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 | B | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 261 | 280 | 194 | 1260 | 0 | 1151 | 0 | 0 | 0 |
| N.S. |
1 | 1.07 | 0.74 | 4.83 | 0.00 | 4.41 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.404 | 0.835 | 11.730 | 0.000 | 0.159 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 320 | 336 | 262 | 1593 | 0 | 1594 | 0 | 0 | 0 |
| N.S. |
1 | 1.05 | 0.82 | 4.98 | 0.00 | 4.98 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.497 | 0.961 | 17.422 | 0.000 | 0.185 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 400 | 419 | 315 | 2083 | 0 | 2449 | 0 | 0 | 0 |
| N.S. |
1 | 1.05 | 0.79 | 5.21 | 0.00 | 6.12 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.670 | 1.630 | 26.634 | 0.000 | 0.259 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 237 | 246 | 295 | 1372 | 0 | 820 | 0 | 0 | 0 |
| N.S. |
1 | 1.04 | 1.24 | 5.79 | 0.00 | 3.46 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.259 | 1.064 | 3.139 | 0.000 | 0.130 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 185 | 186 | 223 | 925 | 0 | 674 | 0 | 0 | 0 |
| N.S. |
1 | 1.01 | 1.21 | 5.00 | 0.00 | 3.64 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.186 | 1.205 | 1.785 | 0.000 | 0.115 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 169 | 170 | 201 | 382 | 0 | 555 | 0 | 0 | 0 |
| N.S. |
1 | 1.01 | 1.19 | 2.26 | 0.00 | 3.28 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.161 | 0.874 | 1.332 | 0.000 | 0.119 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 180 | 181 | 210 | 443 | 0 | 582 | 0 | 0 | 0 |
| N.S. |
1 | 1.01 | 1.17 | 2.46 | 0.00 | 3.23 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.158 | 0.856 | 1.272 | 0.000 | 0.110 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 242 | 244 | 264 | 925 | 0 | 1172 | 0 | 0 | 0 |
| N.S. |
1 | 1.01 | 1.09 | 3.82 | 0.00 | 4.84 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.223 | 1.482 | 1.584 | 0.000 | 0.138 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F(-1) | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 321 | 333 | 364 | 1291 | 0 | 2198 | 0 | 0 | 0 |
| N.S. |
1 | 1.04 | 1.13 | 4.02 | 0.00 | 6.85 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.326 | 3.041 | 3.335 | 0.000 | 0.185 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 247 | 256 | 307 | 1372 | 0 | 1152 | 0 | 0 | 0 |
| N.S. |
1 | 1.04 | 1.24 | 5.55 | 0.00 | 4.66 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.362 | 1.890 | 21.829 | 0.000 | 0.143 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 228 | 237 | 280 | 1049 | 0 | 936 | 0 | 0 | 0 |
| N.S. |
1 | 1.04 | 1.23 | 4.60 | 0.00 | 4.11 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.368 | 1.975 | 2.843 | 0.000 | 0.120 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 224 | 233 | 253 | 906 | 0 | 880 | 0 | 0 | 0 |
| N.S. |
1 | 1.04 | 1.13 | 4.04 | 0.00 | 3.93 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.276 | 1.810 | 2.362 | 0.000 | 0.120 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 248 | 257 | 287 | 507 | 0 | 1043 | 0 | 0 | 0 |
| N.S. |
1 | 1.04 | 1.16 | 2.04 | 0.00 | 4.21 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.299 | 4.332 | 1.724 | 0.000 | 0.138 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 314 | 326 | 402 | 1299 | 0 | 2048 | 0 | 0 | 0 |
| N.S. |
1 | 1.04 | 1.28 | 4.14 | 0.00 | 6.52 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.435 | 5.696 | 3.462 | 0.000 | 0.171 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F(-1) | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
| size | 390 | 405 | 674 | 1758 | 0 | 3271 | 0 | 0 | 0 |
| N.S. |
1 | 1.04 | 1.73 | 4.51 | 0.00 | 8.39 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.565 | 9.129 | 5.197 | 0.000 | 0.257 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 309 | 322 | 382 | 1615 | 0 | 1513 | 0 | 0 | 0 |
