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 | B | F | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 342 | 342 | 251 | 294 | 298 | 1096 | 0 | 0 | 5825 |
| N.S. |
1 | 1.00 | 0.73 | 0.86 | 0.87 | 3.20 | 0.00 | 0.00 | 17.03 |
| time (sec) |
N/A | 0.732 | 3.477 | 0.209 | 0.365 | 0.301 | 0.000 | 0.000 | 9.987 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | B | F | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 213 | 213 | 150 | 166 | 172 | 547 | 0 | 0 | 383 |
| N.S. |
1 | 1.00 | 0.70 | 0.78 | 0.81 | 2.57 | 0.00 | 0.00 | 1.80 |
| time (sec) |
N/A | 0.273 | 0.895 | 0.076 | 0.350 | 0.261 | 0.000 | 0.000 | 8.518 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | B | F | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 213 | 213 | 198 | 166 | 171 | 493 | 0 | 0 | 390 |
| N.S. |
1 | 1.00 | 0.93 | 0.78 | 0.80 | 2.31 | 0.00 | 0.00 | 1.83 |
| time (sec) |
N/A | 0.317 | 0.788 | 0.075 | 0.352 | 0.248 | 0.000 | 0.000 | 8.424 |
| 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 | 290 | 290 | 173 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.60 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.202 | 3.095 | 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 | 205 | 205 | 119 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.58 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.721 | 2.554 | 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 | 132 | 132 | 81 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.61 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.433 | 1.573 | 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 | 70 | 70 | 52 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.74 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.146 | 0.524 | 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(-2) | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 168 | 168 | 137 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.82 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.270 | 1.890 | 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(-2) | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 226 | 226 | 175 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.77 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.611 | 3.218 | 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(-2) | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 308 | 308 | 227 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.74 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.274 | 4.328 | 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(-2) | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 386 | 386 | 277 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.72 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.591 | 3.557 | 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 | 316 | 316 | 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 | 1.131 | 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 | F | F(-1) |
| verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 227 | 227 | 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 | 0.769 | 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 | F | F(-1) |
| verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 159 | 159 | 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 | 0.435 | 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(-2) | F | F | F | F(-1) |
| verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 214 | 214 | 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 | 0.937 | 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(-2) | F | F | F | F(-1) |
| verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 285 | 285 | 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 | 1.167 | 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(-2) | F | F | F | F(-1) |
| verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 363 | 363 | 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 | 1.544 | 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 | F | F(-1) |
| verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 167 | 167 | 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 | 0.348 | 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 | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 245 | 245 | 189 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.77 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.765 | 4.142 | 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 | 164 | 164 | 137 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.84 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.363 | 1.480 | 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 | 111 | 111 | 87 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.78 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.142 | 0.809 | 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 | 78 | 78 | 60 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.77 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.073 | 0.280 | 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 | 97 | 97 | 124 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.28 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.207 | 1.224 | 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 | 131 | 131 | 156 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.19 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.379 | 2.923 | 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 | 185 | 185 | 221 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.19 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.666 | 3.167 | 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 | 383 | 383 | 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 | 1.588 | 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 | 291 | 291 | 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 | 1.159 | 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 | F | F(-1) |
| verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 215 | 215 | 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 | 0.560 | 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 | F | F(-1) |
| verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 158 | 158 | 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 | 0.333 | 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(-1) | F | F | F | F(-1) |
| verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 194 | 194 | 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 | 0.568 | 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 | F | F(-1) |
| verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 247 | 247 | 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 | 0.828 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 87 | 87 | 86 | 88 | 86 | 85 | 136 | 937 | 84 |
| N.S. |
1 | 1.00 | 0.99 | 1.01 | 0.99 | 0.98 | 1.56 | 10.77 | 0.97 |
| time (sec) |
N/A | 0.147 | 0.623 | 0.053 | 0.373 | 0.245 | 0.119 | 0.846 | 7.281 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 65 | 65 | 67 | 69 | 66 | 66 | 104 | 556 | 63 |
| N.S. |
1 | 1.00 | 1.03 | 1.06 | 1.02 | 1.02 | 1.60 | 8.55 | 0.97 |
| time (sec) |
