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 | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | F(-2) | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 14 | 10 | 0 | 0 | 10 | 12 | 11 | 12 |
N.S. |
1 | 1.00 | 1.17 | 0.83 | 0.00 | 0.00 | 0.83 | 1.00 | 0.92 | 1.00 |
time (sec) |
N/A | 0.201 | 0.143 | 0.086 | 0.000 | 0.000 | 0.419 | 0.325 | 0.157 | 0.099 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | F(-2) | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 214 | 337 | 202 | 193 | 0 | 0 | 0 | 355 | 15 | 0 |
N.S. |
1 | 1.57 | 0.94 | 0.90 | 0.00 | 0.00 | 0.00 | 1.66 | 0.07 | 0.00 |
time (sec) |
N/A | 2.344 | 0.043 | 0.118 | 0.000 | 0.000 | 0.000 | 0.182 | 0.203 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | F(-2) | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 157 | 201 | 130 | 121 | 0 | 0 | 0 | 225 | 15 | 0 |
N.S. |
1 | 1.28 | 0.83 | 0.77 | 0.00 | 0.00 | 0.00 | 1.43 | 0.10 | 0.00 |
time (sec) |
N/A | 1.773 | 0.024 | 0.094 | 0.000 | 0.000 | 0.000 | 0.182 | 0.187 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | F(-2) | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 147 | 193 | 136 | 131 | 0 | 0 | 0 | 237 | 15 | 0 |
N.S. |
1 | 1.31 | 0.93 | 0.89 | 0.00 | 0.00 | 0.00 | 1.61 | 0.10 | 0.00 |
time (sec) |
N/A | 1.151 | 0.039 | 0.076 | 0.000 | 0.000 | 0.000 | 0.182 | 0.180 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | F(-2) | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 89 | 95 | 71 | 64 | 0 | 0 | 0 | 107 | 13 | 0 |
N.S. |
1 | 1.07 | 0.80 | 0.72 | 0.00 | 0.00 | 0.00 | 1.20 | 0.15 | 0.00 |
time (sec) |
N/A | 0.832 | 0.013 | 0.051 | 0.000 | 0.000 | 0.000 | 0.167 | 0.173 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | F(-2) | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 75 | 76 | 76 | 72 | 0 | 0 | 0 | 119 | 46 | 0 |
N.S. |
1 | 1.01 | 1.01 | 0.96 | 0.00 | 0.00 | 0.00 | 1.59 | 0.61 | 0.00 |
time (sec) |
N/A | 0.470 | 0.031 | 0.049 | 0.000 | 0.000 | 0.000 | 0.182 | 0.173 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | F(-2) | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 14 | 10 | 0 | 0 | 10 | 12 | 15 | 12 |
N.S. |
1 | 1.00 | 1.17 | 0.83 | 0.00 | 0.00 | 0.83 | 1.00 | 1.25 | 1.00 |
time (sec) |
N/A | 0.172 | 0.124 | 0.082 | 0.000 | 0.000 | 1.496 | 0.401 | 0.167 | 0.097 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | F(-2) | F(-1) | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 263 | 402 | 192 | 233 | 0 | 0 | 0 | 463 | 17 | 0 |
N.S. |
1 | 1.53 | 0.73 | 0.89 | 0.00 | 0.00 | 0.00 | 1.76 | 0.06 | 0.00 |
time (sec) |
N/A | 2.536 | 0.052 | 0.125 | 0.000 | 0.000 | 0.000 | 0.201 | 0.216 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | F(-2) | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 205 | 272 | 131 | 154 | 0 | 0 | 0 | 297 | 17 | 0 |
N.S. |
1 | 1.33 | 0.64 | 0.75 | 0.00 | 0.00 | 0.00 | 1.45 | 0.08 | 0.00 |
time (sec) |
N/A | 2.005 | 0.025 | 0.099 | 0.000 | 0.000 | 0.000 | 0.195 | 0.220 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | F(-2) | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 178 | 235 | 125 | 156 | 0 | 0 | 0 | 309 | 17 | 0 |
N.S. |
1 | 1.32 | 0.70 | 0.88 | 0.00 | 0.00 | 0.00 | 1.74 | 0.10 | 0.00 |
time (sec) |
N/A | 1.742 | 0.030 | 0.082 | 0.000 | 0.000 | 0.000 | 0.198 | 0.194 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | F(-2) | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 119 | 131 | 74 | 79 | 0 | 0 | 0 | 143 | 15 | 0 |
