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 | C | F | F(-2) | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 296 | 351 | 491 | 0 | 0 | 0 | 0 | 0 | 108 | 0 |
N.S. |
1 | 1.19 | 1.66 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.36 | 0.00 |
time (sec) |
N/A | 0.656 | 1.029 | 0.000 | 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 | A | F | F(-2) | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 193 | 248 | 185 | 0 | 0 | 0 | 0 | 0 | 78 | 0 |
N.S. |
1 | 1.28 | 0.96 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.40 | 0.00 |
time (sec) |
N/A | 0.497 | 0.203 | 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 | C | A | C | F(-2) | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 104 | 96 | 107 | 263 | 0 | 0 | 0 | 0 | 48 | 0 |
N.S. |
1 | 0.92 | 1.03 | 2.53 | 0.00 | 0.00 | 0.00 | 0.00 | 0.46 | 0.00 |
time (sec) |
N/A | 0.319 | 0.022 | 0.569 | 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 | A | A | F(-2) | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 24 | 16 | 0 | 67 | 53 | 15 | 23 | 16 |
N.S. |
1 | 1.00 | 1.00 | 0.67 | 0.00 | 2.79 | 2.21 | 0.62 | 0.96 | 0.67 |
time (sec) |
N/A | 0.145 | 0.007 | 0.447 | 0.000 | 0.068 | 0.067 | 0.117 | 0.159 | 0.075 |
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 | 22 | 22 | 24 | 22 | 24 | 31 | 19 | 24 | 35 | 24 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 1.09 | 1.41 | 0.86 | 1.09 | 1.59 | 1.09 |
time (sec) |
N/A | 0.197 | 1.199 | 0.267 | 0.063 | 0.070 | 4.757 | 0.129 | 0.164 | 25.520 |
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 | 22 | 22 | 24 | 22 | 172 | 61 | 20 | 24 | 72 | 24 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 7.82 | 2.77 | 0.91 | 1.09 | 3.27 | 1.09 |
time (sec) |
N/A | 0.186 | 9.171 | 0.017 | 0.070 | 0.071 | 58.306 | 0.116 | 0.177 | 25.789 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F(-2) | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 173 | 173 | 183 | 395 | 0 | 0 | 0 | 0 | 102 | 0 |
N.S. |
1 | 1.00 | 1.06 | 2.28 | 0.00 | 0.00 | 0.00 | 0.00 | 0.59 | 0.00 |
time (sec) |
N/A | 0.433 | 0.264 | 1.269 | 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 | C | A | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 210 | 201 | 188 | 326 | 259 | 0 | 0 | 0 | 260 | 0 |
N.S. |
1 | 0.96 | 0.90 | 1.55 | 1.23 | 0.00 | 0.00 | 0.00 | 1.24 | 0.00 |
time (sec) |
N/A | 0.405 | 0.149 | 12.162 | 0.076 | 0.000 | 0.000 | 0.000 | 0.180 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 178 | 171 | 161 | 284 | 220 | 0 | 0 | 0 | 222 | 0 |
N.S. |
1 | 0.96 | 0.90 | 1.60 | 1.24 | 0.00 | 0.00 | 0.00 | 1.25 | 0.00 |
time (sec) |
N/A | 0.363 | 0.115 | 6.547 | 0.071 | 0.000 | 0.000 | 0.000 | 0.156 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 146 | 141 | 131 | 241 | 178 | 0 | 0 | 0 | 182 | 0 |
N.S. |
1 | 0.97 | 0.90 | 1.65 | 1.22 | 0.00 | 0.00 | 0.00 | 1.25 | 0.00 |
time (sec) |
N/A | 0.328 | 0.094 | 3.461 | 0.072 | 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 | C | A | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 74 | 73 | 90 | 191 | 126 | 0 | 0 | 0 | 133 | 0 |
N.S. |
1 | 0.99 | 1.22 | 2.58 | 1.70 | 0.00 | 0.00 | 0.00 | 1.80 | 0.00 |
time (sec) |
N/A | 0.297 | 0.067 | 1.778 | 0.071 | 0.000 | 0.000 | 0.000 | 0.166 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 34 | 143 | 0 | 0 | 0 | 0 | 52 | 0 |
N.S. |
1 | 1.00 | 1.21 | 5.11 | 0.00 | 0.00 | 0.00 | 0.00 | 1.86 | 0.00 |
time (sec) |
N/A | 0.245 | 0.019 | 1.993 | 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 | C | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 107 | 100 | 69 | 201 | 128 | 0 | 0 | 0 | 112 | 0 |
