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 | A | A | A | F | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 143 | 146 | 252 | 85 | 133 | 142 | 0 | 99 | 91 |
| N.S. |
1 | 1.02 | 1.76 | 0.59 | 0.93 | 0.99 | 0.00 | 0.69 | 0.64 |
| time (sec) |
N/A | 0.502 | 1.638 | 0.637 | 0.304 | 0.275 | 0.000 | 0.396 | 14.088 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | A | A | A | F | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 177 | 184 | 366 | 111 | 177 | 216 | 0 | 131 | 205 |
| N.S. |
1 | 1.04 | 2.07 | 0.63 | 1.00 | 1.22 | 0.00 | 0.74 | 1.16 |
| time (sec) |
N/A | 0.532 | 1.885 | 0.640 | 0.293 | 0.283 | 0.000 | 0.475 | 14.279 |
| 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 | 215 | 218 | 394 | 137 | 218 | 282 | 0 | 160 | 254 |
| N.S. |
1 | 1.01 | 1.83 | 0.64 | 1.01 | 1.31 | 0.00 | 0.74 | 1.18 |
| time (sec) |
N/A | 0.609 | 4.220 | 0.901 | 0.293 | 0.291 | 0.000 | 0.533 | 14.919 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F(-2) | F(-1) | F | F | F(-1) |
| verified |
N/A | No | Yes | No | TBD | TBD | TBD | TBD | TBD |
| size | 310 | 295 | 186 | 580 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.95 | 0.60 | 1.87 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.092 | 2.575 | 6.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F(-2) | F(-1) | F | F | F(-1) |
| verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 282 | 270 | 214 | 372 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.96 | 0.76 | 1.32 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.939 | 2.153 | 5.588 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F(-2) | F(-1) | F | F | F(-1) |
| verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 272 | 253 | 182 | 505 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.93 | 0.67 | 1.86 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.881 | 1.381 | 5.040 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | C | F(-2) | F(-1) | F | F | F(-1) |
| verified |
N/A | No | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 244 | 230 | 220 | 141 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.94 | 0.90 | 0.58 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.765 | 0.870 | 4.422 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F(-2) | F(-1) | F | F | F(-1) |
| verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 305 | 290 | 196 | 511 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.95 | 0.64 | 1.68 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.124 | 2.632 | 4.696 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F(-2) | F(-1) | F | F | F(-1) |
| verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 282 | 270 | 200 | 458 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.96 | 0.71 | 1.62 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.932 | 1.638 | 4.784 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F(-2) | F(-1) | F | F | F(-1) |
| verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 346 | 333 | 254 | 546 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.96 | 0.73 | 1.58 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.296 | 2.748 | 4.590 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F(-2) | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 366 | 366 | 117 | 605 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.32 | 1.65 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.807 | 12.893 | 6.596 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F(-2) | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 335 | 335 | 257 | 397 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.77 | 1.19 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.684 | 26.787 | 6.591 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F(-2) | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 309 | 309 | 106 | 530 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.34 | 1.72 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.625 | 11.676 | 5.431 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F(-2) | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 278 | 278 | 220 | 269 