N.S. |
1 | 1.10 | 0.62 | 0.66 | 0.00 | 0.00 | 0.00 | 1.20 | 0.13 | 0.00 |
time (sec) |
N/A | 1.049 | 0.014 | 0.059 | 0.000 | 0.000 | 0.000 | 0.173 | 0.181 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | F(-2) | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 88 | 95 | 68 | 88 | 0 | 0 | 0 | 155 | 14 | 0 |
N.S. |
1 | 1.08 | 0.77 | 1.00 | 0.00 | 0.00 | 0.00 | 1.76 | 0.16 | 0.00 |
time (sec) |
N/A | 0.642 | 0.025 | 0.052 | 0.000 | 0.000 | 0.000 | 0.208 | 0.210 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | F(-2) | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 14 | 10 | 0 | 0 | 10 | 12 | 17 | 12 |
N.S. |
1 | 1.00 | 1.17 | 0.83 | 0.00 | 0.00 | 0.83 | 1.00 | 1.42 | 1.00 |
time (sec) |
N/A | 0.168 | 0.123 | 0.082 | 0.000 | 0.000 | 19.758 | 0.412 | 0.191 | 0.098 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | F(-2) | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 106 | 101 | 193 | 72 | 0 | 0 | 0 | 139 | 227 | 0 |
N.S. |
1 | 0.95 | 1.82 | 0.68 | 0.00 | 0.00 | 0.00 | 1.31 | 2.14 | 0.00 |
time (sec) |
N/A | 0.326 | 0.037 | 0.106 | 0.000 | 0.000 | 0.000 | 0.159 | 0.298 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | F(-2) | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 65 | 63 | 128 | 44 | 0 | 0 | 0 | 81 | 169 | 0 |
N.S. |
1 | 0.97 | 1.97 | 0.68 | 0.00 | 0.00 | 0.00 | 1.25 | 2.60 | 0.00 |
time (sec) |
N/A | 0.302 | 0.023 | 0.086 | 0.000 | 0.000 | 0.000 | 0.157 | 0.233 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | F(-2) | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 71 | 69 | 128 | 51 | 0 | 0 | 0 | 93 | 97 | 0 |
N.S. |
1 | 0.97 | 1.80 | 0.72 | 0.00 | 0.00 | 0.00 | 1.31 | 1.37 | 0.00 |
time (sec) |
N/A | 0.294 | 0.034 | 0.066 | 0.000 | 0.000 | 0.000 | 0.161 | 0.226 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | F(-2) | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 71 | 21 | 0 | 0 | 0 | 35 | 75 | 0 |
N.S. |
1 | 1.00 | 2.54 | 0.75 | 0.00 | 0.00 | 0.00 | 1.25 | 2.68 | 0.00 |
time (sec) |
N/A | 0.296 | 0.014 | 0.047 | 0.000 | 0.000 | 0.000 | 0.155 | 0.223 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | F(-2) | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 30 | 69 | 25 | 0 | 0 | 0 | 47 | 59 | 0 |
N.S. |
1 | 1.00 | 2.30 | 0.83 | 0.00 | 0.00 | 0.00 | 1.57 | 1.97 | 0.00 |
time (sec) |
N/A | 0.248 | 0.019 | 0.040 | 0.000 | 0.000 | 0.000 | 0.140 | 0.211 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | F(-2) | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 14 | 10 | 0 | 0 | 12 | 12 | 17 | 12 |
N.S. |
1 | 1.00 | 1.17 | 0.83 | 0.00 | 0.00 | 1.00 | 1.00 | 1.42 | 1.00 |
time (sec) |
N/A | 0.172 | 0.140 | 0.083 | 0.000 | 0.000 | 0.447 | 0.241 | 0.216 | 0.096 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | F(-2) | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 14 | 10 | 0 | 0 | 14 | 12 | 17 | 12 |
N.S. |
1 | 1.00 | 1.17 | 0.83 | 0.00 | 0.00 | 1.17 | 1.00 | 1.42 | 1.00 |
time (sec) |
N/A | 0.176 | 1.709 | 0.104 | 0.000 | 0.000 | 0.546 | 0.248 | 0.183 | 0.099 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 171 | 165 | 427 | 184 | 0 | 0 | 0 | 0 | 406 | 0 |
N.S. |
1 | 0.96 | 2.50 | 1.08 | 0.00 | 0.00 | 0.00 | 0.00 | 2.37 | 0.00 |
time (sec) |
N/A | 0.367 | 0.160 | 0.140 | 0.000 | 0.000 | 0.000 | 0.000 | 0.336 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 127 | 126 | 231 | 121 | 0 | 0 | 0 | 0 | 195 | 0 |
