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 | F | F | F | A | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 207 | 197 | 196 | 0 | 0 | 0 | 1329 | 0 | 0 |
| N.S. |
1 | 0.95 | 0.95 | 0.00 | 0.00 | 0.00 | 6.42 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.374 | 0.260 | 0.000 | 0.000 | 0.000 | 17.322 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | B | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 210 | 198 | 196 | 0 | 0 | 0 | 1329 | 0 | 0 |
| N.S. |
1 | 0.94 | 0.93 | 0.00 | 0.00 | 0.00 | 6.33 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.380 | 0.233 | 0.000 | 0.000 | 0.000 | 11.369 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | A | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 167 | 158 | 228 | 0 | 0 | 0 | 440 | 0 | 0 |
| N.S. |
1 | 0.95 | 1.37 | 0.00 | 0.00 | 0.00 | 2.63 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.339 | 0.264 | 0.000 | 0.000 | 0.000 | 9.271 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | B | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 176 | 185 | 223 | 0 | 0 | 0 | 437 | 0 | 0 |
| N.S. |
1 | 1.05 | 1.27 | 0.00 | 0.00 | 0.00 | 2.48 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.339 | 0.262 | 0.000 | 0.000 | 0.000 | 5.711 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | A | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 171 | 166 | 170 | 0 | 0 | 0 | 144 | 0 | 0 |
| N.S. |
1 | 0.97 | 0.99 | 0.00 | 0.00 | 0.00 | 0.84 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.302 | 0.239 | 0.000 | 0.000 | 0.000 | 6.361 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | A | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 159 | 159 | 154 | 0 | 0 | 0 | 143 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.97 | 0.00 | 0.00 | 0.00 | 0.90 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.286 | 0.236 | 0.000 | 0.000 | 0.000 | 5.470 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | C | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 168 | 169 | 174 | 0 | 0 | 0 | 148 | 0 | 0 |
| N.S. |
1 | 1.01 | 1.04 | 0.00 | 0.00 | 0.00 | 0.88 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.292 | 0.252 | 0.000 | 0.000 | 0.000 | 8.174 | 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 | 199 | 198 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.99 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.404 | 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 | 163 | 163 | 260 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.60 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.304 | 0.328 | 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 | 161 | 162 | 227 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.01 | 1.41 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.305 | 0.267 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 173 | 131 | 172 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.76 | 0.99 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.279 | 0.232 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 125 | 125 | 131 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.05 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.254 | 0.130 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 176 | 177 | 170 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.01 | 0.97 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.302 | 0.265 | 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 | 178 | 178 | 214 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.20 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.322 | 0.401 | 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 | 213 | 218 | 256 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.02 | 1.20 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.383 | 0.457 | 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 | 392 | 389 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.99 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.010 | 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 | 321 | 309 | 343 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.96 | 1.07 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.645 | 0.588 | 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 | No | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 281 | 267 | 300 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.95 | 1.07 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.447 | 0.420 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 273 | 249 | 223 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.91 | 0.82 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.405 | 0.241 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 244 | 191 | 141 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.78 | 0.58 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.363 | 0.212 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 368 | 306 | 303 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.83 | 0.82 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.574 | 0.412 | 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 | No | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 421 | 296 | 342 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.70 | 0.81 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.569 | 0.601 | 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 | 449 | 433 | 462 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.96 | 1.03 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.095 | 0.895 | 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 | 416 | 387 | 436 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.93 | 1.05 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.741 | 0.665 | 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 | 396 | 364 | 290 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.92 | 0.73 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.587 | 0.407 | 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 | 336 | 326 | 229 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.97 | 0.68 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.525 | 0.312 | 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 | 322 | 322 | 142 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.44 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.562 | 0.269 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 700 | 464 | 434 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.66 | 0.62 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.813 | 0.691 | 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 | No | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 754 | 460 | 478 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.61 | 0.63 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.814 | 0.773 | 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 | C | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 276 | 291 | 182 | 0 | 0 | 0 | 230 | 0 | 0 |
| N.S. |
1 | 1.05 | 0.66 | 0.00 | 0.00 | 0.00 | 0.83 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.642 | 0.217 | 0.000 | 0.000 | 0.000 | 113.065 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | C | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 205 | 214 | 158 | 0 | 0 | 0 | 168 | 0 | 0 |
| N.S. |
1 | 1.04 | 0.77 | 0.00 | 0.00 | 0.00 | 0.82 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.345 | 0.106 | 0.000 | 0.000 | 0.000 | 70.148 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | C | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 135 | 135 | 106 | 0 | 0 | 0 | 107 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.79 | 0.00 | 0.00 | 0.00 | 0.79 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.238 | 0.059 | 0.000 | 0.000 | 0.000 | 37.017 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | C | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 66 | 66 | 64 | 0 | 0 | 0 | 54 