N.S. |
1 | 0.93 | 0.64 | 1.88 | 1.20 | 0.00 | 0.00 | 0.00 | 1.05 | 0.00 |
time (sec) |
N/A | 0.299 | 0.101 | 2.174 | 0.077 | 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(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 163 | 156 | 215 | 244 | 194 | 0 | 0 | 0 | 144 | 0 |
N.S. |
1 | 0.96 | 1.32 | 1.50 | 1.19 | 0.00 | 0.00 | 0.00 | 0.88 | 0.00 |
time (sec) |
N/A | 0.344 | 0.120 | 2.217 | 0.070 | 0.000 | 0.000 | 0.000 | 0.167 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 195 | 186 | 206 | 282 | 232 | 0 | 0 | 0 | 163 | 0 |
N.S. |
1 | 0.95 | 1.06 | 1.45 | 1.19 | 0.00 | 0.00 | 0.00 | 0.84 | 0.00 |
time (sec) |
N/A | 0.365 | 0.133 | 4.329 | 0.078 | 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 | 456 | 410 | 594 | 0 | 0 | 0 | 0 | 0 | 654 | 0 |
N.S. |
1 | 0.90 | 1.30 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.43 | 0.00 |
time (sec) |
N/A | 0.669 | 0.258 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.309 | 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 | 396 | 356 | 506 | 0 | 0 | 0 | 0 | 0 | 558 | 0 |
N.S. |
1 | 0.90 | 1.28 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.41 | 0.00 |
time (sec) |
N/A | 0.623 | 0.185 | 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 | 327 | 302 | 416 | 0 | 0 | 0 | 0 | 0 | 462 | 0 |
N.S. |
1 | 0.92 | 1.27 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.41 | 0.00 |
time (sec) |
N/A | 0.515 | 0.167 | 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 | 193 | 168 | 294 | 0 | 0 | 0 | 0 | 0 | 341 | 0 |
N.S. |
1 | 0.87 | 1.52 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.77 | 0.00 |
time (sec) |
N/A | 0.590 | 0.108 | 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 | A | A | C | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 55 | 53 | 53 | 352 | 0 | 0 | 0 | 0 | 82 | 0 |
N.S. |
1 | 0.96 | 0.96 | 6.40 | 0.00 | 0.00 | 0.00 | 0.00 | 1.49 | 0.00 |
time (sec) |
N/A | 0.351 | 0.107 | 6.920 | 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 | A | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 203 | 199 | 183 | 576 | 0 | 0 | 0 | 0 | 293 | 0 |
N.S. |
1 | 0.98 | 0.90 | 2.84 | 0.00 | 0.00 | 0.00 | 0.00 | 1.44 | 0.00 |
time (sec) |
N/A | 0.539 | 0.251 | 7.411 | 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 | A | A | C | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 287 | 272 | 513 | 705 | 0 | 0 | 0 | 0 | 348 | 0 |
N.S. |
1 | 0.95 | 1.79 | 2.46 | 0.00 | 0.00 | 0.00 | 0.00 | 1.21 | 0.00 |
time (sec) |
N/A | 0.775 | 0.226 | 7.371 | 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 | 710 | 663 | 1144 | 0 | 0 | 0 | 0 | 0 | 24 | 0 |
N.S. |
1 | 0.93 | 1.61 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.03 | 0.00 |
time (sec) |
N/A | 1.101 | 0.404 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 200.589 | 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 | 615 | 581 | 975 | 0 | 0 | 0 | 0 | 0 | 24 | 0 |
N.S. |
1 | 0.94 | 1.59 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.04 | 0.00 |
time (sec) |
N/A | 0.966 | 0.372 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 200.021 | 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 | 530 | 494 | 806 | 0 | 0 | 0 | 0 | 0 | 867 | 0 |
N.S. |
1 | 0.93 | 1.52 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.64 | 0.00 |
time (sec) |
N/A | 0.830 | 0.306 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.251 | 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 | 327 | 303 | 584 | 0 | 0 | 0 | 0 | 0 | 647 | 0 |
