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 | F | F | F | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 214 | 210 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.383 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 125 | 117 | 120 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.94 | 0.96 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.287 | 0.147 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | F(-1) | F | B |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 67 | 67 | 67 | 0 | 0 | 0 | 0 | 0 | 64 |
| N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.96 |
| time (sec) |
N/A | 0.239 | 0.022 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 2.445 |
| 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 | 78 | 78 | 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 | 0.263 | 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 | 78 | 78 | 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 | 0.264 | 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 | 92 | 92 | 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 | 0.274 | 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 | 92 | 92 | 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 | 0.273 | 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 | 92 | 92 | 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 | 0.245 | 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 | 92 | 92 | 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 | 0.274 | 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 | 92 | 92 | 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 | 0.264 | 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 | F | B | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 259 | 235 | 220 | 262 | 0 | 2595 | 0 | 0 | 0 |
| N.S. |
1 | 0.91 | 0.85 | 1.01 | 0.00 | 10.02 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.533 | 0.306 | 0.223 | 0.000 | 0.858 | 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 | 136 | 124 | 117 | 117 | 0 | 879 | 0 | 0 | 0 |
| N.S. |
1 | 0.91 | 0.86 | 0.86 | 0.00 | 6.46 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.407 | 0.117 | 0.151 | 0.000 | 0.770 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | B | A | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 43 | 41 | 41 | 80 | 0 | 225 | 68 | 0 | 39 |
| N.S. |
1 | 0.95 | 0.95 | 1.86 | 0.00 | 5.23 | 1.58 | 0.00 | 0.91 |
| time (sec) |
N/A | 0.254 | 0.023 | 0.118 | 0.000 | 0.731 | 1.283 | 0.000 | 1.829 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | C | F | B | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 286 | 285 | 229 | 195 | 0 | 5671 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.80 | 0.68 | 0.00 | 19.83 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.756 | 0.190 | 0.239 | 0.000 | 1.154 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-1) | B | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 270 | 249 | 288 | 255 | 0 | 5181 | 0 | 0 | 0 |
| N.S. |
1 | 0.92 | 1.07 | 0.94 | 0.00 | 19.19 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.556 | 0.431 | 0.162 | 0.000 | 0.920 | 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 | 142 | 129 | 123 | 118 | 0 | 2137 | 0 | 0 | 0 |
| N.S. |
1 | 0.91 | 0.87 | 0.83 | 0.00 | 15.05 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.408 | 0.310 | 0.157 | 0.000 | 0.804 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | B | B | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 49 | 46 | 42 | 127 | 0 | 564 | 151 | 0 | 45 |
| N.S. |
1 | 0.94 | 0.86 | 2.59 | 0.00 | 11.51 | 3.08 | 0.00 | 0.92 |
| time (sec) |
N/A | 0.263 | 0.047 | 0.143 | 0.000 | 0.289 | 3.122 | 0.000 | 2.274 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | C | F | B | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 384 | 379 | 300 | 376 | 0 | 10240 | 0 | 0 | 0 |
| N.S. |
