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 | A | C | F | F | F | F | F | F | F(-1) |
verified | N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 148 | 199 | 2524 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.34 | 17.05 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.423 | 5.621 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.181 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | F | F(-1) |
verified | N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 120 | 124 | 895 | 0 | 0 | 0 | 0 | 0 | 1566 | 0 |
N.S. |
1 | 1.03 | 7.46 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 13.05 | 0.00 |
time (sec) |
N/A | 0.251 | 2.183 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.170 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 93 | 93 | 80 | 0 | 0 | 0 | 906 | 0 | 610 | 0 |
N.S. |
1 | 1.00 | 0.86 | 0.00 | 0.00 | 0.00 | 9.74 | 0.00 | 6.56 | 0.00 |
time (sec) |
N/A | 0.202 | 0.141 | 0.000 | 0.000 | 0.000 | 14.187 | 0.000 | 0.169 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 156 | 173 | 127 | 0 | 0 | 0 | 3245 | 0 | 54 | 0 |
N.S. |
1 | 1.11 | 0.81 | 0.00 | 0.00 | 0.00 | 20.80 | 0.00 | 0.35 | 0.00 |
time (sec) |
N/A | 0.344 | 0.081 | 0.000 | 0.000 | 0.000 | 39.423 | 0.000 | 0.148 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 230 | 254 | 173 | 0 | 0 | 0 | 0 | 0 | 95 | 0 |
N.S. |
1 | 1.10 | 0.75 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.41 | 0.00 |
time (sec) |
N/A | 0.518 | 0.592 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.195 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 325 | 373 | 215 | 0 | 0 | 0 | 0 | 0 | 136 | 0 |
N.S. |
1 | 1.15 | 0.66 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.42 | 0.00 |
time (sec) |
N/A | 0.735 | 0.966 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.208 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 268 | 312 | 184 | 0 | 0 | 0 | 0 | 0 | 827 | 0 |
N.S. |
1 | 1.16 | 0.69 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 3.09 | 0.00 |
time (sec) |
N/A | 0.515 | 5.472 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.173 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 191 | 191 | 158 | 0 | 0 | 0 | 150 | 0 | 450 | 0 |
N.S. |
1 | 1.00 | 0.83 | 0.00 | 0.00 | 0.00 | 0.79 | 0.00 | 2.36 | 0.00 |
time (sec) |
N/A | 0.330 | 5.312 | 0.000 | 0.000 | 0.000 | 110.615 | 0.000 | 0.166 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 111 | 118 | 108 | 0 | 0 | 0 | 97 | 0 | 204 | 0 |
N.S. |
1 | 1.06 | 0.97 | 0.00 | 0.00 | 0.00 | 0.87 | 0.00 | 1.84 | 0.00 |
time (sec) |
N/A | 0.225 | 0.122 | 0.000 | 0.000 | 0.000 | 46.508 | 0.000 | 0.160 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 69 | 69 | 65 | 0 | 0 | 0 | 46 | 0 | 73 | 0 |
N.S. |
1 | 1.00 | 0.94 | 0.00 | 0.00 | 0.00 | 0.67 | 0.00 | 1.06 | 0.00 |
time (sec) |
N/A | 0.179 | 0.023 | 0.000 | 0.000 | 0.000 | 8.763 | 0.000 | 0.163 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 124 | 138 | 79 | 0 | 0 | 0 | 0 | 0 | 42 | 0 |
N.S. |
1 | 1.11 | 0.64 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.34 | 0.00 |
time (sec) |
N/A | 0.245 | 0.349 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.171 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified | N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 74 | 72 | 105 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.97 | 1.42 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.195 | 0.097 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.236 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 143 | 162 | 162 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.13 | 1.13 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.245 | 0.234 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.592 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 296 | 324 | 198 | 0 | 0 | 0 | 216 | 0 | 804 | 0 |
N.S. |
1 | 1.09 | 0.67 | 0.00 | 0.00 | 0.00 | 0.73 | 0.00 | 2.72 | 0.00 |
time (sec) |
N/A | 0.484 | 6.313 | 0.000 | 0.000 | 0.000 | 159.970 | 0.000 | 0.160 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 196 | 199 | 179 | 0 | 0 | 0 | 151 | 0 | 437 | 0 |
N.S. |
1 | 1.02 | 0.91 | 0.00 | 0.00 | 0.00 | 0.77 | 0.00 | 2.23 | 0.00 |
time (sec) |
