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 | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 47 | 47 | 47 | 40 | 39 | 39 | 42 | 43 | 38 | 41 |
N.S. |
1 | 1.00 | 1.00 | 0.85 | 0.83 | 0.83 | 0.89 | 0.91 | 0.81 | 0.87 |
time (sec) |
N/A | 0.214 | 0.013 | 0.276 | 0.031 | 0.063 | 0.018 | 0.201 | 0.213 | 0.049 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 47 | 47 | 47 | 40 | 39 | 39 | 42 | 43 | 38 | 41 |
N.S. |
1 | 1.00 | 1.00 | 0.85 | 0.83 | 0.83 | 0.89 | 0.91 | 0.81 | 0.87 |
time (sec) |
N/A | 0.215 | 0.015 | 0.267 | 0.027 | 0.063 | 0.017 | 0.211 | 0.210 | 0.043 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 47 | 47 | 41 | 40 | 39 | 39 | 42 | 43 | 38 | 41 |
N.S. |
1 | 1.00 | 0.87 | 0.85 | 0.83 | 0.83 | 0.89 | 0.91 | 0.81 | 0.87 |
time (sec) |
N/A | 0.209 | 0.014 | 0.269 | 0.028 | 0.062 | 0.021 | 0.221 | 0.214 | 0.043 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 42 | 42 | 42 | 37 | 36 | 36 | 39 | 40 | 36 | 38 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 0.86 | 0.86 | 0.93 | 0.95 | 0.86 | 0.90 |
time (sec) |
N/A | 0.202 | 0.014 | 0.234 | 0.033 | 0.062 | 0.016 | 0.219 | 0.205 | 0.043 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 38 | 38 | 36 | 34 | 34 | 36 | 36 | 34 | 35 |
N.S. |
1 | 1.00 | 1.00 | 0.95 | 0.89 | 0.89 | 0.95 | 0.95 | 0.89 | 0.92 |
time (sec) |
N/A | 0.188 | 0.013 | 0.098 | 0.032 | 0.065 | 0.050 | 0.191 | 0.224 | 0.043 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 36 | 36 | 34 | 34 | 40 | 31 | 34 | 39 | 34 |
N.S. |
1 | 1.00 | 1.00 | 0.94 | 0.94 | 1.11 | 0.86 | 0.94 | 1.08 | 0.94 |
time (sec) |
N/A | 0.192 | 0.019 | 0.096 | 0.029 | 0.064 | 0.078 | 0.221 | 0.293 | 0.040 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 36 | 37 | 35 | 34 | 41 | 36 | 35 | 42 | 34 |
N.S. |
1 | 1.00 | 1.03 | 0.97 | 0.94 | 1.14 | 1.00 | 0.97 | 1.17 | 0.94 |
time (sec) |
N/A | 0.191 | 0.023 | 0.083 | 0.030 | 0.069 | 0.154 | 0.209 | 0.222 | 0.053 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 41 | 41 | 41 | 38 | 38 | 41 | 44 | 39 | 40 | 38 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 0.93 | 1.00 | 1.07 | 0.95 | 0.98 | 0.93 |
time (sec) |
N/A | 0.192 | 0.030 | 0.069 | 0.027 | 0.064 | 0.320 | 0.198 | 0.234 | 0.056 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 45 | 45 | 42 | 40 | 39 | 39 | 46 | 41 | 38 | 40 |
N.S. |
1 | 1.00 | 0.93 | 0.89 | 0.87 | 0.87 | 1.02 | 0.91 | 0.84 | 0.89 |
time (sec) |
N/A | 0.192 | 0.017 | 0.062 | 0.028 | 0.061 | 0.490 | 0.188 | 0.247 | 0.030 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 47 | 47 | 44 | 40 | 39 | 39 | 46 | 41 | 38 | 41 |
N.S. |
1 | 1.00 | 0.94 | 0.85 | 0.83 | 0.83 | 0.98 | 0.87 | 0.81 | 0.87 |
time (sec) |
N/A | 0.191 | 0.017 | 0.070 | 0.034 | 0.065 | 0.884 | 0.213 | 0.230 | 0.030 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 47 | 47 | 45 | 40 | 39 | 39 | 46 | 41 | 38 | 41 |
N.S. |
1 | 1.00 | 0.96 | 0.85 | 0.83 | 0.83 | 0.98 | 0.87 | 0.81 | 0.87 |
time (sec) |
N/A | 0.188 | 0.018 | 0.063 | 0.045 | 0.062 | 1.105 | 0.224 | 0.275 | 0.030 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 47 | 47 | 46 | 40 | 39 | 39 | 46 | 41 | 38 | 41 |
N.S. |
1 | 1.00 | 0.98 | 0.85 | 0.83 | 0.83 | 0.98 | 0.87 | 0.81 | 0.87 |
time (sec) |
N/A | 0.190 | 0.019 | 0.079 | 0.030 | 0.064 | 1.562 | 0.242 | 0.238 | 0.031 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 101 | 101 | 101 | 94 | 93 | 93 | 105 | 103 | 79 | 93 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 0.92 | 0.92 | 1.04 | 1.02 | 0.78 | 0.92 |
