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 | 96 | 96 | 92 | 79 | 78 | 78 | 90 | 78 | 79 | 78 |
N.S. |
1 | 1.00 | 0.96 | 0.82 | 0.81 | 0.81 | 0.94 | 0.81 | 0.82 | 0.81 |
time (sec) |
N/A | 0.211 | 0.002 | 0.168 | 0.228 | 0.218 | 0.026 | 0.299 | 0.000 | 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 | 81 | 81 | 93 | 80 | 79 | 79 | 92 | 79 | 79 | 79 |
N.S. |
1 | 1.00 | 1.15 | 0.99 | 0.98 | 0.98 | 1.14 | 0.98 | 0.98 | 0.98 |
time (sec) |
N/A | 0.200 | 0.002 | 0.160 | 0.244 | 0.214 | 0.034 | 0.291 | 0.000 | 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 | 64 | 64 | 93 | 80 | 79 | 79 | 92 | 79 | 79 | 79 |
N.S. |
1 | 1.00 | 1.45 | 1.25 | 1.23 | 1.23 | 1.44 | 1.23 | 1.23 | 1.23 |
time (sec) |
N/A | 0.184 | 0.002 | 0.168 | 0.202 | 0.218 | 0.031 | 0.281 | 0.001 | 0.062 |
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 | 47 | 47 | 93 | 80 | 79 | 79 | 92 | 79 | 79 | 31 |
N.S. |
1 | 1.00 | 1.98 | 1.70 | 1.68 | 1.68 | 1.96 | 1.68 | 1.68 | 0.66 |
time (sec) |
N/A | 0.171 | 0.002 | 0.169 | 0.206 | 0.216 | 0.028 | 0.294 | 0.000 | 0.065 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 30 | 91 | 80 | 79 | 79 | 90 | 79 | 79 | 25 |
N.S. |
1 | 1.00 | 3.03 | 2.67 | 2.63 | 2.63 | 3.00 | 2.63 | 2.63 | 0.83 |
time (sec) |
N/A | 0.150 | 0.002 | 0.168 | 0.199 | 0.212 | 0.029 | 0.295 | 0.000 | 0.065 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 14 | 13 | 12 | 75 | 83 | 12 | 76 | 75 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 0.86 | 5.36 | 5.93 | 0.86 | 5.43 | 5.36 |
time (sec) |
N/A | 0.124 | 0.001 | 0.167 | 0.227 | 0.226 | 0.026 | 0.288 | 0.000 | 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 | 87 | 87 | 87 | 76 | 75 | 75 | 88 | 76 | 75 | 75 |
N.S. |
1 | 1.00 | 1.00 | 0.87 | 0.86 | 0.86 | 1.01 | 0.87 | 0.86 | 0.86 |
time (sec) |
N/A | 0.189 | 0.003 | 0.170 | 0.214 | 0.223 | 0.065 | 0.300 | 0.000 | 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 | 86 | 86 | 86 | 77 | 76 | 81 | 85 | 77 | 81 | 76 |
N.S. |
1 | 1.00 | 1.00 | 0.90 | 0.88 | 0.94 | 0.99 | 0.90 | 0.94 | 0.88 |
time (sec) |
N/A | 0.193 | 0.003 | 0.162 | 0.200 | 0.217 | 0.077 | 0.288 | 0.001 | 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 | 84 | 84 | 84 | 77 | 75 | 81 | 85 | 76 | 81 | 77 |
N.S. |
1 | 1.00 | 1.00 | 0.92 | 0.89 | 0.96 | 1.01 | 0.90 | 0.96 | 0.92 |
time (sec) |
N/A | 0.195 | 0.003 | 0.162 | 0.212 | 0.224 | 0.098 | 0.289 | 0.000 | 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 | 86 | 86 | 86 | 77 | 77 | 81 | 87 | 78 | 81 | 77 |
N.S. |
1 | 1.00 | 1.00 | 0.90 | 0.90 | 0.94 | 1.01 | 0.91 | 0.94 | 0.90 |
time (sec) |
N/A | 0.195 | 0.004 | 0.170 | 0.214 | 0.217 | 0.121 | 0.300 | 0.000 | 0.033 |
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 | 86 | 86 | 86 | 77 | 77 | 81 | 85 | 78 | 81 | 77 |
N.S. |
1 | 1.00 | 1.00 | 0.90 | 0.90 | 0.94 | 0.99 | 0.91 | 0.94 | 0.90 |
time (sec) |
N/A | 0.195 | 0.003 | 0.161 | 0.205 | 0.222 | 0.167 | 0.281 | 0.000 | 0.063 |
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 | 84 | 84 | 84 | 77 | 77 | 81 | 83 | 78 | 81 | 77 |
N.S. |
1 | 1.00 | 1.00 | 0.92 | 0.92 | 0.96 | 0.99 | 0.93 | 0.96 | 0.92 |
time (sec) |
N/A | 0.194 | 0.003 | 0.153 | 0.207 | 0.220 | 0.212 | 0.302 | 0.001 | 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 | 85 | 85 | 85 | 76 | 76 | 81 | 82 | 77 | 81 | 81 |
N.S. |
1 | 1.00 | 1.00 | 0.89 | 0.89 | 0.95 | 0.96 | 0.91 | 0.95 | 0.95 |
time (sec) |