N.S. |
1 | 0.93 | 1.79 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.98 | 0.00 |
time (sec) |
N/A | 1.033 | 0.211 | 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 | C | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 81 | 77 | 77 | 605 | 0 | 0 | 0 | 0 | 110 | 0 |
N.S. |
1 | 0.95 | 0.95 | 7.47 | 0.00 | 0.00 | 0.00 | 0.00 | 1.36 | 0.00 |
time (sec) |
N/A | 0.432 | 0.165 | 22.319 | 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 | B | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 342 | 334 | 770 | 1080 | 0 | 0 | 0 | 0 | 553 | 0 |
N.S. |
1 | 0.98 | 2.25 | 3.16 | 0.00 | 0.00 | 0.00 | 0.00 | 1.62 | 0.00 |
time (sec) |
N/A | 0.809 | 0.410 | 23.753 | 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 | B | C | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 470 | 448 | 1047 | 1329 | 0 | 0 | 0 | 0 | 636 | 0 |
N.S. |
1 | 0.95 | 2.23 | 2.83 | 0.00 | 0.00 | 0.00 | 0.00 | 1.35 | 0.00 |
time (sec) |
N/A | 1.177 | 0.438 | 23.846 | 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 | C | C | F | F | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 180 | 175 | 348 | 393 | 0 | 0 | 0 | 0 | 228 | 0 |
N.S. |
1 | 0.97 | 1.93 | 2.18 | 0.00 | 0.00 | 0.00 | 0.00 | 1.27 | 0.00 |
time (sec) |
N/A | 0.440 | 0.147 | 54.371 | 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 | C | C | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 114 | 113 | 267 | 340 | 0 | 0 | 0 | 0 | 171 | 0 |
N.S. |
1 | 0.99 | 2.34 | 2.98 | 0.00 | 0.00 | 0.00 | 0.00 | 1.50 | 0.00 |
time (sec) |
N/A | 0.423 | 0.090 | 16.782 | 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 | A | C | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 39 | 39 | 50 | 385 | 0 | 0 | 0 | 0 | 62 | 0 |
N.S. |
1 | 1.00 | 1.28 | 9.87 | 0.00 | 0.00 | 0.00 | 0.00 | 1.59 | 0.00 |
time (sec) |
N/A | 0.257 | 0.017 | 7.911 | 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 | C | C | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 141 | 136 | 239 | 310 | 0 | 0 | 0 | 0 | 145 | 0 |
N.S. |
1 | 0.96 | 1.70 | 2.20 | 0.00 | 0.00 | 0.00 | 0.00 | 1.03 | 0.00 |
time (sec) |
N/A | 0.369 | 0.139 | 7.542 | 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 | A | C | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 241 | 234 | 364 | 422 | 0 | 0 | 0 | 0 | 212 | 0 |
N.S. |
1 | 0.97 | 1.51 | 1.75 | 0.00 | 0.00 | 0.00 | 0.00 | 0.88 | 0.00 |
time (sec) |
N/A | 0.434 | 0.142 | 32.182 | 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 | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 182 | 176 | 254 | 356 | 0 | 0 | 0 | 0 | 148 | 0 |
N.S. |
1 | 0.97 | 1.40 | 1.96 | 0.00 | 0.00 | 0.00 | 0.00 | 0.81 | 0.00 |
time (sec) |
N/A | 0.360 | 0.144 | 8.279 | 0.000 | 0.000 | 0.000 | 0.000 | 0.221 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 169 | 165 | 221 | 316 | 0 | 0 | 0 | 0 | 129 | 0 |
N.S. |
1 | 0.98 | 1.31 | 1.87 | 0.00 | 0.00 | 0.00 | 0.00 | 0.76 | 0.00 |
time (sec) |
N/A | 0.354 | 0.140 | 7.958 | 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 | A | C | C | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 211 | 206 | 285 | 369 | 0 | 0 | 0 | 0 | 157 | 0 |
N.S. |
1 | 0.98 | 1.35 | 1.75 | 0.00 | 0.00 | 0.00 | 0.00 | 0.74 | 0.00 |
time (sec) |
N/A | 0.378 | 0.256 | 15.529 | 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 | F | F | F | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 367 | 338 | 654 | 0 | 0 | 0 | 0 | 0 | 549 | 0 |
N.S. |
1 | 0.92 | 1.78 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.50 | 0.00 |
time (sec) |