N/A | 0.303 | 6.165 | 0.000 | 0.000 | 0.000 | 81.131 | 0.000 | 0.168 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 119 | 126 | 117 | 0 | 0 | 0 | 94 | 0 | 197 | 0 |
N.S. |
1 | 1.06 | 0.98 | 0.00 | 0.00 | 0.00 | 0.79 | 0.00 | 1.66 | 0.00 |
time (sec) |
N/A | 0.221 | 0.140 | 0.000 | 0.000 | 0.000 | 36.595 | 0.000 | 0.167 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 74 | 74 | 66 | 0 | 0 | 0 | 37 | 0 | 68 | 0 |
N.S. |
1 | 1.00 | 0.89 | 0.00 | 0.00 | 0.00 | 0.50 | 0.00 | 0.92 | 0.00 |
time (sec) |
N/A | 0.177 | 0.021 | 0.000 | 0.000 | 0.000 | 6.959 | 0.000 | 0.175 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 87 | 79 | 77 | 0 | 0 | 0 | 0 | 0 | 40 | 0 |
N.S. |
1 | 0.91 | 0.89 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.46 | 0.00 |
time (sec) |
N/A | 0.216 | 0.254 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.169 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 87 | 79 | 79 | 0 | 0 | 0 | 0 | 0 | 56 | 0 |
N.S. |
1 | 0.91 | 0.91 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.64 | 0.00 |
time (sec) |
N/A | 0.217 | 0.300 | 0.000 | 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 | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 87 | 79 | 79 | 0 | 0 | 0 | 0 | 0 | 72 | 0 |
N.S. |
1 | 0.91 | 0.91 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.83 | 0.00 |
time (sec) |
N/A | 0.212 | 0.398 | 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 | F | F | F | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 245 | 285 | 202 | 0 | 0 | 0 | 0 | 0 | 544 | 0 |
N.S. |
1 | 1.16 | 0.82 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 2.22 | 0.00 |
time (sec) |
N/A | 0.477 | 6.212 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.169 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 176 | 179 | 149 | 0 | 0 | 0 | 153 | 0 | 289 | 0 |
N.S. |
1 | 1.02 | 0.85 | 0.00 | 0.00 | 0.00 | 0.87 | 0.00 | 1.64 | 0.00 |
time (sec) |
N/A | 0.323 | 6.146 | 0.000 | 0.000 | 0.000 | 95.854 | 0.000 | 0.165 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 116 | 102 | 101 | 0 | 0 | 0 | 99 | 0 | 138 | 0 |
N.S. |
1 | 0.88 | 0.87 | 0.00 | 0.00 | 0.00 | 0.85 | 0.00 | 1.19 | 0.00 |
time (sec) |
N/A | 0.218 | 0.132 | 0.000 | 0.000 | 0.000 | 41.296 | 0.000 | 0.156 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 61 | 61 | 61 | 0 | 0 | 0 | 46 | 0 | 33 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.75 | 0.00 | 0.54 | 0.00 |
time (sec) |
N/A | 0.180 | 0.013 | 0.000 | 0.000 | 0.000 | 5.519 | 0.000 | 0.161 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified | N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 63 | 63 | 91 | 0 | 0 | 0 | 0 | 0 | 178 | 0 |
N.S. |
1 | 1.00 | 1.44 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 2.83 | 0.00 |
time (sec) |
N/A | 0.194 | 0.085 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.174 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 131 | 143 | 114 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.09 | 0.87 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.243 | 0.180 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.326 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 231 | 243 | 191 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.05 | 0.83 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.351 | 0.379 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 2.971 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 267 | 315 | 201 | 0 | 0 | 0 | 0 | 0 | 789 | 0 |
N.S. |
1 | 1.18 | 0.75 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 2.96 | 0.00 |
time (sec) |
N/A | 0.485 | 6.296 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.163 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 192 | 197 | 181 | 0 | 0 | 0 | 180 | 0 | 410 | 0 |
N.S. |
1 | 1.03 | 0.94 | 0.00 | 0.00 | 0.00 | 0.94 | 0.00 | 2.14 | 0.00 |
time (sec) |
N/A | 0.312 | 6.205 | 0.000 | 0.000 | 0.000 | 99.824 | 0.000 | 0.165 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 128 | 119 | 116 | 0 | 0 | 0 | 119 | 0 | 212 | 0 |
N.S. |
1 | 0.93 | 0.91 | 0.00 | 0.00 | 0.00 | 0.93 | 0.00 | 1.66 | 0.00 |
time (sec) |
N/A | 0.224 | 0.167 | 0.000 | 0.000 | 0.000 | 46.252 | 0.000 | 0.159 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 75 | 75 | 69 | 0 | 0 | 0 | 60 | 0 | 78 | 0 |
N.S. |
1 | 1.00 | 0.92 | 0.00 | 0.00 | 0.00 | 0.80 | 0.00 | 1.04 | 0.00 |