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.79 | 0.97 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.585 | 13.012 | 5.459 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F(-2) | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 310 | 310 | 238 | 536 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.77 | 1.73 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.672 | 7.763 | 4.951 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F(-2) | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 316 | 316 | 224 | 483 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.71 | 1.53 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.685 | 15.823 | 5.554 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F(-2) | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 370 | 370 | 2820 | 571 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 7.62 | 1.54 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.774 | 14.671 | 4.913 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | C | F | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | No | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 330 | 321 | 332 | 1026 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.97 | 1.01 | 3.11 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.297 | 16.028 | 4.637 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | C | F | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | No | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 326 | 303 | 129 | 1166 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.93 | 0.40 | 3.58 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.255 | 17.800 | 3.858 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | C | F | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | No | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 295 | 280 | 271 | 976 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.95 | 0.92 | 3.31 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.086 | 22.333 | 4.027 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | C | F | F(-1) | F | F | F(-1) |
| verified |
N/A | No | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 285 | 262 | 105 | 1100 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.92 | 0.37 | 3.86 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.032 | 16.519 | 3.637 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | C | F | F(-1) | F | F | F(-1) |
| verified |
N/A | No | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 257 | 239 | 1211 | 205 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.93 | 4.71 | 0.80 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.872 | 15.615 | 3.749 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | C | F | F(-1) | F | F | F(-1) |
| verified |
N/A | No | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 315 | 298 | 2715 | 256 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.95 | 8.62 | 0.81 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.287 | 10.581 | 2.362 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | C | F | F(-1) | F | F | F(-1) |
| verified |
N/A | No | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 290 | 280 | 1253 | 611 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.97 | 4.32 | 2.11 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.100 | 10.239 | 3.750 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | C | F | F(-1) | F | F | F(-1) |
| verified |
N/A | No | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 359 | 342 | 180 | 1116 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.95 | 0.50 | 3.11 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.593 | 13.994 | 2.988 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | C | F | F(-1) | F | F | F(-1) |
| verified |
N/A | No | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 328 | 323 | 1299 | 744 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.98 | 3.96 | 2.27 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.326 | 10.617 | 3.870 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | F | C | F(-1) | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | N/A | No | TBD | TBD | TBD | TBD | TBD |