N.S. |
1 | 0.99 | 1.82 | 0.95 | 0.00 | 0.00 | 0.00 | 0.00 | 1.54 | 0.00 |
time (sec) |
N/A | 0.324 | 0.096 | 0.119 | 0.000 | 0.000 | 0.000 | 0.000 | 0.292 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 136 | 133 | 319 | 138 | 0 | 0 | 0 | 0 | 288 | 0 |
N.S. |
1 | 0.98 | 2.35 | 1.01 | 0.00 | 0.00 | 0.00 | 0.00 | 2.12 | 0.00 |
time (sec) |
N/A | 0.318 | 0.091 | 0.086 | 0.000 | 0.000 | 0.000 | 0.000 | 0.262 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 90 | 95 | 154 | 83 | 0 | 0 | 0 | 0 | 204 | 0 |
N.S. |
1 | 1.06 | 1.71 | 0.92 | 0.00 | 0.00 | 0.00 | 0.00 | 2.27 | 0.00 |
time (sec) |
N/A | 0.285 | 0.033 | 0.075 | 0.000 | 0.000 | 0.000 | 0.000 | 0.294 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 96 | 101 | 211 | 95 | 0 | 0 | 0 | 0 | 130 | 0 |
N.S. |
1 | 1.05 | 2.20 | 0.99 | 0.00 | 0.00 | 0.00 | 0.00 | 1.35 | 0.00 |
time (sec) |
N/A | 0.298 | 0.045 | 0.075 | 0.000 | 0.000 | 0.000 | 0.000 | 0.267 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 55 | 55 | 91 | 43 | 0 | 0 | 0 | 0 | 94 | 0 |
N.S. |
1 | 1.00 | 1.65 | 0.78 | 0.00 | 0.00 | 0.00 | 0.00 | 1.71 | 0.00 |
time (sec) |
N/A | 0.303 | 0.021 | 0.059 | 0.000 | 0.000 | 0.000 | 0.000 | 0.239 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 59 | 59 | 87 | 65 | 0 | 0 | 0 | 0 | 78 | 0 |
N.S. |
1 | 1.00 | 1.47 | 1.10 | 0.00 | 0.00 | 0.00 | 0.00 | 1.32 | 0.00 |
time (sec) |
N/A | 0.399 | 0.063 | 0.048 | 0.000 | 0.000 | 0.000 | 0.000 | 0.197 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | F(-2) | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 14 | 10 | 0 | 0 | 12 | 12 | 17 | 12 |
N.S. |
1 | 1.00 | 1.17 | 0.83 | 0.00 | 0.00 | 1.00 | 1.00 | 1.42 | 1.00 |
time (sec) |
N/A | 0.173 | 0.140 | 0.084 | 0.000 | 0.000 | 1.001 | 0.264 | 0.181 | 0.102 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 171 | 251 | 418 | 173 | 0 | 0 | 0 | 0 | 310 | 0 |
N.S. |
1 | 1.47 | 2.44 | 1.01 | 0.00 | 0.00 | 0.00 | 0.00 | 1.81 | 0.00 |
time (sec) |
N/A | 0.857 | 0.203 | 0.123 | 0.000 | 0.000 | 0.000 | 0.000 | 0.379 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | F(-2) | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 126 | 167 | 200 | 109 | 0 | 0 | 0 | 0 | 214 | 0 |
N.S. |
1 | 1.33 | 1.59 | 0.87 | 0.00 | 0.00 | 0.00 | 0.00 | 1.70 | 0.00 |
time (sec) |
N/A | 0.996 | 0.240 | 0.101 | 0.000 | 0.000 | 0.000 | 0.000 | 0.359 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 125 | 176 | 277 | 117 | 0 | 0 | 0 | 0 | 142 | 0 |
N.S. |
1 | 1.41 | 2.22 | 0.94 | 0.00 | 0.00 | 0.00 | 0.00 | 1.14 | 0.00 |
time (sec) |
N/A | 1.079 | 0.105 | 0.080 | 0.000 | 0.000 | 0.000 | 0.000 | 0.329 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 89 | 94 | 112 | 56 | 0 | 0 | 0 | 0 | 100 | 0 |
N.S. |
1 | 1.06 | 1.26 | 0.63 | 0.00 | 0.00 | 0.00 | 0.00 | 1.12 | 0.00 |
time (sec) |
N/A | 0.832 | 0.126 | 0.054 | 0.000 | 0.000 | 0.000 | 0.000 | 0.295 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 76 | 81 | 138 | 83 | 0 | 0 | 0 | 0 | 84 | 0 |
N.S. |
1 | 1.07 | 1.82 | 1.09 | 0.00 | 0.00 | 0.00 | 0.00 | 1.11 | 0.00 |
time (sec) |
N/A | 0.549 | 0.085 | 0.050 | 0.000 | 0.000 | 0.000 | 0.000 | 0.212 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | F(-2) | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 14 | 10 | 0 | 0 | 12 | 12 | 17 | 12 |
N.S. |
1 | 1.00 | 1.17 | 0.83 | 0.00 | 0.00 | 1.00 | 1.00 | 1.42 | 1.00 |