time (sec) |
N/A | 0.315 | 0.028 | 1.157 | 0.031 | 0.068 | 0.026 | 0.190 | 0.232 | 0.046 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 101 | 101 | 101 | 94 | 93 | 93 | 105 | 103 | 79 | 93 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 0.92 | 0.92 | 1.04 | 1.02 | 0.78 | 0.92 |
time (sec) |
N/A | 0.287 | 0.023 | 1.081 | 0.036 | 0.081 | 0.025 | 0.228 | 0.231 | 0.032 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 96 | 96 | 96 | 90 | 90 | 90 | 100 | 99 | 77 | 89 |
N.S. |
1 | 1.00 | 1.00 | 0.94 | 0.94 | 0.94 | 1.04 | 1.03 | 0.80 | 0.93 |
time (sec) |
N/A | 0.281 | 0.022 | 1.093 | 0.032 | 0.077 | 0.036 | 0.219 | 0.216 | 0.032 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 92 | 92 | 92 | 87 | 88 | 88 | 95 | 95 | 74 | 86 |
N.S. |
1 | 1.00 | 1.00 | 0.95 | 0.96 | 0.96 | 1.03 | 1.03 | 0.80 | 0.93 |
time (sec) |
N/A | 0.248 | 0.037 | 0.931 | 0.029 | 0.072 | 0.095 | 0.204 | 0.216 | 0.037 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 90 | 90 | 87 | 90 | 88 | 95 | 88 | 92 | 81 | 86 |
N.S. |
1 | 1.00 | 0.97 | 1.00 | 0.98 | 1.06 | 0.98 | 1.02 | 0.90 | 0.96 |
time (sec) |
N/A | 0.275 | 0.056 | 1.069 | 0.034 | 0.075 | 0.113 | 0.204 | 0.216 | 10.620 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 90 | 90 | 86 | 87 | 88 | 95 | 94 | 89 | 83 | 87 |
N.S. |
1 | 1.00 | 0.96 | 0.97 | 0.98 | 1.06 | 1.04 | 0.99 | 0.92 | 0.97 |
time (sec) |
N/A | 0.263 | 0.053 | 1.073 | 0.029 | 0.073 | 0.227 | 0.213 | 0.232 | 10.581 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 90 | 90 | 90 | 86 | 89 | 95 | 99 | 89 | 83 | 87 |
N.S. |
1 | 1.00 | 1.00 | 0.96 | 0.99 | 1.06 | 1.10 | 0.99 | 0.92 | 0.97 |
time (sec) |
N/A | 0.257 | 0.056 | 1.035 | 0.034 | 0.075 | 0.652 | 0.180 | 0.217 | 10.514 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 90 | 90 | 92 | 85 | 89 | 95 | 99 | 90 | 83 | 86 |
N.S. |
1 | 1.00 | 1.02 | 0.94 | 0.99 | 1.06 | 1.10 | 1.00 | 0.92 | 0.96 |
time (sec) |
N/A | 0.258 | 0.055 | 1.095 | 0.028 | 0.070 | 1.424 | 0.247 | 0.226 | 10.181 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 95 | 95 | 92 | 88 | 92 | 95 | 105 | 93 | 81 | 89 |
N.S. |
1 | 1.00 | 0.97 | 0.93 | 0.97 | 1.00 | 1.11 | 0.98 | 0.85 | 0.94 |
time (sec) |
N/A | 0.249 | 0.063 | 1.053 | 0.026 | 0.069 | 3.186 | 0.211 | 0.217 | 0.067 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 99 | 99 | 97 | 90 | 93 | 93 | 107 | 101 | 79 | 91 |
N.S. |
1 | 1.00 | 0.98 | 0.91 | 0.94 | 0.94 | 1.08 | 1.02 | 0.80 | 0.92 |
time (sec) |
N/A | 0.242 | 0.048 | 0.937 | 0.034 | 0.068 | 6.037 | 0.236 | 0.234 | 10.229 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 101 | 101 | 100 | 90 | 93 | 93 | 107 | 101 | 79 | 93 |
N.S. |
1 | 1.00 | 0.99 | 0.89 | 0.92 | 0.92 | 1.06 | 1.00 | 0.78 | 0.92 |
time (sec) |
N/A | 0.248 | 0.069 | 0.973 | 0.043 | 0.070 | 10.847 | 0.174 | 0.237 | 0.049 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 101 | 101 | 99 | 90 | 93 | 93 | 107 | 101 | 79 | 93 |
N.S. |
1 | 1.00 | 0.98 | 0.89 | 0.92 | 0.92 | 1.06 | 1.00 | 0.78 | 0.92 |
time (sec) |
N/A | 0.247 | 0.042 | 0.923 | 0.036 | 0.071 | 18.917 | 0.233 | 0.231 | 0.048 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 166 | 166 | 166 | 169 | 166 | 166 | 201 | 192 | 134 | 168 |
N.S. |
1 | 1.00 | 1.00 | 1.02 | 1.00 | 1.00 | 1.21 | 1.16 | 0.81 | 1.01 |
time (sec) |
N/A | 0.446 | 0.054 | 1.016 | 0.045 | 0.069 | 0.033 | 0.199 | 0.222 | 10.223 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 166 | 166 | 166 | 168 | 166 | 166 | 199 | 191 | 134 | 167 |