N/A | 0.727 | 0.421 | 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 | C | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 241 | 227 | 519 | 0 | 0 | 0 | 0 | 0 | 411 | 0 |
N.S. |
1 | 0.94 | 2.15 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.71 | 0.00 |
time (sec) |
N/A | 0.776 | 0.317 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.231 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 70 | 68 | 484 | 825 | 0 | 0 | 0 | 0 | 95 | 0 |
N.S. |
1 | 0.97 | 6.91 | 11.79 | 0.00 | 0.00 | 0.00 | 0.00 | 1.36 | 0.00 |
time (sec) |
N/A | 0.348 | 0.281 | 15.658 | 0.000 | 0.000 | 0.000 | 0.000 | 0.189 | 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 | 257 | 254 | 488 | 612 | 0 | 0 | 0 | 0 | 349 | 0 |
N.S. |
1 | 0.99 | 1.90 | 2.38 | 0.00 | 0.00 | 0.00 | 0.00 | 1.36 | 0.00 |
time (sec) |
N/A | 0.599 | 0.402 | 15.790 | 0.000 | 0.000 | 0.000 | 0.000 | 0.192 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | C | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 559 | 625 | 703 | 0 | 0 | 0 | 0 | 0 | 497 | 0 |
N.S. |
1 | 1.12 | 1.26 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.89 | 0.00 |
time (sec) |
N/A | 1.277 | 0.875 | 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 | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 469 | 540 | 544 | 0 | 0 | 0 | 0 | 0 | 351 | 0 |
N.S. |
1 | 1.15 | 1.16 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.75 | 0.00 |
time (sec) |
N/A | 1.081 | 0.412 | 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 | C | C | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 409 | 466 | 414 | 0 | 0 | 0 | 0 | 0 | 315 | 0 |
N.S. |
1 | 1.14 | 1.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.77 | 0.00 |
time (sec) |
N/A | 0.853 | 0.426 | 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 | C | C | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 490 | 544 | 585 | 0 | 0 | 0 | 0 | 0 | 367 | 0 |
N.S. |
1 | 1.11 | 1.19 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.75 | 0.00 |
time (sec) |
N/A | 1.082 | 0.666 | 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 | A | C | F | F | F | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 591 | 562 | 1234 | 0 | 0 | 0 | 0 | 0 | 1008 | 0 |
N.S. |
1 | 0.95 | 2.09 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.71 | 0.00 |
time (sec) |
N/A | 1.139 | 1.773 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.287 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 411 | 394 | 1004 | 0 | 0 | 0 | 0 | 0 | 759 | 0 |
N.S. |
1 | 0.96 | 2.44 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.85 | 0.00 |
time (sec) |
N/A | 1.316 | 0.730 | 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 | C | C | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 101 | 101 | 754 | 1296 | 0 | 0 | 0 | 0 | 126 | 0 |
N.S. |
1 | 1.00 | 7.47 | 12.83 | 0.00 | 0.00 | 0.00 | 0.00 | 1.25 | 0.00 |
time (sec) |
N/A | 0.449 | 0.395 | 46.616 | 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 | C | C | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 425 | 418 | 940 | 1171 | 0 | 0 | 0 | 0 | 639 | 0 |
N.S. |
1 | 0.98 | 2.21 | 2.76 | 0.00 | 0.00 | 0.00 | 0.00 | 1.50 | 0.00 |
time (sec) |
N/A | 0.910 | 0.448 | 46.479 | 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 | C | C | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 836 | 972 | 1027 | 0 | 0 | 0 | 0 | 0 | 641 | 0 |
N.S. |
1 | 1.16 | 1.23 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.77 | 0.00 |
time (sec) |