time (sec) |
N/A | 0.180 | 0.141 | 0.082 | 0.000 | 0.000 | 7.334 | 0.288 | 0.203 | 0.094 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 264 | 327 | 417 | 225 | 0 | 0 | 0 | 0 | 310 | 0 |
N.S. |
1 | 1.24 | 1.58 | 0.85 | 0.00 | 0.00 | 0.00 | 0.00 | 1.17 | 0.00 |
time (sec) |
N/A | 0.757 | 0.456 | 0.137 | 0.000 | 0.000 | 0.000 | 0.000 | 0.290 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | F(-2) | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 190 | 247 | 272 | 139 | 0 | 0 | 0 | 0 | 214 | 0 |
N.S. |
1 | 1.30 | 1.43 | 0.73 | 0.00 | 0.00 | 0.00 | 0.00 | 1.13 | 0.00 |
time (sec) |
N/A | 0.916 | 0.761 | 0.102 | 0.000 | 0.000 | 0.000 | 0.000 | 0.237 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 191 | 253 | 280 | 154 | 0 | 0 | 0 | 0 | 142 | 0 |
N.S. |
1 | 1.32 | 1.47 | 0.81 | 0.00 | 0.00 | 0.00 | 0.00 | 0.74 | 0.00 |
time (sec) |
N/A | 1.169 | 0.257 | 0.083 | 0.000 | 0.000 | 0.000 | 0.000 | 0.232 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 119 | 132 | 146 | 73 | 0 | 0 | 0 | 0 | 100 | 0 |
N.S. |
1 | 1.11 | 1.23 | 0.61 | 0.00 | 0.00 | 0.00 | 0.00 | 0.84 | 0.00 |
time (sec) |
N/A | 0.741 | 0.245 | 0.056 | 0.000 | 0.000 | 0.000 | 0.000 | 0.218 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 105 | 118 | 143 | 110 | 0 | 0 | 0 | 0 | 84 | 0 |
N.S. |
1 | 1.12 | 1.36 | 1.05 | 0.00 | 0.00 | 0.00 | 0.00 | 0.80 | 0.00 |
time (sec) |
N/A | 0.597 | 0.163 | 0.053 | 0.000 | 0.000 | 0.000 | 0.000 | 0.200 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | F(-2) | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 14 | 10 | 0 | 0 | 12 | 12 | 17 | 12 |
N.S. |
1 | 1.00 | 1.17 | 0.83 | 0.00 | 0.00 | 1.00 | 1.00 | 1.42 | 1.00 |
time (sec) |
N/A | 0.175 | 0.143 | 0.084 | 0.000 | 0.000 | 71.893 | 0.292 | 0.182 | 0.099 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | F(-2) | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 242 | 238 | 227 | 361 | 0 | 0 | 0 | 1057 | 15 | 0 |
N.S. |
1 | 0.98 | 0.94 | 1.49 | 0.00 | 0.00 | 0.00 | 4.37 | 0.06 | 0.00 |
time (sec) |
N/A | 0.785 | 0.167 | 0.216 | 0.000 | 0.000 | 0.000 | 0.770 | 0.172 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | F(-2) | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 137 | 132 | 127 | 186 | 0 | 0 | 0 | 448 | 13 | 0 |
N.S. |
1 | 0.96 | 0.93 | 1.36 | 0.00 | 0.00 | 0.00 | 3.27 | 0.09 | 0.00 |
time (sec) |
N/A | 0.621 | 0.041 | 0.083 | 0.000 | 0.000 | 0.000 | 0.533 | 0.172 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | F(-2) | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 120 | 118 | 119 | 187 | 0 | 0 | 0 | 531 | 11 | 0 |
N.S. |
1 | 0.98 | 0.99 | 1.56 | 0.00 | 0.00 | 0.00 | 4.42 | 0.09 | 0.00 |
time (sec) |
N/A | 0.831 | 0.023 | 0.000 | 0.000 | 0.000 | 0.000 | 0.387 | 0.177 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 18 | 14 | 16 | 0 | 14 | 16 | 15 | 16 |
N.S. |
1 | 1.00 | 1.12 | 0.88 | 1.00 | 0.00 | 0.88 | 1.00 | 0.94 | 1.00 |
time (sec) |
N/A | 0.230 | 0.383 | 0.101 | 0.422 | 0.000 | 0.495 | 0.799 | 0.169 | 0.107 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 18 | 14 | 16 | 0 | 15 | 16 | 15 | 16 |
N.S. |
1 | 1.00 | 1.12 | 0.88 | 1.00 | 0.00 | 0.94 | 1.00 | 0.94 | 1.00 |
time (sec) |
N/A | 0.217 | 4.119 | 0.168 | 0.462 | 0.000 | 0.414 | 0.834 | 0.221 | 0.101 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | F(-2) | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 313 | 422 | 245 | 547 | 0 | 0 | 0 | 2295 | 39 | 0 |