N.S. |
1 | 1.00 | 1.00 | 1.01 | 1.00 | 1.00 | 1.20 | 1.15 | 0.81 | 1.01 |
time (sec) |
N/A | 0.404 | 0.041 | 1.107 | 0.027 | 0.072 | 0.033 | 0.225 | 0.282 | 0.048 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 158 | 158 | 158 | 164 | 162 | 162 | 190 | 187 | 132 | 163 |
N.S. |
1 | 1.00 | 1.00 | 1.04 | 1.03 | 1.03 | 1.20 | 1.18 | 0.84 | 1.03 |
time (sec) |
N/A | 0.386 | 0.038 | 1.008 | 0.062 | 0.069 | 0.032 | 0.213 | 0.233 | 0.049 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 157 | 157 | 157 | 163 | 161 | 161 | 192 | 185 | 130 | 162 |
N.S. |
1 | 1.00 | 1.00 | 1.04 | 1.03 | 1.03 | 1.22 | 1.18 | 0.83 | 1.03 |
time (sec) |
N/A | 0.324 | 0.070 | 0.980 | 0.059 | 0.078 | 0.137 | 0.218 | 0.273 | 10.205 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 156 | 156 | 156 | 168 | 162 | 168 | 184 | 183 | 136 | 163 |
N.S. |
1 | 1.00 | 1.00 | 1.08 | 1.04 | 1.08 | 1.18 | 1.17 | 0.87 | 1.04 |
time (sec) |
N/A | 0.328 | 0.086 | 1.066 | 0.036 | 0.074 | 0.166 | 0.219 | 0.216 | 10.329 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 153 | 153 | 153 | 165 | 161 | 168 | 175 | 174 | 138 | 162 |
N.S. |
1 | 1.00 | 1.00 | 1.08 | 1.05 | 1.10 | 1.14 | 1.14 | 0.90 | 1.06 |
time (sec) |
N/A | 0.338 | 0.077 | 0.987 | 0.042 | 0.074 | 0.300 | 0.219 | 0.217 | 0.058 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 155 | 155 | 160 | 162 | 162 | 168 | 187 | 169 | 138 | 164 |
N.S. |
1 | 1.00 | 1.03 | 1.05 | 1.05 | 1.08 | 1.21 | 1.09 | 0.89 | 1.06 |
time (sec) |
N/A | 0.360 | 0.066 | 1.017 | 0.038 | 0.077 | 0.665 | 0.222 | 0.215 | 10.592 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 156 | 156 | 154 | 159 | 163 | 168 | 189 | 166 | 140 | 164 |
N.S. |
1 | 1.00 | 0.99 | 1.02 | 1.04 | 1.08 | 1.21 | 1.06 | 0.90 | 1.05 |
time (sec) |
N/A | 0.341 | 0.067 | 1.022 | 0.037 | 0.071 | 2.085 | 0.176 | 0.231 | 10.398 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 154 | 154 | 161 | 151 | 163 | 168 | 182 | 162 | 138 | 162 |
N.S. |
1 | 1.00 | 1.05 | 0.98 | 1.06 | 1.09 | 1.18 | 1.05 | 0.90 | 1.05 |
time (sec) |
N/A | 0.335 | 0.095 | 1.000 | 0.037 | 0.075 | 5.456 | 0.220 | 0.237 | 0.072 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 155 | 155 | 169 | 149 | 162 | 168 | 187 | 162 | 138 | 163 |
N.S. |
1 | 1.00 | 1.09 | 0.96 | 1.05 | 1.08 | 1.21 | 1.05 | 0.89 | 1.05 |
time (sec) |
N/A | 0.333 | 0.096 | 1.038 | 0.032 | 0.070 | 13.282 | 0.168 | 0.226 | 10.425 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 160 | 160 | 175 | 152 | 165 | 168 | 194 | 165 | 136 | 165 |
N.S. |
1 | 1.00 | 1.09 | 0.95 | 1.03 | 1.05 | 1.21 | 1.03 | 0.85 | 1.03 |
time (sec) |
N/A | 0.330 | 0.087 | 0.937 | 0.035 | 0.072 | 26.691 | 0.219 | 0.232 | 10.463 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 162 | 162 | 172 | 154 | 166 | 166 | 196 | 191 | 134 | 165 |
N.S. |
1 | 1.00 | 1.06 | 0.95 | 1.02 | 1.02 | 1.21 | 1.18 | 0.83 | 1.02 |
time (sec) |
N/A | 0.340 | 0.069 | 0.951 | 0.037 | 0.070 | 59.224 | 0.217 | 0.218 | 0.075 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 166 | 166 | 175 | 154 | 166 | 166 | 196 | 191 | 134 | 167 |
N.S. |
1 | 1.00 | 1.05 | 0.93 | 1.00 | 1.00 | 1.18 | 1.15 | 0.81 | 1.01 |
time (sec) |
N/A | 0.334 | 0.066 | 0.960 | 0.041 | 0.070 | 121.609 | 0.245 | 0.206 | 0.074 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 166 | 166 | 176 | 154 | 166 | 166 | 0 | 191 | 134 | 168 |
N.S. |
1 | 1.00 | 1.06 | 0.93 | 1.00 | 1.00 | 0.00 | 1.15 | 0.81 | 1.01 |
time (sec) |