N/A | 1.832 | 0.964 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.199 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | C | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 747 | 866 | 794 | 0 | 0 | 0 | 0 | 0 | 585 | 0 |
N.S. |
1 | 1.16 | 1.06 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.78 | 0.00 |
time (sec) |
N/A | 1.410 | 0.457 | 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 | 350 | 337 | 263 | 0 | 0 | 0 | 0 | 0 | 439 | 0 |
N.S. |
1 | 0.96 | 0.75 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.25 | 0.00 |
time (sec) |
N/A | 0.609 | 0.423 | 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 | 268 | 258 | 191 | 0 | 0 | 0 | 0 | 0 | 347 | 0 |
N.S. |
1 | 0.96 | 0.71 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.29 | 0.00 |
time (sec) |
N/A | 0.502 | 0.316 | 0.000 | 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 | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 172 | 168 | 117 | 0 | 0 | 0 | 0 | 0 | 255 | 0 |
N.S. |
1 | 0.98 | 0.68 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.48 | 0.00 |
time (sec) |
N/A | 0.396 | 0.250 | 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 | 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 | 39 | 39 | 50 | 0 | 0 | 0 | 0 | 0 | 98 | 0 |
N.S. |
1 | 1.00 | 1.28 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 2.51 | 0.00 |
time (sec) |
N/A | 0.276 | 0.015 | 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 | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 196 | 189 | 124 | 0 | 0 | 0 | 0 | 0 | 322 | 0 |
N.S. |
1 | 0.96 | 0.63 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.64 | 0.00 |
time (sec) |
N/A | 0.453 | 0.282 | 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 | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 289 | 279 | 207 | 0 | 0 | 0 | 0 | 0 | 430 | 0 |
N.S. |
1 | 0.97 | 0.72 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.49 | 0.00 |
time (sec) |
N/A | 0.519 | 0.349 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.266 | 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 | 372 | 357 | 288 | 0 | 0 | 0 | 0 | 0 | 530 | 0 |
N.S. |
1 | 0.96 | 0.77 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.42 | 0.00 |
time (sec) |
N/A | 0.596 | 0.500 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.199 | 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 | 708 | 650 | 995 | 0 | 0 | 0 | 0 | 0 | 1116 | 0 |
N.S. |
1 | 0.92 | 1.41 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.58 | 0.00 |
time (sec) |
N/A | 1.089 | 0.663 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.426 | 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 | 557 | 513 | 769 | 0 | 0 | 0 | 0 | 0 | 876 | 0 |
N.S. |
1 | 0.92 | 1.38 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.57 | 0.00 |
time (sec) |
N/A | 0.836 | 0.511 | 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 | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 374 | 349 | 527 | 0 | 0 | 0 | 0 | 0 | 636 | 0 |
N.S. |
1 | 0.93 | 1.41 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.70 | 0.00 |
time (sec) |
N/A | 0.621 | 0.427 | 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 | 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 | 70 | 69 | 70 | 0 | 0 | 0 | 0 | 0 | 132 | 0 |
N.S. |
1 | 0.99 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.89 | 0.00 |
time (sec) |
N/A | 0.355 | 0.216 | 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 | 389 | 412 | 627 | 0 | 0 | 0 | 0 | 0 | 509 | 0 |
N.S. |
1 | 1.06 | 1.61 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.31 | 0.00 |
time (sec) |