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.97 | 0.00 | 0.00 | 0.00 | 0.82 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.179 | 0.026 | 0.000 | 0.000 | 0.000 | 9.519 | 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 | 157 | 164 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.04 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.316 | 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 | 238 | 242 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.448 | 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 | 321 | 322 | 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 | 0.524 | 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 | B | F(-2) | A | F | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 345 | 369 | 304 | 955 | 0 | 678 | 0 | 305 | 0 |
| N.S. |
1 | 1.07 | 0.88 | 2.77 | 0.00 | 1.97 | 0.00 | 0.88 | 0.00 |
| time (sec) |
N/A | 0.642 | 11.128 | 0.681 | 0.000 | 0.380 | 0.000 | 0.363 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F(-2) | A | F | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 251 | 259 | 245 | 512 | 0 | 536 | 0 | 224 | 0 |
| N.S. |
1 | 1.03 | 0.98 | 2.04 | 0.00 | 2.14 | 0.00 | 0.89 | 0.00 |
| time (sec) |
N/A | 0.458 | 10.564 | 0.655 | 0.000 | 0.327 | 0.000 | 0.370 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | F | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 207 | 173 | 181 | 291 | 0 | 418 | 0 | 164 | 0 |
| N.S. |
1 | 0.84 | 0.87 | 1.41 | 0.00 | 2.02 | 0.00 | 0.79 | 0.00 |
| time (sec) |
N/A | 0.317 | 0.773 | 0.569 | 0.000 | 0.311 | 0.000 | 0.338 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | F | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 131 | 131 | 112 | 131 | 0 | 337 | 0 | 114 | 0 |
| N.S. |
1 | 1.00 | 0.85 | 1.00 | 0.00 | 2.57 | 0.00 | 0.87 | 0.00 |
| time (sec) |
N/A | 0.253 | 0.061 | 0.545 | 0.000 | 0.311 | 0.000 | 0.342 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | B | F(-2) | A | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 168 | 162 | 476 | 308 | 0 | 947 | 0 | 0 | 0 |
| N.S. |
1 | 0.96 | 2.83 | 1.83 | 0.00 | 5.64 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.326 | 1.413 | 0.533 | 0.000 | 0.429 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | B | F | A | F | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 137 | 137 | 841 | 708 | 0 | 355 | 0 | 220 | 0 |
| N.S. |
1 | 1.00 | 6.14 | 5.17 | 0.00 | 2.59 | 0.00 | 1.61 | 0.00 |
| time (sec) |
N/A | 0.310 | 9.249 | 0.720 | 0.000 | 0.359 | 0.000 | 0.327 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | A | F | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 202 | 211 | 162 | 1353 | 0 | 442 | 0 | 505 | 0 |
| N.S. |
1 | 1.04 | 0.80 | 6.70 | 0.00 | 2.19 | 0.00 | 2.50 | 0.00 |
| time (sec) |
N/A | 0.448 | 10.119 | 0.759 | 0.000 | 0.630 | 0.000 | 0.314 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | A | F(-1) | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 286 | 307 | 210 | 2059 | 0 | 558 | 0 | 912 | 0 |
| N.S. |
1 | 1.07 | 0.73 | 7.20 | 0.00 | 1.95 | 0.00 | 3.19 | 0.00 |
| time (sec) |
N/A | 0.586 | 10.171 | 1.155 | 0.000 | 1.230 | 0.000 | 0.333 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | A | F(-1) | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 389 | 421 | 273 | 3471 | 0 | 702 | 0 | 1483 | 0 |
| N.S. |
1 | 1.08 | 0.70 | 8.92 | 0.00 | 1.80 | 0.00 | 3.81 | 0.00 |
| time (sec) |
N/A | 0.779 | 10.243 | 1.121 | 0.000 | 8.549 | 0.000 | 0.338 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F(-2) | A | F(-1) | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 449 | 446 | 385 | 1426 | 0 | 1044 | 0 | 513 | 0 |
| N.S. |
1 | 0.99 | 0.86 | 3.18 | 0.00 | 2.33 | 0.00 | 1.14 | 0.00 |
| time (sec) |
N/A | 0.702 | 1.239 | 0.636 | 0.000 | 0.343 | 0.000 | 0.367 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F(-2) | A | F(-1) | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 352 | 347 | 303 | 797 | 0 | 846 | 0 | 405 | 0 |
| N.S. |
