | 0.000 | 0.000 | 0.000 | 0.236 | 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 | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 585 | 448 | 818 | 0 | 0 | 0 | 0 | 0 | 460 | 0 |
N.S. |
1 | 0.77 | 1.40 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.79 | 0.00 |
time (sec) |
N/A | 5.322 | 9.391 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.244 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | B | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 464 | 469 | 457 | 2857 | 0 | 0 | 0 | 0 | 392 | 0 |
N.S. |
1 | 1.01 | 0.98 | 6.16 | 0.00 | 0.00 | 0.00 | 0.00 | 0.84 | 0.00 |
time (sec) |
N/A | 4.878 | 2.757 | 0.821 | 0.000 | 0.000 | 0.000 | 0.000 | 0.247 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 243 | 295 | 116 | 488 | 0 | 0 | 0 | 0 | 25 | 0 |
N.S. |
1 | 1.21 | 0.48 | 2.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.10 | 0.00 |
time (sec) |
N/A | 1.149 | 0.344 | 0.392 | 0.000 | 0.000 | 0.000 | 0.000 | 0.223 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | C | A | F | F(-2) | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 198 | 215 | 123 | 343 | 105 | 150 | 0 | 0 | 25 | 0 |
N.S. |
1 | 1.09 | 0.62 | 1.73 | 0.53 | 0.76 | 0.00 | 0.00 | 0.13 | 0.00 |
time (sec) |
N/A | 1.255 | 0.112 | 0.463 | 0.120 | 0.113 | 0.000 | 0.000 | 0.211 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 151 | 140 | 87 | 239 | 0 | 0 | 0 | 0 | 25 | 0 |
N.S. |
1 | 0.93 | 0.58 | 1.58 | 0.00 | 0.00 | 0.00 | 0.00 | 0.17 | 0.00 |
time (sec) |
N/A | 0.560 | 0.162 | 0.308 | 0.000 | 0.000 | 0.000 | 0.000 | 0.227 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 74 | 80 | 54 | 82 | 50 | 114 | 0 | 80 | 23 | 0 |
N.S. |
1 | 1.08 | 0.73 | 1.11 | 0.68 | 1.54 | 0.00 | 1.08 | 0.31 | 0.00 |
time (sec) |
N/A | 0.315 | 0.076 | 0.371 | 0.038 | 0.103 | 0.000 | 0.142 | 0.202 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 32 | 45 | 51 | 0 | 0 | 0 | 0 | 22 | 0 |
N.S. |
1 | 1.00 | 1.41 | 1.59 | 0.00 | 0.00 | 0.00 | 0.00 | 0.69 | 0.00 |
time (sec) |
N/A | 0.220 | 0.018 | 0.191 | 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 | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 183 | 106 | 151 | 0 | 0 | 0 | 0 | 0 | 25 | 0 |
N.S. |
1 | 0.58 | 0.83 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.14 | 0.00 |
time (sec) |
N/A | 0.545 | 0.171 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.196 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 124 | 103 | 111 | 241 | 0 | 0 | 0 | 0 | 25 | 0 |
N.S. |
1 | 0.83 | 0.90 | 1.94 | 0.00 | 0.00 | 0.00 | 0.00 | 0.20 | 0.00 |
time (sec) |
N/A | 0.786 | 0.368 | 0.451 | 0.000 | 0.000 | 0.000 | 0.000 | 0.201 | 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 | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 297 | 194 | 233 | 0 | 0 | 0 | 0 | 0 | 25 | 0 |
N.S. |
1 | 0.65 | 0.78 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 1.823 | 0.758 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.214 | 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) | F(-2) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 31 | 33 | 29 | 31 | 136 | 0 | 0 | 267 | 31 |
N.S. |
1 | 1.00 | 1.06 | 0.94 | 1.00 | 4.39 | 0.00 | 0.00 | 8.61 | 1.00 |
time (sec) |
N/A | 5.431 | 2.125 | 1.860 | 0.254 | 0.107 | 0.000 | 0.000 | 0.642 | 3.557 |
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) | F(-2) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 31 | 33 | 29 | 31 | 87 | 0 | 0 | 174 | 31 |
N.S. |
1 | 1.00 | 1.06 | 0.94 | 1.00 | 2.81 | 0.00 | 0.00 | 5.61 | 1.00 |