N/A | 0.072 | 0.308 | 0.041 | 0.404 | 0.256 | 0.120 | 0.510 | 8.431 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 42 | 42 | 59 | 47 | 50 | 50 | 73 | 289 | 55 |
| N.S. |
1 | 1.00 | 1.40 | 1.12 | 1.19 | 1.19 | 1.74 | 6.88 | 1.31 |
| time (sec) |
N/A | 0.034 | 0.035 | 0.025 | 0.374 | 0.252 | 0.083 | 0.394 | 7.178 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 37 | 37 | 49 | 47 | 52 | 59 | 78 | 53 | 69 |
| N.S. |
1 | 1.00 | 1.32 | 1.27 | 1.41 | 1.59 | 2.11 | 1.43 | 1.86 |
| time (sec) |
N/A | 0.089 | 0.065 | 0.114 | 0.401 | 0.275 | 0.211 | 0.421 | 7.384 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | A | A | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 43 | 43 | 88 | 65 | 68 | 73 | 121 | 119 | 87 |
| N.S. |
1 | 1.00 | 2.05 | 1.51 | 1.58 | 1.70 | 2.81 | 2.77 | 2.02 |
| time (sec) |
N/A | 0.099 | 0.046 | 0.123 | 0.375 | 0.252 | 0.322 | 0.538 | 8.479 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | A | A | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 66 | 66 | 77 | 89 | 86 | 95 | 148 | 179 | 108 |
| N.S. |
1 | 1.00 | 1.17 | 1.35 | 1.30 | 1.44 | 2.24 | 2.71 | 1.64 |
| time (sec) |
N/A | 0.138 | 0.502 | 0.152 | 0.388 | 0.249 | 0.559 | 0.628 | 7.277 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | A | A | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 87 | 87 | 101 | 106 | 104 | 121 | 178 | 237 | 127 |
| N.S. |
1 | 1.00 | 1.16 | 1.22 | 1.20 | 1.39 | 2.05 | 2.72 | 1.46 |
| time (sec) |
N/A | 0.190 | 1.095 | 0.184 | 0.349 | 0.260 | 0.848 | 0.756 | 7.537 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | A | A | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 108 | 108 | 100 | 124 | 122 | 138 | 209 | 299 | 145 |
| N.S. |
1 | 1.00 | 0.93 | 1.15 | 1.13 | 1.28 | 1.94 | 2.77 | 1.34 |
| time (sec) |
N/A | 0.227 | 1.250 | 0.201 | 0.322 | 0.262 | 1.119 | 0.905 | 7.873 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | A | A | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 148 | 148 | 221 | 148 | 147 | 146 | 246 | 2078 | 151 |
| N.S. |
1 | 1.00 | 1.49 | 1.00 | 0.99 | 0.99 | 1.66 | 14.04 | 1.02 |
| time (sec) |
N/A | 0.319 | 6.223 | 0.075 | 0.383 | 0.250 | 0.149 | 1.843 | 7.331 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | A | A | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 112 | 112 | 172 | 120 | 120 | 119 | 192 | 1389 | 121 |
| N.S. |
1 | 1.00 | 1.54 | 1.07 | 1.07 | 1.06 | 1.71 | 12.40 | 1.08 |
| time (sec) |
N/A | 0.152 | 1.909 | 0.056 | 0.325 | 0.257 | 0.129 | 1.046 | 7.322 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | A | A | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 87 | 87 | 96 | 90 | 91 | 91 | 143 | 811 | 91 |
| N.S. |
1 | 1.00 | 1.10 | 1.03 | 1.05 | 1.05 | 1.64 | 9.32 | 1.05 |
| time (sec) |
N/A | 0.092 | 0.477 | 0.040 | 0.380 | 0.244 | 0.104 | 0.696 | 8.347 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | A | A | A | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 70 | 70 | 93 | 80 | 85 | 92 | 129 | 86 | 90 |
| N.S. |
1 | 1.00 | 1.33 | 1.14 | 1.21 | 1.31 | 1.84 | 1.23 | 1.29 |
| time (sec) |
N/A | 0.136 | 0.319 | 0.132 | 0.337 | 0.261 | 0.305 | 0.697 | 7.512 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | A | A | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 72 | 72 | 100 | 84 | 93 | 112 | 167 | 118 | 100 |
| N.S. |
1 | 1.00 | 1.39 | 1.17 | 1.29 | 1.56 | 2.32 | 1.64 | 1.39 |
| time (sec) |
N/A | 0.159 | 0.297 | 0.201 | 0.324 | 0.286 | 0.458 | 0.874 | 7.532 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | A | A | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 88 | 88 | 123 | 107 | 120 | 122 | 214 | 237 | 127 |