N.S. |
1 | 1.35 | 0.78 | 1.75 | 0.00 | 0.00 | 0.00 | 7.33 | 0.12 | 0.00 |
time (sec) |
N/A | 2.700 | 0.188 | 0.148 | 0.000 | 0.000 | 0.000 | 1.521 | 0.270 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | F(-2) | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 172 | 178 | 126 | 281 | 0 | 0 | 0 | 911 | 35 | 0 |
N.S. |
1 | 1.03 | 0.73 | 1.63 | 0.00 | 0.00 | 0.00 | 5.30 | 0.20 | 0.00 |
time (sec) |
N/A | 1.674 | 0.049 | 0.087 | 0.000 | 0.000 | 0.000 | 0.819 | 0.243 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | F(-2) | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 159 | 155 | 289 | 278 | 0 | 0 | 0 | 1157 | 32 | 0 |
N.S. |
1 | 0.97 | 1.82 | 1.75 | 0.00 | 0.00 | 0.00 | 7.28 | 0.20 | 0.00 |
time (sec) |
N/A | 0.822 | 1.020 | 0.000 | 0.000 | 0.000 | 0.000 | 1.034 | 0.226 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 18 | 14 | 16 | 0 | 14 | 16 | 39 | 16 |
N.S. |
1 | 1.00 | 1.12 | 0.88 | 1.00 | 0.00 | 0.88 | 1.00 | 2.44 | 1.00 |
time (sec) |
N/A | 0.207 | 0.402 | 0.089 | 0.523 | 0.000 | 13.484 | 0.919 | 0.236 | 0.110 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 18 | 14 | 16 | 0 | 15 | 16 | 16 | 16 |
N.S. |
1 | 1.00 | 1.12 | 0.88 | 1.00 | 0.00 | 0.94 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.207 | 3.141 | 0.173 | 0.487 | 0.000 | 3.381 | 0.936 | 200.023 | 0.107 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | F(-2) | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 358 | 474 | 228 | 798 | 0 | 0 | 0 | 3096 | 68 | 0 |
N.S. |
1 | 1.32 | 0.64 | 2.23 | 0.00 | 0.00 | 0.00 | 8.65 | 0.19 | 0.00 |
time (sec) |
N/A | 2.941 | 0.182 | 0.161 | 0.000 | 0.000 | 0.000 | 2.172 | 0.406 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | F(-2) | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 216 | 223 | 129 | 408 | 0 | 0 | 0 | 1521 | 62 | 0 |
N.S. |
1 | 1.03 | 0.60 | 1.89 | 0.00 | 0.00 | 0.00 | 7.04 | 0.29 | 0.00 |
time (sec) |
N/A | 1.665 | 0.046 | 0.105 | 0.000 | 0.000 | 0.000 | 1.127 | 0.344 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | F(-2) | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 179 | 179 | 366 | 401 | 0 | 0 | 0 | 1519 | 58 | 0 |
N.S. |
1 | 1.00 | 2.04 | 2.24 | 0.00 | 0.00 | 0.00 | 8.49 | 0.32 | 0.00 |
time (sec) |
N/A | 1.263 | 0.578 | 0.000 | 0.000 | 0.000 | 0.000 | 1.335 | 0.314 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 18 | 14 | 16 | 0 | 14 | 16 | 68 | 16 |
N.S. |
1 | 1.00 | 1.12 | 0.88 | 1.00 | 0.00 | 0.88 | 1.00 | 4.25 | 1.00 |
time (sec) |
N/A | 0.216 | 0.482 | 0.091 | 0.603 | 0.000 | 36.330 | 1.001 | 0.265 | 0.106 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 18 | 14 | 16 | 0 | 15 | 16 | 16 | 16 |
N.S. |
1 | 1.00 | 1.12 | 0.88 | 1.00 | 0.00 | 0.94 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.230 | 3.153 | 0.171 | 0.702 | 0.000 | 26.819 | 1.057 | 200.028 | 0.103 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | F(-2) | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 223 | 218 | 228 | 196 | 0 | 0 | 0 | 317 | 25 | 0 |
N.S. |
1 | 0.98 | 1.02 | 0.88 | 0.00 | 0.00 | 0.00 | 1.42 | 0.11 | 0.00 |
time (sec) |
N/A | 0.592 | 0.168 | 0.126 | 0.000 | 0.000 | 0.000 | 0.292 | 0.253 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | F(-2) | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 99 | 98 | 123 | 91 | 0 | 0 | 0 | 132 | 23 | 0 |
N.S. |
