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 | A | C | F | C | F(-1) | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 182 | 179 | 207 | 1477 | 0 | 174 | 0 | 0 | 0 |
N.S. |
1 | 0.98 | 1.14 | 8.12 | 0.00 | 0.96 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.316 | 9.130 | 1.400 | 0.000 | 0.128 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | C | F(-1) | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 186 | 184 | 191 | 2547 | 0 | 219 | 0 | 0 | 0 |
N.S. |
1 | 0.99 | 1.03 | 13.69 | 0.00 | 1.18 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.339 | 6.285 | 1.500 | 0.000 | 0.121 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | C | F(-1) | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 243 | 243 | 218 | 2064 | 0 | 282 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.90 | 8.49 | 0.00 | 1.16 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.792 | 5.122 | 1.645 | 0.000 | 0.126 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | C | F(-1) | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 300 | 302 | 464 | 1389 | 0 | 342 | 0 | 0 | 0 |
N.S. |
1 | 1.01 | 1.55 | 4.63 | 0.00 | 1.14 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.279 | 10.350 | 1.692 | 0.000 | 0.144 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | C | F(-1) | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 357 | 361 | 532 | 1578 | 0 | 396 | 0 | 0 | 0 |
N.S. |
1 | 1.01 | 1.49 | 4.42 | 0.00 | 1.11 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.700 | 10.550 | 3.760 | 0.000 | 0.161 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | C | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 406 | 412 | 120 | 511 | 0 | 171 | 0 | 0 | 0 |
N.S. |
1 | 1.01 | 0.30 | 1.26 | 0.00 | 0.42 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 3.168 | 4.515 | 4.916 | 0.000 | 0.140 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | C | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 352 | 354 | 189 | 497 | 0 | 164 | 0 | 0 | 0 |
N.S. |
1 | 1.01 | 0.54 | 1.41 | 0.00 | 0.47 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.699 | 7.524 | 6.845 | 0.000 | 0.139 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | C | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 290 | 296 | 281 | 496 | 0 | 159 | 0 | 0 | 0 |
N.S. |
1 | 1.02 | 0.97 | 1.71 | 0.00 | 0.55 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.161 | 3.087 | 4.417 | 0.000 | 0.123 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | C | F(-1) | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 234 | 238 | 158 | 510 | 0 | 151 | 0 | 0 | 0 |
N.S. |
1 | 1.02 | 0.68 | 2.18 | 0.00 | 0.65 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.797 | 9.048 | 2.473 | 0.000 | 0.133 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | C | F(-1) | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 241 | 237 | 240 | 1511 | 0 | 201 | 0 | 0 | 0 |
N.S. |
1 | 0.98 | 1.00 | 6.27 | 0.00 | 0.83 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.788 | 11.453 | 2.754 | 0.000 | 0.122 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | C | F(-1) | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 243 | 240 | 245 | 2573 | 0 | 249 | 0 | 0 | 0 |
N.S. |
1 | 0.99 | 1.01 | 10.59 | 0.00 | 1.02 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.810 | 9.705 | 2.397 | 0.000 | 0.152 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | C | F(-1) | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 243 | 245 | 246 | 3149 | 0 | 304 | 0 | 0 | 0 |
N.S. |
1 | 1.01 | 1.01 | 12.96 | 0.00 | 1.25 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.852 | 9.778 | 2.475 | 0.000 | 0.157 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | C | F(-1) | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 300 | 304 | 464 | 2675 | 0 | 370 | 0 | 0 | 0 |
N.S. |
1 | 1.01 | 1.55 | 8.92 | 0.00 | 1.23 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.287 | 10.493 | 2.424 | 0.000 | 0.142 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | C | F(-1) | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 357 | 363 | 532 | 1580 | 0 | 430 | 0 | 0 | 0 |
N.S. |
1 | 1.02 | 1.49 | 4.43 | 0.00 | 1.20 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.776 | 10.894 | 2.539 | 0.000 | 0.167 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | C | F(-1) | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 414 | 422 | 600 | 1991 | 0 | 495 | 0 | 0 | 0 |
N.S. |
1 | 1.02 | 1.45 | 4.81 | 0.00 | 1.20 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 3.302 | 11.782 | 5.081 | 0.000 | 0.186 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | C | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 463 | 470 | 226 | 531 | 0 | 191 | 0 | 0 | 0 |