| size | 372 | 373 | 0 | 1181 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.00 | 3.17 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.842 | 0.000 | 5.192 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | F | C | F(-1) | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | N/A | No | TBD | TBD | TBD | TBD | TBD |
| size | 339 | 342 | 0 | 1007 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.01 | 0.00 | 2.97 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.774 | 0.000 | 4.508 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | F | C | F | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | N/A | No | TBD | TBD | TBD | TBD | TBD |
| size | 312 | 316 | 0 | 1141 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.01 | 0.00 | 3.66 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.735 | 0.000 | 4.916 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | F | C | F(-1) | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | N/A | No | TBD | TBD | TBD | TBD | TBD |
| size | 281 | 285 | 0 | 961 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.01 | 0.00 | 3.42 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.676 | 0.000 | 6.340 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | C | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 310 | 317 | 812 | 261 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.02 | 2.62 | 0.84 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.757 | 8.364 | 4.490 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | F | C | F(-1) | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | N/A | No | TBD | TBD | TBD | TBD | TBD |
| size | 316 | 323 | 0 | 638 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.02 | 0.00 | 2.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.783 | 0.000 | 5.271 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | C | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 363 | 377 | 2792 | 705 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.04 | 7.69 | 1.94 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.843 | 10.039 | 4.229 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | C | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 365 | 379 | 1281 | 633 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.04 | 3.51 | 1.73 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.852 | 12.508 | 5.598 | 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 | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 147 | 134 | 102 | 101 | 145 | 299 | 0 | 0 | 0 |
| N.S. |
1 | 0.91 | 0.69 | 0.69 | 0.99 | 2.03 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.325 | 0.625 | 5.028 | 0.283 | 0.402 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 99 | 95 | 80 | 81 | 107 | 259 | 0 | 0 | 0 |
| N.S. |
1 | 0.96 | 0.81 | 0.82 | 1.08 | 2.62 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.280 | 0.275 | 4.745 | 0.273 | 0.332 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 51 | 49 | 60 | 42 | 67 | 184 | 0 | 0 | 47 |
| N.S. |
1 | 0.96 | 1.18 | 0.82 | 1.31 | 3.61 | 0.00 | 0.00 | 0.92 |
| time (sec) |
N/A | 0.234 | 0.101 | 0.934 | 0.288 | 0.312 | 0.000 | 0.000 | 14.576 |
| 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 | 73 | 72 | 72 | 92 | 0 | 242 | 0 | 0 | 0 |
| N.S. |
1 | 0.99 | 0.99 | 1.26 | 0.00 | 3.32 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.281 | 0.078 | 2.374 | 0.000 | 0.332 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | A | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 131 | 138 | 87 | 137 | 0 | 426 | 0 | 0 | 0 |
| N.S. |
1 | 1.05 | 0.66 | 1.05 | 0.00 | 3.25 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.334 | 0.551 | 2.620 | 0.000 | 0.378 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F(-1) | A | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 193 | 207 | 102 | 173 | 0 | 529 | 0 | 0 | 0 |
| N.S. |
1 | 1.07 | 0.53 | 0.90 | 0.00 | 2.74 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.386 | 0.585 | 3.038 | 0.000 | 0.373 | 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 | 222 | 205 | 134 | 233 | 0 | 371 | 0 | 0 | 0 |
| N.S. |