| N.S. |
1 | 1.04 | 1.24 | 5.23 | 0.00 | 4.90 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.565 | 4.115 | 175.868 | 0.000 | 0.150 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 310 | 323 | 438 | 1462 | 0 | 1589 | 0 | 0 | 0 |
| N.S. |
1 | 1.04 | 1.41 | 4.72 | 0.00 | 5.13 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.614 | 4.289 | 4.434 | 0.000 | 0.143 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 321 | 334 | 446 | 1056 | 0 | 1658 | 0 | 0 | 0 |
| N.S. |
1 | 1.04 | 1.39 | 3.29 | 0.00 | 5.17 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.530 | 4.217 | 3.925 | 0.000 | 0.162 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
| size | 331 | 344 | 442 | 593 | 0 | 1744 | 0 | 0 | 0 |
| N.S. |
1 | 1.04 | 1.34 | 1.79 | 0.00 | 5.27 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.525 | 8.959 | 2.928 | 0.000 | 0.161 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F(-1) | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
| size | 407 | 423 | 745 | 1851 | 0 | 3067 | 0 | 0 | 0 |
| N.S. |
1 | 1.04 | 1.83 | 4.55 | 0.00 | 7.54 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.696 | 11.702 | 6.196 | 0.000 | 0.230 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F(-1) | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
| size | 499 | 518 | 828 | 2311 | 0 | 4788 | 0 | 0 | 0 |
| N.S. |
1 | 1.04 | 1.66 | 4.63 | 0.00 | 9.60 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.842 | 11.935 | 8.158 | 0.000 | 0.369 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | A | F | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 156 | 161 | 149 | 141 | 0 | 240 | 0 | 252 | 0 |
| N.S. |
1 | 1.03 | 0.96 | 0.90 | 0.00 | 1.54 | 0.00 | 1.62 | 0.00 |
| time (sec) |
N/A | 0.186 | 0.657 | 2.493 | 0.000 | 0.258 | 0.000 | 0.408 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | A | F | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 108 | 112 | 114 | 92 | 0 | 157 | 0 | 158 | 0 |
| N.S. |
1 | 1.04 | 1.06 | 0.85 | 0.00 | 1.45 | 0.00 | 1.46 | 0.00 |
| time (sec) |
N/A | 0.116 | 0.408 | 1.833 | 0.000 | 0.254 | 0.000 | 0.492 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | A | F | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 59 | 62 | 83 | 58 | 0 | 85 | 0 | 85 | 0 |
| N.S. |
1 | 1.05 | 1.41 | 0.98 | 0.00 | 1.44 | 0.00 | 1.44 | 0.00 |
| time (sec) |
N/A | 0.040 | 0.197 | 1.399 | 0.000 | 0.253 | 0.000 | 0.494 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | A | F | B | F | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 25 | 26 | 68 | 43 | 0 | 50 | 0 | 36 | 33 |
| N.S. |
1 | 1.04 | 2.72 | 1.72 | 0.00 | 2.00 | 0.00 | 1.44 | 1.32 |
| time (sec) |
N/A | 0.010 | 0.022 | 0.696 | 0.000 | 0.258 | 0.000 | 0.507 | 0.227 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | A | F | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 61 | 61 | 660 | 80 | 0 | 464 | 0 | 63 | 0 |
| N.S. |
1 | 1.00 | 10.82 | 1.31 | 0.00 | 7.61 | 0.00 | 1.03 | 0.00 |
| time (sec) |
N/A | 0.080 | 3.917 | 0.894 | 0.000 | 0.331 | 0.000 | 0.432 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | B | F(-1) | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 104 | 105 | 874 | 155 | 0 | 786 | 0 | 134 | 0 |
| N.S. |
1 | 1.01 | 8.40 | 1.49 | 0.00 | 7.56 | 0.00 | 1.29 | 0.00 |
| time (sec) |
N/A | 0.142 | 4.567 | 1.170 | 0.000 | 0.356 | 0.000 | 0.379 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | B | F(-1) | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 152 | 154 | 923 | 254 | 0 | 1250 | 0 | 213 | 0 |
| N.S. |
1 | 1.01 | 6.07 | 1.67 | 0.00 | 8.22 | 0.00 | 1.40 | 0.00 |
| time (sec) |