| N.S. |
1 | 1.00 | 1.40 | 1.22 | 1.36 | 1.39 | 2.43 | 2.69 | 1.44 |
| time (sec) |
N/A | 0.239 | 0.367 | 0.265 | 0.318 | 0.256 | 0.822 | 1.104 | 8.041 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | A | A | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 118 | 118 | 152 | 136 | 149 | 157 | 260 | 334 | 156 |
| N.S. |
1 | 1.00 | 1.29 | 1.15 | 1.26 | 1.33 | 2.20 | 2.83 | 1.32 |
| time (sec) |
N/A | 0.286 | 1.253 | 0.250 | 0.344 | 0.261 | 1.128 | 1.431 | 7.955 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | A | A | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 151 | 151 | 180 | 162 | 175 | 191 | 313 | 435 | 182 |
| N.S. |
1 | 1.00 | 1.19 | 1.07 | 1.16 | 1.26 | 2.07 | 2.88 | 1.21 |
| time (sec) |
N/A | 0.483 | 3.099 | 0.285 | 0.335 | 0.267 | 1.846 | 1.180 | 8.040 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | A | A | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 201 | 201 | 241 | 207 | 214 | 213 | 384 | 3757 | 217 |
| N.S. |
1 | 1.00 | 1.20 | 1.03 | 1.06 | 1.06 | 1.91 | 18.69 | 1.08 |
| time (sec) |
N/A | 0.605 | 2.373 | 0.096 | 0.324 | 0.260 | 0.183 | 3.792 | 7.309 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | A | A | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 165 | 165 | 209 | 180 | 179 | 178 | 311 | 2670 | 181 |
| N.S. |
1 | 1.00 | 1.27 | 1.09 | 1.08 | 1.08 | 1.88 | 16.18 | 1.10 |
| time (sec) |
N/A | 0.336 | 1.580 | 0.088 | 0.347 | 0.252 | 0.159 | 2.182 | 8.244 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | A | A | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 140 | 140 | 130 | 141 | 143 | 142 | 240 | 1751 | 142 |
| N.S. |
1 | 1.00 | 0.93 | 1.01 | 1.02 | 1.01 | 1.71 | 12.51 | 1.01 |
| time (sec) |
N/A | 0.269 | 1.036 | 0.069 | 0.329 | 0.255 | 0.137 | 1.396 | 8.272 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | A | A | A | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 117 | 117 | 115 | 121 | 124 | 133 | 204 | 129 | 118 |
| N.S. |
1 | 1.00 | 0.98 | 1.03 | 1.06 | 1.14 | 1.74 | 1.10 | 1.01 |
| time (sec) |
N/A | 0.393 | 0.626 | 0.214 | 0.365 | 0.281 | 0.458 | 1.133 | 8.484 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | A | A | A | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 119 | 119 | 113 | 118 | 125 | 145 | 223 | 152 | 114 |
| N.S. |
1 | 1.00 | 0.95 | 0.99 | 1.05 | 1.22 | 1.87 | 1.28 | 0.96 |
| time (sec) |
N/A | 0.314 | 0.589 | 0.225 | 0.349 | 0.281 | 0.769 | 1.435 | 7.700 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | A | A | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 127 | 127 | 126 | 136 | 142 | 162 | 262 | 193 | 135 |
| N.S. |
1 | 1.00 | 0.99 | 1.07 | 1.12 | 1.28 | 2.06 | 1.52 | 1.06 |
| time (sec) |
N/A | 0.326 | 0.454 | 0.214 | 0.295 | 0.275 | 1.081 | 1.403 | 8.152 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | A | A | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 154 | 154 | 164 | 172 | 180 | 181 | 332 | 390 | 169 |
| N.S. |
1 | 1.00 | 1.06 | 1.12 | 1.17 | 1.18 | 2.16 | 2.53 | 1.10 |
| time (sec) |
N/A | 0.417 | 1.284 | 0.204 | 0.286 | 0.288 | 1.810 | 0.971 | 8.168 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | A | A | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 191 | 191 | 199 | 209 | 215 | 225 | 400 | 528 | 204 |
| N.S. |
1 | 1.00 | 1.04 | 1.09 | 1.13 | 1.18 | 2.09 | 2.76 | 1.07 |
| time (sec) |
N/A | 0.499 | 0.783 | 0.245 | 0.298 | 0.273 | 2.315 | 1.093 | 7.831 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | A | A | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 233 | 233 | 237 | 243 | 250 | 266 | 471 | 670 | 238 |
| N.S. |