1 | 0.99 | 0.86 | 2.26 | 0.00 | 2.40 | 0.00 | 1.15 | 0.00 |
| time (sec) |
N/A | 0.536 | 0.732 | 0.644 | 0.000 | 0.323 | 0.000 | 0.350 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | A | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 295 | 255 | 236 | 483 | 0 | 676 | 1093 | 310 | 0 |
| N.S. |
1 | 0.86 | 0.80 | 1.64 | 0.00 | 2.29 | 3.71 | 1.05 | 0.00 |
| time (sec) |
N/A | 0.388 | 0.518 | 0.549 | 0.000 | 0.311 | 10.979 | 0.355 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | A | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 201 | 215 | 180 | 230 | 0 | 532 | 751 | 229 | 0 |
| N.S. |
1 | 1.07 | 0.90 | 1.14 | 0.00 | 2.65 | 3.74 | 1.14 | 0.00 |
| time (sec) |
N/A | 0.328 | 0.071 | 0.590 | 0.000 | 0.329 | 3.611 | 0.347 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F(-2) | A | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 251 | 257 | 232 | 607 | 0 | 1327 | 0 | 0 | 0 |
| N.S. |
1 | 1.02 | 0.92 | 2.42 | 0.00 | 5.29 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.499 | 0.532 | 0.638 | 0.000 | 2.598 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | A | F | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 240 | 240 | 213 | 1300 | 0 | 1221 | 0 | 339 | 0 |
| N.S. |
1 | 1.00 | 0.89 | 5.42 | 0.00 | 5.09 | 0.00 | 1.41 | 0.00 |
| time (sec) |
N/A | 0.483 | 0.398 | 0.721 | 0.000 | 1.327 | 0.000 | 0.374 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | A | F(-1) | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 256 | 263 | 243 | 2438 | 0 | 1375 | 0 | 626 | 0 |
| N.S. |
1 | 1.03 | 0.95 | 9.52 | 0.00 | 5.37 | 0.00 | 2.45 | 0.00 |
| time (sec) |
N/A | 0.522 | 0.504 | 0.767 | 0.000 | 1.435 | 0.000 | 0.442 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | A | F(-1) | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 211 | 225 | 201 | 4330 | 0 | 558 | 0 | 1005 | 0 |
| N.S. |
1 | 1.07 | 0.95 | 20.52 | 0.00 | 2.64 | 0.00 | 4.76 | 0.00 |
| time (sec) |
N/A | 0.406 | 0.343 | 1.011 | 0.000 | 0.956 | 0.000 | 0.341 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | A | F(-1) | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 295 | 304 | 247 | 7421 | 0 | 704 | 0 | 1618 | 0 |
| N.S. |
1 | 1.03 | 0.84 | 25.16 | 0.00 | 2.39 | 0.00 | 5.48 | 0.00 |
| time (sec) |
N/A | 0.531 | 0.529 | 1.062 | 0.000 | 4.941 | 0.000 | 0.366 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | A | F(-1) | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 395 | 402 | 317 | 10575 | 0 | 872 | 0 | 2352 | 0 |
| N.S. |
1 | 1.02 | 0.80 | 26.77 | 0.00 | 2.21 | 0.00 | 5.95 | 0.00 |
| time (sec) |
N/A | 0.695 | 0.791 | 1.651 | 0.000 | 14.930 | 0.000 | 0.403 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | A | F(-1) | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 498 | 505 | 402 | 16883 | 0 | 1072 | 0 | 3251 | 0 |
| N.S. |
1 | 1.01 | 0.81 | 33.90 | 0.00 | 2.15 | 0.00 | 6.53 | 0.00 |
| time (sec) |
N/A | 0.891 | 1.092 | 1.928 | 0.000 | 37.471 | 0.000 | 0.484 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F(-2) | A | F(-1) | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 574 | 543 | 549 | 1895 | 0 | 1524 | 0 | 784 | 0 |
| N.S. |
1 | 0.95 | 0.96 | 3.30 | 0.00 | 2.66 | 0.00 | 1.37 | 0.00 |
| time (sec) |
N/A | 0.835 | 1.396 | 0.658 | 0.000 | 0.510 | 0.000 | 0.376 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F(-2) | A | F(-1) | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 452 | 434 | 479 | 1080 | 0 | 1272 | 0 | 648 | 0 |
| N.S. |
1 | 0.96 | 1.06 | 2.39 | 0.00 | 2.81 | 0.00 | 1.43 | 0.00 |
| time (sec) |
N/A | 0.643 | 1.200 | 0.662 | 0.000 | 0.671 | 0.000 | 0.376 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 381 | 342 | 388 | 673 | 0 | 1046 | 0 | 526 | 0 |
| N.S. |
1 | 0.90 | 1.02 | 1.77 | 0.00 | 2.75 | 0.00 | 1.38 | 0.00 |
| time (sec) |
N/A | 0.485 | 0.890 | 0.547 | 0.000 | 0.360 | 0.000 | 0.381 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 274 | 302 | 295 | 327 | 0 | 844 | 0 | 415 | 0 |
| N.S. |