N/A | 0.331 | 0.071 | 0.964 | 0.083 | 0.069 | 0.000 | 0.210 | 0.296 | 0.074 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 229 | 229 | 222 | 260 | 0 | 730 | 1100 | 235 | 587 | 302 |
N.S. |
1 | 1.00 | 0.97 | 1.14 | 0.00 | 3.19 | 4.80 | 1.03 | 2.56 | 1.32 |
time (sec) |
N/A | 0.576 | 0.143 | 1.334 | 0.000 | 0.102 | 1.998 | 0.229 | 0.227 | 10.531 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 169 | 169 | 165 | 183 | 0 | 563 | 840 | 169 | 447 | 221 |
N.S. |
1 | 1.00 | 0.98 | 1.08 | 0.00 | 3.33 | 4.97 | 1.00 | 2.64 | 1.31 |
time (sec) |
N/A | 0.413 | 0.100 | 1.358 | 0.000 | 0.101 | 1.708 | 0.217 | 0.237 | 10.479 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 121 | 121 | 119 | 127 | 0 | 414 | 609 | 116 | 321 | 168 |
N.S. |
1 | 1.00 | 0.98 | 1.05 | 0.00 | 3.42 | 5.03 | 0.96 | 2.65 | 1.39 |
time (sec) |
N/A | 0.327 | 0.079 | 1.348 | 0.000 | 0.090 | 1.125 | 0.175 | 0.240 | 0.181 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 85 | 85 | 86 | 90 | 0 | 289 | 423 | 84 | 215 | 127 |
N.S. |
1 | 1.00 | 1.01 | 1.06 | 0.00 | 3.40 | 4.98 | 0.99 | 2.53 | 1.49 |
time (sec) |
N/A | 0.264 | 0.090 | 1.266 | 0.000 | 0.086 | 0.744 | 0.240 | 0.229 | 0.231 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 66 | 66 | 66 | 62 | 0 | 204 | 280 | 63 | 123 | 162 |
N.S. |
1 | 1.00 | 1.00 | 0.94 | 0.00 | 3.09 | 4.24 | 0.95 | 1.86 | 2.45 |
time (sec) |
N/A | 0.227 | 0.056 | 1.233 | 0.000 | 0.085 | 0.413 | 0.226 | 0.230 | 0.082 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 71 | 71 | 71 | 70 | 0 | 228 | 0 | 71 | 137 | 375 |
N.S. |
1 | 1.00 | 1.00 | 0.99 | 0.00 | 3.21 | 0.00 | 1.00 | 1.93 | 5.28 |
time (sec) |
N/A | 0.267 | 0.113 | 1.281 | 0.000 | 0.109 | 0.000 | 0.231 | 0.215 | 11.377 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 104 | 104 | 100 | 122 | 0 | 361 | 0 | 102 | 261 | 791 |
N.S. |
1 | 1.00 | 0.96 | 1.17 | 0.00 | 3.47 | 0.00 | 0.98 | 2.51 | 7.61 |
time (sec) |
N/A | 0.328 | 0.087 | 1.342 | 0.000 | 0.156 | 0.000 | 0.205 | 0.232 | 12.332 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 145 | 145 | 141 | 174 | 0 | 517 | 0 | 147 | 407 | 814 |
N.S. |
1 | 1.00 | 0.97 | 1.20 | 0.00 | 3.57 | 0.00 | 1.01 | 2.81 | 5.61 |
time (sec) |
N/A | 0.401 | 0.132 | 1.326 | 0.000 | 0.317 | 0.000 | 0.212 | 0.275 | 11.666 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 204 | 204 | 196 | 243 | 0 | 687 | 0 | 206 | 559 | 1063 |
N.S. |
1 | 1.00 | 0.96 | 1.19 | 0.00 | 3.37 | 0.00 | 1.01 | 2.74 | 5.21 |
time (sec) |
N/A | 0.486 | 0.146 | 1.330 | 0.000 | 0.737 | 0.000 | 0.220 | 0.231 | 12.104 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 266 | 266 | 249 | 349 | 0 | 1696 | 1572 | 284 | 1610 | 427 |
N.S. |
1 | 1.00 | 0.94 | 1.31 | 0.00 | 6.38 | 5.91 | 1.07 | 6.05 | 1.61 |
time (sec) |
N/A | 0.723 | 0.395 | 1.349 | 0.000 | 0.173 | 3.946 | 0.205 | 0.221 | 11.666 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 202 | 204 | 190 | 269 | 0 | 1283 | 1248 | 225 | 1294 | 360 |
N.S. |
1 | 1.01 | 0.94 | 1.33 | 0.00 | 6.35 | 6.18 | 1.11 | 6.41 | 1.78 |
time (sec) |
N/A | 0.515 | 0.309 | 1.302 | 0.000 | 0.104 | 2.890 | 0.202 | 0.224 | 11.499 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 132 | 157 | 146 | 200 | 0 | 813 | 901 | 162 | 766 | 895 |
N.S. |
1 | 1.19 | 1.11 | 1.52 | 0.00 | 6.16 | 6.83 | 1.23 | 5.80 | 6.78 |
time (sec) |
N/A | 0.363 | 0.189 | 1.295 | 0.000 | 0.087 | 1.493 | 0.217 | 0.287 | 11.121 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 87 | 99 | 99 | 118 | 0 | 521 | 379 | 109 | 406 | 177 |
N.S. |