1 | 1.00 | 1.02 | 1.04 | 1.07 | 1.14 | 2.02 | 2.88 | 1.02 |
| time (sec) |
N/A | 0.572 | 1.240 | 0.283 | 0.299 | 0.270 | 4.175 | 1.121 | 8.430 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | A | A | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 263 | 263 | 290 | 274 | 290 | 289 | 536 | 6042 | 300 |
| N.S. |
1 | 1.00 | 1.10 | 1.04 | 1.10 | 1.10 | 2.04 | 22.97 | 1.14 |
| time (sec) |
N/A | 0.520 | 6.104 | 0.152 | 0.298 | 0.266 | 0.249 | 7.744 | 7.985 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | A | A | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 226 | 226 | 257 | 242 | 246 | 245 | 437 | 4489 | 251 |
| N.S. |
1 | 1.00 | 1.14 | 1.07 | 1.09 | 1.08 | 1.93 | 19.86 | 1.11 |
| time (sec) |
N/A | 0.332 | 3.536 | 0.134 | 0.298 | 0.274 | 0.193 | 4.841 | 8.516 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | A | A | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 202 | 202 | 240 | 201 | 202 | 201 | 347 | 3133 | 205 |
| N.S. |
1 | 1.00 | 1.19 | 1.00 | 1.00 | 1.00 | 1.72 | 15.51 | 1.01 |
| time (sec) |
N/A | 0.269 | 3.995 | 0.098 | 0.285 | 0.252 | 0.165 | 2.814 | 7.078 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | A | A | A | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 172 | 172 | 149 | 172 | 175 | 185 | 291 | 191 | 151 |
| N.S. |
1 | 1.00 | 0.87 | 1.00 | 1.02 | 1.08 | 1.69 | 1.11 | 0.88 |
| time (sec) |
N/A | 0.522 | 1.521 | 0.230 | 0.294 | 0.270 | 0.755 | 1.743 | 7.466 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | A | A | A | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 175 | 175 | 134 | 159 | 164 | 193 | 289 | 195 | 142 |
| N.S. |
1 | 1.00 | 0.77 | 0.91 | 0.94 | 1.10 | 1.65 | 1.11 | 0.81 |
| time (sec) |
N/A | 0.551 | 1.106 | 0.236 | 0.307 | 0.277 | 1.001 | 1.282 | 7.975 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | A | A | A | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 186 | 186 | 140 | 168 | 173 | 199 | 309 | 224 | 149 |
| N.S. |
1 | 1.00 | 0.75 | 0.90 | 0.93 | 1.07 | 1.66 | 1.20 | 0.80 |
| time (sec) |
N/A | 0.666 | 0.704 | 0.234 | 0.321 | 0.270 | 1.791 | 1.388 | 7.400 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | A | A | A | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 187 | 187 | 167 | 195 | 202 | 222 | 369 | 281 | 177 |
| N.S. |
1 | 1.00 | 0.89 | 1.04 | 1.08 | 1.19 | 1.97 | 1.50 | 0.95 |
| time (sec) |
N/A | 0.834 | 1.175 | 0.243 | 0.272 | 0.284 | 2.290 | 1.511 | 8.016 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | A | A | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 225 | 225 | 211 | 240 | 246 | 249 | 459 | 584 | 218 |
| N.S. |
1 | 1.00 | 0.94 | 1.07 | 1.09 | 1.11 | 2.04 | 2.60 | 0.97 |
| time (sec) |
N/A | 1.030 | 0.988 | 0.294 | 0.277 | 0.266 | 4.169 | 1.680 | 8.512 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | A | A | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 273 | 273 | 257 | 284 | 289 | 300 | 546 | 763 | 263 |
| N.S. |
1 | 1.00 | 0.94 | 1.04 | 1.06 | 1.10 | 2.00 | 2.79 | 0.96 |
| time (sec) |
N/A | 0.835 | 1.724 | 0.308 | 0.274 | 0.276 | 5.550 | 1.724 | 8.617 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | A | A | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 323 | 323 | 299 | 330 | 333 | 350 | 643 | 943 | 307 |
| N.S. |
1 | 1.00 | 0.93 | 1.02 | 1.03 | 1.08 | 1.99 | 2.92 | 0.95 |
| time (sec) |
N/A | 0.990 | 1.376 | 0.370 | 0.272 | 0.266 | 12.579 | 1.855 | 8.105 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | A | A | C | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 127 | 127 | 138 | 127 | 130 | 190 | 1297 | 135 | 144 |
| N.S. |