1 | 0.92 | 0.60 | 1.05 | 0.00 | 1.67 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.305 | 7.811 | 5.352 | 0.000 | 0.342 | 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 | 160 | 149 | 110 | 201 | 0 | 331 | 0 | 0 | 0 |
| N.S. |
1 | 0.93 | 0.69 | 1.26 | 0.00 | 2.07 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.284 | 6.658 | 5.176 | 0.000 | 0.342 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | A | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 96 | 93 | 226 | 186 | 0 | 283 | 0 | 0 | 0 |
| N.S. |
1 | 0.97 | 2.35 | 1.94 | 0.00 | 2.95 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.254 | 3.484 | 4.731 | 0.000 | 0.297 | 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 | 109 | 113 | 124 | 161 | 0 | 422 | 0 | 0 | 0 |
| N.S. |
1 | 1.04 | 1.14 | 1.48 | 0.00 | 3.87 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.273 | 3.344 | 2.809 | 0.000 | 0.390 | 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 | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 196 | 206 | 232 | 196 | 0 | 547 | 0 | 0 | 0 |
| N.S. |
1 | 1.05 | 1.18 | 1.00 | 0.00 | 2.79 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.346 | 7.207 | 2.781 | 0.000 | 0.408 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-1) | A | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 280 | 295 | 210 | 226 | 0 | 646 | 0 | 0 | 0 |
| N.S. |
1 | 1.05 | 0.75 | 0.81 | 0.00 | 2.31 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.429 | 4.657 | 2.653 | 0.000 | 0.418 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 169 | 155 | 112 | 112 | 162 | 334 | 0 | 0 | 0 |
| N.S. |
1 | 0.92 | 0.66 | 0.66 | 0.96 | 1.98 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.350 | 0.430 | 4.931 | 0.268 | 0.362 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 121 | 116 | 92 | 92 | 124 | 290 | 0 | 0 | 0 |
| N.S. |
1 | 0.96 | 0.76 | 0.76 | 1.02 | 2.40 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.292 | 0.217 | 4.260 | 0.269 | 0.346 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 73 | 70 | 70 | 57 | 86 | 238 | 0 | 0 | 67 |
| N.S. |
1 | 0.96 | 0.96 | 0.78 | 1.18 | 3.26 | 0.00 | 0.00 | 0.92 |
| time (sec) |
N/A | 0.250 | 0.122 | 0.749 | 0.268 | 0.355 | 0.000 | 0.000 | 14.334 |
| 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 | 73 | 73 | 72 | 91 | 0 | 243 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.99 | 1.25 | 0.00 | 3.33 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.279 | 0.082 | 1.528 | 0.000 | 0.332 | 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 | 109 | 112 | 100 | 138 | 0 | 378 | 0 | 0 | 0 |
| N.S. |
1 | 1.03 | 0.92 | 1.27 | 0.00 | 3.47 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.314 | 0.313 | 1.939 | 0.000 | 0.329 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F(-1) | B | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 171 | 178 | 104 | 174 | 0 | 589 | 0 | 0 | 0 |
| N.S. |
1 | 1.04 | 0.61 | 1.02 | 0.00 | 3.44 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.369 | 0.721 | 1.963 | 0.000 | 0.422 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-1) | A | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 258 | 236 | 147 | 250 | 0 | 415 | 0 | 0 | 0 |
| N.S. |
1 | 0.91 | 0.57 | 0.97 | 0.00 | 1.61 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.304 | 9.384 | 4.029 | 0.000 | 0.358 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-1) | A | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 194 | 178 | 123 | 218 | 0 | 371 | 0 | 0 | 0 |
| N.S. |
1 | 0.92 | 0.63 | 1.12 | 0.00 | 1.91 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.300 | 7.148 | 3.724 | 0.000 | 0.310 | 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 | No | TBD | TBD | TBD | TBD | TBD |
| size | 128 | 118 | 97 | 187 | 0 | 321 | 0 | 0 | 0 |
| N.S. |
1 | 0.92 | 0.76 | 1.46 | 0.00 | 2.51 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.290 | 6.787 | 3.482 | 0.000 | 0.326 | 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 | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 64 | 61 | 102 | 85 | 0 | 264 | 0 | 0 | 0 |
| N.S. |