1 | 1.14 | 1.14 | 1.36 | 0.00 | 5.99 | 4.36 | 1.25 | 4.67 | 2.03 |
time (sec) |
N/A | 0.246 | 0.077 | 1.197 | 0.000 | 0.083 | 0.679 | 0.190 | 0.225 | 10.887 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 87 | 87 | 88 | 89 | 0 | 459 | 359 | 96 | 404 | 159 |
N.S. |
1 | 1.00 | 1.01 | 1.02 | 0.00 | 5.28 | 4.13 | 1.10 | 4.64 | 1.83 |
time (sec) |
N/A | 0.235 | 0.078 | 1.204 | 0.000 | 0.083 | 0.514 | 0.214 | 0.211 | 0.118 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 135 | 166 | 134 | 200 | 0 | 955 | 0 | 157 | 873 | 920 |
N.S. |
1 | 1.23 | 0.99 | 1.48 | 0.00 | 7.07 | 0.00 | 1.16 | 6.47 | 6.81 |
time (sec) |
N/A | 0.430 | 0.204 | 1.283 | 0.000 | 0.316 | 0.000 | 0.180 | 0.218 | 12.198 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 201 | 232 | 192 | 293 | 0 | 1615 | 0 | 238 | 1575 | 1366 |
N.S. |
1 | 1.15 | 0.96 | 1.46 | 0.00 | 8.03 | 0.00 | 1.18 | 7.84 | 6.80 |
time (sec) |
N/A | 0.567 | 0.352 | 1.441 | 0.000 | 1.063 | 0.000 | 0.231 | 0.236 | 12.989 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 266 | 294 | 253 | 375 | 0 | 2003 | 0 | 334 | 1989 | 1661 |
N.S. |
1 | 1.11 | 0.95 | 1.41 | 0.00 | 7.53 | 0.00 | 1.26 | 7.48 | 6.24 |
time (sec) |
N/A | 0.760 | 0.447 | 1.371 | 0.000 | 2.146 | 0.000 | 0.195 | 0.232 | 12.857 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 55 | 55 | 45 | 40 | 39 | 44 | 70 | 43 | 40 | 41 |
N.S. |
1 | 1.00 | 0.82 | 0.73 | 0.71 | 0.80 | 1.27 | 0.78 | 0.73 | 0.75 |
time (sec) |
N/A | 0.200 | 0.056 | 0.525 | 0.033 | 0.083 | 0.572 | 0.251 | 0.299 | 0.052 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 55 | 55 | 48 | 40 | 39 | 44 | 70 | 43 | 40 | 41 |
N.S. |
1 | 1.00 | 0.87 | 0.73 | 0.71 | 0.80 | 1.27 | 0.78 | 0.73 | 0.75 |
time (sec) |
N/A | 0.198 | 0.052 | 0.518 | 0.050 | 0.095 | 0.315 | 0.253 | 0.209 | 0.047 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 55 | 55 | 48 | 40 | 39 | 44 | 70 | 43 | 40 | 41 |
N.S. |
1 | 1.00 | 0.87 | 0.73 | 0.71 | 0.80 | 1.27 | 0.78 | 0.73 | 0.75 |
time (sec) |
N/A | 0.206 | 0.052 | 0.473 | 0.034 | 0.081 | 0.206 | 0.259 | 0.227 | 0.045 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 55 | 55 | 47 | 40 | 39 | 42 | 53 | 43 | 38 | 41 |
N.S. |
1 | 1.00 | 0.85 | 0.73 | 0.71 | 0.76 | 0.96 | 0.78 | 0.69 | 0.75 |
time (sec) |
N/A | 0.201 | 0.051 | 0.461 | 0.029 | 0.076 | 0.609 | 0.239 | 0.232 | 0.047 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 53 | 53 | 46 | 40 | 39 | 39 | 68 | 43 | 37 | 41 |
N.S. |
1 | 1.00 | 0.87 | 0.75 | 0.74 | 0.74 | 1.28 | 0.81 | 0.70 | 0.77 |
time (sec) |
N/A | 0.199 | 0.054 | 0.362 | 0.028 | 0.074 | 0.126 | 0.263 | 0.228 | 0.046 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 51 | 51 | 45 | 42 | 39 | 39 | 65 | 43 | 39 | 41 |
N.S. |
1 | 1.00 | 0.88 | 0.82 | 0.76 | 0.76 | 1.27 | 0.84 | 0.76 | 0.80 |
time (sec) |
N/A | 0.193 | 0.054 | 0.129 | 0.040 | 0.081 | 0.187 | 0.246 | 0.223 | 0.051 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 51 | 51 | 44 | 41 | 39 | 38 | 63 | 41 | 41 | 41 |
N.S. |
1 | 1.00 | 0.86 | 0.80 | 0.76 | 0.75 | 1.24 | 0.80 | 0.80 | 0.80 |
time (sec) |
N/A | 0.197 | 0.068 | 0.139 | 0.037 | 0.076 | 0.204 | 0.243 | 0.223 | 0.047 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 51 | 51 | 42 | 40 | 40 | 39 | 65 | 42 | 42 | 42 |
N.S. |
1 | 1.00 | 0.82 | 0.78 | 0.78 | 0.76 | 1.27 | 0.82 | 0.82 | 0.82 |
time (sec) |
N/A | 0.202 | 0.068 | 0.122 | 0.032 | 0.082 | 0.261 | 0.243 | 0.282 | 0.052 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 53 | 53 | 45 | 40 | 39 | 39 | 70 | 41 | 42 | 41 |