N/A | 0.194 | 5.784 | 1.276 | 0.000 | 0.392 | 0.000 | 0.399 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | A | F | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 219 | 231 | 205 | 195 | 0 | 339 | 0 | 355 | 0 |
| N.S. |
1 | 1.05 | 0.94 | 0.89 | 0.00 | 1.55 | 0.00 | 1.62 | 0.00 |
| time (sec) |
N/A | 0.268 | 4.507 | 3.020 | 0.000 | 0.281 | 0.000 | 0.402 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | A | F | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 150 | 157 | 138 | 130 | 0 | 229 | 0 | 237 | 0 |
| N.S. |
1 | 1.05 | 0.92 | 0.87 | 0.00 | 1.53 | 0.00 | 1.58 | 0.00 |
| time (sec) |
N/A | 0.158 | 3.279 | 2.299 | 0.000 | 0.255 | 0.000 | 0.372 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | A | F | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 97 | 101 | 103 | 77 | 0 | 136 | 0 | 139 | 0 |
| N.S. |
1 | 1.04 | 1.06 | 0.79 | 0.00 | 1.40 | 0.00 | 1.43 | 0.00 |
| time (sec) |
N/A | 0.059 | 1.243 | 1.816 | 0.000 | 0.268 | 0.000 | 0.342 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | A | F | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 51 | 59 | 90 | 53 | 0 | 76 | 0 | 67 | 0 |
| N.S. |
1 | 1.16 | 1.76 | 1.04 | 0.00 | 1.49 | 0.00 | 1.31 | 0.00 |
| time (sec) |
N/A | 0.021 | 0.362 | 0.683 | 0.000 | 0.257 | 0.000 | 0.350 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | B | F(-1) | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 95 | 98 | 744 | 137 | 0 | 651 | 0 | 125 | 0 |
| N.S. |
1 | 1.03 | 7.83 | 1.44 | 0.00 | 6.85 | 0.00 | 1.32 | 0.00 |
| time (sec) |
N/A | 0.131 | 7.204 | 1.319 | 0.000 | 0.341 | 0.000 | 0.370 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | B | F(-1) | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 117 | 119 | 762 | 233 | 0 | 970 | 0 | 196 | 0 |
| N.S. |
1 | 1.02 | 6.51 | 1.99 | 0.00 | 8.29 | 0.00 | 1.68 | 0.00 |
| time (sec) |
N/A | 0.134 | 7.620 | 1.076 | 0.000 | 0.359 | 0.000 | 0.367 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | B | F(-1) | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 173 | 179 | 891 | 429 | 0 | 1558 | 0 | 311 | 0 |
| N.S. |
1 | 1.03 | 5.15 | 2.48 | 0.00 | 9.01 | 0.00 | 1.80 | 0.00 |
| time (sec) |
N/A | 0.205 | 8.133 | 1.168 | 0.000 | 0.426 | 0.000 | 0.381 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | A | F | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 312 | 328 | 246 | 249 | 0 | 493 | 0 | 486 | 0 |
| N.S. |
1 | 1.05 | 0.79 | 0.80 | 0.00 | 1.58 | 0.00 | 1.56 | 0.00 |
| time (sec) |
N/A | 0.446 | 8.520 | 37.721 | 0.000 | 0.285 | 0.000 | 0.453 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | A | F | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 192 | 202 | 180 | 168 | 0 | 339 | 0 | 331 | 0 |
| N.S. |
1 | 1.05 | 0.94 | 0.88 | 0.00 | 1.77 | 0.00 | 1.72 | 0.00 |
| time (sec) |
N/A | 0.188 | 5.194 | 7.776 | 0.000 | 0.288 | 0.000 | 0.556 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | A | F | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 131 | 138 | 119 | 99 | 0 | 206 | 0 | 202 | 0 |
| N.S. |
1 | 1.05 | 0.91 | 0.76 | 0.00 | 1.57 | 0.00 | 1.54 | 0.00 |
| time (sec) |
N/A | 0.075 | 3.278 | 2.435 | 0.000 | 0.294 | 0.000 | 0.503 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | A | F | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 82 | 89 | 120 | 65 | 0 | 115 | 0 | 102 | 0 |
| N.S. |
1 | 1.09 | 1.46 | 0.79 | 0.00 | 1.40 | 0.00 | 1.24 | 0.00 |
| time (sec) |
N/A | 0.036 | 0.902 | 0.755 | 0.000 | 0.263 | 0.000 | 0.474 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | B | F(-1) | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 132 | 142 | 804 | 228 | 0 | 868 | 0 | 229 | 0 |
| N.S. |
1 | 1.08 | 6.09 | 1.73 | 0.00 | 6.58 | 0.00 | 1.73 | 0.00 |
| time (sec) |
N/A | 0.278 | 7.532 | 2.036 | 0.000 | 0.369 | 0.000 | 0.681 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | B | F(-1) | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 162 | 166 | 895 | 392 | 0 | 1322 | 0 | 301 | 0 |