1 | 0.95 | 1.59 | 1.33 | 0.00 | 4.12 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.251 | 0.381 | 1.939 | 0.000 | 0.344 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-1) | A | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 144 | 145 | 226 | 197 | 0 | 531 | 0 | 0 | 0 |
| N.S. |
1 | 1.01 | 1.57 | 1.37 | 0.00 | 3.69 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.314 | 6.687 | 1.739 | 0.000 | 0.404 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-1) | A | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 226 | 238 | 235 | 227 | 0 | 708 | 0 | 0 | 0 |
| N.S. |
1 | 1.05 | 1.04 | 1.00 | 0.00 | 3.13 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.400 | 7.457 | 1.846 | 0.000 | 0.405 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 193 | 176 | 156 | 124 | 181 | 386 | 0 | 0 | 0 |
| N.S. |
1 | 0.91 | 0.81 | 0.64 | 0.94 | 2.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.342 | 0.547 | 262.509 | 0.282 | 0.375 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 145 | 137 | 102 | 104 | 143 | 334 | 0 | 0 | 0 |
| N.S. |
1 | 0.94 | 0.70 | 0.72 | 0.99 | 2.30 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.337 | 0.435 | 55.967 | 0.280 | 0.368 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 97 | 91 | 82 | 74 | 105 | 282 | 0 | 0 | 92 |
| N.S. |
1 | 0.94 | 0.85 | 0.76 | 1.08 | 2.91 | 0.00 | 0.00 | 0.95 |
| time (sec) |
N/A | 0.253 | 0.160 | 7.177 | 0.277 | 0.336 | 0.000 | 0.000 | 13.961 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | A | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 95 | 95 | 83 | 116 | 0 | 300 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.87 | 1.22 | 0.00 | 3.16 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.299 | 0.077 | 5.423 | 0.000 | 0.349 | 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 | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 106 | 107 | 96 | 240 | 0 | 398 | 0 | 0 | 0 |
| N.S. |
1 | 1.01 | 0.91 | 2.26 | 0.00 | 3.75 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.314 | 0.334 | 15.210 | 0.000 | 0.339 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F(-1) | B | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 147 | 151 | 109 | 272 | 0 | 503 | 0 | 0 | 0 |
| N.S. |
1 | 1.03 | 0.74 | 1.85 | 0.00 | 3.42 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.343 | 0.693 | 88.517 | 0.000 | 0.331 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-1) | A | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 290 | 265 | 173 | 268 | 0 | 477 | 0 | 0 | 0 |
| N.S. |
1 | 0.91 | 0.60 | 0.92 | 0.00 | 1.64 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.322 | 8.758 | 1.253 | 0.000 | 0.359 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-1) | A | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 224 | 205 | 149 | 236 | 0 | 425 | 0 | 0 | 0 |
| N.S. |
1 | 0.92 | 0.67 | 1.05 | 0.00 | 1.90 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.293 | 7.813 | 129.408 | 0.000 | 0.366 | 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 | No | TBD | TBD | TBD | TBD | TBD |
| size | 160 | 147 | 125 | 233 | 0 | 374 | 0 | 0 | 0 |
| N.S. |
1 | 0.92 | 0.78 | 1.46 | 0.00 | 2.34 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.284 | 6.417 | 13.545 | 0.000 | 0.344 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | B | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 66 | 64 | 124 | 89 | 0 | 270 | 0 | 0 | 0 |
| N.S. |
1 | 0.97 | 1.88 | 1.35 | 0.00 | 4.09 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.247 | 0.584 | 6.621 | 0.000 | 0.352 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | A | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 96 | 91 | 81 | 180 | 0 | 355 | 0 | 0 | 0 |
| N.S. |
1 | 0.95 | 0.84 | 1.88 | 0.00 | 3.70 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.252 | 0.196 | 40.391 | 0.000 | 0.343 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F(-1) | A | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 176 | 177 | 203 | 372 | 0 | 650 | 0 | 0 | 0 |
| N.S. |
1 | 1.01 | 1.15 | 2.11 | 0.00 | 3.69 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.346 | 6.396 | 194.437 | 0.000 | 0.400 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 126 | 113 | 88 | 94 | 129 | 285 | 0 | 167 | 0 |