N.S. |
1 | 1.00 | 0.85 | 0.75 | 0.74 | 0.74 | 1.32 | 0.77 | 0.79 | 0.77 |
time (sec) |
N/A | 0.196 | 0.078 | 0.135 | 0.033 | 0.076 | 0.406 | 0.221 | 0.234 | 0.041 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 113 | 113 | 102 | 94 | 93 | 98 | 162 | 103 | 81 | 93 |
N.S. |
1 | 1.00 | 0.90 | 0.83 | 0.82 | 0.87 | 1.43 | 0.91 | 0.72 | 0.82 |
time (sec) |
N/A | 0.263 | 0.123 | 1.107 | 0.030 | 0.081 | 0.729 | 0.243 | 0.270 | 0.056 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 113 | 113 | 102 | 94 | 93 | 98 | 162 | 103 | 81 | 93 |
N.S. |
1 | 1.00 | 0.90 | 0.83 | 0.82 | 0.87 | 1.43 | 0.91 | 0.72 | 0.82 |
time (sec) |
N/A | 0.255 | 0.113 | 1.046 | 0.033 | 0.078 | 0.484 | 0.231 | 0.228 | 0.037 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 113 | 113 | 102 | 94 | 93 | 98 | 162 | 103 | 81 | 93 |
N.S. |
1 | 1.00 | 0.90 | 0.83 | 0.82 | 0.87 | 1.43 | 0.91 | 0.72 | 0.82 |
time (sec) |
N/A | 0.264 | 0.121 | 1.135 | 0.034 | 0.088 | 0.313 | 0.264 | 0.227 | 0.035 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 113 | 113 | 102 | 94 | 93 | 96 | 121 | 103 | 79 | 93 |
N.S. |
1 | 1.00 | 0.90 | 0.83 | 0.82 | 0.85 | 1.07 | 0.91 | 0.70 | 0.82 |
time (sec) |
N/A | 0.267 | 0.115 | 1.007 | 0.027 | 0.088 | 0.871 | 0.261 | 0.249 | 0.035 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 111 | 111 | 100 | 94 | 93 | 93 | 160 | 103 | 78 | 93 |
N.S. |
1 | 1.00 | 0.90 | 0.85 | 0.84 | 0.84 | 1.44 | 0.93 | 0.70 | 0.84 |
time (sec) |
N/A | 0.260 | 0.115 | 1.069 | 0.037 | 0.086 | 0.209 | 0.243 | 0.225 | 0.036 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 109 | 109 | 97 | 102 | 93 | 93 | 156 | 103 | 80 | 93 |
N.S. |
1 | 1.00 | 0.89 | 0.94 | 0.85 | 0.85 | 1.43 | 0.94 | 0.73 | 0.85 |
time (sec) |
N/A | 0.256 | 0.153 | 0.985 | 0.030 | 0.084 | 0.279 | 0.261 | 0.220 | 0.038 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 109 | 109 | 94 | 101 | 93 | 93 | 153 | 101 | 83 | 94 |
N.S. |
1 | 1.00 | 0.86 | 0.93 | 0.85 | 0.85 | 1.40 | 0.93 | 0.76 | 0.86 |
time (sec) |
N/A | 0.252 | 0.164 | 1.045 | 0.034 | 0.084 | 0.307 | 0.252 | 0.215 | 0.039 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 109 | 109 | 95 | 97 | 94 | 93 | 151 | 102 | 83 | 94 |
N.S. |
1 | 1.00 | 0.87 | 0.89 | 0.86 | 0.85 | 1.39 | 0.94 | 0.76 | 0.86 |
time (sec) |
N/A | 0.253 | 0.167 | 1.075 | 0.032 | 0.097 | 0.370 | 0.231 | 0.220 | 0.060 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 109 | 109 | 95 | 93 | 94 | 93 | 153 | 102 | 83 | 94 |
N.S. |
1 | 1.00 | 0.87 | 0.85 | 0.86 | 0.85 | 1.40 | 0.94 | 0.76 | 0.86 |
time (sec) |
N/A | 0.254 | 0.154 | 1.040 | 0.027 | 0.081 | 0.446 | 0.261 | 0.222 | 0.066 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 182 | 182 | 178 | 192 | 166 | 171 | 294 | 193 | 136 | 169 |
N.S. |
1 | 1.00 | 0.98 | 1.05 | 0.91 | 0.94 | 1.62 | 1.06 | 0.75 | 0.93 |
time (sec) |
N/A | 0.339 | 0.241 | 1.184 | 0.034 | 0.081 | 1.037 | 0.217 | 0.213 | 10.917 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 182 | 182 | 178 | 192 | 166 | 171 | 294 | 193 | 136 | 169 |
N.S. |
1 | 1.00 | 0.98 | 1.05 | 0.91 | 0.94 | 1.62 | 1.06 | 0.75 | 0.93 |
time (sec) |
N/A | 0.340 | 0.259 | 1.116 | 0.034 | 0.085 | 0.731 | 0.248 | 0.215 | 0.053 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 182 | 182 | 178 | 192 | 166 | 171 | 294 | 193 | 136 | 169 |
N.S. |
1 | 1.00 | 0.98 | 1.05 | 0.91 | 0.94 | 1.62 | 1.06 | 0.75 | 0.93 |
time (sec) |
N/A | 0.334 | 0.231 | 1.029 | 0.035 | 0.086 | 0.638 | 0.240 | 0.230 | 0.053 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 182 | 182 | 178 | 192 | 166 | 169 | 216 | 193 | 134 | 169 |