1 | 1.00 | 1.09 | 1.00 | 1.02 | 1.50 | 10.21 | 1.06 | 1.13 |
| time (sec) |
N/A | 0.453 | 1.562 | 0.135 | 0.276 | 0.287 | 0.953 | 0.646 | 7.613 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | A | A | C | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 101 | 101 | 118 | 101 | 109 | 149 | 1015 | 110 | 117 |
| N.S. |
1 | 1.00 | 1.17 | 1.00 | 1.08 | 1.48 | 10.05 | 1.09 | 1.16 |
| time (sec) |
N/A | 0.235 | 0.660 | 0.089 | 0.292 | 0.284 | 0.688 | 0.495 | 7.844 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | A | A | C | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 80 | 80 | 98 | 87 | 94 | 110 | 700 | 95 | 100 |
| N.S. |
1 | 1.00 | 1.22 | 1.09 | 1.18 | 1.38 | 8.75 | 1.19 | 1.25 |
| time (sec) |
N/A | 0.166 | 0.180 | 0.079 | 0.268 | 0.288 | 0.548 | 0.366 | 7.706 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | C | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 58 | 58 | 66 | 82 | 88 | 76 | 524 | 94 | 93 |
| N.S. |
1 | 1.00 | 1.14 | 1.41 | 1.52 | 1.31 | 9.03 | 1.62 | 1.60 |
| time (sec) |
N/A | 0.085 | 0.110 | 0.047 | 0.267 | 0.275 | 0.468 | 0.348 | 7.797 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | A | A | C | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 80 | 80 | 113 | 95 | 107 | 118 | 952 | 113 | 115 |
| N.S. |
1 | 1.00 | 1.41 | 1.19 | 1.34 | 1.48 | 11.90 | 1.41 | 1.44 |
| time (sec) |
N/A | 0.132 | 0.426 | 0.192 | 0.269 | 0.270 | 1.050 | 0.441 | 9.399 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | A | A | C | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 103 | 103 | 138 | 122 | 131 | 177 | 2071 | 157 | 140 |
| N.S. |
1 | 1.00 | 1.34 | 1.18 | 1.27 | 1.72 | 20.11 | 1.52 | 1.36 |
| time (sec) |
N/A | 0.299 | 0.947 | 0.214 | 0.278 | 0.288 | 1.997 | 0.568 | 9.865 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | A | A | C | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 137 | 137 | 163 | 152 | 158 | 234 | 2599 | 214 | 175 |
| N.S. |
1 | 1.00 | 1.19 | 1.11 | 1.15 | 1.71 | 18.97 | 1.56 | 1.28 |
| time (sec) |
N/A | 0.621 | 1.488 | 0.297 | 0.273 | 0.294 | 2.853 | 0.702 | 10.898 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | A | A | C | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 169 | 169 | 194 | 189 | 200 | 293 | 3016 | 285 | 208 |
| N.S. |
1 | 1.00 | 1.15 | 1.12 | 1.18 | 1.73 | 17.85 | 1.69 | 1.23 |
| time (sec) |
N/A | 1.241 | 2.955 | 0.304 | 0.281 | 0.295 | 4.199 | 0.866 | 10.065 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | A | B | C | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 208 | 208 | 193 | 172 | 220 | 434 | 4534 | 290 | 210 |
| N.S. |
1 | 1.00 | 0.93 | 0.83 | 1.06 | 2.09 | 21.80 | 1.39 | 1.01 |
| time (sec) |
N/A | 0.724 | 6.004 | 0.161 | 0.284 | 0.336 | 1.399 | 0.708 | 8.326 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | A | B | C | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 157 | 157 | 146 | 155 | 197 | 311 | 3485 | 244 | 165 |
| N.S. |
1 | 1.00 | 0.93 | 0.99 | 1.25 | 1.98 | 22.20 | 1.55 | 1.05 |
| time (sec) |
N/A | 0.491 | 2.892 | 0.119 | 0.318 | 0.308 | 1.049 | 0.578 | 7.843 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | A | A | C | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 115 | 115 | 140 | 145 | 185 | 221 | 2987 | 241 | 163 |
| N.S. |
1 | 1.00 | 1.22 | 1.26 | 1.61 | 1.92 | 25.97 | 2.10 | 1.42 |
| time (sec) |
N/A | 0.256 | 2.269 | 0.070 | 0.301 | 0.265 | 0.843 | 0.430 | 8.187 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | A | A | C | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 111 | 111 | 190 | 141 | 177 | 222 | 2878 | 234 | 153 |
| N.S. |