1 | 0.99 | 0.78 | 0.98 | 0.00 | 26.67 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.876 | 0.522 | 0.443 | 0.000 | 5.153 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 130 | 125 | 119 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.96 | 0.92 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.371 | 0.111 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 84 | 82 | 82 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.98 | 0.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.328 | 0.042 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | F(-1) | F | B |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 37 | 37 | 37 | 0 | 0 | 0 | 0 | 0 | 38 |
| N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.03 |
| time (sec) |
N/A | 0.233 | 0.010 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 1.747 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 130 | 125 | 119 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.96 | 0.92 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.369 | 0.091 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 84 | 82 | 82 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.98 | 0.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.319 | 0.049 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | F(-1) | F | B |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 37 | 37 | 37 | 0 | 0 | 0 | 0 | 0 | 38 |
| N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.03 |
| time (sec) |
N/A | 0.238 | 0.009 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 1.708 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | B | F | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 17 | 21 | 23 | 24 | 45 | 47 | 0 | 25 | 27 |
| N.S. |
1 | 1.24 | 1.35 | 1.41 | 2.65 | 2.76 | 0.00 | 1.47 | 1.59 |
| time (sec) |
N/A | 0.209 | 0.013 | 0.325 | 0.173 | 0.255 | 0.000 | 0.260 | 0.095 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | B | F | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 63 | 70 | 44 | 49 | 292 | 875 | 0 | 70 | 252 |
| N.S. |
1 | 1.11 | 0.70 | 0.78 | 4.63 | 13.89 | 0.00 | 1.11 | 4.00 |
| time (sec) |
N/A | 0.373 | 0.206 | 0.323 | 0.306 | 0.266 | 0.000 | 0.305 | 0.182 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | B | F | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 38 | 49 | 29 | 28 | 106 | 311 | 0 | 44 | 67 |
| N.S. |
1 | 1.29 | 0.76 | 0.74 | 2.79 | 8.18 | 0.00 | 1.16 | 1.76 |
| time (sec) |
N/A | 0.353 | 0.130 | 0.184 | 0.307 | 0.246 | 0.000 | 0.279 | 1.625 |
| 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 | 18 | 18 | 18 | 19 | 32 | 139 | 0 | 24 | 18 |
| N.S. |
1 | 1.00 | 1.00 | 1.06 | 1.78 | 7.72 | 0.00 | 1.33 | 1.00 |
| time (sec) |
N/A | 0.301 | 0.034 | 0.134 | 0.303 | 0.248 | 0.000 | 0.266 | 1.545 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | B | F | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 50 | 52 | 49 | 54 | 68 | 200 | 0 | 47 | 0 |
| N.S. |
1 | 1.04 | 0.98 | 1.08 | 1.36 | 4.00 | 0.00 | 0.94 | 0.00 |
| time (sec) |
N/A | 0.321 | 0.074 | 0.198 | 0.305 | 0.257 | 0.000 | 0.272 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | A | B | F | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 87 | 90 | 40 | 102 | 126 | 764 | 0 | 108 | 0 |
| N.S. |
1 | 1.03 | 0.46 | 1.17 | 1.45 | 8.78 | 0.00 | 1.24 | 0.00 |
| time (sec) |
N/A | 0.360 | 0.108 | 0.222 | 0.305 | 0.274 | 0.000 | 0.308 | 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 | 120 | 99 | 75 | 169 | 891 | 1645 | 0 | 124 | 0 |
| N.S. |
1 | 0.82 | 0.62 | 1.41 | 7.42 | 13.71 | 0.00 | 1.03 | 0.00 |
| time (sec) |
N/A | 0.455 | 0.189 | 0.287 | 0.315 | 0.272 | 0.000 | 0.308 | 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 | 91 | 69 | 55 | 141 | 387 | 742 | 0 | 100 | 0 |
| N.S. |
1 | 0.76 | 0.60 | 1.55 | 4.25 | 8.15 | 0.00 | 1.10 | 0.00 |
| time (sec) |
N/A | 0.399 | 0.147 | 0.249 | 0.292 | 0.264 | 0.000 | 0.279 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | B | F | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 57 | 41 | 40 | 102 | 50 | 182 | 0 | 35 | 0 |
| N.S. |
1 | 0.72 | 0.70 | 1.79 | 0.88 | 3.19 | 0.00 | 0.61 | 0.00 |
| time (sec) |
N/A | 0.397 | 0.038 | 0.224 | 0.292 | 0.251 | 0.000 | 0.277 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | C | A | A | B | B | F | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 56 | 48 | 35 | 42 | 125 | 317 | 0 | 48 | 67 |