N.S. |
1 | 1.00 | 0.98 | 1.05 | 0.91 | 0.93 | 1.19 | 1.06 | 0.74 | 0.93 |
time (sec) |
N/A | 0.334 | 0.243 | 1.072 | 0.039 | 0.075 | 0.978 | 0.249 | 0.226 | 0.053 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 180 | 180 | 176 | 191 | 166 | 166 | 291 | 193 | 133 | 169 |
N.S. |
1 | 1.00 | 0.98 | 1.06 | 0.92 | 0.92 | 1.62 | 1.07 | 0.74 | 0.94 |
time (sec) |
N/A | 0.323 | 0.237 | 1.088 | 0.034 | 0.082 | 0.329 | 0.239 | 0.250 | 0.053 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 176 | 176 | 173 | 192 | 166 | 166 | 284 | 193 | 135 | 169 |
N.S. |
1 | 1.00 | 0.98 | 1.09 | 0.94 | 0.94 | 1.61 | 1.10 | 0.77 | 0.96 |
time (sec) |
N/A | 0.324 | 0.263 | 1.053 | 0.028 | 0.085 | 0.436 | 0.240 | 0.252 | 0.056 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 178 | 178 | 170 | 191 | 166 | 166 | 280 | 191 | 138 | 170 |
N.S. |
1 | 1.00 | 0.96 | 1.07 | 0.93 | 0.93 | 1.57 | 1.07 | 0.78 | 0.96 |
time (sec) |
N/A | 0.324 | 0.272 | 1.027 | 0.036 | 0.080 | 0.471 | 0.227 | 0.247 | 0.055 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 178 | 178 | 169 | 181 | 167 | 166 | 275 | 192 | 138 | 170 |
N.S. |
1 | 1.00 | 0.95 | 1.02 | 0.94 | 0.93 | 1.54 | 1.08 | 0.78 | 0.96 |
time (sec) |
N/A | 0.329 | 0.250 | 0.994 | 0.037 | 0.090 | 0.561 | 0.262 | 0.320 | 0.056 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 174 | 174 | 168 | 174 | 167 | 166 | 270 | 192 | 138 | 170 |
N.S. |
1 | 1.00 | 0.97 | 1.00 | 0.96 | 0.95 | 1.55 | 1.10 | 0.79 | 0.98 |
time (sec) |
N/A | 0.322 | 0.285 | 1.037 | 0.034 | 0.126 | 0.656 | 0.236 | 0.311 | 10.653 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 178 | 178 | 172 | 167 | 167 | 166 | 275 | 192 | 138 | 170 |
N.S. |
1 | 1.00 | 0.97 | 0.94 | 0.94 | 0.93 | 1.54 | 1.08 | 0.78 | 0.96 |
time (sec) |
N/A | 0.329 | 0.266 | 0.966 | 0.033 | 0.077 | 0.929 | 0.257 | 0.272 | 0.078 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 347 | 363 | 411 | 381 | 0 | 7707 | 40613 | 5319 | 1213 | 14120 |
N.S. |
1 | 1.05 | 1.18 | 1.10 | 0.00 | 22.21 | 117.04 | 15.33 | 3.50 | 40.69 |
time (sec) |
N/A | 0.810 | 1.656 | 1.220 | 0.000 | 12.948 | 75.315 | 0.864 | 0.251 | 12.130 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 275 | 287 | 333 | 291 | 0 | 5148 | 17734 | 4399 | 975 | 10204 |
N.S. |
1 | 1.04 | 1.21 | 1.06 | 0.00 | 18.72 | 64.49 | 16.00 | 3.55 | 37.11 |
time (sec) |
N/A | 0.589 | 1.432 | 1.218 | 0.000 | 4.420 | 18.140 | 0.787 | 0.269 | 11.756 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 221 | 225 | 264 | 218 | 0 | 2642 | 13942 | 3186 | 741 | 6401 |
N.S. |
1 | 1.02 | 1.19 | 0.99 | 0.00 | 11.95 | 63.09 | 14.42 | 3.35 | 28.96 |
time (sec) |
N/A | 0.459 | 0.783 | 1.228 | 0.000 | 0.886 | 6.900 | 0.712 | 0.251 | 11.924 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 180 | 182 | 181 | 168 | 0 | 1577 | 4488 | 1404 | 533 | 4141 |
N.S. |
1 | 1.01 | 1.01 | 0.93 | 0.00 | 8.76 | 24.93 | 7.80 | 2.96 | 23.01 |
time (sec) |
N/A | 0.355 | 0.539 | 1.121 | 0.000 | 0.411 | 9.139 | 0.661 | 0.244 | 11.905 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 199 | 197 | 214 | 175 | 0 | 2925 | 305978 | 2809 | 377 | 6367 |
N.S. |
1 | 0.99 | 1.08 | 0.88 | 0.00 | 14.70 | 1537.58 | 14.12 | 1.89 | 31.99 |
time (sec) |
N/A | 0.430 | 0.901 | 1.019 | 0.000 | 0.884 | 59.492 | 0.709 | 0.285 | 12.635 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F | B | F(-1) | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 284 | 0 | 276 | 233 | 0 | 5453 | 0 | 2870 | 403 | 10133 |