time (sec) |
N/A | 2.976 | 1.073 | 1.292 | 0.179 | 0.103 | 0.000 | 0.000 | 0.464 | 3.637 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 31 | 33 | 29 | 31 | 43 | 32 | 0 | 80 | 31 |
N.S. |
1 | 1.00 | 1.06 | 0.94 | 1.00 | 1.39 | 1.03 | 0.00 | 2.58 | 1.00 |
time (sec) |
N/A | 1.030 | 0.746 | 1.273 | 0.174 | 0.102 | 56.704 | 0.000 | 0.285 | 3.593 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | 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 | TBD |
size | 31 | 31 | 33 | 29 | 31 | 58 | 32 | 31 | 88 | 31 |
N.S. |
1 | 1.00 | 1.06 | 0.94 | 1.00 | 1.87 | 1.03 | 1.00 | 2.84 | 1.00 |
time (sec) |
N/A | 0.334 | 3.685 | 0.428 | 0.178 | 0.093 | 17.264 | 0.189 | 0.221 | 3.610 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | 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 | TBD |
size | 31 | 31 | 33 | 29 | 31 | 70 | 32 | 31 | 156 | 31 |
N.S. |
1 | 1.00 | 1.06 | 0.94 | 1.00 | 2.26 | 1.03 | 1.00 | 5.03 | 1.00 |
time (sec) |
N/A | 0.351 | 4.405 | 0.618 | 0.238 | 0.088 | 21.933 | 0.208 | 0.229 | 3.778 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | 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 | TBD |
size | 26 | 26 | 28 | 24 | 26 | 38 | 27 | 26 | 29 | 26 |
N.S. |
1 | 1.00 | 1.08 | 0.92 | 1.00 | 1.46 | 1.04 | 1.00 | 1.12 | 1.00 |
time (sec) |
N/A | 0.277 | 0.720 | 0.411 | 0.166 | 0.087 | 9.583 | 0.184 | 0.199 | 3.545 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 315 | 345 | 136 | 520 | 0 | 0 | 0 | 0 | 25 | 0 |
N.S. |
1 | 1.10 | 0.43 | 1.65 | 0.00 | 0.00 | 0.00 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 4.448 | 0.509 | 0.444 | 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 | A | A | A | C | A | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 243 | 259 | 140 | 375 | 131 | 205 | 0 | 0 | 25 | 0 |
N.S. |
1 | 1.07 | 0.58 | 1.54 | 0.54 | 0.84 | 0.00 | 0.00 | 0.10 | 0.00 |
time (sec) |
N/A | 2.057 | 0.118 | 0.516 | 0.124 | 0.095 | 0.000 | 0.000 | 0.186 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 188 | 158 | 98 | 255 | 0 | 0 | 0 | 0 | 25 | 0 |
N.S. |
1 | 0.84 | 0.52 | 1.36 | 0.00 | 0.00 | 0.00 | 0.00 | 0.13 | 0.00 |
time (sec) |
N/A | 1.131 | 0.198 | 0.368 | 0.000 | 0.000 | 0.000 | 0.000 | 0.185 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 105 | 95 | 101 | 111 | 65 | 159 | 0 | 104 | 23 | 0 |
N.S. |
1 | 0.90 | 0.96 | 1.06 | 0.62 | 1.51 | 0.00 | 0.99 | 0.22 | 0.00 |
time (sec) |
N/A | 0.788 | 0.079 | 0.440 | 0.041 | 0.092 | 0.000 | 0.187 | 0.194 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 32 | 45 | 51 | 0 | 0 | 0 | 0 | 22 | 0 |
N.S. |
1 | 1.00 | 1.41 | 1.59 | 0.00 | 0.00 | 0.00 | 0.00 | 0.69 | 0.00 |
time (sec) |
N/A | 0.372 | 0.018 | 0.254 | 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 | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 265 | 154 | 488 | 0 | 0 | 0 | 0 | 0 | 25 | 0 |
N.S. |
1 | 0.58 | 1.84 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 1.104 | 0.471 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.190 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 167 | 125 | 137 | 313 | 0 | 0 | 0 | 0 | 25 | 0 |
N.S. |
1 | 0.75 | 0.82 | 1.87 | 0.00 | 0.00 | 0.00 | 0.00 | 0.15 | 0.00 |
time (sec) |
N/A | 0.908 | 0.403 | 0.528 | 0.000 | 0.000 | 0.000 | 0.000 | 0.227 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 461 | 273 | 1051 | 0 | 0 | 0 | 0 | 0 | 25 | 0 |
N.S. |