1 | 1.10 | 1.08 | 1.19 | 0.00 | 3.08 | 0.00 | 1.51 | 0.00 |
| time (sec) |
N/A | 0.419 | 0.204 | 0.561 | 0.000 | 0.322 | 0.000 | 0.377 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F(-2) | A | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 394 | 414 | 342 | 997 | 0 | 1873 | 0 | 0 | 0 |
| N.S. |
1 | 1.05 | 0.87 | 2.53 | 0.00 | 4.75 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.745 | 0.948 | 0.595 | 0.000 | 30.623 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | A | F(-1) | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 352 | 361 | 309 | 2076 | 0 | 1717 | 0 | 473 | 0 |
| N.S. |
1 | 1.03 | 0.88 | 5.90 | 0.00 | 4.88 | 0.00 | 1.34 | 0.00 |
| time (sec) |
N/A | 0.723 | 1.038 | 0.746 | 0.000 | 10.887 | 0.000 | 0.409 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | A | F(-1) | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 339 | 342 | 287 | 3893 | 0 | 1569 | 0 | 746 | 0 |
| N.S. |
1 | 1.01 | 0.85 | 11.48 | 0.00 | 4.63 | 0.00 | 2.20 | 0.00 |
| time (sec) |
N/A | 0.667 | 0.864 | 0.812 | 0.000 | 4.423 | 0.000 | 0.458 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | A | F(-1) | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 371 | 375 | 316 | 6850 | 0 | 1741 | 0 | 1195 | 0 |
| N.S. |
1 | 1.01 | 0.85 | 18.46 | 0.00 | 4.69 | 0.00 | 3.22 | 0.00 |
| time (sec) |
N/A | 0.745 | 1.024 | 1.060 | 0.000 | 5.776 | 0.000 | 0.498 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | A | F(-1) | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 404 | 426 | 358 | 11685 | 0 | 1917 | 0 | 1750 | 0 |
| N.S. |
1 | 1.05 | 0.89 | 28.92 | 0.00 | 4.75 | 0.00 | 4.33 | 0.00 |
| time (sec) |
N/A | 0.776 | 1.041 | 1.197 | 0.000 | 16.145 | 0.000 | 0.680 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | A | F(-1) | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 289 | 317 | 271 | 19539 | 0 | 872 | 0 | 2449 | 0 |
| N.S. |
1 | 1.10 | 0.94 | 67.61 | 0.00 | 3.02 | 0.00 | 8.47 | 0.00 |
| time (sec) |
N/A | 0.518 | 0.711 | 1.566 | 0.000 | 13.959 | 0.000 | 0.395 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | A | F(-1) | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 386 | 396 | 404 | 32291 | 0 | 1072 | 0 | 3388 | 0 |
| N.S. |
1 | 1.03 | 1.05 | 83.66 | 0.00 | 2.78 | 0.00 | 8.78 | 0.00 |
| time (sec) |
N/A | 0.666 | 0.912 | 1.973 | 0.000 | 41.437 | 0.000 | 0.510 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | A | F(-1) | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 500 | 494 | 497 | 45106 | 0 | 1300 | 0 | 4452 | 0 |
| N.S. |
1 | 0.99 | 0.99 | 90.21 | 0.00 | 2.60 | 0.00 | 8.90 | 0.00 |
| time (sec) |
N/A | 0.830 | 1.217 | 3.187 | 0.000 | 78.301 | 0.000 | 0.775 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | A | F(-1) | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 628 | 608 | 572 | 70736 | 0 | 1550 | 0 | 5681 | 0 |
| N.S. |
1 | 0.97 | 0.91 | 112.64 | 0.00 | 2.47 | 0.00 | 9.05 | 0.00 |
| time (sec) |
N/A | 1.035 | 1.539 | 3.286 | 0.000 | 176.453 | 0.000 | 1.301 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F(-2) | A | F | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 271 | 274 | 277 | 514 | 0 | 758 | 0 | 228 | 0 |
| N.S. |
1 | 1.01 | 1.02 | 1.90 | 0.00 | 2.80 | 0.00 | 0.84 | 0.00 |
| time (sec) |
N/A | 0.545 | 0.438 | 0.686 | 0.000 | 0.665 | 0.000 | 0.369 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | F | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 195 | 202 | 201 | 259 | 0 | 586 | 0 | 182 | 0 |
| N.S. |
1 | 1.04 | 1.03 | 1.33 | 0.00 | 3.01 | 0.00 | 0.93 | 0.00 |
| time (sec) |
N/A | 0.345 | 0.277 | 0.697 | 0.000 | 0.402 | 0.000 | 0.366 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 139 | 139 | 130 | 131 | 0 | 443 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.94 | 0.94 | 0.00 | 3.19 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.271 | 0.190 | 0.556 | 0.000 | 0.392 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | F | F(-2) | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 52 | 52 | 42 | 50 | 0 | 59 | 0 | 0 | 50 |