N/A | 0.801 | 0.509 | 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 | 555 | 567 | 881 | 0 | 0 | 0 | 0 | 0 | 618 | 0 |
N.S. |
1 | 1.02 | 1.59 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.11 | 0.00 |
time (sec) |
N/A | 0.951 | 0.672 | 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 | 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 | 858 | 810 | 1432 | 0 | 0 | 0 | 0 | 0 | 28 | 0 |
N.S. |
1 | 0.94 | 1.67 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.03 | 0.00 |
time (sec) |
N/A | 1.343 | 0.765 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 200.017 | 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 | 604 | 567 | 986 | 0 | 0 | 0 | 0 | 0 | 1205 | 0 |
N.S. |
1 | 0.94 | 1.63 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 2.00 | 0.00 |
time (sec) |
N/A | 0.909 | 0.607 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.256 | 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 | 101 | 99 | 98 | 0 | 0 | 0 | 0 | 0 | 162 | 0 |
N.S. |
1 | 0.98 | 0.97 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.60 | 0.00 |
time (sec) |
N/A | 0.461 | 0.279 | 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 | 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 | 610 | 640 | 1455 | 0 | 0 | 0 | 0 | 0 | 949 | 0 |
N.S. |
1 | 1.05 | 2.39 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.56 | 0.00 |
time (sec) |
N/A | 1.249 | 1.075 | 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 | 849 | 870 | 2009 | 0 | 0 | 0 | 0 | 0 | 1112 | 0 |
N.S. |
1 | 1.02 | 2.37 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.31 | 0.00 |
time (sec) |
N/A | 1.587 | 1.280 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.220 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | C | F | B | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 137 | 140 | 1700 | 1968 | 0 | 523 | 0 | 0 | 169 | 0 |
N.S. |
1 | 1.02 | 12.41 | 14.36 | 0.00 | 3.82 | 0.00 | 0.00 | 1.23 | 0.00 |
time (sec) |
N/A | 0.577 | 0.775 | 0.036 | 0.000 | 0.088 | 0.000 | 0.000 | 0.170 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | C | F | B | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 105 | 107 | 1035 | 1261 | 0 | 285 | 0 | 0 | 137 | 0 |
N.S. |
1 | 1.02 | 9.86 | 12.01 | 0.00 | 2.71 | 0.00 | 0.00 | 1.30 | 0.00 |
time (sec) |
N/A | 0.476 | 0.471 | 0.072 | 0.000 | 0.086 | 0.000 | 0.000 | 0.161 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | C | F | A | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 73 | 74 | 526 | 684 | 0 | 131 | 0 | 0 | 105 | 0 |
N.S. |
1 | 1.01 | 7.21 | 9.37 | 0.00 | 1.79 | 0.00 | 0.00 | 1.44 | 0.00 |
time (sec) |
N/A | 0.374 | 0.305 | 136.576 | 0.000 | 0.106 | 0.000 | 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(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 40 | 40 | 52 | 248 | 0 | 42 | 0 | 0 | 71 | 0 |
N.S. |
1 | 1.00 | 1.30 | 6.20 | 0.00 | 1.05 | 0.00 | 0.00 | 1.78 | 0.00 |
time (sec) |
N/A | 0.267 | 0.016 | 25.569 | 0.000 | 0.080 | 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 | 27 | 0 | 30 | 27 | 30 |
N.S. |
1 | 1.00 | 1.07 | 1.00 | 1.07 | 0.96 | 0.00 | 1.07 | 0.96 | 1.07 |
time (sec) |
N/A | 0.206 | 0.121 | 0.041 | 0.120 | 0.082 | 0.000 | 0.133 | 0.162 | 25.465 |
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 | 106 | 44 | 0 | 30 | 164 | 30 |
N.S. |
1 | 1.00 | 1.07 | 1.00 | 3.79 | 1.57 | 0.00 | 1.07 | 5.86 | 1.07 |
time (sec) |
N/A | 0.206 | 9.225 | 0.041 | 0.097 | 0.074 | 0.000 | 0.146 | 0.176 | 25.715 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 283 | 272 | 290 | 1248 | 381 | 0 | 0 | 0 | 329 | 0 |