1 | 0.59 | 2.28 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 2.546 | 3.951 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.214 | 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 | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 30 | 32 | 28 | 30 | 68 | 31 | 30 | 117 | 30 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 1.00 | 2.27 | 1.03 | 1.00 | 3.90 | 1.00 |
time (sec) |
N/A | 0.316 | 3.219 | 0.414 | 0.197 | 0.092 | 58.782 | 0.194 | 0.265 | 3.719 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 339 | 190 | 188 | 297 | 0 | 0 | 0 | 0 | 27 | 0 |
N.S. |
1 | 0.56 | 0.55 | 0.88 | 0.00 | 0.00 | 0.00 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 0.676 | 0.372 | 0.287 | 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 | A | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 297 | 173 | 171 | 254 | 0 | 0 | 0 | 0 | 27 | 0 |
N.S. |
1 | 0.58 | 0.58 | 0.86 | 0.00 | 0.00 | 0.00 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 0.883 | 0.331 | 0.648 | 0.000 | 0.000 | 0.000 | 0.000 | 0.206 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 139 | 90 | 103 | 165 | 0 | 0 | 0 | 0 | 27 | 0 |
N.S. |
1 | 0.65 | 0.74 | 1.19 | 0.00 | 0.00 | 0.00 | 0.00 | 0.19 | 0.00 |
time (sec) |
N/A | 0.827 | 0.287 | 0.195 | 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 | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 197 | 123 | 127 | 0 | 0 | 0 | 0 | 0 | 25 | 0 |
N.S. |
1 | 0.62 | 0.64 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.13 | 0.00 |
time (sec) |
N/A | 0.773 | 0.292 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.215 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 139 | 90 | 105 | 165 | 0 | 0 | 0 | 0 | 24 | 0 |
N.S. |
1 | 0.65 | 0.76 | 1.19 | 0.00 | 0.00 | 0.00 | 0.00 | 0.17 | 0.00 |
time (sec) |
N/A | 0.559 | 0.298 | 0.241 | 0.000 | 0.000 | 0.000 | 0.000 | 0.224 | 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 | N/A | F(-2) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 30 | 26 | 28 | 28 | 26 | 0 | 27 | 28 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 1.00 | 1.00 | 0.93 | 0.00 | 0.96 | 1.00 |
time (sec) |
N/A | 0.690 | 1.412 | 0.311 | 0.110 | 0.082 | 0.908 | 0.000 | 0.213 | 3.314 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | 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 | TBD |
size | 28 | 28 | 30 | 26 | 28 | 32 | 27 | 28 | 31 | 28 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 1.00 | 1.14 | 0.96 | 1.00 | 1.11 | 1.00 |
time (sec) |
N/A | 0.529 | 1.707 | 0.313 | 0.110 | 0.091 | 1.405 | 0.145 | 0.245 | 3.242 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 397 | 224 | 215 | 318 | 0 | 0 | 0 | 0 | 60 | 0 |
N.S. |
1 | 0.56 | 0.54 | 0.80 | 0.00 | 0.00 | 0.00 | 0.00 | 0.15 | 0.00 |
time (sec) |
N/A | 0.749 | 0.656 | 0.305 | 0.000 | 0.000 | 0.000 | 0.000 | 0.284 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 339 | 191 | 188 | 297 | 0 | 0 | 0 | 0 | 60 | 0 |
N.S. |
1 | 0.56 | 0.55 | 0.88 | 0.00 | 0.00 | 0.00 | 0.00 | 0.18 | 0.00 |
time (sec) |
N/A | 0.667 | 0.598 | 0.224 | 0.000 | 0.000 | 0.000 | 0.000 | 0.290 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 297 | 174 | 172 | 252 | 0 | 0 | 0 | 0 | 58 | 0 |
N.S. |
1 | 0.59 | 0.58 | 0.85 | 0.00 | 0.00 | 0.00 | 0.00 | 0.20 | 0.00 |
time (sec) |
N/A | 0.574 | 0.570 | 0.543 | 0.000 | 0.000 | 0.000 | 0.000 | 0.248 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 239 | 141 | 147 | 231 | 0 | 0 | 0 | 0 | 57 | 0 |
N.S. |
1 | 0.59 | 0.62 | 0.97 | 0.00 | 0.00 | 0.00 | 0.00 | 0.24 | 0.00 |
time (sec) |