N.S. |
1 | 1.02 | 0.49 | 1.15 | 0.00 | 0.41 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 3.716 | 10.468 | 11.983 | 0.000 | 0.151 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | C | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 409 | 412 | 212 | 529 | 0 | 179 | 0 | 0 | 0 |
N.S. |
1 | 1.01 | 0.52 | 1.29 | 0.00 | 0.44 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 3.304 | 9.691 | 9.494 | 0.000 | 0.139 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | C | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 343 | 354 | 360 | 516 | 0 | 172 | 0 | 0 | 0 |
N.S. |
1 | 1.03 | 1.05 | 1.50 | 0.00 | 0.50 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.752 | 5.479 | 6.037 | 0.000 | 0.112 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | C | F(-1) | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 288 | 296 | 181 | 542 | 0 | 167 | 0 | 0 | 0 |
N.S. |
1 | 1.03 | 0.63 | 1.88 | 0.00 | 0.58 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.204 | 10.512 | 4.470 | 0.000 | 0.126 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | C | F(-1) | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 294 | 295 | 284 | 1527 | 0 | 216 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.97 | 5.19 | 0.00 | 0.73 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.216 | 14.350 | 3.906 | 0.000 | 0.132 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | C | F(-1) | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 298 | 296 | 267 | 2596 | 0 | 264 | 0 | 0 | 0 |
N.S. |
1 | 0.99 | 0.90 | 8.71 | 0.00 | 0.89 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.211 | 11.298 | 3.255 | 0.000 | 0.138 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | C | F(-1) | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 300 | 301 | 406 | 3173 | 0 | 320 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.35 | 10.58 | 0.00 | 1.07 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.263 | 14.818 | 2.857 | 0.000 | 0.138 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | C | F(-1) | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 300 | 306 | 464 | 3799 | 0 | 370 | 0 | 0 | 0 |
N.S. |
1 | 1.02 | 1.55 | 12.66 | 0.00 | 1.23 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.262 | 15.292 | 2.949 | 0.000 | 0.146 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | C | F(-1) | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 357 | 365 | 532 | 3093 | 0 | 431 | 0 | 0 | 0 |
N.S. |
1 | 1.02 | 1.49 | 8.66 | 0.00 | 1.21 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.724 | 11.459 | 2.897 | 0.000 | 0.176 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | C | F(-1) | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 414 | 424 | 600 | 1991 | 0 | 495 | 0 | 0 | 0 |
N.S. |
1 | 1.02 | 1.45 | 4.81 | 0.00 | 1.20 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 3.250 | 12.425 | 2.934 | 0.000 | 0.162 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | C | F(-1) | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 471 | 483 | 668 | 2170 | 0 | 555 | 0 | 0 | 0 |
N.S. |
1 | 1.03 | 1.42 | 4.61 | 0.00 | 1.18 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 3.723 | 13.848 | 5.725 | 0.000 | 0.195 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | C | F(-1) | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 234 | 238 | 174 | 510 | 0 | 151 | 0 | 0 | 0 |
N.S. |
1 | 1.02 | 0.74 | 2.18 | 0.00 | 0.65 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.723 | 8.872 | 2.415 | 0.000 | 0.125 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | C | F(-1) | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 180 | 180 | 157 | 488 | 0 | 129 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.87 | 2.71 | 0.00 | 0.72 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.315 | 6.930 | 1.361 | 0.000 | 0.107 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | C | F(-1) | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 122 | 122 | 215 | 451 | 0 | 113 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.76 | 3.70 | 0.00 | 0.93 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.899 | 3.383 | 0.813 | 0.000 | 0.109 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | C | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 68 | 68 | 111 | 424 | 0 | 77 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.63 | 6.24 | 0.00 | 1.13 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.522 | 3.088 | 0.580 | 0.000 | 0.102 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | C | F(-1) | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 121 | 121 | 148 | 799 | 0 | 159 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.22 | 6.60 | 0.00 | 1.31 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.924 | 3.827 | 0.832 | 0.000 | 0.117 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | C | F(-1) | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 179 | 180 | 204 | 834 | 0 | 211 | 0 | 0 | 0 |