N.S. |
1 | 0.96 | 1.02 | 4.41 | 1.35 | 0.00 | 0.00 | 0.00 | 1.16 | 0.00 |
time (sec) |
N/A | 0.505 | 0.294 | 158.181 | 0.129 | 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 | A | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 243 | 234 | 252 | 1067 | 328 | 0 | 0 | 0 | 279 | 0 |
N.S. |
1 | 0.96 | 1.04 | 4.39 | 1.35 | 0.00 | 0.00 | 0.00 | 1.15 | 0.00 |
time (sec) |
N/A | 0.439 | 0.217 | 72.408 | 0.123 | 0.000 | 0.000 | 0.000 | 0.214 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 203 | 196 | 208 | 885 | 269 | 0 | 0 | 0 | 227 | 0 |
N.S. |
1 | 0.97 | 1.02 | 4.36 | 1.33 | 0.00 | 0.00 | 0.00 | 1.12 | 0.00 |
time (sec) |
N/A | 0.386 | 0.179 | 28.783 | 0.125 | 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 | C | A | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 117 | 111 | 152 | 686 | 188 | 0 | 0 | 0 | 166 | 0 |
N.S. |
1 | 0.95 | 1.30 | 5.86 | 1.61 | 0.00 | 0.00 | 0.00 | 1.42 | 0.00 |
time (sec) |
N/A | 0.396 | 0.128 | 10.818 | 0.120 | 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 | C | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 100 | 112 | 147 | 793 | 0 | 0 | 0 | 0 | 75 | 0 |
N.S. |
1 | 1.12 | 1.47 | 7.93 | 0.00 | 0.00 | 0.00 | 0.00 | 0.75 | 0.00 |
time (sec) |
N/A | 0.484 | 0.127 | 9.578 | 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 | A | A | C | A | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 164 | 158 | 117 | 737 | 199 | 0 | 0 | 0 | 150 | 0 |
N.S. |
1 | 0.96 | 0.71 | 4.49 | 1.21 | 0.00 | 0.00 | 0.00 | 0.91 | 0.00 |
time (sec) |
N/A | 0.376 | 0.168 | 11.299 | 0.126 | 0.000 | 0.000 | 0.000 | 0.163 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 234 | 225 | 232 | 945 | 285 | 0 | 0 | 0 | 196 | 0 |
N.S. |
1 | 0.96 | 0.99 | 4.04 | 1.22 | 0.00 | 0.00 | 0.00 | 0.84 | 0.00 |
time (sec) |
N/A | 0.440 | 0.205 | 11.155 | 0.126 | 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(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 274 | 263 | 280 | 1127 | 342 | 0 | 0 | 0 | 223 | 0 |
N.S. |
1 | 0.96 | 1.02 | 4.11 | 1.25 | 0.00 | 0.00 | 0.00 | 0.81 | 0.00 |
time (sec) |
N/A | 0.490 | 0.227 | 30.994 | 0.128 | 0.000 | 0.000 | 0.000 | 0.172 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 452 | 450 | 788 | 5917 | 0 | 0 | 0 | 0 | 675 | 0 |
N.S. |
1 | 1.00 | 1.74 | 13.09 | 0.00 | 0.00 | 0.00 | 0.00 | 1.49 | 0.00 |
time (sec) |
N/A | 0.956 | 0.400 | 0.091 | 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 | C | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 373 | 374 | 674 | 4845 | 0 | 0 | 0 | 0 | 555 | 0 |
N.S. |
1 | 1.00 | 1.81 | 12.99 | 0.00 | 0.00 | 0.00 | 0.00 | 1.49 | 0.00 |
time (sec) |
N/A | 0.813 | 0.325 | 163.314 | 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 | A | C | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 288 | 297 | 507 | 3710 | 0 | 0 | 0 | 0 | 410 | 0 |
N.S. |
1 | 1.03 | 1.76 | 12.88 | 0.00 | 0.00 | 0.00 | 0.00 | 1.42 | 0.00 |
time (sec) |
N/A | 0.653 | 0.215 | 72.062 | 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 | B | C | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 131 | 140 | 329 | 3957 | 0 | 0 | 0 | 0 | 110 | 0 |
N.S. |
1 | 1.07 | 2.51 | 30.21 | 0.00 | 0.00 | 0.00 | 0.00 | 0.84 | 0.00 |
time (sec) |
N/A | 0.604 | 0.219 | 61.188 | 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 | B | C | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 248 | 238 | 600 | 3983 | 0 | 0 | 0 | 0 | 369 | 0 |
N.S. |
1 | 0.96 | 2.42 | 16.06 | 0.00 | 0.00 | 0.00 | 0.00 | 1.49 | 0.00 |
time (sec) |