| N.S. |
1 | 0.86 | 0.62 | 0.75 | 2.23 | 5.66 | 0.00 | 0.86 | 1.20 |
| time (sec) |
N/A | 0.449 | 0.056 | 0.196 | 0.284 | 0.241 | 0.000 | 0.279 | 1.638 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | C | A | A | B | B | F | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 91 | 62 | 47 | 75 | 487 | 885 | 0 | 74 | 281 |
| N.S. |
1 | 0.68 | 0.52 | 0.82 | 5.35 | 9.73 | 0.00 | 0.81 | 3.09 |
| time (sec) |
N/A | 0.416 | 0.065 | 0.209 | 0.289 | 0.246 | 0.000 | 0.298 | 1.588 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | C | A | A | B | B | F(-1) | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 124 | 74 | 67 | 85 | 1050 | 1696 | 0 | 96 | 427 |
| N.S. |
1 | 0.60 | 0.54 | 0.69 | 8.47 | 13.68 | 0.00 | 0.77 | 3.44 |
| time (sec) |
N/A | 0.435 | 0.142 | 0.223 | 0.312 | 0.278 | 0.000 | 0.305 | 1.624 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | B | F | F(-2) | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 66 | 72 | 43 | 48 | 446 | 1387 | 0 | 0 | 381 |
| N.S. |
1 | 1.09 | 0.65 | 0.73 | 6.76 | 21.02 | 0.00 | 0.00 | 5.77 |
| time (sec) |
N/A | 0.375 | 0.173 | 0.187 | 0.331 | 0.269 | 0.000 | 0.000 | 1.636 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | B | F | F(-2) | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 42 | 51 | 31 | 38 | 184 | 641 | 0 | 0 | 82 |
| N.S. |
1 | 1.21 | 0.74 | 0.90 | 4.38 | 15.26 | 0.00 | 0.00 | 1.95 |
| time (sec) |
N/A | 0.357 | 0.133 | 0.190 | 0.316 | 0.240 | 0.000 | 0.000 | 0.137 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | B | F | F(-2) | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 19 | 19 | 19 | 20 | 33 | 168 | 0 | 0 | 30 |
| N.S. |
1 | 1.00 | 1.00 | 1.05 | 1.74 | 8.84 | 0.00 | 0.00 | 1.58 |
| time (sec) |
N/A | 0.297 | 0.026 | 0.138 | 0.298 | 0.250 | 0.000 | 0.000 | 1.554 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | B | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 31 | 31 | 31 | 31 | 40 | 174 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.00 | 1.00 | 1.29 | 5.61 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.321 | 0.039 | 0.163 | 0.300 | 0.278 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | B | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 66 | 68 | 56 | 83 | 100 | 529 | 0 | 0 | 0 |
| N.S. |
1 | 1.03 | 0.85 | 1.26 | 1.52 | 8.02 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.360 | 0.188 | 0.217 | 0.316 | 0.256 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | B | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 91 | 81 | 66 | 145 | 628 | 1328 | 0 | 0 | 0 |
| N.S. |
1 | 0.89 | 0.73 | 1.59 | 6.90 | 14.59 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.568 | 0.091 | 0.268 | 0.313 | 0.284 | 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(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 62 | 56 | 44 | 116 | 217 | 504 | 0 | 0 | 0 |
| N.S. |
1 | 0.90 | 0.71 | 1.87 | 3.50 | 8.13 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.491 | 0.044 | 0.250 | 0.288 | 0.272 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | B | F | F(-2) | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 25 | 25 | 25 | 32 | 101 | 170 | 0 | 0 | 76 |
| N.S. |
1 | 1.00 | 1.00 | 1.28 | 4.04 | 6.80 | 0.00 | 0.00 | 3.04 |
| time (sec) |
N/A | 0.406 | 0.030 | 0.176 | 0.284 | 0.261 | 0.000 | 0.000 | 0.117 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | C | A | A | B | B | F | F(-2) | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 61 | 52 | 37 | 64 | 556 | 647 | 0 | 0 | 95 |
| N.S. |
1 | 0.85 | 0.61 | 1.05 | 9.11 | 10.61 | 0.00 | 0.00 | 1.56 |
| time (sec) |
N/A | 0.423 | 0.048 | 0.209 | 0.321 | 0.261 | 0.000 | 0.000 | 1.662 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | C | A | A | B | B | F | F(-2) | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 96 | 66 | 49 | 74 | 1231 | 1399 | 0 | 0 | 381 |
| N.S. |
1 | 0.69 | 0.51 | 0.77 | 12.82 | 14.57 | 0.00 | 0.00 | 3.97 |
| time (sec) |