| N.S. |
1 | 1.00 | 0.81 | 0.96 | 0.00 | 1.13 | 0.00 | 0.00 | 0.96 |
| time (sec) |
N/A | 0.181 | 0.010 | 0.575 | 0.000 | 0.340 | 0.000 | 0.000 | 11.710 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | A | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 143 | 142 | 131 | 136 | 0 | 454 | 0 | 0 | 0 |
| N.S. |
1 | 0.99 | 0.92 | 0.95 | 0.00 | 3.17 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.302 | 0.174 | 0.586 | 0.000 | 0.511 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | A | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 229 | 206 | 201 | 270 | 0 | 610 | 0 | 0 | 0 |
| N.S. |
1 | 0.90 | 0.88 | 1.18 | 0.00 | 2.66 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.384 | 0.260 | 0.687 | 0.000 | 0.972 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | A | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 329 | 281 | 283 | 545 | 0 | 792 | 0 | 0 | 0 |
| N.S. |
1 | 0.85 | 0.86 | 1.66 | 0.00 | 2.41 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.635 | 0.431 | 0.687 | 0.000 | 2.251 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F(-2) | B | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 515 | 511 | 388 | 1923 | 0 | 2120 | 0 | 0 | 0 |
| N.S. |
1 | 0.99 | 0.75 | 3.73 | 0.00 | 4.12 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.795 | 0.833 | 0.869 | 0.000 | 4.284 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F(-2) | B | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 438 | 431 | 300 | 1112 | 0 | 1782 | 0 | 0 | 0 |
| N.S. |
1 | 0.98 | 0.68 | 2.54 | 0.00 | 4.07 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.676 | 0.531 | 0.862 | 0.000 | 1.669 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F(-2) | B | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 297 | 309 | 218 | 639 | 0 | 1466 | 0 | 0 | 0 |
| N.S. |
1 | 1.04 | 0.73 | 2.15 | 0.00 | 4.94 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.477 | 0.319 | 0.694 | 0.000 | 2.061 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | B | F | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 126 | 126 | 95 | 145 | 0 | 308 | 0 | 0 | 1071 |
| N.S. |
1 | 1.00 | 0.75 | 1.15 | 0.00 | 2.44 | 0.00 | 0.00 | 8.50 |
| time (sec) |
N/A | 0.296 | 0.136 | 0.658 | 0.000 | 1.676 | 0.000 | 0.000 | 12.581 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | B | F | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 138 | 138 | 100 | 149 | 0 | 314 | 0 | 0 | 499 |
| N.S. |
1 | 1.00 | 0.72 | 1.08 | 0.00 | 2.28 | 0.00 | 0.00 | 3.62 |
| time (sec) |
N/A | 0.276 | 0.132 | 0.536 | 0.000 | 1.866 | 0.000 | 0.000 | 12.477 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | B | F | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 121 | 121 | 95 | 138 | 0 | 306 | 0 | 0 | 120 |
| N.S. |
1 | 1.00 | 0.79 | 1.14 | 0.00 | 2.53 | 0.00 | 0.00 | 0.99 |
| time (sec) |
N/A | 0.236 | 0.017 | 0.574 | 0.000 | 2.119 | 0.000 | 0.000 | 12.275 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | B | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 271 | 303 | 217 | 360 | 0 | 1476 | 0 | 0 | 0 |
| N.S. |
1 | 1.12 | 0.80 | 1.33 | 0.00 | 5.45 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.478 | 0.334 | 0.593 | 0.000 | 5.464 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | B | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 394 | 437 | 303 | 716 | 0 | 1812 | 0 | 0 | 0 |
| N.S. |
1 | 1.11 | 0.77 | 1.82 | 0.00 | 4.60 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.711 | 0.526 | 0.744 | 0.000 | 11.466 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | B | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 522 | 565 | 390 | 1354 | 0 | 2162 | 0 | 0 | 0 |
| N.S. |
1 | 1.08 | 0.75 | 2.59 | 0.00 | 4.14 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.946 | 0.783 | 0.773 | 0.000 | 28.523 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | B | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 664 | 708 | 493 | 2409 | 0 | 2526 | 0 | 0 | 0 |