N/A | 0.606 | 0.353 | 66.460 | 0.000 | 0.000 | 0.000 | 0.000 | 0.160 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | C | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 344 | 320 | 796 | 5174 | 0 | 0 | 0 | 0 | 452 | 0 |
N.S. |
1 | 0.93 | 2.31 | 15.04 | 0.00 | 0.00 | 0.00 | 0.00 | 1.31 | 0.00 |
time (sec) |
N/A | 0.835 | 0.451 | 65.483 | 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 | B | C | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 420 | 403 | 909 | 6242 | 0 | 0 | 0 | 0 | 501 | 0 |
N.S. |
1 | 0.96 | 2.16 | 14.86 | 0.00 | 0.00 | 0.00 | 0.00 | 1.19 | 0.00 |
time (sec) |
N/A | 1.114 | 0.497 | 66.918 | 0.000 | 0.000 | 0.000 | 0.000 | 0.504 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | C | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 603 | 601 | 1431 | 19601 | 0 | 0 | 0 | 0 | 1025 | 0 |
N.S. |
1 | 1.00 | 2.37 | 32.51 | 0.00 | 0.00 | 0.00 | 0.00 | 1.70 | 0.00 |
time (sec) |
N/A | 1.299 | 0.657 | 0.201 | 0.000 | 0.000 | 0.000 | 0.000 | 0.213 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | C | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 473 | 480 | 1122 | 15385 | 0 | 0 | 0 | 0 | 765 | 0 |
N.S. |
1 | 1.01 | 2.37 | 32.53 | 0.00 | 0.00 | 0.00 | 0.00 | 1.62 | 0.00 |
time (sec) |
N/A | 0.988 | 0.462 | 0.167 | 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 | B | C | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 161 | 167 | 602 | 15171 | 0 | 0 | 0 | 0 | 143 | 0 |
N.S. |
1 | 1.04 | 3.74 | 94.23 | 0.00 | 0.00 | 0.00 | 0.00 | 0.89 | 0.00 |
time (sec) |
N/A | 0.739 | 0.308 | 281.678 | 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 | A | B | C | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 411 | 393 | 1347 | 16533 | 0 | 0 | 0 | 0 | 680 | 0 |
N.S. |
1 | 0.96 | 3.28 | 40.23 | 0.00 | 0.00 | 0.00 | 0.00 | 1.65 | 0.00 |
time (sec) |
N/A | 0.918 | 0.748 | 181.466 | 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 | B | C | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 555 | 519 | 1736 | 21008 | 0 | 0 | 0 | 0 | 809 | 0 |
N.S. |
1 | 0.94 | 3.13 | 37.85 | 0.00 | 0.00 | 0.00 | 0.00 | 1.46 | 0.00 |
time (sec) |
N/A | 1.302 | 1.111 | 175.784 | 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 | A | C | C | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 221 | 214 | 324 | 1031 | 0 | 0 | 0 | 0 | 243 | 0 |
N.S. |
1 | 0.97 | 1.47 | 4.67 | 0.00 | 0.00 | 0.00 | 0.00 | 1.10 | 0.00 |
time (sec) |
N/A | 0.519 | 0.241 | 213.383 | 0.000 | 0.000 | 0.000 | 0.000 | 0.155 | 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 | 148 | 145 | 266 | 828 | 0 | 0 | 0 | 0 | 189 | 0 |
N.S. |
1 | 0.98 | 1.80 | 5.59 | 0.00 | 0.00 | 0.00 | 0.00 | 1.28 | 0.00 |
time (sec) |
N/A | 0.469 | 0.143 | 46.083 | 0.000 | 0.000 | 0.000 | 0.000 | 0.157 | 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 | 113 | 126 | 297 | 649 | 0 | 0 | 0 | 0 | 81 | 0 |
N.S. |
1 | 1.12 | 2.63 | 5.74 | 0.00 | 0.00 | 0.00 | 0.00 | 0.72 | 0.00 |
time (sec) |
N/A | 0.506 | 0.151 | 18.553 | 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 | 195 | 188 | 298 | 862 | 0 | 0 | 0 | 0 | 173 | 0 |
N.S. |
1 | 0.96 | 1.53 | 4.42 | 0.00 | 0.00 | 0.00 | 0.00 | 0.89 | 0.00 |
time (sec) |
N/A | 0.448 | 0.192 | 19.700 | 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 | C | C | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 248 | 239 | 363 | 1074 | 0 | 0 | 0 | 0 | 210 | 0 |
N.S. |
1 | 0.96 | 1.46 | 4.33 | 0.00 | 0.00 | 0.00 | 0.00 | 0.85 | 0.00 |
time (sec) |
N/A | 0.525 | 0.215 | 106.098 | 0.000 | 0.000 | 0.000 | 0.000 | 0.161 | 0.000 |