N/A | 0.439 | 0.070 | 0.224 | 0.361 | 0.263 | 0.000 | 0.000 | 1.661 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | C | B | B | F | F(-2) | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 68 | 74 | 51 | 44 | 586 | 2507 | 0 | 0 | 457 |
| N.S. |
1 | 1.09 | 0.75 | 0.65 | 8.62 | 36.87 | 0.00 | 0.00 | 6.72 |
| time (sec) |
N/A | 0.405 | 0.199 | 0.261 | 0.343 | 0.310 | 0.000 | 0.000 | 0.168 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | C | B | B | F | F(-2) | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 44 | 53 | 34 | 44 | 268 | 1400 | 0 | 0 | 305 |
| N.S. |
1 | 1.20 | 0.77 | 1.00 | 6.09 | 31.82 | 0.00 | 0.00 | 6.93 |
| time (sec) |
N/A | 0.358 | 0.184 | 0.187 | 0.334 | 0.274 | 0.000 | 0.000 | 1.658 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | B | F | F(-2) | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 21 | 21 | 21 | 20 | 61 | 608 | 0 | 0 | 58 |
| N.S. |
1 | 1.00 | 1.00 | 0.95 | 2.90 | 28.95 | 0.00 | 0.00 | 2.76 |
| time (sec) |
N/A | 0.311 | 0.031 | 0.132 | 0.326 | 0.241 | 0.000 | 0.000 | 1.694 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | C | A | B | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 53 | 55 | 37 | 44 | 76 | 271 | 0 | 0 | 0 |
| N.S. |
1 | 1.04 | 0.70 | 0.83 | 1.43 | 5.11 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.342 | 0.078 | 0.180 | 0.310 | 0.272 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | C | A | B | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 66 | 70 | 61 | 36 | 100 | 565 | 0 | 0 | 0 |
| N.S. |
1 | 1.06 | 0.92 | 0.55 | 1.52 | 8.56 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.371 | 0.102 | 0.182 | 0.323 | 0.266 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | B | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 106 | 85 | 58 | 69 | 369 | 1423 | 0 | 0 | 0 |
| N.S. |
1 | 0.80 | 0.55 | 0.65 | 3.48 | 13.42 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.600 | 0.082 | 0.243 | 0.297 | 0.283 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | C | C | B | B | B | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 64 | 52 | 46 | 135 | 321 | 254 | 0 | 0 | 0 |
| N.S. |
1 | 0.81 | 0.72 | 2.11 | 5.02 | 3.97 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.429 | 0.059 | 0.287 | 0.297 | 0.278 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | B | F | F(-2) | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 38 | 38 | 29 | 35 | 823 | 612 | 0 | 0 | 71 |
| N.S. |
1 | 1.00 | 0.76 | 0.92 | 21.66 | 16.11 | 0.00 | 0.00 | 1.87 |
| time (sec) |
N/A | 0.410 | 0.038 | 0.196 | 0.330 | 0.269 | 0.000 | 0.000 | 1.738 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | C | A | A | B | B | F | F(-2) | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 77 | 59 | 41 | 47 | 1531 | 1410 | 0 | 0 | 305 |
| N.S. |
1 | 0.77 | 0.53 | 0.61 | 19.88 | 18.31 | 0.00 | 0.00 | 3.96 |
| time (sec) |
N/A | 0.448 | 0.083 | 0.190 | 0.385 | 0.286 | 0.000 | 0.000 | 0.180 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | C | A | A | B | B | F(-1) | F(-2) | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 115 | 73 | 51 | 57 | 2216 | 2511 | 0 | 0 | 457 |
| N.S. |
1 | 0.63 | 0.44 | 0.50 | 19.27 | 21.83 | 0.00 | 0.00 | 3.97 |
| time (sec) |
N/A | 0.445 | 0.101 | 0.210 | 0.439 | 0.299 | 0.000 | 0.000 | 1.764 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | C | F | B | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 187 | 186 | 151 | 43 | 0 | 4704 | 0 | 0 | 0 |
| N.S. |
1 | 0.99 | 0.81 | 0.23 | 0.00 | 25.16 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.374 | 0.430 | 0.282 | 0.000 | 0.726 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | C | F | B | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 126 | 119 | 88 | 43 | 0 | 1670 | 0 | 0 | 0 |
| N.S. |
1 | 0.94 | 0.70 | 0.34 | 0.00 | 13.25 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.299 | 0.308 | 0.224 | 0.000 | 0.620 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | C | F | B | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 62 | 64 | 65 | 41 | 0 | 624 | 0 | 0 | 0 |
| N.S. |
1 | 1.03 | 1.05 | 0.66 | 0.00 | 10.06 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.249 | 0.049 | 0.200 | 0.000 | 0.588 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | C | F | B | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 54 | 56 | 53 | 46 | 0 | 605 | 0 | 0 | 0 |