time (sec) |
N/A | 0.183 | 0.021 | 0.000 | 0.000 | 0.000 | 8.701 | 0.000 | 0.152 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 88 | 82 | 80 | 0 | 0 | 0 | 0 | 0 | 46 | 0 |
N.S. |
1 | 0.93 | 0.91 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.52 | 0.00 |
time (sec) |
N/A | 0.220 | 0.289 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.189 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 88 | 82 | 82 | 0 | 0 | 0 | 0 | 0 | 62 | 0 |
N.S. |
1 | 0.93 | 0.93 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.70 | 0.00 |
time (sec) |
N/A | 0.214 | 0.303 | 0.000 | 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 | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 88 | 82 | 82 | 0 | 0 | 0 | 0 | 0 | 78 | 0 |
N.S. |
1 | 0.93 | 0.93 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.89 | 0.00 |
time (sec) |
N/A | 0.213 | 0.354 | 0.000 | 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 | A | F | F | F | F(-1) | F | F | F(-1) |
verified | N/A | No | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 230 | 232 | 195 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.01 | 0.85 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.371 | 0.336 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 1.027 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 134 | 145 | 118 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.08 | 0.88 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.242 | 0.211 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.453 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 70 | 85 | 84 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.21 | 1.20 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.203 | 0.080 | 0.000 | 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 | F | F | F | F | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 96 | 97 | 95 | 0 | 0 | 0 | 0 | 0 | 845 | 0 |
N.S. |
1 | 1.01 | 0.99 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 8.80 | 0.00 |
time (sec) |
N/A | 0.228 | 0.129 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.199 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 97 | 98 | 100 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.01 | 1.03 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.232 | 0.136 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.477 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 99 | 100 | 100 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.01 | 1.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.230 | 0.166 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.627 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 84 | 84 | 86 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.230 | 0.115 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.366 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 84 | 84 | 86 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.219 | 0.097 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.208 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F | F(-1) | F | F | F(-1) |
verified | N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 79 | 79 | 172 | 0 | 0 | 0 | 0 | 0 | 1249 | 0 |
N.S. |
1 | 1.00 | 2.18 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 15.81 | 0.00 |
time (sec) |
N/A | 0.198 | 0.067 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.184 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 82 | 82 | 84 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.221 | 0.109 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.209 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 84 | 84 | 86 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.218 | 0.136 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.286 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 91 | 91 | 91 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.229 | 0.575 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 14.411 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 91 | 91 | 91 | 0 | 0 | 0 | 0 | 0 | 1320 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 14.51 | 0.00 |
time (sec) |