| N.S. |
1 | 1.02 | 5.52 | 2.42 | 0.00 | 8.16 | 0.00 | 1.86 | 0.00 |
| time (sec) |
N/A | 0.289 | 7.922 | 10.365 | 0.000 | 0.377 | 0.000 | 0.371 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | B | F(-1) | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 188 | 194 | 923 | 567 | 0 | 1994 | 0 | 429 | 0 |
| N.S. |
1 | 1.03 | 4.91 | 3.02 | 0.00 | 10.61 | 0.00 | 2.28 | 0.00 |
| time (sec) |
N/A | 0.311 | 8.646 | 62.656 | 0.000 | 0.472 | 0.000 | 0.372 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | B | F | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 169 | 178 | 158 | 285 | 0 | 387 | 0 | 284 | 0 |
| N.S. |
1 | 1.05 | 0.93 | 1.69 | 0.00 | 2.29 | 0.00 | 1.68 | 0.00 |
| time (sec) |
N/A | 0.337 | 1.632 | 2.635 | 0.000 | 0.274 | 0.000 | 0.382 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | B | F | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 114 | 123 | 128 | 185 | 0 | 286 | 0 | 192 | 0 |
| N.S. |
1 | 1.08 | 1.12 | 1.62 | 0.00 | 2.51 | 0.00 | 1.68 | 0.00 |
| time (sec) |
N/A | 0.148 | 1.798 | 2.144 | 0.000 | 0.284 | 0.000 | 0.345 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | B | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 73 | 79 | 109 | 128 | 0 | 214 | 0 | 143 | 151 |
| N.S. |
1 | 1.08 | 1.49 | 1.75 | 0.00 | 2.93 | 0.00 | 1.96 | 2.07 |
| time (sec) |
N/A | 0.058 | 0.574 | 3.250 | 0.000 | 0.276 | 0.000 | 0.458 | 9.429 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | A | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 41 | 47 | 76 | 75 | 0 | 167 | 0 | 111 | 49 |
| N.S. |
1 | 1.15 | 1.85 | 1.83 | 0.00 | 4.07 | 0.00 | 2.71 | 1.20 |
| time (sec) |
N/A | 0.018 | 0.120 | 0.799 | 0.000 | 0.270 | 0.000 | 0.423 | 7.774 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | B | F | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 117 | 123 | 601 | 131 | 0 | 685 | 0 | 197 | 0 |
| N.S. |
1 | 1.05 | 5.14 | 1.12 | 0.00 | 5.85 | 0.00 | 1.68 | 0.00 |
| time (sec) |
N/A | 0.165 | 1.767 | 1.194 | 0.000 | 0.369 | 0.000 | 0.533 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | B | F(-1) | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 169 | 175 | 649 | 449 | 0 | 1494 | 0 | 363 | 0 |
| N.S. |
1 | 1.04 | 3.84 | 2.66 | 0.00 | 8.84 | 0.00 | 2.15 | 0.00 |
| time (sec) |
N/A | 0.318 | 3.589 | 0.980 | 0.000 | 0.504 | 0.000 | 0.523 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | B | F(-1) | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 241 | 247 | 779 | 1066 | 0 | 2903 | 0 | 559 | 0 |
| N.S. |
1 | 1.02 | 3.23 | 4.42 | 0.00 | 12.05 | 0.00 | 2.32 | 0.00 |
| time (sec) |
N/A | 0.525 | 4.570 | 1.448 | 0.000 | 0.730 | 0.000 | 0.427 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | B | F | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 178 | 192 | 331 | 490 | 0 | 494 | 0 | 362 | 0 |
| N.S. |
1 | 1.08 | 1.86 | 2.75 | 0.00 | 2.78 | 0.00 | 2.03 | 0.00 |
| time (sec) |
N/A | 0.336 | 1.662 | 3.175 | 0.000 | 0.304 | 0.000 | 0.393 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | B | F | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 127 | 138 | 242 | 316 | 0 | 380 | 0 | 266 | 0 |
| N.S. |
1 | 1.09 | 1.91 | 2.49 | 0.00 | 2.99 | 0.00 | 2.09 | 0.00 |
| time (sec) |
N/A | 0.157 | 1.248 | 2.697 | 0.000 | 0.322 | 0.000 | 0.346 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | B | F | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 79 | 87 | 153 | 176 | 0 | 293 | 0 | 184 | 0 |
| N.S. |
1 | 1.10 | 1.94 | 2.23 | 0.00 | 3.71 | 0.00 | 2.33 | 0.00 |
| time (sec) |
N/A | 0.059 | 0.626 | 2.180 | 0.000 | 0.290 | 0.000 | 0.375 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | B | F | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 69 | 77 | 111 | 125 | 0 | 252 | 0 | 133 | 0 |