N/A | 0.196 | 0.004 | 0.170 | 0.204 | 0.214 | 0.244 | 0.296 | 0.000 | 0.085 |
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 | 89 | 89 | 89 | 78 | 78 | 81 | 83 | 79 | 81 | 78 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 0.88 | 0.91 | 0.93 | 0.89 | 0.91 | 0.88 |
time (sec) |
N/A | 0.197 | 0.003 | 0.166 | 0.238 | 0.221 | 0.249 | 0.282 | 0.000 | 0.038 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 17 | 87 | 78 | 77 | 77 | 83 | 77 | 79 | 77 |
N.S. |
1 | 1.00 | 5.12 | 4.59 | 4.53 | 4.53 | 4.88 | 4.53 | 4.65 | 4.53 |
time (sec) |
N/A | 0.129 | 0.003 | 0.169 | 0.191 | 0.218 | 0.272 | 0.290 | 0.000 | 0.040 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 36 | 91 | 79 | 79 | 79 | 85 | 79 | 79 | 23 |
N.S. |
1 | 1.00 | 2.53 | 2.19 | 2.19 | 2.19 | 2.36 | 2.19 | 2.19 | 0.64 |
time (sec) |
N/A | 0.139 | 0.003 | 0.160 | 0.200 | 0.215 | 0.338 | 0.308 | 0.000 | 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 | 56 | 62 | 93 | 79 | 79 | 79 | 85 | 79 | 79 | 79 |
N.S. |
1 | 1.11 | 1.66 | 1.41 | 1.41 | 1.41 | 1.52 | 1.41 | 1.41 | 1.41 |
time (sec) |
N/A | 0.148 | 0.003 | 0.169 | 0.209 | 0.215 | 0.327 | 0.307 | 0.000 | 0.065 |
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 | 76 | 88 | 93 | 79 | 79 | 79 | 85 | 79 | 79 | 79 |
N.S. |
1 | 1.16 | 1.22 | 1.04 | 1.04 | 1.04 | 1.12 | 1.04 | 1.04 | 1.04 |
time (sec) |
N/A | 0.163 | 0.003 | 0.173 | 0.204 | 0.227 | 0.346 | 0.292 | 0.001 | 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 | 96 | 114 | 93 | 79 | 79 | 79 | 85 | 79 | 79 | 79 |
N.S. |
1 | 1.19 | 0.97 | 0.82 | 0.82 | 0.82 | 0.89 | 0.82 | 0.82 | 0.82 |
time (sec) |
N/A | 0.175 | 0.003 | 0.174 | 0.214 | 0.227 | 0.372 | 0.313 | 0.000 | 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 | 93 | 93 | 93 | 79 | 79 | 79 | 85 | 79 | 79 | 78 |
N.S. |
1 | 1.00 | 1.00 | 0.85 | 0.85 | 0.85 | 0.91 | 0.85 | 0.85 | 0.84 |
time (sec) |
N/A | 0.193 | 0.005 | 0.170 | 0.216 | 0.213 | 0.340 | 0.282 | 0.001 | 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 | 95 | 95 | 95 | 79 | 79 | 79 | 85 | 79 | 79 | 79 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 0.83 | 0.83 | 0.89 | 0.83 | 0.83 | 0.83 |
time (sec) |
N/A | 0.193 | 0.003 | 0.167 | 0.208 | 0.217 | 0.363 | 0.297 | 0.000 | 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 | 95 | 95 | 95 | 79 | 79 | 79 | 85 | 79 | 79 | 79 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 0.83 | 0.83 | 0.89 | 0.83 | 0.83 | 0.83 |
time (sec) |
N/A | 0.192 | 0.003 | 0.188 | 0.202 | 0.213 | 0.374 | 0.311 | 0.000 | 0.068 |
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 | 132 | 132 | 132 | 113 | 112 | 112 | 133 | 112 | 112 | 112 |
N.S. |
1 | 1.00 | 1.00 | 0.86 | 0.85 | 0.85 | 1.01 | 0.85 | 0.85 | 0.85 |
time (sec) |
N/A | 0.247 | 0.003 | 0.170 | 0.197 | 0.221 | 0.025 | 0.297 | 0.000 | 0.098 |
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 | 132 | 132 | 132 | 113 | 112 | 112 | 131 | 112 | 112 | 112 |
N.S. |
1 | 1.00 | 1.00 | 0.86 | 0.85 | 0.85 | 0.99 | 0.85 | 0.85 | 0.85 |
time (sec) |
N/A | 0.244 | 0.002 | 0.175 | 0.216 | 0.218 | 0.029 | 0.303 | 0.000 | 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 | 132 | 132 | 132 | 113 | 112 | 112 | 133 | 112 | 112 | 112 |
N.S. |
1 | 1.00 | 1.00 | 0.86 | 0.85 | 0.85 | 1.01 | 0.85 | 0.85 | 0.85 |
time (sec) |
N/A | 0.240 | 0.002 | 0.170 | 0.219 | 0.219 | 0.033 | 0.299 | 0.000 | 0.085 |
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 | 147 | 147 | 125 | 112 | 111 | 111 | 126 | 111 | 112 | 111 |