N/A | 0.469 | 0.474 | 0.231 | 0.000 | 0.000 | 0.000 | 0.000 | 0.255 | 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 | N/A | F(-2) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 30 | 26 | 28 | 28 | 26 | 0 | 58 | 28 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 1.00 | 1.00 | 0.93 | 0.00 | 2.07 | 1.00 |
time (sec) |
N/A | 1.300 | 1.382 | 0.221 | 0.112 | 0.087 | 7.768 | 0.000 | 0.248 | 3.239 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | 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 | TBD |
size | 28 | 28 | 30 | 26 | 28 | 32 | 27 | 28 | 61 | 28 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 1.00 | 1.14 | 0.96 | 1.00 | 2.18 | 1.00 |
time (sec) |
N/A | 1.251 | 2.279 | 0.285 | 0.118 | 0.084 | 9.627 | 0.147 | 0.276 | 3.418 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 397 | 223 | 216 | 318 | 0 | 0 | 0 | 0 | 91 | 0 |
N.S. |
1 | 0.56 | 0.54 | 0.80 | 0.00 | 0.00 | 0.00 | 0.00 | 0.23 | 0.00 |
time (sec) |
N/A | 1.013 | 0.943 | 0.312 | 0.000 | 0.000 | 0.000 | 0.000 | 0.274 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 439 | 240 | 233 | 363 | 0 | 0 | 0 | 0 | 91 | 0 |
N.S. |
1 | 0.55 | 0.53 | 0.83 | 0.00 | 0.00 | 0.00 | 0.00 | 0.21 | 0.00 |
time (sec) |
N/A | 0.714 | 0.952 | 0.256 | 0.000 | 0.000 | 0.000 | 0.000 | 0.307 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 397 | 223 | 216 | 318 | 0 | 0 | 0 | 0 | 89 | 0 |
N.S. |
1 | 0.56 | 0.54 | 0.80 | 0.00 | 0.00 | 0.00 | 0.00 | 0.22 | 0.00 |
time (sec) |
N/A | 0.661 | 0.900 | 0.341 | 0.000 | 0.000 | 0.000 | 0.000 | 0.269 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 339 | 190 | 191 | 297 | 0 | 0 | 0 | 0 | 88 | 0 |
N.S. |
1 | 0.56 | 0.56 | 0.88 | 0.00 | 0.00 | 0.00 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 0.552 | 0.704 | 0.256 | 0.000 | 0.000 | 0.000 | 0.000 | 0.281 | 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) | F(-2) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 30 | 26 | 28 | 45 | 0 | 0 | 89 | 28 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 1.00 | 1.61 | 0.00 | 0.00 | 3.18 | 1.00 |
time (sec) |
N/A | 1.357 | 1.394 | 0.256 | 0.136 | 0.082 | 0.000 | 0.000 | 0.269 | 3.615 |
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 | 26 | 28 | 49 | 0 | 28 | 92 | 28 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 1.00 | 1.75 | 0.00 | 1.00 | 3.29 | 1.00 |
time (sec) |
N/A | 1.621 | 2.077 | 0.265 | 0.140 | 0.090 | 0.000 | 0.154 | 0.304 | 3.721 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 98 | 55 | 69 | 87 | 0 | 0 | 0 | 0 | 25 | 0 |
N.S. |
1 | 0.56 | 0.70 | 0.89 | 0.00 | 0.00 | 0.00 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 0.679 | 0.097 | 0.246 | 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 | A | A | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 65 | 44 | 60 | 78 | 0 | 0 | 0 | 0 | 25 | 0 |
N.S. |
1 | 0.68 | 0.92 | 1.20 | 0.00 | 0.00 | 0.00 | 0.00 | 0.38 | 0.00 |
time (sec) |
N/A | 0.564 | 0.080 | 0.329 | 0.000 | 0.000 | 0.000 | 0.000 | 0.200 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 65 | 44 | 60 | 67 | 0 | 0 | 0 | 0 | 25 | 0 |
N.S. |
1 | 0.68 | 0.92 | 1.03 | 0.00 | 0.00 | 0.00 | 0.00 | 0.38 | 0.00 |
time (sec) |
N/A | 0.486 | 0.089 | 0.178 | 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 | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 50 | 0 | 0 | 0 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.00 | 1.79 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.82 | 0.00 |
time (sec) |
N/A | 0.338 | 0.075 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.191 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 28 | 47 | 48 | 0 | 55 | 0 | 0 | 22 | 0 |