1 | 1.00 | 1.71 | 1.27 | 1.59 | 2.00 | 25.93 | 2.11 | 1.38 |
| time (sec) |
N/A | 0.174 | 2.333 | 0.062 | 0.285 | 0.268 | 0.827 | 0.404 | 8.467 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | A | B | C | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 137 | 137 | 183 | 163 | 208 | 323 | 4488 | 279 | 180 |
| N.S. |
1 | 1.00 | 1.34 | 1.19 | 1.52 | 2.36 | 32.76 | 2.04 | 1.31 |
| time (sec) |
N/A | 0.408 | 0.961 | 0.279 | 0.288 | 0.298 | 1.798 | 0.657 | 9.157 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | A | B | C | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 192 | 192 | 193 | 196 | 262 | 465 | 8145 | 362 | 230 |
| N.S. |
1 | 1.00 | 1.01 | 1.02 | 1.36 | 2.42 | 42.42 | 1.89 | 1.20 |
| time (sec) |
N/A | 0.637 | 3.770 | 0.417 | 0.287 | 0.321 | 2.921 | 0.873 | 10.847 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | A | B | C | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 250 | 250 | 220 | 227 | 325 | 590 | 9896 | 402 | 284 |
| N.S. |
1 | 1.00 | 0.88 | 0.91 | 1.30 | 2.36 | 39.58 | 1.61 | 1.14 |
| time (sec) |
N/A | 0.937 | 4.961 | 0.486 | 0.289 | 0.349 | 4.008 | 0.907 | 11.861 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | A | B | F(-2) | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 331 | 331 | 275 | 263 | 389 | 890 | 0 | 505 | 335 |
| N.S. |
1 | 1.00 | 0.83 | 0.79 | 1.18 | 2.69 | 0.00 | 1.53 | 1.01 |
| time (sec) |
N/A | 0.864 | 5.220 | 0.196 | 0.299 | 0.380 | 0.000 | 1.116 | 9.001 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | A | B | F(-2) | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 250 | 250 | 235 | 242 | 366 | 666 | 0 | 458 | 307 |
| N.S. |
1 | 1.00 | 0.94 | 0.97 | 1.46 | 2.66 | 0.00 | 1.83 | 1.23 |
| time (sec) |
N/A | 0.788 | 6.374 | 0.166 | 0.308 | 0.343 | 0.000 | 0.854 | 8.271 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | A | B | F(-2) | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 189 | 189 | 288 | 223 | 333 | 478 | 0 | 410 | 280 |
| N.S. |
1 | 1.00 | 1.52 | 1.18 | 1.76 | 2.53 | 0.00 | 2.17 | 1.48 |
| time (sec) |
N/A | 0.595 | 5.746 | 0.110 | 0.297 | 0.275 | 0.000 | 0.704 | 7.825 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | A | B | F(-2) | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 179 | 179 | 188 | 213 | 330 | 488 | 0 | 410 | 282 |
| N.S. |
1 | 1.00 | 1.05 | 1.19 | 1.84 | 2.73 | 0.00 | 2.29 | 1.58 |
| time (sec) |
N/A | 0.475 | 3.970 | 0.118 | 0.307 | 0.276 | 0.000 | 0.577 | 7.878 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | A | B | F(-2) | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 175 | 175 | 243 | 208 | 321 | 482 | 0 | 409 | 279 |
| N.S. |
1 | 1.00 | 1.39 | 1.19 | 1.83 | 2.75 | 0.00 | 2.34 | 1.59 |
| time (sec) |
N/A | 0.347 | 4.042 | 0.110 | 0.305 | 0.272 | 0.000 | 0.538 | 8.251 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | A | B | F(-2) | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 215 | 215 | 254 | 243 | 372 | 683 | 0 | 479 | 315 |
| N.S. |
1 | 1.00 | 1.18 | 1.13 | 1.73 | 3.18 | 0.00 | 2.23 | 1.47 |
| time (sec) |
N/A | 0.665 | 3.877 | 0.442 | 0.305 | 0.331 | 0.000 | 1.000 | 10.319 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | A | B | F(-2) | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 287 | 287 | 288 | 289 | 454 | 917 | 0 | 560 | 380 |
| N.S. |
1 | 1.00 | 1.00 | 1.01 | 1.58 | 3.20 | 0.00 | 1.95 | 1.32 |
| time (sec) |
N/A | 0.951 | 6.459 | 0.724 | 0.386 | 0.371 | 0.000 | 0.920 | 13.087 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | A | B | F(-2) | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 352 | 352 | 320 | 320 | 541 | 1065 | 0 | 812 | 434 |