N.S. |
1 | 1.00 | 0.85 | 0.76 | 0.76 | 0.76 | 0.86 | 0.76 | 0.76 | 0.76 |
time (sec) |
N/A | 0.262 | 0.002 | 0.181 | 0.211 | 0.216 | 0.039 | 0.288 | 0.000 | 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 | 132 | 132 | 130 | 113 | 112 | 112 | 131 | 112 | 112 | 112 |
N.S. |
1 | 1.00 | 0.98 | 0.86 | 0.85 | 0.85 | 0.99 | 0.85 | 0.85 | 0.85 |
time (sec) |
N/A | 0.247 | 0.002 | 0.185 | 0.207 | 0.215 | 0.032 | 0.308 | 0.000 | 0.050 |
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 | 112 | 112 | 126 | 113 | 112 | 112 | 128 | 112 | 112 | 112 |
N.S. |
1 | 1.00 | 1.12 | 1.01 | 1.00 | 1.00 | 1.14 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.231 | 0.002 | 0.129 | 0.206 | 0.220 | 0.034 | 0.310 | 0.001 | 0.078 |
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 | 98 | 98 | 132 | 113 | 112 | 112 | 133 | 112 | 112 | 112 |
N.S. |
1 | 1.00 | 1.35 | 1.15 | 1.14 | 1.14 | 1.36 | 1.14 | 1.14 | 1.14 |
time (sec) |
N/A | 0.218 | 0.002 | 0.130 | 0.214 | 0.215 | 0.031 | 0.301 | 0.000 | 0.079 |
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 | 81 | 81 | 130 | 113 | 112 | 112 | 131 | 112 | 112 | 112 |
N.S. |
1 | 1.00 | 1.60 | 1.40 | 1.38 | 1.38 | 1.62 | 1.38 | 1.38 | 1.38 |
time (sec) |
N/A | 0.202 | 0.002 | 0.170 | 0.204 | 0.224 | 0.030 | 0.312 | 0.000 | 0.079 |
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 | 64 | 64 | 128 | 113 | 112 | 112 | 129 | 112 | 112 | 112 |
N.S. |
1 | 1.00 | 2.00 | 1.77 | 1.75 | 1.75 | 2.02 | 1.75 | 1.75 | 1.75 |
time (sec) |
N/A | 0.187 | 0.002 | 0.171 | 0.208 | 0.218 | 0.034 | 0.309 | 0.000 | 0.078 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 47 | 47 | 126 | 113 | 112 | 112 | 128 | 112 | 112 | 31 |
N.S. |
1 | 1.00 | 2.68 | 2.40 | 2.38 | 2.38 | 2.72 | 2.38 | 2.38 | 0.66 |
time (sec) |
N/A | 0.173 | 0.002 | 0.165 | 0.202 | 0.220 | 0.034 | 0.290 | 0.000 | 0.040 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 30 | 128 | 113 | 112 | 112 | 129 | 112 | 112 | 25 |
N.S. |
1 | 1.00 | 4.27 | 3.77 | 3.73 | 3.73 | 4.30 | 3.73 | 3.73 | 0.83 |
time (sec) |
N/A | 0.149 | 0.002 | 0.176 | 0.209 | 0.211 | 0.045 | 0.299 | 0.000 | 0.060 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 14 | 13 | 12 | 108 | 114 | 12 | 109 | 108 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 0.86 | 7.71 | 8.14 | 0.86 | 7.79 | 7.71 |
time (sec) |
N/A | 0.122 | 0.001 | 0.199 | 0.210 | 0.214 | 0.034 | 0.303 | 0.000 | 0.084 |
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 | 122 | 122 | 122 | 109 | 108 | 108 | 126 | 109 | 108 | 108 |
N.S. |
1 | 1.00 | 1.00 | 0.89 | 0.89 | 0.89 | 1.03 | 0.89 | 0.89 | 0.89 |
time (sec) |
N/A | 0.219 | 0.003 | 0.227 | 0.210 | 0.210 | 0.082 | 0.291 | 0.000 | 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 | 115 | 115 | 115 | 110 | 109 | 114 | 117 | 110 | 114 | 109 |
N.S. |
1 | 1.00 | 1.00 | 0.96 | 0.95 | 0.99 | 1.02 | 0.96 | 0.99 | 0.95 |
time (sec) |
N/A | 0.227 | 0.007 | 0.185 | 0.197 | 0.214 | 0.108 | 0.286 | 0.000 | 0.077 |
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 | 119 | 119 | 119 | 110 | 108 | 114 | 122 | 109 | 114 | 110 |
N.S. |
1 | 1.00 | 1.00 | 0.92 | 0.91 | 0.96 | 1.03 | 0.92 | 0.96 | 0.92 |
time (sec) |
N/A | 0.222 | 0.004 | 0.137 | 0.216 | 0.218 | 0.133 | 0.290 | 0.000 | 0.042 |
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 | 115 | 115 | 115 | 110 | 108 | 114 | 119 | 109 | 114 | 110 |
N.S. |