| N.S. |
1 | 0.90 | 0.70 | 0.75 | 1.02 | 2.26 | 0.00 | 1.33 | 0.00 |
| time (sec) |
N/A | 0.305 | 0.155 | 3.783 | 0.275 | 0.359 | 0.000 | 2.037 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 78 | 74 | 66 | 74 | 91 | 241 | 0 | 126 | 0 |
| N.S. |
1 | 0.95 | 0.85 | 0.95 | 1.17 | 3.09 | 0.00 | 1.62 | 0.00 |
| time (sec) |
N/A | 0.277 | 0.075 | 3.142 | 0.280 | 0.374 | 0.000 | 1.087 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | B | F | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 31 | 31 | 44 | 26 | 49 | 137 | 0 | 48 | 27 |
| N.S. |
1 | 1.00 | 1.42 | 0.84 | 1.58 | 4.42 | 0.00 | 1.55 | 0.87 |
| time (sec) |
N/A | 0.228 | 0.033 | 0.693 | 0.274 | 0.318 | 0.000 | 0.784 | 15.183 |
| 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 | 92 | 98 | 57 | 229 | 0 | 384 | 0 | 111 | 0 |
| N.S. |
1 | 1.07 | 0.62 | 2.49 | 0.00 | 4.17 | 0.00 | 1.21 | 0.00 |
| time (sec) |
N/A | 0.298 | 0.062 | 1.802 | 0.000 | 0.347 | 0.000 | 0.752 | 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 | 152 | 168 | 90 | 272 | 0 | 546 | 0 | 174 | 0 |
| N.S. |
1 | 1.11 | 0.59 | 1.79 | 0.00 | 3.59 | 0.00 | 1.14 | 0.00 |
| time (sec) |
N/A | 0.357 | 0.160 | 1.752 | 0.000 | 0.353 | 0.000 | 0.843 | 0.000 |
| 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 | 214 | 236 | 102 | 308 | 0 | 705 | 0 | 241 | 0 |
| N.S. |
1 | 1.10 | 0.48 | 1.44 | 0.00 | 3.29 | 0.00 | 1.13 | 0.00 |
| time (sec) |
N/A | 0.404 | 0.257 | 1.577 | 0.000 | 0.394 | 0.000 | 0.890 | 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 | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 189 | 178 | 167 | 220 | 0 | 355 | 0 | 266 | 0 |
| N.S. |
1 | 0.94 | 0.88 | 1.16 | 0.00 | 1.88 | 0.00 | 1.41 | 0.00 |
| time (sec) |
N/A | 0.296 | 14.085 | 3.719 | 0.000 | 0.304 | 0.000 | 2.839 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | A | F | B | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 125 | 122 | 238 | 188 | 0 | 311 | 0 | 228 | 0 |
| N.S. |
1 | 0.98 | 1.90 | 1.50 | 0.00 | 2.49 | 0.00 | 1.82 | 0.00 |
| time (sec) |
N/A | 0.270 | 2.465 | 3.689 | 0.000 | 0.292 | 0.000 | 1.601 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | A | F | B | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 63 | 65 | 119 | 95 | 0 | 235 | 0 | 187 | 0 |
| N.S. |
1 | 1.03 | 1.89 | 1.51 | 0.00 | 3.73 | 0.00 | 2.97 | 0.00 |
| time (sec) |
N/A | 0.248 | 0.586 | 3.159 | 0.000 | 0.272 | 0.000 | 1.142 | 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 | 165 | 172 | 187 | 336 | 0 | 503 | 0 | 269 | 0 |
| N.S. |
1 | 1.04 | 1.13 | 2.04 | 0.00 | 3.05 | 0.00 | 1.63 | 0.00 |
| time (sec) |
N/A | 0.322 | 5.046 | 2.013 | 0.000 | 0.343 | 0.000 | 1.095 | 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 | 251 | 263 | 229 | 372 | 0 | 666 | 0 | 385 | 0 |
| N.S. |
1 | 1.05 | 0.91 | 1.48 | 0.00 | 2.65 | 0.00 | 1.53 | 0.00 |
| time (sec) |
N/A | 0.399 | 1.656 | 2.104 | 0.000 | 0.360 | 0.000 | 1.206 | 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 | 335 | 352 | 263 | 408 | 0 | 823 | 0 | 500 | 0 |
| N.S. |
1 | 1.05 | 0.79 | 1.22 | 0.00 | 2.46 | 0.00 | 1.49 | 0.00 |
| time (sec) |
N/A | 0.482 | 3.251 | 1.949 | 0.000 | 0.391 | 0.000 | 1.322 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 100 | 92 | 79 | 82 | 110 | 261 | 0 | 154 | 0 |
| N.S. |
1 | 0.92 | 0.79 | 0.82 | 1.10 | 2.61 | 0.00 | 1.54 | 0.00 |
| time (sec) |
N/A | 0.302 | 0.108 | 3.593 | 0.290 | 0.312 | 0.000 | 2.290 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 54 | 56 | 56 | 65 | 71 | 191 | 0 | 85 | 0 |
| N.S. |
1 | 1.04 | 1.04 | 1.20 | 1.31 | 3.54 | 0.00 | 1.57 | 0.00 |
| time (sec) |
N/A | 0.275 | 0.052 | 3.292 | 0.277 | 0.305 | 0.000 | 1.252 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | A | B | F | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 54 | 52 | 38 | 45 | 70 | 244 | 0 | 87 | 50 |
| N.S. |
1 | 0.96 | 0.70 | 0.83 | 1.30 | 4.52 | 0.00 | 1.61 | 0.93 |
| time (sec) |
N/A | 0.241 | 0.029 | 0.872 | 0.276 | 0.312 | 0.000 | 0.927 | 14.466 |
| 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 | 120 | 128 | 60 | 304 | 0 | 485 | 0 | 164 | 0 |
| N.S. |
1 | 1.07 | 0.50 | 2.53 | 0.00 | 4.04 | 0.00 | 1.37 | 0.00 |