1 | 0.99 | 1.24 | 0.92 | 0.00 | 0.00 | 0.00 | 1.33 | 0.23 | 0.00 |
time (sec) |
N/A | 0.685 | 0.042 | 0.079 | 0.000 | 0.000 | 0.000 | 0.247 | 0.225 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | F(-2) | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 101 | 102 | 121 | 90 | 0 | 0 | 0 | 159 | 22 | 0 |
N.S. |
1 | 1.01 | 1.20 | 0.89 | 0.00 | 0.00 | 0.00 | 1.57 | 0.22 | 0.00 |
time (sec) |
N/A | 0.555 | 0.024 | 0.000 | 0.000 | 0.000 | 0.000 | 0.193 | 0.287 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 18 | 14 | 16 | 0 | 15 | 16 | 25 | 16 |
N.S. |
1 | 1.00 | 1.12 | 0.88 | 1.00 | 0.00 | 0.94 | 1.00 | 1.56 | 1.00 |
time (sec) |
N/A | 0.217 | 0.856 | 0.090 | 0.519 | 0.000 | 0.486 | 0.476 | 0.237 | 0.111 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 18 | 14 | 16 | 0 | 17 | 16 | 29 | 16 |
N.S. |
1 | 1.00 | 1.12 | 0.88 | 1.00 | 0.00 | 1.06 | 1.00 | 1.81 | 1.00 |
time (sec) |
N/A | 0.217 | 3.435 | 0.156 | 0.427 | 0.000 | 0.611 | 0.517 | 0.247 | 0.102 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 250 | 257 | 343 | 301 | 0 | 0 | 0 | 0 | 39 | 0 |
N.S. |
1 | 1.03 | 1.37 | 1.20 | 0.00 | 0.00 | 0.00 | 0.00 | 0.16 | 0.00 |
time (sec) |
N/A | 0.529 | 0.274 | 0.130 | 0.000 | 0.000 | 0.000 | 0.000 | 0.258 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 130 | 131 | 155 | 156 | 0 | 0 | 0 | 0 | 37 | 0 |
N.S. |
1 | 1.01 | 1.19 | 1.20 | 0.00 | 0.00 | 0.00 | 0.00 | 0.28 | 0.00 |
time (sec) |
N/A | 0.641 | 0.102 | 0.090 | 0.000 | 0.000 | 0.000 | 0.000 | 0.261 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 137 | 139 | 167 | 158 | 0 | 0 | 0 | 0 | 169 | 0 |
N.S. |
1 | 1.01 | 1.22 | 1.15 | 0.00 | 0.00 | 0.00 | 0.00 | 1.23 | 0.00 |
time (sec) |
N/A | 0.765 | 0.091 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.261 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | F(-2) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 18 | 14 | 16 | 0 | 15 | 0 | 40 | 16 |
N.S. |
1 | 1.00 | 1.12 | 0.88 | 1.00 | 0.00 | 0.94 | 0.00 | 2.50 | 1.00 |
time (sec) |
N/A | 0.212 | 0.702 | 0.129 | 0.421 | 0.000 | 1.904 | 0.000 | 0.238 | 0.106 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 18 | 14 | 16 | 0 | 17 | 16 | 46 | 16 |
N.S. |
1 | 1.00 | 1.12 | 0.88 | 1.00 | 0.00 | 1.06 | 1.00 | 2.88 | 1.00 |
time (sec) |
N/A | 0.216 | 3.307 | 0.162 | 0.427 | 0.000 | 2.730 | 0.954 | 0.267 | 0.111 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 291 | 424 | 370 | 672 | 0 | 0 | 0 | 0 | 53 | 0 |
N.S. |
1 | 1.46 | 1.27 | 2.31 | 0.00 | 0.00 | 0.00 | 0.00 | 0.18 | 0.00 |
time (sec) |
N/A | 2.123 | 1.285 | 0.148 | 0.000 | 0.000 | 0.000 | 0.000 | 0.233 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 180 | 188 | 173 | 340 | 0 | 0 | 0 | 0 | 51 | 0 |
N.S. |
1 | 1.04 | 0.96 | 1.89 | 0.00 | 0.00 | 0.00 | 0.00 | 0.28 | 0.00 |
time (sec) |
N/A | 1.641 | 0.777 | 0.099 | 0.000 | 0.000 | 0.000 | 0.000 | 0.245 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 163 | 170 | 214 | 340 | 0 | 0 | 0 | 0 | 359 | 0 |
N.S. |
1 | 1.04 | 1.31 | 2.09 | 0.00 | 0.00 | 0.00 | 0.00 | 2.20 | 0.00 |
time (sec) |
N/A | 1.015 | 0.265 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.310 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | F(-2) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 18 | 14 | 16 | 0 | 15 | 0 | 55 | 16 |
N.S. |
1 | 1.00 | 1.12 | 0.88 | 1.00 | 0.00 | 0.94 | 0.00 | 3.44 | 1.00 |
time (sec) |