N.S. |
1 | 0.97 | 1.62 | 1.66 | 0.00 | 1.90 | 0.00 | 0.00 | 0.76 | 0.00 |
time (sec) |
N/A | 0.213 | 0.054 | 0.234 | 0.000 | 0.086 | 0.000 | 0.000 | 0.181 | 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 | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 26 | 22 | 24 | 35 | 24 | 24 | 25 | 24 |
N.S. |
1 | 1.00 | 1.08 | 0.92 | 1.00 | 1.46 | 1.00 | 1.00 | 1.04 | 1.00 |
time (sec) |
N/A | 0.263 | 0.589 | 0.414 | 0.108 | 0.093 | 1.112 | 0.138 | 0.189 | 3.223 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | 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 | TBD |
size | 24 | 24 | 26 | 22 | 24 | 37 | 26 | 24 | 25 | 24 |
N.S. |
1 | 1.00 | 1.08 | 0.92 | 1.00 | 1.54 | 1.08 | 1.00 | 1.04 | 1.00 |
time (sec) |
N/A | 0.318 | 0.766 | 0.309 | 0.105 | 0.082 | 3.701 | 0.133 | 0.194 | 3.170 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 197 | 123 | 130 | 182 | 0 | 0 | 0 | 0 | 39 | 0 |
N.S. |
1 | 0.62 | 0.66 | 0.92 | 0.00 | 0.00 | 0.00 | 0.00 | 0.20 | 0.00 |
time (sec) |
N/A | 0.558 | 0.437 | 0.351 | 0.000 | 0.000 | 0.000 | 0.000 | 0.197 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 139 | 90 | 99 | 161 | 0 | 0 | 0 | 0 | 39 | 0 |
N.S. |
1 | 0.65 | 0.71 | 1.16 | 0.00 | 0.00 | 0.00 | 0.00 | 0.28 | 0.00 |
time (sec) |
N/A | 0.484 | 0.369 | 0.217 | 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 | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 92 | 68 | 81 | 0 | 0 | 0 | 0 | 0 | 50 | 0 |
N.S. |
1 | 0.74 | 0.88 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.54 | 0.00 |
time (sec) |
N/A | 0.511 | 0.262 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.206 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 35 | 54 | 55 | 0 | 65 | 0 | 0 | 49 | 0 |
N.S. |
1 | 0.97 | 1.50 | 1.53 | 0.00 | 1.81 | 0.00 | 0.00 | 1.36 | 0.00 |
time (sec) |
N/A | 0.235 | 0.134 | 0.238 | 0.000 | 0.091 | 0.000 | 0.000 | 0.194 | 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 | N/A | F(-2) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 30 | 26 | 28 | 49 | 27 | 0 | 37 | 28 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 1.00 | 1.75 | 0.96 | 0.00 | 1.32 | 1.00 |
time (sec) |
N/A | 0.303 | 1.511 | 0.290 | 0.109 | 0.083 | 1.737 | 0.000 | 0.198 | 3.236 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | 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 | TBD |
size | 28 | 28 | 30 | 26 | 28 | 53 | 29 | 28 | 41 | 28 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 1.00 | 1.89 | 1.04 | 1.00 | 1.46 | 1.00 |
time (sec) |
N/A | 0.305 | 2.230 | 0.329 | 0.112 | 0.090 | 3.080 | 0.139 | 0.212 | 3.121 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | 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 | TBD |
size | 28 | 28 | 30 | 26 | 28 | 63 | 27 | 28 | 277 | 28 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 1.00 | 2.25 | 0.96 | 1.00 | 9.89 | 1.00 |
time (sec) |
N/A | 0.359 | 4.489 | 0.300 | 0.140 | 0.100 | 7.171 | 0.166 | 0.258 | 3.196 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 28 | 24 | 26 | 61 | 26 | 0 | 83 | 26 |
N.S. |
1 | 1.00 | 1.08 | 0.92 | 1.00 | 2.35 | 1.00 | 0.00 | 3.19 | 1.00 |
time (sec) |
N/A | 0.343 | 6.379 | 0.289 | 0.131 | 0.092 | 6.749 | 0.000 | 0.218 | 3.156 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | 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 | TBD |
size | 25 | 25 | 27 | 23 | 25 | 60 | 26 | 25 | 81 | 25 |
N.S. |
1 | 1.00 | 1.08 | 0.92 | 1.00 | 2.40 | 1.04 | 1.00 | 3.24 | 1.00 |
time (sec) |