N.S. |
1 | 1.01 | 1.14 | 4.66 | 0.00 | 1.18 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.362 | 4.597 | 0.533 | 0.000 | 0.146 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | C | F(-1) | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 233 | 239 | 240 | 1128 | 0 | 275 | 0 | 0 | 0 |
N.S. |
1 | 1.03 | 1.03 | 4.84 | 0.00 | 1.18 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.797 | 5.239 | 0.903 | 0.000 | 0.165 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | C | F(-1) | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 294 | 295 | 282 | 1527 | 0 | 216 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.96 | 5.19 | 0.00 | 0.73 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.190 | 14.507 | 4.263 | 0.000 | 0.133 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | C | F(-1) | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 241 | 237 | 238 | 1511 | 0 | 200 | 0 | 0 | 0 |
N.S. |
1 | 0.98 | 0.99 | 6.27 | 0.00 | 0.83 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.766 | 11.153 | 2.711 | 0.000 | 0.117 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | C | F(-1) | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 182 | 179 | 200 | 1473 | 0 | 173 | 0 | 0 | 0 |
N.S. |
1 | 0.98 | 1.10 | 8.09 | 0.00 | 0.95 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.330 | 4.161 | 1.451 | 0.000 | 0.119 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | C | F(-1) | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 123 | 123 | 213 | 1190 | 0 | 156 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.73 | 9.67 | 0.00 | 1.27 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.917 | 3.181 | 1.263 | 0.000 | 0.101 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | C | F(-1) | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 121 | 121 | 170 | 798 | 0 | 158 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.40 | 6.60 | 0.00 | 1.31 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.929 | 3.761 | 0.763 | 0.000 | 0.106 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | C | F(-1) | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 176 | 175 | 92 | 425 | 0 | 145 | 0 | 0 | 0 |
N.S. |
1 | 0.99 | 0.52 | 2.41 | 0.00 | 0.82 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.359 | 4.091 | 0.708 | 0.000 | 0.109 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | C | F(-1) | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 237 | 235 | 134 | 841 | 0 | 234 | 0 | 0 | 0 |
N.S. |
1 | 0.99 | 0.57 | 3.55 | 0.00 | 0.99 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.809 | 4.719 | 0.937 | 0.000 | 0.117 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | C | F(-1) | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 294 | 294 | 155 | 1131 | 0 | 293 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.53 | 3.85 | 0.00 | 1.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.208 | 5.845 | 1.259 | 0.000 | 0.137 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | C | F(-1) | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 357 | 356 | 356 | 2627 | 0 | 279 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.00 | 7.36 | 0.00 | 0.78 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.659 | 15.397 | 3.821 | 0.000 | 0.147 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | C | F(-1) | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 298 | 296 | 250 | 2599 | 0 | 265 | 0 | 0 | 0 |
N.S. |
1 | 0.99 | 0.84 | 8.72 | 0.00 | 0.89 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.282 | 7.405 | 3.236 | 0.000 | 0.186 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | C | F(-1) | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 243 | 240 | 230 | 2575 | 0 | 249 | 0 | 0 | 0 |
N.S. |
1 | 0.99 | 0.95 | 10.60 | 0.00 | 1.02 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.798 | 4.973 | 2.265 | 0.000 | 0.126 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | C | F(-1) | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 186 | 184 | 180 | 2549 | 0 | 219 | 0 | 0 | 0 |
N.S. |