1 | 1.00 | 1.00 | 0.96 | 0.94 | 0.99 | 1.03 | 0.95 | 0.99 | 0.96 |
time (sec) |
N/A | 0.224 | 0.007 | 0.143 | 0.208 | 0.216 | 0.141 | 0.290 | 0.000 | 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 | 119 | 119 | 119 | 110 | 110 | 114 | 121 | 111 | 114 | 110 |
N.S. |
1 | 1.00 | 1.00 | 0.92 | 0.92 | 0.96 | 1.02 | 0.93 | 0.96 | 0.92 |
time (sec) |
N/A | 0.227 | 0.007 | 0.209 | 0.203 | 0.214 | 0.177 | 0.285 | 0.000 | 0.070 |
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 | 117 | 117 | 117 | 110 | 110 | 114 | 121 | 111 | 114 | 110 |
N.S. |
1 | 1.00 | 1.00 | 0.94 | 0.94 | 0.97 | 1.03 | 0.95 | 0.97 | 0.94 |
time (sec) |
N/A | 0.226 | 0.008 | 0.176 | 0.208 | 0.222 | 0.210 | 0.291 | 0.000 | 0.064 |
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 | 119 | 119 | 119 | 110 | 110 | 114 | 122 | 111 | 114 | 110 |
N.S. |
1 | 1.00 | 1.00 | 0.92 | 0.92 | 0.96 | 1.03 | 0.93 | 0.96 | 0.92 |
time (sec) |
N/A | 0.229 | 0.004 | 0.192 | 0.202 | 0.220 | 0.256 | 0.286 | 0.000 | 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 | 115 | 115 | 115 | 110 | 110 | 114 | 119 | 111 | 114 | 110 |
N.S. |
1 | 1.00 | 1.00 | 0.96 | 0.96 | 0.99 | 1.03 | 0.97 | 0.99 | 0.96 |
time (sec) |
N/A | 0.230 | 0.007 | 0.191 | 0.203 | 0.223 | 0.286 | 0.307 | 0.001 | 0.065 |
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 | 119 | 119 | 119 | 110 | 110 | 114 | 119 | 111 | 114 | 110 |
N.S. |
1 | 1.00 | 1.00 | 0.92 | 0.92 | 0.96 | 1.00 | 0.93 | 0.96 | 0.92 |
time (sec) |
N/A | 0.231 | 0.004 | 0.147 | 0.206 | 0.222 | 0.340 | 0.304 | 0.000 | 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 | 114 | 114 | 114 | 109 | 109 | 114 | 117 | 110 | 114 | 114 |
N.S. |
1 | 1.00 | 1.00 | 0.96 | 0.96 | 1.00 | 1.03 | 0.96 | 1.00 | 1.00 |
time (sec) |
N/A | 0.228 | 0.005 | 0.174 | 0.204 | 0.216 | 0.380 | 0.287 | 0.000 | 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 | 124 | 124 | 124 | 111 | 111 | 114 | 119 | 112 | 114 | 111 |
N.S. |
1 | 1.00 | 1.00 | 0.90 | 0.90 | 0.92 | 0.96 | 0.90 | 0.92 | 0.90 |
time (sec) |
N/A | 0.228 | 0.004 | 0.176 | 0.193 | 0.224 | 0.469 | 0.300 | 0.000 | 0.046 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 17 | 114 | 111 | 110 | 110 | 119 | 110 | 112 | 110 |
N.S. |
1 | 1.00 | 6.71 | 6.53 | 6.47 | 6.47 | 7.00 | 6.47 | 6.59 | 6.47 |
time (sec) |
N/A | 0.126 | 0.007 | 0.168 | 0.214 | 0.214 | 0.531 | 0.284 | 0.000 | 0.099 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 36 | 128 | 112 | 112 | 112 | 121 | 112 | 112 | 23 |
N.S. |
1 | 1.00 | 3.56 | 3.11 | 3.11 | 3.11 | 3.36 | 3.11 | 3.11 | 0.64 |
time (sec) |
N/A | 0.137 | 0.004 | 0.175 | 0.205 | 0.220 | 0.528 | 0.294 | 0.000 | 0.078 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 56 | 62 | 126 | 112 | 112 | 112 | 121 | 112 | 112 | 112 |
N.S. |
1 | 1.11 | 2.25 | 2.00 | 2.00 | 2.00 | 2.16 | 2.00 | 2.00 | 2.00 |
time (sec) |
N/A | 0.151 | 0.008 | 0.173 | 0.203 | 0.220 | 0.574 | 0.295 | 0.000 | 0.092 |
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 | 76 | 88 | 128 | 112 | 112 | 112 | 121 | 112 | 112 | 112 |
N.S. |
1 | 1.16 | 1.68 | 1.47 | 1.47 | 1.47 | 1.59 | 1.47 | 1.47 | 1.47 |
time (sec) |
N/A | 0.165 | 0.006 | 0.173 | 0.214 | 0.224 | 0.562 | 0.293 | 0.001 | 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 | 96 | 114 | 130 | 112 | 112 | 112 | 121 | 112 | 112 | 112 |
N.S. |
1 | 1.19 | 1.35 | 1.17 | 1.17 | 1.17 | 1.26 | 1.17 | 1.17 | 1.17 |
time (sec) |
N/A | 0.181 | 0.008 | 0.173 | 0.204 | 0.213 | 0.610 | 0.292 | 0.000 | 0.090 |