| N.S. |
1 | 1.04 | 0.98 | 0.85 | 0.00 | 11.20 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.261 | 0.035 | 0.204 | 0.000 | 0.437 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | C | F | B | F | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 106 | 98 | 69 | 58 | 0 | 1445 | 0 | 1026 | 0 |
| N.S. |
1 | 0.92 | 0.65 | 0.55 | 0.00 | 13.63 | 0.00 | 9.68 | 0.00 |
| time (sec) |
N/A | 0.295 | 0.262 | 0.253 | 0.000 | 0.491 | 0.000 | 8.360 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | C | F | B | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 167 | 154 | 102 | 80 | 0 | 3880 | 0 | 0 | 0 |
| N.S. |
1 | 0.92 | 0.61 | 0.48 | 0.00 | 23.23 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.338 | 0.407 | 0.289 | 0.000 | 0.602 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | F | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 292 | 350 | 214 | 369 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.20 | 0.73 | 1.26 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.513 | 1.694 | 3.021 | 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 | F | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 168 | 267 | 150 | 233 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.59 | 0.89 | 1.39 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.402 | 0.721 | 1.947 | 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 | F | F | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 60 | 60 | 69 | 140 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.15 | 2.33 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.285 | 0.051 | 1.118 | 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 | F | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 202 | 273 | 154 | 215 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.35 | 0.76 | 1.06 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.429 | 0.771 | 1.789 | 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 | F | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 270 | 338 | 210 | 519 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.25 | 0.78 | 1.92 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.491 | 2.371 | 2.611 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | C | F | B | F(-1) | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 232 | 213 | 169 | 71 | 0 | 6380 | 0 | 2986 | 0 |
| N.S. |
1 | 0.92 | 0.73 | 0.31 | 0.00 | 27.50 | 0.00 | 12.87 | 0.00 |
| time (sec) |
N/A | 0.393 | 1.111 | 0.348 | 0.000 | 0.777 | 0.000 | 55.106 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | C | F | B | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 156 | 146 | 122 | 71 | 0 | 2454 | 0 | 0 | 0 |
| N.S. |
1 | 0.94 | 0.78 | 0.46 | 0.00 | 15.73 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.323 | 0.385 | 0.300 | 0.000 | 0.667 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | C | F | B | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 90 | 91 | 86 | 69 | 0 | 1052 | 0 | 0 | 0 |
| N.S. |
1 | 1.01 | 0.96 | 0.77 | 0.00 | 11.69 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.267 | 0.113 | 0.228 | 0.000 | 0.621 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | C | F | B | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 78 | 79 | 69 | 62 | 0 | 1000 | 0 | 0 | 0 |
| N.S. |
1 | 1.01 | 0.88 | 0.79 | 0.00 | 12.82 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.273 | 0.091 | 0.201 | 0.000 | 0.437 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | C | F | B | F(-1) | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 140 | 123 | 90 | 84 | 0 | 2406 | 0 | 0 | 0 |
| N.S. |
1 | 0.88 | 0.64 | 0.60 | 0.00 | 17.19 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.311 | 0.332 | 0.284 | 0.000 | 0.541 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | C | F | B | F(-1) | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 203 | 174 | 123 | 113 | 0 | 5509 | 0 | 0 | 0 |
| N.S. |