| N.S. |
1 | 1.12 | 1.61 | 1.81 | 0.00 | 3.65 | 0.00 | 1.93 | 0.00 |
| time (sec) |
N/A | 0.032 | 0.209 | 0.871 | 0.000 | 0.293 | 0.000 | 0.354 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | B | F | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 158 | 164 | 750 | 348 | 0 | 1299 | 0 | 403 | 0 |
| N.S. |
1 | 1.04 | 4.75 | 2.20 | 0.00 | 8.22 | 0.00 | 2.55 | 0.00 |
| time (sec) |
N/A | 0.302 | 3.400 | 1.201 | 0.000 | 0.483 | 0.000 | 0.419 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F(-1) | B | F(-1) | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 234 | 243 | 856 | 978 | 0 | 2515 | 0 | 0 | 0 |
| N.S. |
1 | 1.04 | 3.66 | 4.18 | 0.00 | 10.75 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.526 | 5.745 | 1.638 | 0.000 | 0.775 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F(-1) | B | F(-1) | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 304 | 318 | 935 | 2219 | 0 | 4133 | 0 | 998 | 0 |
| N.S. |
1 | 1.05 | 3.08 | 7.30 | 0.00 | 13.60 | 0.00 | 3.28 | 0.00 |
| time (sec) |
N/A | 0.769 | 7.234 | 2.309 | 0.000 | 1.290 | 0.000 | 0.610 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | B | F(-1) | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 180 | 194 | 403 | 688 | 0 | 608 | 0 | 404 | 0 |
| N.S. |
1 | 1.08 | 2.24 | 3.82 | 0.00 | 3.38 | 0.00 | 2.24 | 0.00 |
| time (sec) |
N/A | 0.341 | 1.932 | 4.152 | 0.000 | 0.296 | 0.000 | 0.474 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | B | F(-1) | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 136 | 147 | 255 | 378 | 0 | 492 | 0 | 297 | 0 |
| N.S. |
1 | 1.08 | 1.88 | 2.78 | 0.00 | 3.62 | 0.00 | 2.18 | 0.00 |
| time (sec) |
N/A | 0.165 | 1.474 | 2.981 | 0.000 | 0.283 | 0.000 | 0.457 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | B | F | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 115 | 126 | 230 | 279 | 0 | 392 | 0 | 236 | 0 |
| N.S. |
1 | 1.10 | 2.00 | 2.43 | 0.00 | 3.41 | 0.00 | 2.05 | 0.00 |
| time (sec) |
N/A | 0.073 | 0.756 | 2.677 | 0.000 | 0.286 | 0.000 | 0.400 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | B | F | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 96 | 107 | 152 | 199 | 0 | 320 | 0 | 153 | 0 |
| N.S. |
1 | 1.11 | 1.58 | 2.07 | 0.00 | 3.33 | 0.00 | 1.59 | 0.00 |
| time (sec) |
N/A | 0.050 | 0.262 | 0.865 | 0.000 | 0.275 | 0.000 | 0.384 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | B | F(-1) | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 209 | 218 | 866 | 732 | 0 | 2015 | 0 | 596 | 0 |
| N.S. |
1 | 1.04 | 4.14 | 3.50 | 0.00 | 9.64 | 0.00 | 2.85 | 0.00 |
| time (sec) |
N/A | 0.524 | 6.413 | 1.251 | 0.000 | 0.673 | 0.000 | 0.474 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F(-1) | B | F(-1) | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 302 | 313 | 935 | 1972 | 0 | 3719 | 0 | 902 | 0 |
| N.S. |
1 | 1.04 | 3.10 | 6.53 | 0.00 | 12.31 | 0.00 | 2.99 | 0.00 |
| time (sec) |
N/A | 0.776 | 9.515 | 2.043 | 0.000 | 1.229 | 0.000 | 0.607 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F(-1) | B | F(-1) | B | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 383 | 400 | 1048 | 3535 | 0 | 5999 | 0 | 1399 | 0 |
| N.S. |
1 | 1.04 | 2.74 | 9.23 | 0.00 | 15.66 | 0.00 | 3.65 | 0.00 |
| time (sec) |
N/A | 1.051 | 14.004 | 2.876 | 0.000 | 2.081 | 0.000 | 0.780 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | F(-1) | F | B | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 198 | 203 | 395 | 0 | 0 | 1257 | 0 | 0 | 0 |
| N.S. |
1 | 1.03 | 1.99 | 0.00 | 0.00 | 6.35 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.270 | 1.948 | 0.000 | 0.000 | 0.649 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | F(-1) | F | B | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 154 | 156 | 363 | 0 | 0 | 1069 | 0 | 0 | 0 |