| N.S. |
1 | 1.07 | 0.74 | 3.63 | 0.00 | 3.80 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.210 | 0.977 | 1.145 | 0.000 | 64.197 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | B | F(-1) | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 259 | 265 | 235 | 366 | 0 | 820 | 0 | 0 | 3099 |
| N.S. |
1 | 1.02 | 0.91 | 1.41 | 0.00 | 3.17 | 0.00 | 0.00 | 11.97 |
| time (sec) |
N/A | 0.447 | 0.219 | 0.684 | 0.000 | 16.877 | 0.000 | 0.000 | 13.602 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F(-2) | B | F(-1) | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 341 | 353 | 440 | 663 | 0 | 1540 | 0 | 0 | 11469 |
| N.S. |
1 | 1.04 | 1.29 | 1.94 | 0.00 | 4.52 | 0.00 | 0.00 | 33.63 |
| time (sec) |
N/A | 0.528 | 0.346 | 0.657 | 0.000 | 115.684 | 0.000 | 0.000 | 16.999 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 170 | 170 | 221 | 169 | 0 | 33 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.30 | 0.99 | 0.00 | 0.19 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.271 | 32.665 | 0.684 | 0.000 | 0.091 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 23 | 23 | 23 | 18 | 22 | 22 | 0 | 67 | 22 |
| N.S. |
1 | 1.00 | 1.00 | 0.78 | 0.96 | 0.96 | 0.00 | 2.91 | 0.96 |
| time (sec) |
N/A | 0.156 | 10.025 | 0.581 | 0.286 | 0.317 | 0.000 | 0.299 | 11.905 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 294 | 289 | 347 | 216 | 0 | 30 | 0 | 0 | 0 |
| N.S. |
1 | 0.98 | 1.18 | 0.73 | 0.00 | 0.10 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.364 | 20.404 | 0.660 | 0.000 | 0.179 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 144 | 149 | 169 | 157 | 0 | 25 | 0 | 0 | 0 |
| N.S. |
1 | 1.03 | 1.17 | 1.09 | 0.00 | 0.17 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.240 | 20.351 | 0.637 | 0.000 | 0.081 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | A | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 66 | 56 | 48 | 43 | 0 | 60 | 0 | 0 | 0 |
| N.S. |
1 | 0.85 | 0.73 | 0.65 | 0.00 | 0.91 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.203 | 15.354 | 0.549 | 0.000 | 0.264 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 287 | 287 | 349 | 216 | 0 | 32 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.22 | 0.75 | 0.00 | 0.11 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.369 | 10.297 | 0.634 | 0.000 | 0.077 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 146 | 151 | 185 | 159 | 0 | 32 | 0 | 0 | 0 |
| N.S. |
1 | 1.03 | 1.27 | 1.09 | 0.00 | 0.22 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.248 | 20.309 | 0.654 | 0.000 | 0.073 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 201 | 191 | 235 | 176 | 0 | 38 | 0 | 0 | 0 |
| N.S. |
1 | 0.95 | 1.17 | 0.88 | 0.00 | 0.19 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.279 | 21.557 | 0.711 | 0.000 | 0.081 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 23 | 23 | 23 | 18 | 27 | 27 | 0 | 173 | 25 |
| N.S. |
1 | 1.00 | 1.00 | 0.78 | 1.17 | 1.17 | 0.00 | 7.52 | 1.09 |
| time (sec) |
N/A | 0.166 | 10.029 | 0.565 | 0.288 | 0.267 | 0.000 | 0.314 | 0.120 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 325 | 310 | 244 | 230 | 0 | 38 | 0 | 0 | 0 |
| N.S. |
1 | 0.95 | 0.75 | 0.71 | 0.00 | 0.12 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.393 | 10.333 | 0.645 | 0.000 | 0.077 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | F(-1) | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 173 | 168 | 176 | 0 | 0 | 33 | 0 | 0 | 0 |
| N.S. |
1 | 0.97 | 1.02 | 0.00 | 0.00 | 0.19 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.256 | 20.484 | 180.000 | 0.000 | 0.074 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | A | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 94 | 69 | 53 | 57 | 0 | 65 | 0 | 0 | 0 |
| N.S. |
1 | 0.73 | 0.56 | 0.61 | 0.00 | 0.69 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.202 | 10.057 | 0.783 | 0.000 | 0.264 | 0.000 | 0.000 | 0.000 |