N/A | 0.234 | 0.741 | 0.129 | 0.498 | 0.000 | 8.651 | 0.000 | 0.237 | 0.101 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 18 | 14 | 16 | 0 | 17 | 16 | 63 | 16 |
N.S. |
1 | 1.00 | 1.12 | 0.88 | 1.00 | 0.00 | 1.06 | 1.00 | 3.94 | 1.00 |
time (sec) |
N/A | 0.234 | 3.502 | 0.165 | 0.511 | 0.000 | 16.011 | 1.387 | 0.258 | 0.099 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | F(-2) | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 16 | 12 | 0 | 0 | 14 | 14 | 19 | 14 |
N.S. |
1 | 1.00 | 1.14 | 0.86 | 0.00 | 0.00 | 1.00 | 1.00 | 1.36 | 1.00 |
time (sec) |
N/A | 0.209 | 0.494 | 0.082 | 0.000 | 0.000 | 65.780 | 1.807 | 0.257 | 0.109 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | F(-2) | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 16 | 12 | 0 | 0 | 14 | 14 | 15 | 14 |
N.S. |
1 | 1.00 | 1.14 | 0.86 | 0.00 | 0.00 | 1.00 | 1.00 | 1.07 | 1.00 |
time (sec) |
N/A | 0.224 | 0.551 | 0.071 | 0.000 | 0.000 | 1.336 | 1.090 | 0.246 | 0.103 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | F(-2) | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 16 | 12 | 0 | 0 | 14 | 14 | 145 | 14 |
N.S. |
1 | 1.00 | 1.14 | 0.86 | 0.00 | 0.00 | 1.00 | 1.00 | 10.36 | 1.00 |
time (sec) |
N/A | 0.200 | 0.592 | 0.074 | 0.000 | 0.000 | 0.581 | 0.963 | 0.281 | 0.101 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | F(-2) | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 16 | 12 | 0 | 0 | 14 | 14 | 189 | 14 |
N.S. |
1 | 1.00 | 1.14 | 0.86 | 0.00 | 0.00 | 1.00 | 1.00 | 13.50 | 1.00 |
time (sec) |
N/A | 0.215 | 0.552 | 0.071 | 0.000 | 0.000 | 4.384 | 0.870 | 0.273 | 0.103 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F(-2) | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 167 | 159 | 132 | 0 | 0 | 0 | 0 | 0 | 12 | 0 |
N.S. |
1 | 0.95 | 0.79 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.07 | 0.00 |
time (sec) |
N/A | 0.460 | 0.056 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.252 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F(-2) | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 171 | 163 | 137 | 0 | 0 | 0 | 0 | 0 | 12 | 0 |
N.S. |
1 | 0.95 | 0.80 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.07 | 0.00 |
time (sec) |
N/A | 0.416 | 0.045 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.224 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F(-2) | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 85 | 86 | 75 | 138 | 0 | 0 | 0 | 0 | 10 | 0 |
N.S. |
1 | 1.01 | 0.88 | 1.62 | 0.00 | 0.00 | 0.00 | 0.00 | 0.12 | 0.00 |
time (sec) |
N/A | 0.365 | 0.014 | 0.095 | 0.000 | 0.000 | 0.000 | 0.000 | 0.215 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F(-2) | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 79 | 77 | 73 | 240 | 0 | 0 | 0 | 0 | 8 | 0 |
N.S. |
1 | 0.97 | 0.92 | 3.04 | 0.00 | 0.00 | 0.00 | 0.00 | 0.10 | 0.00 |
time (sec) |
N/A | 0.298 | 0.027 | 0.078 | 0.000 | 0.000 | 0.000 | 0.000 | 0.230 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 10 | 10 | 12 | 10 | 0 | 12 | 8 | 12 | 12 | 12 |
N.S. |
1 | 1.00 | 1.20 | 1.00 | 0.00 | 1.20 | 0.80 | 1.20 | 1.20 | 1.20 |
time (sec) |
N/A | 0.188 | 0.188 | 0.081 | 0.000 | 0.091 | 0.426 | 0.190 | 0.230 | 0.143 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 10 | 10 | 12 | 10 | 0 | 12 | 10 | 12 | 12 | 12 |
N.S. |
1 | 1.00 | 1.20 | 1.00 | 0.00 | 1.20 | 1.00 | 1.20 | 1.20 | 1.20 |
time (sec) |