| N.S. |
1 | 1.01 | 2.36 | 0.00 | 0.00 | 6.94 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.195 | 1.256 | 0.000 | 0.000 | 0.585 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | F(-1) | F | B | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 104 | 105 | 345 | 0 | 0 | 945 | 0 | 0 | 0 |
| N.S. |
1 | 1.01 | 3.32 | 0.00 | 0.00 | 9.09 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.121 | 0.928 | 0.000 | 0.000 | 0.585 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | B | F | F | F(-1) |
| verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
| size | 61 | 61 | 290 | 1141 | 0 | 777 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 4.75 | 18.70 | 0.00 | 12.74 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.062 | 0.967 | 1.754 | 0.000 | 0.532 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | B | B | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 44 | 45 | 87 | 84 | 179 | 129 | 0 | 151 | 145 |
| N.S. |
1 | 1.02 | 1.98 | 1.91 | 4.07 | 2.93 | 0.00 | 3.43 | 3.30 |
| time (sec) |
N/A | 0.061 | 0.487 | 3.365 | 0.321 | 0.272 | 0.000 | 0.563 | 9.510 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | B | B | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 89 | 95 | 101 | 197 | 340 | 300 | 0 | 471 | 353 |
| N.S. |
1 | 1.07 | 1.13 | 2.21 | 3.82 | 3.37 | 0.00 | 5.29 | 3.97 |
| time (sec) |
N/A | 0.130 | 0.548 | 3.874 | 0.338 | 0.291 | 0.000 | 0.832 | 15.146 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | B | B | F(-1) | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 139 | 142 | 131 | 375 | 544 | 556 | 0 | 1050 | 501 |
| N.S. |
1 | 1.02 | 0.94 | 2.70 | 3.91 | 4.00 | 0.00 | 7.55 | 3.60 |
| time (sec) |
N/A | 0.201 | 0.753 | 3.580 | 0.365 | 0.307 | 0.000 | 1.220 | 17.148 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F(-1) | F | B | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 273 | 285 | 321 | 0 | 0 | 1579 | 0 | 0 | 0 |
| N.S. |
1 | 1.04 | 1.18 | 0.00 | 0.00 | 5.78 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.399 | 3.705 | 0.000 | 0.000 | 0.987 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F(-1) | F | B | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 217 | 228 | 284 | 0 | 0 | 1337 | 0 | 0 | 0 |
| N.S. |
1 | 1.05 | 1.31 | 0.00 | 0.00 | 6.16 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.324 | 2.223 | 0.000 | 0.000 | 0.679 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F(-1) | F | B | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 165 | 171 | 250 | 0 | 0 | 1127 | 0 | 0 | 0 |
| N.S. |
1 | 1.04 | 1.52 | 0.00 | 0.00 | 6.83 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.214 | 1.345 | 0.000 | 0.000 | 0.611 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | F | F | B | F | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 109 | 111 | 304 | 0 | 0 | 989 | 0 | 0 | 0 |
| N.S. |
1 | 1.02 | 2.79 | 0.00 | 0.00 | 9.07 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.150 | 1.552 | 0.000 | 0.000 | 0.621 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | B | F | B | F | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
| size | 114 | 117 | 380 | 4782 | 0 | 1297 | 0 | 0 | 0 |
| N.S. |
1 | 1.03 | 3.33 | 41.95 | 0.00 | 11.38 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.156 | 5.369 | 1.086 | 0.000 | 0.614 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | B | B | F | F(-1) | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 105 | 115 | 104 | 254 | 307 | 323 | 0 | 0 | 387 |
| N.S. |
1 | 1.10 | 0.99 | 2.42 | 2.92 | 3.08 | 0.00 | 0.00 | 3.69 |
| time (sec) |