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 | 116 | 140 | 132 | 112 | 112 | 112 | 121 | 112 | 112 | 112 |
N.S. |
1 | 1.21 | 1.14 | 0.97 | 0.97 | 0.97 | 1.04 | 0.97 | 0.97 | 0.97 |
time (sec) |
N/A | 0.190 | 0.004 | 0.173 | 0.206 | 0.216 | 0.646 | 0.290 | 0.001 | 0.095 |
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 | 136 | 166 | 126 | 112 | 112 | 112 | 121 | 112 | 112 | 112 |
N.S. |
1 | 1.22 | 0.93 | 0.82 | 0.82 | 0.82 | 0.89 | 0.82 | 0.82 | 0.82 |
time (sec) |
N/A | 0.203 | 0.007 | 0.172 | 0.206 | 0.214 | 0.659 | 0.294 | 0.000 | 0.188 |
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 | 130 | 130 | 130 | 112 | 112 | 112 | 121 | 112 | 112 | 112 |
N.S. |
1 | 1.00 | 1.00 | 0.86 | 0.86 | 0.86 | 0.93 | 0.86 | 0.86 | 0.86 |
time (sec) |
N/A | 0.225 | 0.004 | 0.173 | 0.201 | 0.227 | 0.684 | 0.294 | 0.000 | 0.103 |
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 | 126 | 126 | 126 | 112 | 112 | 112 | 121 | 112 | 112 | 111 |
N.S. |
1 | 1.00 | 1.00 | 0.89 | 0.89 | 0.89 | 0.96 | 0.89 | 0.89 | 0.88 |
time (sec) |
N/A | 0.227 | 0.005 | 0.172 | 0.195 | 0.224 | 0.701 | 0.288 | 0.000 | 0.152 |
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 | 15 | 15 | 14 | 12 | 13 | 12 | 12 | 13 | 11 | 11 |
N.S. |
1 | 1.00 | 0.93 | 0.80 | 0.87 | 0.80 | 0.80 | 0.87 | 0.73 | 0.73 |
time (sec) |
N/A | 0.124 | 0.000 | 0.004 | 0.202 | 0.193 | 0.015 | 0.288 | 0.000 | 0.023 |
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 | 20 | 20 | 19 | 17 | 18 | 27 | 22 | 18 | 23 | 16 |
N.S. |
1 | 1.00 | 0.95 | 0.85 | 0.90 | 1.35 | 1.10 | 0.90 | 1.15 | 0.80 |
time (sec) |
N/A | 0.131 | 0.001 | 0.004 | 0.203 | 0.219 | 0.022 | 0.298 | 0.000 | 0.080 |
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 | 70 | 70 | 70 | 63 | 64 | 63 | 61 | 65 | 63 | 62 |
N.S. |
1 | 1.00 | 1.00 | 0.90 | 0.91 | 0.90 | 0.87 | 0.93 | 0.90 | 0.89 |
time (sec) |
N/A | 0.193 | 0.004 | 0.144 | 0.198 | 0.226 | 0.065 | 0.305 | 0.001 | 0.092 |
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 | 57 | 57 | 57 | 52 | 52 | 52 | 49 | 53 | 52 | 51 |
N.S. |
1 | 1.00 | 1.00 | 0.91 | 0.91 | 0.91 | 0.86 | 0.93 | 0.91 | 0.89 |
time (sec) |
N/A | 0.178 | 0.004 | 0.190 | 0.198 | 0.217 | 0.080 | 0.302 | 0.000 | 0.108 |
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 | 44 | 44 | 44 | 41 | 42 | 41 | 37 | 43 | 41 | 40 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 0.95 | 0.93 | 0.84 | 0.98 | 0.93 | 0.91 |
time (sec) |
N/A | 0.168 | 0.003 | 0.179 | 0.203 | 0.219 | 0.065 | 0.306 | 0.000 | 0.042 |
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 | 31 | 31 | 31 | 30 | 29 | 29 | 26 | 30 | 29 | 29 |
N.S. |
1 | 1.00 | 1.00 | 0.97 | 0.94 | 0.94 | 0.84 | 0.97 | 0.94 | 0.94 |
time (sec) |
N/A | 0.157 | 0.002 | 0.173 | 0.198 | 0.214 | 0.053 | 0.288 | 0.000 | 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 | 18 | 18 | 18 | 19 | 18 | 17 | 14 | 19 | 17 | 18 |
N.S. |
1 | 1.00 | 1.00 | 1.06 | 1.00 | 0.94 | 0.78 | 1.06 | 0.94 | 1.00 |
time (sec) |
N/A | 0.145 | 0.002 | 0.185 | 0.211 | 0.217 | 0.046 | 0.314 | 0.000 | 0.091 |
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 | 10 | 10 | 10 | 11 | 10 | 10 | 7 | 11 | 10 | 10 |
N.S. |
1 | 1.00 | 1.00 | 1.10 | 1.00 | 1.00 | 0.70 | 1.10 | 1.00 | 1.00 |
time (sec) |
N/A | 0.122 | 0.000 | 0.173 | 0.216 | 0.214 | 0.019 | 0.307 | 0.000 | 0.022 |
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 | 18 | 18 | 18 | 16 | 18 | 16 | 10 | 20 | 15 | 15 |