N/A | 0.290 | 0.172 | 0.270 | 0.125 | 0.092 | 5.980 | 0.163 | 0.207 | 3.095 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 30 | 26 | 28 | 64 | 27 | 0 | 83 | 28 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 1.00 | 2.29 | 0.96 | 0.00 | 2.96 | 1.00 |
time (sec) |
N/A | 0.439 | 8.076 | 0.393 | 0.141 | 0.095 | 17.872 | 0.000 | 0.213 | 3.188 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | 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 | TBD |
size | 28 | 28 | 30 | 26 | 28 | 68 | 29 | 28 | 87 | 28 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 1.00 | 2.43 | 1.04 | 1.00 | 3.11 | 1.00 |
time (sec) |
N/A | 0.480 | 9.583 | 0.366 | 0.148 | 0.095 | 38.702 | 0.167 | 0.243 | 3.165 |
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) | F(-2) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 30 | 26 | 28 | 38 | 0 | 0 | 63 | 28 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 1.00 | 1.36 | 0.00 | 0.00 | 2.25 | 1.00 |
time (sec) |
N/A | 0.509 | 1.340 | 0.549 | 0.109 | 0.084 | 0.000 | 0.000 | 0.293 | 3.116 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 30 | 26 | 28 | 28 | 27 | 0 | 27 | 28 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 1.00 | 1.00 | 0.96 | 0.00 | 0.96 | 1.00 |
time (sec) |
N/A | 0.471 | 0.256 | 0.599 | 0.106 | 0.096 | 2.254 | 0.000 | 0.238 | 3.032 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | 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 | TBD |
size | 28 | 28 | 30 | 26 | 28 | 50 | 27 | 28 | 39 | 28 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 1.00 | 1.79 | 0.96 | 1.00 | 1.39 | 1.00 |
time (sec) |
N/A | 0.315 | 0.923 | 0.325 | 0.112 | 0.104 | 2.415 | 0.152 | 0.197 | 3.629 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | 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 | TBD |
size | 28 | 28 | 30 | 26 | 28 | 63 | 27 | 28 | 85 | 28 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 1.00 | 2.25 | 0.96 | 1.00 | 3.04 | 1.00 |
time (sec) |
N/A | 0.332 | 1.358 | 0.510 | 0.139 | 0.089 | 65.616 | 0.174 | 0.616 | 3.722 |
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 | 26 | 28 | 86 | 0 | 28 | 125 | 28 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 1.00 | 3.07 | 0.00 | 1.00 | 4.46 | 1.00 |
time (sec) |
N/A | 0.306 | 1.728 | 0.540 | 0.144 | 0.111 | 0.000 | 0.184 | 0.230 | 3.740 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 350 | 352 | 322 | 555 | 0 | 0 | 0 | 0 | 41 | 0 |
N.S. |
1 | 1.01 | 0.92 | 1.59 | 0.00 | 0.00 | 0.00 | 0.00 | 0.12 | 0.00 |
time (sec) |
N/A | 1.040 | 0.533 | 0.823 | 0.000 | 0.000 | 0.000 | 0.000 | 0.210 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 154 | 262 | 130 | 279 | 0 | 0 | 0 | 0 | 41 | 0 |
N.S. |
1 | 1.70 | 0.84 | 1.81 | 0.00 | 0.00 | 0.00 | 0.00 | 0.27 | 0.00 |
time (sec) |
N/A | 1.294 | 0.413 | 0.229 | 0.000 | 0.000 | 0.000 | 0.000 | 0.214 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 248 | 252 | 217 | 0 | 0 | 0 | 0 | 0 | 39 | 0 |
N.S. |
1 | 1.02 | 0.88 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.16 | 0.00 |
time (sec) |
N/A | 1.652 | 0.360 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.200 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 146 | 131 | 121 | 269 | 0 | 0 | 0 | 0 | 38 | 0 |
N.S. |
1 | 0.90 | 0.83 | 1.84 | 0.00 | 0.00 | 0.00 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 1.274 | 0.203 | 0.275 | 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 | N/A | N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 30 | 26 | 442 | 43 | 27 | 0 | 42 | 28 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 15.79 | 1.54 | 0.96 | 0.00 | 1.50 | 1.00 |