N/A | 0.154 | 1.619 | 3.214 | 0.348 | 0.288 | 0.000 | 0.000 | 15.497 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | B | B | F(-1) | F(-1) | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 163 | 172 | 142 | 471 | 505 | 598 | 0 | 0 | 541 |
| N.S. |
1 | 1.06 | 0.87 | 2.89 | 3.10 | 3.67 | 0.00 | 0.00 | 3.32 |
| time (sec) |
N/A | 0.237 | 1.974 | 3.781 | 0.355 | 0.326 | 0.000 | 0.000 | 18.534 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | B | B | F(-1) | F(-1) | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 217 | 229 | 195 | 764 | 750 | 937 | 0 | 0 | 807 |
| N.S. |
1 | 1.06 | 0.90 | 3.52 | 3.46 | 4.32 | 0.00 | 0.00 | 3.72 |
| time (sec) |
N/A | 0.329 | 2.340 | 3.812 | 0.406 | 0.373 | 0.000 | 0.000 | 21.530 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F(-1) | F | B | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 362 | 377 | 398 | 0 | 0 | 2083 | 0 | 0 | 0 |
| N.S. |
1 | 1.04 | 1.10 | 0.00 | 0.00 | 5.75 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.623 | 7.496 | 0.000 | 0.000 | 1.240 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F(-1) | F | B | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 300 | 312 | 330 | 0 | 0 | 1751 | 0 | 0 | 0 |
| N.S. |
1 | 1.04 | 1.10 | 0.00 | 0.00 | 5.84 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.510 | 6.556 | 0.000 | 0.000 | 1.032 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F(-1) | F | B | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 230 | 241 | 288 | 0 | 0 | 1455 | 0 | 0 | 0 |
| N.S. |
1 | 1.05 | 1.25 | 0.00 | 0.00 | 6.33 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.386 | 2.377 | 0.000 | 0.000 | 0.763 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | B | F(-1) | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 172 | 178 | 259 | 0 | 0 | 1219 | 0 | 0 | 0 |
| N.S. |
1 | 1.03 | 1.51 | 0.00 | 0.00 | 7.09 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.305 | 2.992 | 0.000 | 0.000 | 0.649 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | B | F(-1) | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 175 | 180 | 266 | 0 | 0 | 1665 | 0 | 0 | 0 |
| N.S. |
1 | 1.03 | 1.52 | 0.00 | 0.00 | 9.51 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.311 | 3.080 | 0.000 | 0.000 | 0.648 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | B | F(-1) | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
| size | 173 | 183 | 265 | 13122 | 0 | 2297 | 0 | 0 | 0 |
| N.S. |
1 | 1.06 | 1.53 | 75.85 | 0.00 | 13.28 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.328 | 7.159 | 1.293 | 0.000 | 0.671 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | B | B | F(-1) | F(-1) | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 180 | 189 | 152 | 552 | 464 | 654 | 0 | 0 | 590 |
| N.S. |
1 | 1.05 | 0.84 | 3.07 | 2.58 | 3.63 | 0.00 | 0.00 | 3.28 |
| time (sec) |
N/A | 0.334 | 3.759 | 4.236 | 0.360 | 0.330 | 0.000 | 0.000 | 17.937 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | B | B | F(-1) | F(-1) | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 242 | 254 | 216 | 885 | 703 | 1033 | 0 | 0 | 862 |
| N.S. |
1 | 1.05 | 0.89 | 3.66 | 2.90 | 4.27 | 0.00 | 0.00 | 3.56 |
| time (sec) |
N/A | 0.427 | 4.808 | 4.247 | 0.397 | 0.393 | 0.000 | 0.000 | 21.734 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | B | B | F(-1) | F(-1) | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 300 | 317 | 304 | 1280 | 984 | 1492 | 0 | 0 | 1155 |
| N.S. |
1 | 1.06 | 1.01 | 4.27 | 3.28 | 4.97 | 0.00 | 0.00 | 3.85 |
| time (sec) |
N/A | 0.535 | 6.238 | 3.022 | 0.447 | 0.415 | 0.000 | 0.000 | 28.868 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | F | F | B | F(-1) | F(-1) | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 243 | 249 | 1893 | 0 | 0 | 2925 | 0 | 0 | 0 |
| N.S. |