N.S. |
1 | 1.00 | 1.00 | 0.89 | 1.00 | 0.89 | 0.56 | 1.11 | 0.83 | 0.83 |
time (sec) |
N/A | 0.131 | 0.002 | 0.174 | 0.211 | 0.224 | 0.071 | 0.280 | 0.000 | 0.095 |
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 | 28 | 28 | 28 | 26 | 28 | 26 | 19 | 30 | 26 | 25 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 1.00 | 0.93 | 0.68 | 1.07 | 0.93 | 0.89 |
time (sec) |
N/A | 0.152 | 0.003 | 0.181 | 0.208 | 0.221 | 0.099 | 0.294 | 0.001 | 0.059 |
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 | 41 | 40 | 41 | 31 | 45 | 43 | 38 |
N.S. |
1 | 1.00 | 1.00 | 0.98 | 0.95 | 0.98 | 0.74 | 1.07 | 1.02 | 0.90 |
time (sec) |
N/A | 0.165 | 0.004 | 0.183 | 0.207 | 0.229 | 0.107 | 0.307 | 0.000 | 0.070 |
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 | 56 | 56 | 56 | 53 | 51 | 54 | 44 | 56 | 54 | 48 |
N.S. |
1 | 1.00 | 1.00 | 0.95 | 0.91 | 0.96 | 0.79 | 1.00 | 0.96 | 0.86 |
time (sec) |
N/A | 0.177 | 0.004 | 0.183 | 0.208 | 0.222 | 0.110 | 0.285 | 0.000 | 0.115 |
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 | 68 | 68 | 68 | 63 | 62 | 65 | 56 | 67 | 65 | 60 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 0.91 | 0.96 | 0.82 | 0.99 | 0.96 | 0.88 |
time (sec) |
N/A | 0.187 | 0.004 | 0.185 | 0.195 | 0.218 | 0.157 | 0.300 | 0.000 | 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 | 81 | 81 | 77 | 78 | 82 | 96 | 78 | 103 | 94 | 83 |
N.S. |
1 | 1.00 | 0.95 | 0.96 | 1.01 | 1.19 | 0.96 | 1.27 | 1.16 | 1.02 |
time (sec) |
N/A | 0.216 | 0.016 | 0.181 | 0.217 | 0.221 | 0.122 | 0.300 | 0.000 | 0.145 |
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 | 72 | 72 | 66 | 67 | 70 | 85 | 71 | 90 | 83 | 72 |
N.S. |
1 | 1.00 | 0.92 | 0.93 | 0.97 | 1.18 | 0.99 | 1.25 | 1.15 | 1.00 |
time (sec) |
N/A | 0.204 | 0.013 | 0.181 | 0.203 | 0.216 | 0.106 | 0.288 | 0.001 | 0.115 |
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 | 58 | 58 | 54 | 57 | 59 | 73 | 54 | 79 | 71 | 62 |
N.S. |
1 | 1.00 | 0.93 | 0.98 | 1.02 | 1.26 | 0.93 | 1.36 | 1.22 | 1.07 |
time (sec) |
N/A | 0.188 | 0.014 | 0.174 | 0.209 | 0.215 | 0.101 | 0.308 | 0.000 | 0.098 |
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 | 46 | 46 | 43 | 45 | 47 | 62 | 44 | 66 | 60 | 50 |
N.S. |
1 | 1.00 | 0.93 | 0.98 | 1.02 | 1.35 | 0.96 | 1.43 | 1.30 | 1.09 |
time (sec) |
N/A | 0.173 | 0.009 | 0.178 | 0.197 | 0.225 | 0.089 | 0.305 | 0.000 | 0.097 |
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 | 33 | 33 | 29 | 34 | 36 | 47 | 31 | 50 | 46 | 36 |
N.S. |
1 | 1.00 | 0.88 | 1.03 | 1.09 | 1.42 | 0.94 | 1.52 | 1.39 | 1.09 |
time (sec) |
N/A | 0.161 | 0.009 | 0.176 | 0.203 | 0.222 | 0.091 | 0.285 | 0.001 | 0.088 |
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 | 23 | 23 | 20 | 24 | 26 | 28 | 20 | 42 | 33 | 23 |
N.S. |
1 | 1.00 | 0.87 | 1.04 | 1.13 | 1.22 | 0.87 | 1.83 | 1.43 | 1.00 |
time (sec) |
N/A | 0.153 | 0.005 | 0.188 | 0.191 | 0.231 | 0.067 | 0.299 | 0.000 | 0.042 |
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 | 12 | 12 | 12 | 13 | 12 | 13 | 10 | 12 | 12 | 12 |
N.S. |
1 | 1.00 | 1.00 | 1.08 | 1.00 | 1.08 | 0.83 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.122 | 0.001 | 0.206 | 0.202 | 0.218 | 0.069 | 0.302 | 0.000 | 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 | 29 | 29 | 24 | 30 | 28 | 39 | 22 | 38 | 44 | 26 |
N.S. |
1 | 1.00 | 0.83 | 1.03 | 0.97 | 1.34 | 0.76 | 1.31 | 1.52 | 0.90 |
time (sec) |