1 | 0.86 | 0.61 | 0.56 | 0.00 | 27.14 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.354 | 0.572 | 0.408 | 0.000 | 0.646 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | F | F(-1) | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 305 | 379 | 224 | 389 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.24 | 0.73 | 1.28 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.568 | 2.346 | 3.409 | 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 | F | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 260 | 326 | 188 | 414 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.25 | 0.72 | 1.59 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.454 | 2.508 | 2.876 | 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 | F | F | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 174 | 175 | 169 | 428 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.01 | 0.97 | 2.46 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.847 | 0.574 | 1.927 | 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 | F | F(-1) | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 256 | 324 | 184 | 327 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.27 | 0.72 | 1.28 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.463 | 2.047 | 2.615 | 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 | F | F(-1) | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 306 | 380 | 229 | 540 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.24 | 0.75 | 1.76 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.546 | 3.622 | 3.014 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | C | F | B | F | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 142 | 155 | 116 | 43 | 0 | 4100 | 0 | 2265 | 0 |
| N.S. |
1 | 1.09 | 0.82 | 0.30 | 0.00 | 28.87 | 0.00 | 15.95 | 0.00 |
| time (sec) |
N/A | 0.344 | 0.360 | 0.286 | 0.000 | 0.432 | 0.000 | 10.848 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | C | F | B | F | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 89 | 89 | 85 | 43 | 0 | 1320 | 0 | 702 | 0 |
| N.S. |
1 | 1.00 | 0.96 | 0.48 | 0.00 | 14.83 | 0.00 | 7.89 | 0.00 |
| time (sec) |
N/A | 0.298 | 0.088 | 0.284 | 0.000 | 0.333 | 0.000 | 2.829 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | C | F | B | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 41 | 41 | 44 | 41 | 0 | 433 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.07 | 1.00 | 0.00 | 10.56 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.242 | 0.035 | 0.270 | 0.000 | 0.305 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | C | F | B | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 33 | 33 | 33 | 35 | 0 | 410 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.00 | 1.06 | 0.00 | 12.42 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.253 | 0.029 | 0.202 | 0.000 | 0.299 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | C | F | B | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 77 | 74 | 72 | 44 | 0 | 1144 | 0 | 0 | 0 |
| N.S. |
1 | 0.96 | 0.94 | 0.57 | 0.00 | 14.86 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.278 | 0.141 | 0.259 | 0.000 | 0.339 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | C | F | B | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 126 | 128 | 100 | 54 | 0 | 3086 | 0 | 0 | 0 |
| N.S. |
1 | 1.02 | 0.79 | 0.43 | 0.00 | 24.49 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.325 | 0.269 | 0.281 | 0.000 | 0.349 | 0.000 | 0.000 | 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 | 219 | 270 | 206 | 366 | 0 | 2755 | 0 | 1227 | 0 |
| N.S. |
1 | 1.23 | 0.94 | 1.67 | 0.00 | 12.58 | 0.00 | 5.60 | 0.00 |
| time (sec) |
N/A | 0.413 | 1.800 | 1.946 | 0.000 | 0.129 | 0.000 | 4.979 | 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 | 156 | 282 | 109 | 239 | 0 | 703 | 0 | 350 | 0 |
| N.S. |
1 | 1.81 | 0.70 | 1.53 | 0.00 | 4.51 | 0.00 | 2.24 | 0.00 |
| time (sec) |