1 | 1.02 | 7.79 | 0.00 | 0.00 | 12.04 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.646 | 15.474 | 0.000 | 0.000 | 0.787 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | F | F | B | F | F(-1) | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 182 | 188 | 1639 | 0 | 0 | 2525 | 0 | 0 | 0 |
| N.S. |
1 | 1.03 | 9.01 | 0.00 | 0.00 | 13.87 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.424 | 15.383 | 0.000 | 0.000 | 0.673 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | B | F | F(-1) | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 135 | 141 | 1251 | 3361 | 0 | 1944 | 0 | 0 | 0 |
| N.S. |
1 | 1.04 | 9.27 | 24.90 | 0.00 | 14.40 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.205 | 14.204 | 1.477 | 0.000 | 0.616 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | B | F | A | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 73 | 79 | 283 | 191 | 0 | 475 | 0 | 0 | 0 |
| N.S. |
1 | 1.08 | 3.88 | 2.62 | 0.00 | 6.51 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.078 | 1.998 | 9.789 | 0.000 | 0.407 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | B | F | B | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 125 | 131 | 309 | 444 | 0 | 1016 | 0 | 0 | 0 |
| N.S. |
1 | 1.05 | 2.47 | 3.55 | 0.00 | 8.13 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.173 | 3.258 | 5.365 | 0.000 | 0.487 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | B | F | B | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 185 | 191 | 390 | 2407 | 0 | 1855 | 0 | 0 | 0 |
| N.S. |
1 | 1.03 | 2.11 | 13.01 | 0.00 | 10.03 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.335 | 3.104 | 5.532 | 0.000 | 0.579 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | F | F | B | F(-1) | F(-1) | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 242 | 251 | 1844 | 0 | 0 | 3420 | 0 | 0 | 0 |
| N.S. |
1 | 1.04 | 7.62 | 0.00 | 0.00 | 14.13 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.658 | 15.348 | 0.000 | 0.000 | 0.815 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | B | F | F(-1) | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 188 | 194 | 1625 | 8333 | 0 | 2883 | 0 | 0 | 0 |
| N.S. |
1 | 1.03 | 8.64 | 44.32 | 0.00 | 15.34 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.404 | 15.342 | 1.164 | 0.000 | 0.720 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | B | F | B | F | F(-1) | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 118 | 126 | 375 | 736 | 0 | 896 | 0 | 0 | 0 |
| N.S. |
1 | 1.07 | 3.18 | 6.24 | 0.00 | 7.59 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.150 | 2.381 | 3.715 | 0.000 | 0.480 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | B | F | B | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 127 | 135 | 384 | 643 | 0 | 1008 | 0 | 0 | 0 |
| N.S. |
1 | 1.06 | 3.02 | 5.06 | 0.00 | 7.94 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.168 | 3.511 | 4.912 | 0.000 | 0.517 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | B | F | B | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 186 | 197 | 404 | 1984 | 0 | 1954 | 0 | 0 | 0 |
| N.S. |
1 | 1.06 | 2.17 | 10.67 | 0.00 | 10.51 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.338 | 4.803 | 5.026 | 0.000 | 0.687 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | B | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 257 | 271 | 481 | 4707 | 0 | 3182 | 0 | 0 | 0 |
| N.S. |
1 | 1.05 | 1.87 | 18.32 | 0.00 | 12.38 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.595 | 6.340 | 4.609 | 0.000 | 0.848 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | B | F(-1) | F(-1) | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 251 | 260 | 1845 | 13853 | 0 | 3855 | 0 | 0 | 0 |
| N.S. |
1 | 1.04 | 7.35 | 55.19 | 0.00 | 15.36 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.595 | 15.401 | 1.822 | 0.000 | 0.855 | 0.000 | 0.000 | 0.000 |