N/A | 0.156 | 0.008 | 0.173 | 0.214 | 0.219 | 0.113 | 0.285 | 0.000 | 0.132 |
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 | 35 | 43 | 45 | 63 | 37 | 52 | 70 | 45 |
N.S. |
1 | 1.00 | 0.83 | 1.02 | 1.07 | 1.50 | 0.88 | 1.24 | 1.67 | 1.07 |
time (sec) |
N/A | 0.170 | 0.027 | 0.183 | 0.204 | 0.220 | 0.138 | 0.296 | 0.000 | 0.132 |
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 | 58 | 58 | 53 | 57 | 64 | 86 | 54 | 74 | 86 | 57 |
N.S. |
1 | 1.00 | 0.91 | 0.98 | 1.10 | 1.48 | 0.93 | 1.28 | 1.48 | 0.98 |
time (sec) |
N/A | 0.184 | 0.033 | 0.182 | 0.201 | 0.231 | 0.199 | 0.304 | 0.000 | 0.120 |
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 | 69 | 69 | 66 | 68 | 73 | 95 | 66 | 90 | 97 | 69 |
N.S. |
1 | 1.00 | 0.96 | 0.99 | 1.06 | 1.38 | 0.96 | 1.30 | 1.41 | 1.00 |
time (sec) |
N/A | 0.200 | 0.039 | 0.178 | 0.204 | 0.220 | 0.174 | 0.287 | 0.001 | 0.086 |
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 | 84 | 84 | 79 | 79 | 86 | 108 | 80 | 104 | 108 | 79 |
N.S. |
1 | 1.00 | 0.94 | 0.94 | 1.02 | 1.29 | 0.95 | 1.24 | 1.29 | 0.94 |
time (sec) |
N/A | 0.217 | 0.031 | 0.183 | 0.207 | 0.234 | 0.192 | 0.294 | 0.000 | 0.138 |
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 | 89 | 90 | 103 | 129 | 109 | 95 | 131 | 91 |
N.S. |
1 | 1.00 | 0.90 | 0.91 | 1.04 | 1.30 | 1.10 | 0.96 | 1.32 | 0.92 |
time (sec) |
N/A | 0.237 | 0.017 | 0.181 | 0.202 | 0.231 | 0.191 | 0.290 | 0.000 | 0.266 |
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 | 86 | 86 | 77 | 79 | 91 | 117 | 92 | 83 | 119 | 78 |
N.S. |
1 | 1.00 | 0.90 | 0.92 | 1.06 | 1.36 | 1.07 | 0.97 | 1.38 | 0.91 |
time (sec) |
N/A | 0.217 | 0.016 | 0.181 | 0.206 | 0.213 | 0.197 | 0.306 | 0.000 | 0.180 |
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 | 77 | 77 | 67 | 68 | 81 | 107 | 85 | 73 | 109 | 67 |
N.S. |
1 | 1.00 | 0.87 | 0.88 | 1.05 | 1.39 | 1.10 | 0.95 | 1.42 | 0.87 |
time (sec) |
N/A | 0.202 | 0.014 | 0.174 | 0.212 | 0.218 | 0.182 | 0.289 | 0.000 | 0.138 |
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 | 64 | 64 | 55 | 57 | 69 | 95 | 70 | 61 | 97 | 54 |
N.S. |
1 | 1.00 | 0.86 | 0.89 | 1.08 | 1.48 | 1.09 | 0.95 | 1.52 | 0.84 |
time (sec) |
N/A | 0.194 | 0.013 | 0.179 | 0.207 | 0.216 | 0.154 | 0.296 | 0.000 | 0.089 |
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 | 50 | 50 | 40 | 45 | 57 | 83 | 58 | 44 | 85 | 43 |
N.S. |
1 | 1.00 | 0.80 | 0.90 | 1.14 | 1.66 | 1.16 | 0.88 | 1.70 | 0.86 |
time (sec) |
N/A | 0.189 | 0.027 | 0.170 | 0.203 | 0.219 | 0.138 | 0.293 | 0.000 | 0.159 |
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 | 33 | 36 | 48 | 61 | 46 | 37 | 71 | 46 |
N.S. |
1 | 1.00 | 0.80 | 0.88 | 1.17 | 1.49 | 1.12 | 0.90 | 1.73 | 1.12 |
time (sec) |
N/A | 0.177 | 0.010 | 0.179 | 0.219 | 0.212 | 0.102 | 0.290 | 0.000 | 0.106 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 17 | 20 | 19 | 32 | 32 | 32 | 18 | 26 | 32 |
N.S. |
1 | 1.00 | 1.18 | 1.12 | 1.88 | 1.88 | 1.88 | 1.06 | 1.53 | 1.88 |
time (sec) |
N/A | 0.126 | 0.004 | 0.182 | 0.201 | 0.221 | 0.104 | 0.279 | 0.000 | 0.096 |
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 | 14 | 14 | 14 | 13 | 12 | 24 | 26 | 12 | 23 | 26 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 0.86 | 1.71 | 1.86 | 0.86 | 1.64 | 1.86 |
time (sec) |
N/A | 0.122 | 0.001 | 0.179 | 0.226 | 0.210 | 0.107 | 0.291 | 0.000 | 0.089 |
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 | 43 | 43 | 37 | 41 | 51 | 80 | 46 | 43 | 97 | 43 |
N.S. |