N/A | 0.191 | 0.447 | 0.055 | 0.000 | 0.091 | 0.601 | 0.180 | 0.226 | 0.135 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | N/A | F(-1) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 16 | 12 | 0 | 16 | 0 | 14 | 16 | 14 |
N.S. |
1 | 1.00 | 1.14 | 0.86 | 0.00 | 1.14 | 0.00 | 1.00 | 1.14 | 1.00 |
time (sec) |
N/A | 0.194 | 1.486 | 0.162 | 0.000 | 0.098 | 0.000 | 0.437 | 0.259 | 0.137 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 16 | 12 | 0 | 14 | 14 | 14 | 14 | 14 |
N.S. |
1 | 1.00 | 1.14 | 0.86 | 0.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.188 | 2.422 | 0.131 | 0.000 | 0.102 | 4.104 | 0.421 | 0.250 | 0.127 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 16 | 12 | 0 | 20 | 14 | 14 | 20 | 14 |
N.S. |
1 | 1.00 | 1.14 | 0.86 | 0.00 | 1.43 | 1.00 | 1.00 | 1.43 | 1.00 |
time (sec) |
N/A | 0.186 | 0.970 | 0.112 | 0.000 | 0.108 | 1.800 | 0.300 | 0.240 | 0.126 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 16 | 12 | 0 | 20 | 14 | 14 | 67 | 14 |
N.S. |
1 | 1.00 | 1.14 | 0.86 | 0.00 | 1.43 | 1.00 | 1.00 | 4.79 | 1.00 |
time (sec) |
N/A | 0.184 | 0.963 | 0.199 | 0.000 | 0.104 | 13.550 | 0.362 | 0.273 | 0.122 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 14 | 12 | 0 | 14 | 12 | 14 | 16 | 14 |
N.S. |
1 | 1.00 | 1.17 | 1.00 | 0.00 | 1.17 | 1.00 | 1.17 | 1.33 | 1.17 |
time (sec) |
N/A | 0.185 | 0.378 | 0.845 | 0.000 | 0.099 | 4.106 | 0.707 | 0.230 | 0.126 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F | A | A | B | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 215 | 0 | 224 | 322 | 0 | 194 | 343 | 742 | 157 | 0 |
N.S. |
1 | 0.00 | 1.04 | 1.50 | 0.00 | 0.90 | 1.60 | 3.45 | 0.73 | 0.00 |
time (sec) |
N/A | 0.000 | 0.208 | 3.149 | 0.000 | 0.103 | 1.313 | 0.184 | 0.235 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | F | A | A | B | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 169 | 0 | 216 | 318 | 0 | 159 | 286 | 587 | 136 | 0 |
N.S. |
1 | 0.00 | 1.28 | 1.88 | 0.00 | 0.94 | 1.69 | 3.47 | 0.80 | 0.00 |
time (sec) |
N/A | 0.000 | 0.134 | 0.512 | 0.000 | 0.100 | 0.658 | 0.171 | 0.228 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | F | A | A | B | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 137 | 0 | 165 | 257 | 0 | 143 | 226 | 534 | 172 | 0 |
N.S. |
1 | 0.00 | 1.20 | 1.88 | 0.00 | 1.04 | 1.65 | 3.90 | 1.26 | 0.00 |
time (sec) |
N/A | 0.000 | 0.120 | 0.480 | 0.000 | 0.099 | 0.558 | 0.175 | 0.228 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | F | A | A | B | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 79 | 0 | 147 | 160 | 0 | 96 | 134 | 359 | 113 | 0 |
N.S. |
1 | 0.00 | 1.86 | 2.03 | 0.00 | 1.22 | 1.70 | 4.54 | 1.43 | 0.00 |
time (sec) |
N/A | 0.000 | 0.063 | 0.360 | 0.000 | 0.097 | 0.168 | 0.155 | 0.259 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | C | N/A | N/A | N/A | F(-1) | N/A | N/A | N/A |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 167 | 20 | 84 | 33 | 0 | 3 | 49 | 22 |
N.S. |
1 | 1.00 | 8.35 | 1.00 | 4.20 | 1.65 | 0.00 | 0.15 | 2.45 | 1.10 |
time (sec) |
N/A | 0.405 | 0.092 | 0.054 | 0.637 | 0.084 | 0.000 | 10.881 | 0.214 | 0.265 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | C | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 163 | 20 | 139 | 33 | 20 | 3 | 70 | 22 |
N.S. |
1 | 1.00 | 8.15 | 1.00 | 6.95 | 1.65 | 1.00 | 0.15 | 3.50 | 1.10 |
time (sec) |
N/A | 0.283 | 0.135 | 0.051 | 0.435 | 0.098 | 62.180 | 11.531 | 0.223 | 0.431 |