1 | 0.99 | 0.97 | 13.70 | 0.00 | 1.18 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.327 | 4.010 | 1.486 | 0.000 | 0.115 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | C | F(-1) | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 182 | 182 | 230 | 1492 | 0 | 209 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.26 | 8.20 | 0.00 | 1.15 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.296 | 3.485 | 0.947 | 0.000 | 0.114 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | C | F(-1) | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 179 | 180 | 189 | 834 | 0 | 213 | 0 | 0 | 0 |
N.S. |
1 | 1.01 | 1.06 | 4.66 | 0.00 | 1.19 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.326 | 4.552 | 0.584 | 0.000 | 0.130 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | C | F(-1) | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 237 | 235 | 133 | 841 | 0 | 233 | 0 | 0 | 0 |
N.S. |
1 | 0.99 | 0.56 | 3.55 | 0.00 | 0.98 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.778 | 4.712 | 0.891 | 0.000 | 0.125 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | C | F(-1) | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 291 | 291 | 104 | 447 | 0 | 158 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.36 | 1.54 | 0.00 | 0.54 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.288 | 5.120 | 1.063 | 0.000 | 0.119 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | C | F(-1) | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 350 | 353 | 171 | 885 | 0 | 257 | 0 | 0 | 0 |
N.S. |
1 | 1.01 | 0.49 | 2.53 | 0.00 | 0.73 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.789 | 8.300 | 2.049 | 0.000 | 0.151 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | F | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 119 | 161 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.35 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.591 | 0.000 | 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 | 93 | 93 | 96 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.03 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.543 | 0.742 | 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 | 93 | 93 | 96 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.03 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.512 | 0.519 | 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 | 91 | 91 | 108 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.19 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.450 | 1.309 | 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 | 88 | 88 | 85 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.97 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.274 | 0.100 | 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 | 84 | 84 | 84 | 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 | 0.489 | 0.102 | 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 | 93 | 93 | 96 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.03 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.494 | 0.158 | 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 | 93 | 93 | 96 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.03 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.501 | 0.165 | 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 | F | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 114 | 114 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.623 | 0.000 | 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 | F | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 112 | 112 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.610 | 0.000 | 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 | F | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 109 | 109 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.580 | 0.000 | 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 | F | F | F | F | F(-1) | F(-1) | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 106 | 106 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.555 | 0.000 | 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 | F | F | F | F | F(-1) | F(-1) | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 106 | 106 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.602 | 0.000 | 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 | F | F | F | F | F(-1) | F(-1) | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 114 | 114 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.602 | 0.000 | 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 | F | F | F | F | F(-1) | F(-1) | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 106 | 106 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.539 | 0.000 | 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 | F | F | F | F | F(-1) | F(-1) | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 106 | 106 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.545 | 0.000 | 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 | F | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 123 | 161 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.31 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.678 | 0.000 | 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 | F | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 123 | 158 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.28 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.626 | 0.000 | 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 | F | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 120 | 159 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.32 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.621 | 0.000 | 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 | F | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 121 | 159 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.31 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.551 | 0.000 | 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 | F | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 123 | 161 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.31 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.603 | 0.000 | 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 | F | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 123 | 161 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.31 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.633 | 0.000 | 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 | F | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 135 | 192 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.42 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.572 | 0.000 | 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 | C | F | A | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 57 | 58 | 76 | 3232 | 0 | 30 | 0 | 934 | 0 |
N.S. |
1 | 1.02 | 1.33 | 56.70 | 0.00 | 0.53 | 0.00 | 16.39 | 0.00 |
time (sec) |
N/A | 0.435 | 16.339 | 2.040 | 0.000 | 0.295 | 0.000 | 0.686 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | B | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 203 | 197 | 210 | 0 | 978 | 651 | 0 | 86180 | 1149 |
N.S. |
1 | 0.97 | 1.03 | 0.00 | 4.82 | 3.21 | 0.00 | 424.53 | 5.66 |
time (sec) |
N/A | 1.042 | 6.292 | 0.000 | 0.507 | 0.336 | 0.000 | 30.458 | 18.610 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | B | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 127 | 127 | 143 | 0 | 485 | 298 | 0 | 28307 | 476 |
N.S. |
1 | 1.00 | 1.13 | 0.00 | 3.82 | 2.35 | 0.00 | 222.89 | 3.75 |
time (sec) |
N/A | 0.680 | 2.474 | 0.000 | 0.375 | 0.299 | 0.000 | 9.464 | 19.082 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 58 | 58 | 96 | 60 | 207 | 129 | 0 | 4499 | 74 |
N.S. |
1 | 1.00 | 1.66 | 1.03 | 3.57 | 2.22 | 0.00 | 77.57 | 1.28 |
time (sec) |
N/A | 0.340 | 1.800 | 39.977 | 0.330 | 0.286 | 0.000 | 2.046 | 9.972 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | F | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 81 | 85 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.05 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.472 | 0.000 | 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 | F | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 85 | 89 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.05 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.479 | 0.000 | 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 | F | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 88 | 92 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.05 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.481 | 0.000 | 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 | A | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 51 | 51 | 94 | 0 | 0 | 48 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.84 | 0.00 | 0.00 | 0.94 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.388 | 2.216 | 0.000 | 0.000 | 0.265 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | F | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 134 | 164 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.22 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.651 | 0.000 | 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 | F | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 134 | 184 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.37 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.634 | 0.000 | 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 | C | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 131 | 184 | 207 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.40 | 1.58 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.624 | 13.911 | 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 | B | A | F(-1) | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 55 | 55 | 55 | 0 | 145 | 83 | 0 | 0 | 53 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 2.64 | 1.51 | 0.00 | 0.00 | 0.96 |