1 | 1.00 | 0.86 | 0.95 | 1.19 | 1.86 | 1.07 | 1.00 | 2.26 | 1.00 |
time (sec) |
N/A | 0.170 | 0.018 | 0.184 | 0.221 | 0.221 | 0.147 | 0.302 | 0.001 | 0.119 |
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 | 57 | 57 | 53 | 56 | 69 | 109 | 66 | 60 | 119 | 63 |
N.S. |
1 | 1.00 | 0.93 | 0.98 | 1.21 | 1.91 | 1.16 | 1.05 | 2.09 | 1.11 |
time (sec) |
N/A | 0.183 | 0.032 | 0.176 | 0.211 | 0.218 | 0.198 | 0.289 | 0.000 | 0.132 |
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 | 76 | 76 | 68 | 72 | 86 | 130 | 78 | 73 | 138 | 79 |
N.S. |
1 | 1.00 | 0.89 | 0.95 | 1.13 | 1.71 | 1.03 | 0.96 | 1.82 | 1.04 |
time (sec) |
N/A | 0.201 | 0.034 | 0.185 | 0.215 | 0.222 | 0.208 | 0.306 | 0.000 | 0.303 |
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 | 89 | 89 | 79 | 83 | 97 | 141 | 92 | 86 | 149 | 91 |
N.S. |
1 | 1.00 | 0.89 | 0.93 | 1.09 | 1.58 | 1.03 | 0.97 | 1.67 | 1.02 |
time (sec) |
N/A | 0.211 | 0.043 | 0.173 | 0.235 | 0.224 | 0.216 | 0.289 | 0.001 | 0.145 |
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 | 97 | 97 | 90 | 94 | 108 | 152 | 102 | 97 | 160 | 101 |
N.S. |
1 | 1.00 | 0.93 | 0.97 | 1.11 | 1.57 | 1.05 | 1.00 | 1.65 | 1.04 |
time (sec) |
N/A | 0.228 | 0.035 | 0.179 | 0.202 | 0.222 | 0.265 | 0.280 | 0.000 | 0.100 |
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 | 114 | 114 | 101 | 99 | 125 | 162 | 131 | 106 | 166 | 103 |
N.S. |
1 | 1.00 | 0.89 | 0.87 | 1.10 | 1.42 | 1.15 | 0.93 | 1.46 | 0.90 |
time (sec) |
N/A | 0.254 | 0.022 | 0.181 | 0.197 | 0.221 | 0.264 | 0.303 | 0.001 | 0.405 |
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 | 105 | 105 | 90 | 88 | 114 | 151 | 119 | 95 | 155 | 90 |
N.S. |
1 | 1.00 | 0.86 | 0.84 | 1.09 | 1.44 | 1.13 | 0.90 | 1.48 | 0.86 |
time (sec) |
N/A | 0.247 | 0.019 | 0.185 | 0.214 | 0.220 | 0.245 | 0.297 | 0.000 | 0.239 |
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 | 77 | 102 | 139 | 107 | 83 | 143 | 79 |
N.S. |
1 | 1.00 | 1.00 | 0.86 | 1.13 | 1.54 | 1.19 | 0.92 | 1.59 | 0.88 |
time (sec) |
N/A | 0.233 | 0.014 | 0.171 | 0.200 | 0.222 | 0.288 | 0.287 | 0.001 | 0.167 |
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 | 81 | 81 | 68 | 66 | 91 | 129 | 94 | 72 | 133 | 66 |
N.S. |
1 | 1.00 | 0.84 | 0.81 | 1.12 | 1.59 | 1.16 | 0.89 | 1.64 | 0.81 |
time (sec) |
N/A | 0.222 | 0.024 | 0.171 | 0.201 | 0.218 | 0.235 | 0.297 | 0.000 | 0.135 |
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 | 65 | 65 | 51 | 54 | 79 | 116 | 82 | 55 | 120 | 55 |
N.S. |
1 | 1.00 | 0.78 | 0.83 | 1.22 | 1.78 | 1.26 | 0.85 | 1.85 | 0.85 |
time (sec) |
N/A | 0.198 | 0.030 | 0.178 | 0.224 | 0.222 | 0.199 | 0.290 | 0.000 | 0.194 |
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 | 58 | 58 | 44 | 47 | 70 | 94 | 70 | 46 | 108 | 45 |
N.S. |
1 | 1.00 | 0.76 | 0.81 | 1.21 | 1.62 | 1.21 | 0.79 | 1.86 | 0.78 |
time (sec) |
N/A | 0.185 | 0.011 | 0.179 | 0.205 | 0.221 | 0.154 | 0.287 | 0.001 | 0.078 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 17 | 31 | 30 | 54 | 54 | 56 | 29 | 37 | 56 |
N.S. |
1 | 1.00 | 1.82 | 1.76 | 3.18 | 3.18 | 3.29 | 1.71 | 2.18 | 3.29 |
time (sec) |
N/A | 0.141 | 0.010 | 0.180 | 0.246 | 0.221 | 0.126 | 0.299 | 0.001 | 0.094 |
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 | 30 | 30 | 20 | 19 | 43 | 43 | 44 | 18 | 42 | 44 |
N.S. |
1 | 1.00 | 0.67 | 0.63 | 1.43 | 1.43 | 1.47 | 0.60 | 1.40 | 1.47 |
time (sec) |
N/A | 0.160 | 0.005 | 0.178 | 0.197 | 0.218 | 0.120 | 0.289 | 0.000 | 0.085 |