N/A | 0.226 | 0.386 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 1.081 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 89 | 89 | 89 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.229 | 0.429 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 3.231 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 89 | 89 | 89 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.228 | 0.661 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 2.376 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 91 | 91 | 91 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.228 | 0.695 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 4.679 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 101 | 101 | 97 | 0 | 0 | 0 | 0 | 0 | 1026 | 0 |
N.S. |
1 | 1.00 | 0.96 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 10.16 | 0.00 |
time (sec) |
N/A | 0.238 | 0.228 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.196 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 41 | 41 | 39 | 0 | 0 | 0 | 0 | 0 | 226 | 0 |
N.S. |
1 | 1.00 | 0.95 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 5.51 | 0.00 |
time (sec) |
N/A | 0.173 | 0.082 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.160 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 80 | 80 | 82 | 0 | 0 | 0 | 0 | 0 | 262 | 0 |
N.S. |
1 | 1.00 | 1.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 3.28 | 0.00 |
time (sec) |
N/A | 0.217 | 0.063 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.159 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | F | F | F | F(-1) | F | F | F(-1) |
verified | N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 263 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 30 | 0 |
N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.11 | 0.00 |
time (sec) |
N/A | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 200.031 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F(-1) | F | F | F(-1) |
verified | N/A | No | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 167 | 217 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.30 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 19.502 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.284 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified | N/A | No | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 107 | 111 | 107 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.04 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.244 | 0.103 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.210 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 96 | 96 | 98 | 0 | 0 | 0 | 0 | 0 | 42 | 0 |
N.S. |
1 | 1.00 | 1.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.44 | 0.00 |
time (sec) |
N/A | 0.238 | 0.233 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.153 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 106 | 106 | 102 | 0 | 0 | 0 | 0 | 0 | 911 | 0 |
N.S. |
1 | 1.00 | 0.96 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 8.59 | 0.00 |
time (sec) |
N/A | 0.245 | 0.268 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.172 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 101 | 101 | 97 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.96 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.234 | 0.228 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.204 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 61 | 56 | 45 | 66 | 77 | 65 | 202 | 103 | 63 | 124 |
N.S. |
1 | 0.92 | 0.74 | 1.08 | 1.26 | 1.07 | 3.31 | 1.69 | 1.03 | 2.03 |
time (sec) |
N/A | 0.200 | 0.037 | 2.034 | 0.033 | 0.084 | 0.958 | 0.127 | 0.152 | 1.649 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 61 | 81 | 45 | 66 | 77 | 65 | 202 | 103 | 63 | 124 |
N.S. |
1 | 1.33 | 0.74 | 1.08 | 1.26 | 1.07 | 3.31 | 1.69 | 1.03 | 2.03 |
time (sec) |
N/A | 0.411 | 0.020 | 1.613 | 0.034 | 0.085 | 0.997 | 0.129 | 0.151 | 1.466 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 61 | 81 | 45 | 66 | 77 | 65 | 202 | 103 | 63 | 124 |
N.S. |
1 | 1.33 | 0.74 | 1.08 | 1.26 | 1.07 | 3.31 | 1.69 | 1.03 | 2.03 |
time (sec) |
N/A | 0.394 | 0.020 | 1.652 | 0.033 | 0.087 | 0.977 | 0.126 | 0.158 | 0.093 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 61 | 81 | 45 | 66 | 77 | 65 | 202 | 103 | 63 | 124 |
N.S. |
1 | 1.33 | 0.74 | 1.08 | 1.26 | 1.07 | 3.31 | 1.69 | 1.03 | 2.03 |
time (sec) |
N/A | 0.306 | 0.019 | 1.657 | 0.032 | 0.081 | 0.955 | 0.124 | 0.154 | 1.424 |