| N.S. |
1 | 1.00 | 0.91 | 0.91 | 1.54 | 3.03 | 0.00 | 2.31 | 1.23 |
| time (sec) |
N/A | 1.442 | 6.687 | 0.706 | 0.398 | 0.398 | 0.000 | 1.239 | 14.255 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | A | B | F(-2) | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 351 | 351 | 307 | 343 | 583 | 1113 | 0 | 719 | 486 |
| N.S. |
1 | 1.00 | 0.87 | 0.98 | 1.66 | 3.17 | 0.00 | 2.05 | 1.38 |
| time (sec) |
N/A | 1.226 | 3.560 | 0.275 | 0.387 | 0.357 | 0.000 | 1.260 | 8.805 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | A | B | F(-2) | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 298 | 298 | 465 | 318 | 550 | 813 | 0 | 670 | 470 |
| N.S. |
1 | 1.00 | 1.56 | 1.07 | 1.85 | 2.73 | 0.00 | 2.25 | 1.58 |
| time (sec) |
N/A | 0.866 | 6.367 | 0.210 | 0.418 | 0.293 | 0.000 | 0.983 | 9.101 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | B | B | F(-2) | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 261 | 261 | 411 | 301 | 526 | 836 | 0 | 632 | 446 |
| N.S. |
1 | 1.00 | 1.57 | 1.15 | 2.02 | 3.20 | 0.00 | 2.42 | 1.71 |
| time (sec) |
N/A | 0.579 | 6.322 | 0.209 | 0.398 | 0.325 | 0.000 | 0.828 | 7.871 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | B | B | F(-2) | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 250 | 250 | 248 | 287 | 523 | 838 | 0 | 638 | 447 |
| N.S. |
1 | 1.00 | 0.99 | 1.15 | 2.09 | 3.35 | 0.00 | 2.55 | 1.79 |
| time (sec) |
N/A | 0.473 | 1.323 | 0.220 | 0.368 | 0.303 | 0.000 | 0.694 | 8.454 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | B | B | F(-2) | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 247 | 247 | 327 | 284 | 514 | 815 | 0 | 630 | 442 |
| N.S. |
1 | 1.00 | 1.32 | 1.15 | 2.08 | 3.30 | 0.00 | 2.55 | 1.79 |
| time (sec) |
N/A | 0.469 | 6.281 | 0.209 | 0.530 | 0.303 | 0.000 | 0.675 | 8.430 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | A | B | F(-2) | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 302 | 302 | 308 | 335 | 580 | 1126 | 0 | 722 | 484 |
| N.S. |
1 | 1.00 | 1.02 | 1.11 | 1.92 | 3.73 | 0.00 | 2.39 | 1.60 |
| time (sec) |
N/A | 1.085 | 3.542 | 0.681 | 0.304 | 0.379 | 0.000 | 0.991 | 11.613 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | A | B | F(-2) | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 399 | 399 | 357 | 400 | 698 | 1510 | 0 | 846 | 576 |
| N.S. |
1 | 1.00 | 0.89 | 1.00 | 1.75 | 3.78 | 0.00 | 2.12 | 1.44 |
| time (sec) |
N/A | 1.725 | 6.576 | 1.340 | 0.307 | 0.443 | 0.000 | 1.308 | 12.846 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | A | B | F(-2) | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 477 | 477 | 417 | 429 | 815 | 1732 | 0 | 903 | 664 |
| N.S. |
1 | 1.00 | 0.87 | 0.90 | 1.71 | 3.63 | 0.00 | 1.89 | 1.39 |
| time (sec) |
N/A | 2.141 | 6.730 | 1.081 | 0.314 | 0.533 | 0.000 | 1.112 | 14.986 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 29 | 29 | 26 | 30 | 30 | 31 | 53 | 187 | 28 |
| N.S. |
1 | 1.00 | 0.90 | 1.03 | 1.03 | 1.07 | 1.83 | 6.45 | 0.97 |
| time (sec) |
N/A | 0.022 | 0.024 | 0.043 | 0.390 | 0.253 | 0.574 | 0.569 | 7.506 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 16 | 16 | 25 | 17 | 22 | 19 | 36 | 22 | 16 |
| N.S. |
1 | 1.00 | 1.56 | 1.06 | 1.38 | 1.19 | 2.25 | 1.38 | 1.00 |
| time (sec) |
N/A | 0.014 | 0.008 | 0.028 | 0.377 | 0.246 | 0.400 | 0.440 | 7.978 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 13 | 13 | 13 | 18 | 17 | 19 | 37 | 99 | 17 |
| N.S. |
1 | 1.00 | 1.00 | 1.38 | 1.31 | 1.46 | 2.85 | 7.62 | 1.31 |
| time (sec) |
N/A | 0.009 | 0.005 | 0.025 | 0.339 | 0.261 | 0.333 | 0.329 | 7.228 |