N/A | 0.420 | 0.662 | 1.045 | 0.000 | 0.091 | 0.000 | 1.383 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | B | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 60 | 60 | 68 | 86 | 0 | 147 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.13 | 1.43 | 0.00 | 2.45 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.283 | 0.039 | 0.383 | 0.000 | 0.084 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | B | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 207 | 274 | 105 | 216 | 0 | 674 | 0 | 0 | 0 |
| N.S. |
1 | 1.32 | 0.51 | 1.04 | 0.00 | 3.26 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.409 | 0.617 | 1.048 | 0.000 | 0.101 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | B | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 285 | 349 | 208 | 522 | 0 | 2584 | 0 | 0 | 0 |
| N.S. |
1 | 1.22 | 0.73 | 1.83 | 0.00 | 9.07 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.511 | 2.772 | 1.780 | 0.000 | 0.117 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | C | F | B | F | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 187 | 193 | 113 | 103 | 0 | 10168 | 0 | 2452 | 0 |
| N.S. |
1 | 1.03 | 0.60 | 0.55 | 0.00 | 54.37 | 0.00 | 13.11 | 0.00 |
| time (sec) |
N/A | 0.385 | 0.354 | 7.191 | 0.000 | 0.713 | 0.000 | 17.593 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | C | F | B | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 122 | 124 | 79 | 103 | 0 | 4050 | 0 | 0 | 0 |
| N.S. |
1 | 1.02 | 0.65 | 0.84 | 0.00 | 33.20 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.320 | 0.087 | 0.693 | 0.000 | 0.419 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | C | F | B | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 69 | 71 | 58 | 93 | 0 | 1370 | 0 | 0 | 0 |
| N.S. |
1 | 1.03 | 0.84 | 1.35 | 0.00 | 19.86 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.265 | 0.057 | 0.212 | 0.000 | 0.330 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | C | F | B | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 57 | 59 | 46 | 35 | 0 | 1137 | 0 | 0 | 0 |
| N.S. |
1 | 1.04 | 0.81 | 0.61 | 0.00 | 19.95 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.271 | 0.045 | 0.208 | 0.000 | 0.310 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | C | F | B | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 110 | 103 | 69 | 43 | 0 | 3228 | 0 | 0 | 0 |
| N.S. |
1 | 0.94 | 0.63 | 0.39 | 0.00 | 29.35 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.300 | 0.078 | 0.739 | 0.000 | 0.362 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | C | F | B | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 167 | 157 | 94 | 43 | 0 | 7562 | 0 | 0 | 0 |
| N.S. |
1 | 0.94 | 0.56 | 0.26 | 0.00 | 45.28 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.351 | 0.233 | 5.163 | 0.000 | 0.531 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | B | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 275 | 345 | 212 | 354 | 0 | 7400 | 0 | 0 | 0 |
| N.S. |
1 | 1.25 | 0.77 | 1.29 | 0.00 | 26.91 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.464 | 1.936 | 5.516 | 0.000 | 0.265 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | B | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 217 | 275 | 158 | 256 | 0 | 2612 | 0 | 0 | 0 |
| N.S. |
1 | 1.27 | 0.73 | 1.18 | 0.00 | 12.04 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.419 | 1.325 | 2.242 | 0.000 | 0.134 | 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(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 115 | 115 | 100 | 253 | 0 | 1464 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.87 | 2.20 | 0.00 | 12.73 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.448 | 0.106 | 0.732 | 0.000 | 0.102 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | B | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 237 | 320 | 153 | 219 | 0 | 2436 | 0 | 0 | 0 |
| N.S. |
1 | 1.35 | 0.65 | 0.92 | 0.00 | 10.28 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.472 | 0.966 | 2.185 | 0.000 | 0.117 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | B | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 341 | 416 | 214 | 523 | 0 | 6862 | 0 | 0 | 0 |
| N.S. |
1 | 1.22 | 0.63 | 1.53 | 0.00 | 20.12 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.599 | 2.609 | 4.222 | 0.000 | 0.219 | 0.000 | 0.000 | 0.000 |