| time (sec) |
N/A | 0.323 | 0.048 | 1.579 | 0.000 | 0.360 | 0.000 | 0.922 | 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 | 176 | 197 | 90 | 400 | 0 | 592 | 0 | 253 | 0 |
| N.S. |
1 | 1.12 | 0.51 | 2.27 | 0.00 | 3.36 | 0.00 | 1.44 | 0.00 |
| time (sec) |
N/A | 0.381 | 0.128 | 1.915 | 0.000 | 0.376 | 0.000 | 1.092 | 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 | 238 | 263 | 99 | 436 | 0 | 837 | 0 | 322 | 0 |
| N.S. |
1 | 1.11 | 0.42 | 1.83 | 0.00 | 3.52 | 0.00 | 1.35 | 0.00 |
| time (sec) |
N/A | 0.434 | 0.207 | 1.817 | 0.000 | 0.396 | 0.000 | 1.010 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | A | F | B | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 157 | 151 | 248 | 233 | 0 | 343 | 0 | 296 | 0 |
| N.S. |
1 | 0.96 | 1.58 | 1.48 | 0.00 | 2.18 | 0.00 | 1.89 | 0.00 |
| time (sec) |
N/A | 0.293 | 1.928 | 3.740 | 0.000 | 0.299 | 0.000 | 3.748 | 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 | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 95 | 94 | 162 | 174 | 0 | 295 | 0 | 230 | 0 |
| N.S. |
1 | 0.99 | 1.71 | 1.83 | 0.00 | 3.11 | 0.00 | 2.42 | 0.00 |
| time (sec) |
N/A | 0.272 | 3.316 | 3.756 | 0.000 | 0.291 | 0.000 | 2.444 | 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 | 85 | 83 | 132 | 136 | 0 | 295 | 0 | 72 | 0 |
| N.S. |
1 | 0.98 | 1.55 | 1.60 | 0.00 | 3.47 | 0.00 | 0.85 | 0.00 |
| time (sec) |
N/A | 0.260 | 0.780 | 1.821 | 0.000 | 0.294 | 0.000 | 1.141 | 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 | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 215 | 227 | 210 | 497 | 0 | 603 | 0 | 143 | 0 |
| N.S. |
1 | 1.06 | 0.98 | 2.31 | 0.00 | 2.80 | 0.00 | 0.67 | 0.00 |
| time (sec) |
N/A | 0.362 | 6.510 | 2.004 | 0.000 | 0.344 | 0.000 | 1.091 | 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 | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 303 | 320 | 240 | 541 | 0 | 712 | 0 | 261 | 0 |
| N.S. |
1 | 1.06 | 0.79 | 1.79 | 0.00 | 2.35 | 0.00 | 0.86 | 0.00 |
| time (sec) |
N/A | 0.455 | 2.524 | 1.870 | 0.000 | 0.367 | 0.000 | 1.089 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-1) | A | F | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 387 | 409 | 264 | 577 | 0 | 955 | 0 | 379 | 0 |
| N.S. |
1 | 1.06 | 0.68 | 1.49 | 0.00 | 2.47 | 0.00 | 0.98 | 0.00 |
| time (sec) |
N/A | 0.534 | 5.129 | 1.587 | 0.000 | 0.439 | 0.000 | 1.333 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | A | F | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 78 | 76 | 69 | 72 | 163 | 241 | 0 | 126 | 0 |
| N.S. |
1 | 0.97 | 0.88 | 0.92 | 2.09 | 3.09 | 0.00 | 1.62 | 0.00 |
| time (sec) |
N/A | 0.294 | 0.232 | 3.747 | 0.285 | 0.310 | 0.000 | 2.788 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | B | F | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 54 | 56 | 50 | 87 | 125 | 245 | 0 | 90 | 0 |
| N.S. |
1 | 1.04 | 0.93 | 1.61 | 2.31 | 4.54 | 0.00 | 1.67 | 0.00 |
| time (sec) |
N/A | 0.272 | 0.056 | 1.784 | 0.276 | 0.308 | 0.000 | 1.706 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | A | B | F | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 78 | 78 | 40 | 62 | 87 | 321 | 0 | 116 | 69 |
| N.S. |
1 | 1.00 | 0.51 | 0.79 | 1.12 | 4.12 | 0.00 | 1.49 | 0.88 |
| time (sec) |
N/A | 0.254 | 0.084 | 0.876 | 0.274 | 0.304 | 0.000 | 1.227 | 14.759 |
| 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 | 144 | 154 | 60 | 378 | 0 | 573 | 0 | 206 | 0 |
| N.S. |
1 | 1.07 | 0.42 | 2.62 | 0.00 | 3.98 | 0.00 | 1.43 | 0.00 |
| time (sec) |
N/A | 0.342 | 0.143 | 1.732 | 0.000 | 0.356 | 0.000 | 0.928 | 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 | 200 | 226 | 90 | 528 | 0 | 748 | 0 | 295 | 0 |
| N.S. |
1 | 1.13 | 0.45 | 2.64 | 0.00 | 3.74 | 0.00 | 1.48 | 0.00 |
| time (sec) |
N/A | 0.400 | 0.286 | 1.758 | 0.000 | 0.376 | 0.000 | 1.081 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F(-1) | B | F | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 262 | 292 | 99 | 564 | 0 | 905 | 0 | 364 | 0 |
| N.S. |
1 | 1.11 | 0.38 | 2.15 | 0.00 | 3.45 | 0.00 | 1.39 | 0.00 |
| time (sec) |
N/A | 0.461 | 0.347 | 1.675 | 0.000 | 0.395 | 0.000 | 1.273 | 0.000 |