N.S. |
1 | 0.00 | 0.97 | 0.82 | 0.00 | 19.20 | 0.00 | 10.11 | 1.42 | 35.68 |
time (sec) |
N/A | 0.000 | 1.284 | 1.528 | 0.000 | 1.418 | 0.000 | 0.830 | 0.292 | 2.143 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F | B | F(-1) | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 307 | 0 | 354 | 314 | 0 | 7971 | 0 | 5013 | 653 | 13983 |
N.S. |
1 | 0.00 | 1.15 | 1.02 | 0.00 | 25.96 | 0.00 | 16.33 | 2.13 | 45.55 |
time (sec) |
N/A | 0.000 | 1.589 | 1.303 | 0.000 | 4.322 | 0.000 | 1.164 | 0.362 | 14.524 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F | B | F(-1) | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 381 | 0 | 445 | 412 | 0 | 10514 | 0 | 4090 | 896 | 17910 |
N.S. |
1 | 0.00 | 1.17 | 1.08 | 0.00 | 27.60 | 0.00 | 10.73 | 2.35 | 47.01 |
time (sec) |
N/A | 0.000 | 2.135 | 1.184 | 0.000 | 6.373 | 0.000 | 1.062 | 0.464 | 15.335 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 403 | 404 | 461 | 455 | 0 | 7251 | 0 | 5685 | 3675 | 16631 |
N.S. |
1 | 1.00 | 1.14 | 1.13 | 0.00 | 17.99 | 0.00 | 14.11 | 9.12 | 41.27 |
time (sec) |
N/A | 0.771 | 4.690 | 1.155 | 0.000 | 15.666 | 0.000 | 1.161 | 3.930 | 15.147 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 321 | 316 | 366 | 364 | 0 | 4653 | 0 | 4544 | 3001 | 12408 |
N.S. |
1 | 0.98 | 1.14 | 1.13 | 0.00 | 14.50 | 0.00 | 14.16 | 9.35 | 38.65 |
time (sec) |
N/A | 0.592 | 3.332 | 1.126 | 0.000 | 4.331 | 0.000 | 1.121 | 0.512 | 16.459 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 276 | 268 | 298 | 295 | 0 | 3462 | 0 | 3781 | 1813 | 9434 |
N.S. |
1 | 0.97 | 1.08 | 1.07 | 0.00 | 12.54 | 0.00 | 13.70 | 6.57 | 34.18 |
time (sec) |
N/A | 0.481 | 2.181 | 1.262 | 0.000 | 2.144 | 0.000 | 0.979 | 0.430 | 15.446 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 292 | 281 | 311 | 468 | 0 | 4884 | 0 | 4434 | 2372 | 12364 |
N.S. |
1 | 0.96 | 1.07 | 1.60 | 0.00 | 16.73 | 0.00 | 15.18 | 8.12 | 42.34 |
time (sec) |
N/A | 0.590 | 2.131 | 1.181 | 0.000 | 6.118 | 0.000 | 1.116 | 0.464 | 15.913 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 406 | 384 | 399 | 383 | 0 | 7597 | 0 | 5405 | 3153 | 17623 |
N.S. |
1 | 0.95 | 0.98 | 0.94 | 0.00 | 18.71 | 0.00 | 13.31 | 7.77 | 43.41 |
time (sec) |
N/A | 0.725 | 3.840 | 1.171 | 0.000 | 23.343 | 0.000 | 1.150 | 1.285 | 16.100 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 521 | 524 | 518 | 485 | 0 | 10203 | 0 | 6335 | 3914 | 21585 |
N.S. |
1 | 1.01 | 0.99 | 0.93 | 0.00 | 19.58 | 0.00 | 12.16 | 7.51 | 41.43 |
time (sec) |
N/A | 0.981 | 5.903 | 1.236 | 0.000 | 51.362 | 0.000 | 1.323 | 2.024 | 15.768 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 528 | 533 | 745 | 714 | 0 | 9631 | 0 | 3997 | 7823 | 22943 |
N.S. |
1 | 1.01 | 1.41 | 1.35 | 0.00 | 18.24 | 0.00 | 7.57 | 14.82 | 43.45 |
time (sec) |
N/A | 1.017 | 12.897 | 1.194 | 0.000 | 39.634 | 0.000 | 1.242 | 5.128 | 15.117 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 459 | 458 | 519 | 595 | 0 | 7056 | 0 | 7586 | 6753 | 19073 |
N.S. |
1 | 1.00 | 1.13 | 1.30 | 0.00 | 15.37 | 0.00 | 16.53 | 14.71 | 41.55 |
time (sec) |
N/A | 0.855 | 10.539 | 1.229 | 0.000 | 11.865 | 0.000 | 1.955 | 5.017 | 13.887 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 414 | 416 | 448 | 500 | 0 | 5646 | 0 | 3170 | 5680 | 16720 |
N.S. |
1 | 1.00 | 1.08 | 1.21 | 0.00 | 13.64 | 0.00 | 7.66 | 13.72 | 40.39 |
time (sec) |
N/A | 0.821 | 11.153 | 1.142 | 0.000 | 7.147 | 0.000 | 1.224 | 4.830 | 14.031 |