time (sec) |
N/A | 0.356 | 2.071 | 0.000 | 0.312 | 0.278 | 0.000 | 0.000 | 9.420 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F(-2) | A | F(-1) | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 125 | 125 | 88 | 0 | 0 | 126 | 0 | 0 | 128 |
N.S. |
1 | 1.00 | 0.70 | 0.00 | 0.00 | 1.01 | 0.00 | 0.00 | 1.02 |
time (sec) |
N/A | 0.694 | 23.901 | 0.000 | 0.000 | 0.278 | 0.000 | 0.000 | 11.277 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F(-2) | A | F(-1) | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 204 | 197 | 126 | 0 | 0 | 183 | 0 | 0 | 887 |
N.S. |
1 | 0.97 | 0.62 | 0.00 | 0.00 | 0.90 | 0.00 | 0.00 | 4.35 |
time (sec) |
N/A | 1.032 | 21.411 | 0.000 | 0.000 | 0.354 | 0.000 | 0.000 | 16.631 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F(-2) | A | F(-1) | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 290 | 269 | 194 | 0 | 0 | 264 | 0 | 0 | 1623 |
N.S. |
1 | 0.93 | 0.67 | 0.00 | 0.00 | 0.91 | 0.00 | 0.00 | 5.60 |
time (sec) |
N/A | 1.445 | 21.859 | 0.000 | 0.000 | 0.393 | 0.000 | 0.000 | 19.778 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | F | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 138 | 190 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.38 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.785 | 0.000 | 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 | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 33 | 38 | 33 | 28 | 28 | 50 | 42 | 28 | 24 |
N.S. |
1 | 1.15 | 1.00 | 0.85 | 0.85 | 1.52 | 1.27 | 0.85 | 0.73 |
time (sec) |
N/A | 0.228 | 0.014 | 0.161 | 0.194 | 0.269 | 0.166 | 0.315 | 0.058 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 33 | 38 | 30 | 28 | 28 | 39 | 41 | 28 | 24 |
N.S. |
1 | 1.15 | 0.91 | 0.85 | 0.85 | 1.18 | 1.24 | 0.85 | 0.73 |
time (sec) |
N/A | 0.217 | 0.105 | 0.067 | 0.216 | 0.336 | 0.106 | 0.311 | 0.047 |
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 | 24 | 24 | 47 | 25 | 22 | 24 | 0 | 23 | 38 |
N.S. |
1 | 1.00 | 1.96 | 1.04 | 0.92 | 1.00 | 0.00 | 0.96 | 1.58 |
time (sec) |
N/A | 0.198 | 0.016 | 0.096 | 0.193 | 0.257 | 0.000 | 0.307 | 8.882 |
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 | 25 | 23 | 37 | 21 | 25 | 33 | 0 | 26 | 55 |
N.S. |
1 | 0.92 | 1.48 | 0.84 | 1.00 | 1.32 | 0.00 | 1.04 | 2.20 |
time (sec) |
N/A | 0.226 | 0.016 | 0.118 | 0.191 | 0.275 | 0.000 | 0.304 | 9.023 |
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 | 30 | 30 | 29 | 24 | 24 | 29 | 0 | 24 | 25 |
N.S. |
1 | 1.00 | 0.97 | 0.80 | 0.80 | 0.97 | 0.00 | 0.80 | 0.83 |
time (sec) |
N/A | 0.212 | 0.013 | 0.086 | 0.194 | 0.250 | 0.000 | 0.312 | 9.153 |
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 | 33 | 38 | 33 | 28 | 26 | 39 | 0 | 26 | 39 |
N.S. |
1 | 1.15 | 1.00 | 0.85 | 0.79 | 1.18 | 0.00 | 0.79 | 1.18 |
time (sec) |
N/A | 0.230 | 0.015 | 0.110 | 0.200 | 0.266 | 0.000 | 0.306 | 9.885 |
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 | 33 | 38 | 33 | 28 | 26 | 40 | 0 | 26 | 26 |
N.S. |
1 | 1.15 | 1.00 | 0.85 | 0.79 | 1.21 | 0.00 | 0.79 | 0.79 |
time (sec) |
N/A | 0.239 | 0.011 | 0.135 | 0.193 | 0.319 | 0.000 | 0.298 | 9.579 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 55 | 53 | 53 | 45 | 45 | 72 | 63 | 45 | 36 |
N.S. |
1 | 0.96 | 0.96 | 0.82 | 0.82 | 1.31 | 1.15 | 0.82 | 0.65 |
time (sec) |
N/A | 0.254 | 0.233 | 0.138 | 0.199 | 0.263 | 0.217 | 0.314 | 9.061 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 55 | 53 | 56 | 45 | 45 | 58 | 63 | 45 | 36 |
N.S. |
1 | 0.96 | 1.02 | 0.82 | 0.82 | 1.05 | 1.15 | 0.82 | 0.65 |
time (sec) |
N/A | 0.243 | 0.024 | 0.105 | 0.203 | 0.265 | 0.156 | 0.322 | 8.953 |
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 | 47 | 44 | 47 | 37 | 41 | 43 | 0 | 42 | 119 |
N.S. |
1 | 0.94 | 1.00 | 0.79 | 0.87 | 0.91 | 0.00 | 0.89 | 2.53 |
time (sec) |
N/A | 0.220 | 0.022 | 0.205 | 0.197 | 0.318 | 0.000 | 0.317 | 9.297 |
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 | 43 | 35 | 38 | 35 | 40 | 46 | 0 | 41 | 111 |
N.S. |
1 | 0.81 | 0.88 | 0.81 | 0.93 | 1.07 | 0.00 | 0.95 | 2.58 |
time (sec) |
N/A | 0.245 | 0.019 | 0.137 | 0.202 | 0.271 | 0.000 | 0.311 | 9.404 |