time (sec) |
N/A | 1.109 | 9.142 | 0.405 | 0.531 | 0.114 | 2.295 | 0.000 | 0.202 | 3.248 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | 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 | TBD |
size | 28 | 28 | 30 | 26 | 427 | 49 | 29 | 28 | 48 | 28 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 15.25 | 1.75 | 1.04 | 1.00 | 1.71 | 1.00 |
time (sec) |
N/A | 0.467 | 3.553 | 0.346 | 0.402 | 0.104 | 5.927 | 0.150 | 0.231 | 3.196 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 354 | 310 | 338 | 599 | 0 | 0 | 0 | 0 | 88 | 0 |
N.S. |
1 | 0.88 | 0.95 | 1.69 | 0.00 | 0.00 | 0.00 | 0.00 | 0.25 | 0.00 |
time (sec) |
N/A | 1.332 | 0.808 | 0.303 | 0.000 | 0.000 | 0.000 | 0.000 | 0.298 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 348 | 360 | 327 | 583 | 0 | 0 | 0 | 0 | 86 | 0 |
N.S. |
1 | 1.03 | 0.94 | 1.68 | 0.00 | 0.00 | 0.00 | 0.00 | 0.25 | 0.00 |
time (sec) |
N/A | 2.156 | 0.715 | 0.626 | 0.000 | 0.000 | 0.000 | 0.000 | 0.232 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 246 | 179 | 232 | 445 | 0 | 0 | 0 | 0 | 85 | 0 |
N.S. |
1 | 0.73 | 0.94 | 1.81 | 0.00 | 0.00 | 0.00 | 0.00 | 0.35 | 0.00 |
time (sec) |
N/A | 1.281 | 0.458 | 0.257 | 0.000 | 0.000 | 0.000 | 0.000 | 0.264 | 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 | N/A | F(-2) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 30 | 26 | 476 | 43 | 27 | 0 | 87 | 28 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 17.00 | 1.54 | 0.96 | 0.00 | 3.11 | 1.00 |
time (sec) |
N/A | 2.196 | 18.224 | 0.303 | 0.700 | 0.102 | 16.435 | 0.000 | 0.222 | 3.181 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | 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 | TBD |
size | 28 | 28 | 30 | 26 | 484 | 49 | 29 | 28 | 92 | 28 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 17.29 | 1.75 | 1.04 | 1.00 | 3.29 | 1.00 |
time (sec) |
N/A | 0.898 | 20.084 | 0.515 | 0.728 | 0.090 | 56.981 | 0.153 | 0.261 | 3.131 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 454 | 460 | 446 | 773 | 0 | 0 | 0 | 0 | 133 | 0 |
N.S. |
1 | 1.01 | 0.98 | 1.70 | 0.00 | 0.00 | 0.00 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 1.785 | 1.309 | 0.349 | 0.000 | 0.000 | 0.000 | 0.000 | 0.342 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 448 | 464 | 436 | 759 | 0 | 0 | 0 | 0 | 131 | 0 |
N.S. |
1 | 1.04 | 0.97 | 1.69 | 0.00 | 0.00 | 0.00 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 3.810 | 1.071 | 0.497 | 0.000 | 0.000 | 0.000 | 0.000 | 0.264 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 351 | 229 | 343 | 623 | 0 | 0 | 0 | 0 | 130 | 0 |
N.S. |
1 | 0.65 | 0.98 | 1.77 | 0.00 | 0.00 | 0.00 | 0.00 | 0.37 | 0.00 |
time (sec) |
N/A | 0.942 | 0.756 | 0.312 | 0.000 | 0.000 | 0.000 | 0.000 | 0.306 | 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) | F(-2) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 30 | 26 | 524 | 60 | 0 | 0 | 132 | 28 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 18.71 | 2.14 | 0.00 | 0.00 | 4.71 | 1.00 |
time (sec) |
N/A | 2.570 | 16.198 | 0.383 | 0.903 | 0.089 | 0.000 | 0.000 | 0.262 | 3.253 |
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 | 26 | 534 | 66 | 0 | 28 | 137 | 28 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 19.07 | 2.36 | 0.00 | 1.00 | 4.89 | 1.00 |
time (sec) |
N/A | 1.208 | 22.182 | 0.360 | 0.900 | 0.106 | 0.000 | 0.161 | 0.308 | 3.226 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 337 | 215 | 190 | 519 | 0 | 0 | 0 | 0 | 64 | 0 |
N.S. |
1 | 0.64 | 0.56 | 1.54 | 0.00 | 0.00 | 0.00 | 0.00 | 0.19 | 0.00 |
time (sec) |
N/A | 0.950 | 0.488 | 0.464 | 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 | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 236 | 169 | 149 | 387 | 0 | 0 | 0 | 0 | 64 | 0 |
N.S. |
1 | 0.72 | 0.63 | 1.64 | 0.00 | 0.00 | 0.00 | 0.00 | 0.27 | 0.00 |
time (sec) |
N/A | 1.140 | 0.365 | 0.253 | 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 | A | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 237 | 165 | 144 | 375 | 0 | 0 | 0 | 0 | 64 | 0 |
N.S. |
1 | 0.70 | 0.61 | 1.58 | 0.00 | 0.00 | 0.00 | 0.00 | 0.27 | 0.00 |
time (sec) |
N/A | 0.818 | 0.313 | 0.411 | 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 | C | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 136 | 121 | 117 | 243 | 0 | 0 | 0 | 0 | 64 | 0 |
N.S. |
1 | 0.89 | 0.86 | 1.79 | 0.00 | 0.00 | 0.00 | 0.00 | 0.47 | 0.00 |
time (sec) |
N/A | 0.887 | 0.270 | 0.238 | 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 | C | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 130 | 115 | 107 | 0 | 0 | 0 | 0 | 0 | 62 | 0 |
N.S. |
1 | 0.88 | 0.82 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.48 | 0.00 |
time (sec) |
N/A | 0.675 | 0.214 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.188 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 37 | 50 | 57 | 0 | 75 | 0 | 0 | 60 | 59 |
N.S. |
1 | 1.03 | 1.39 | 1.58 | 0.00 | 2.08 | 0.00 | 0.00 | 1.67 | 1.64 |
time (sec) |
N/A | 0.250 | 0.026 | 0.106 | 0.000 | 0.085 | 0.000 | 0.000 | 0.201 | 3.229 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 30 | 26 | 481 | 80 | 29 | 0 | 63 | 28 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 17.18 | 2.86 | 1.04 | 0.00 | 2.25 | 1.00 |
time (sec) |
N/A | 0.465 | 3.954 | 0.306 | 0.592 | 0.090 | 5.964 | 0.000 | 0.215 | 3.355 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | 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 | TBD |
size | 28 | 28 | 30 | 26 | 491 | 86 | 31 | 28 | 69 | 28 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 17.54 | 3.07 | 1.11 | 1.00 | 2.46 | 1.00 |
time (sec) |
N/A | 0.508 | 1.307 | 0.292 | 0.593 | 0.079 | 17.837 | 0.158 | 0.207 | 3.372 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | 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 | TBD |
size | 28 | 28 | 30 | 26 | 503 | 106 | 29 | 28 | 141 | 28 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 17.96 | 3.79 | 1.04 | 1.00 | 5.04 | 1.00 |
time (sec) |
N/A | 0.927 | 5.121 | 0.304 | 0.720 | 0.086 | 56.438 | 0.183 | 0.251 | 3.415 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 28 | 24 | 511 | 104 | 27 | 0 | 139 | 26 |
N.S. |
1 | 1.00 | 1.08 | 0.92 | 19.65 | 4.00 | 1.04 | 0.00 | 5.35 | 1.00 |
time (sec) |
N/A | 0.313 | 20.221 | 0.280 | 0.731 | 0.099 | 50.437 | 0.000 | 0.248 | 3.408 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | 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 | TBD |
size | 25 | 25 | 27 | 23 | 502 | 103 | 27 | 25 | 137 | 25 |
N.S. |
1 | 1.00 | 1.08 | 0.92 | 20.08 | 4.12 | 1.08 | 1.00 | 5.48 | 1.00 |
time (sec) |
N/A | 0.720 | 3.605 | 0.270 | 0.673 | 0.092 | 40.247 | 0.180 | 0.239 | 3.579 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 30 | 26 | 530 | 108 | 29 | 0 | 140 | 28 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 18.93 | 3.86 | 1.04 | 0.00 | 5.00 | 1.00 |
time (sec) |
N/A | 0.316 | 18.778 | 0.437 | 0.975 | 0.092 | 108.196 | 0.000 | 0.233 | 3.834 |