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 | 18 | 17 | 17 | 16 | 15 | 15 | 15 | 17 | 17 | 15 |
N.S. |
1 | 0.94 | 0.94 | 0.89 | 0.83 | 0.83 | 0.83 | 0.94 | 0.94 | 0.83 |
time (sec) |
N/A | 0.231 | 0.005 | 0.262 | 0.030 | 0.060 | 0.659 | 0.109 | 0.161 | 0.125 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | C | A | A | F(-1) | A | B | F(-1) |
verified | N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 29 | 443 | 33 | 26 | 0 | 28 | 27 | 0 |
N.S. |
1 | 0.00 | 1.00 | 15.28 | 1.14 | 0.90 | 0.00 | 0.97 | 0.93 | 0.00 |
time (sec) |
N/A | 0.000 | 4.487 | 0.410 | 0.210 | 0.074 | 0.000 | 2.027 | 0.179 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 17 | 17 | 16 | 17 | 20 | 12 | 20 | 22 | 15 |
N.S. |
1 | 0.52 | 0.52 | 0.48 | 0.52 | 0.61 | 0.36 | 0.61 | 0.67 | 0.45 |
time (sec) |
N/A | 0.359 | 0.011 | 0.306 | 0.062 | 0.074 | 0.076 | 0.115 | 0.195 | 1.714 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | B | A | B | A | B | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 153 | 43 | 27 | 99 | 33 | 48 | 70 | 30 | 26 |
N.S. |
1 | 7.65 | 2.15 | 1.35 | 4.95 | 1.65 | 2.40 | 3.50 | 1.50 | 1.30 |
time (sec) |
N/A | 1.073 | 0.104 | 0.839 | 0.081 | 0.067 | 0.152 | 0.113 | 0.208 | 1.773 |
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 | 19 | 33 | 15 | 14 | 13 | 13 | 15 | 13 | 18 | 14 |
N.S. |
1 | 1.74 | 0.79 | 0.74 | 0.68 | 0.68 | 0.79 | 0.68 | 0.95 | 0.74 |
time (sec) |
N/A | 0.201 | 0.011 | 0.168 | 0.086 | 0.072 | 0.128 | 0.117 | 0.173 | 0.054 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | B | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 15 | 17 | 24 | 16 | 31 | 16 | 18 | 14 |
N.S. |
1 | 1.00 | 1.00 | 1.13 | 1.60 | 1.07 | 2.07 | 1.07 | 1.20 | 0.93 |
time (sec) |
N/A | 0.187 | 0.024 | 0.277 | 0.061 | 0.060 | 0.067 | 0.108 | 0.170 | 0.054 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | B | B | B | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 0 | 19 | 63 | 43 | 48 | 49 | 109 | 46 | 17 |
N.S. |
1 | 0.00 | 1.00 | 3.32 | 2.26 | 2.53 | 2.58 | 5.74 | 2.42 | 0.89 |
time (sec) |
N/A | 0.000 | 0.069 | 0.752 | 0.151 | 0.065 | 0.216 | 0.121 | 0.169 | 1.753 |
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 | 14 | 11 | 11 | 10 | 12 | 5 | 10 | 14 | 10 |
N.S. |
1 | 1.17 | 0.92 | 0.92 | 0.83 | 1.00 | 0.42 | 0.83 | 1.17 | 0.83 |
time (sec) |
N/A | 0.180 | 0.008 | 0.098 | 0.036 | 0.065 | 0.040 | 0.112 | 0.173 | 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 | 26 | 21 | 21 | 21 | 20 | 20 | 20 | 20 | 21 | 20 |
N.S. |
1 | 0.81 | 0.81 | 0.81 | 0.77 | 0.77 | 0.77 | 0.77 | 0.81 | 0.77 |
time (sec) |
N/A | 0.521 | 0.037 | 1.302 | 0.038 | 0.073 | 0.109 | 0.114 | 0.188 | 1.728 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 23 | 26 | 27 | 27 | 22 | 27 | 31 | 67 |
N.S. |
1 | 0.00 | 0.88 | 1.00 | 1.04 | 1.04 | 0.85 | 1.04 | 1.19 | 2.58 |
time (sec) |
N/A | 0.000 | 0.398 | 0.282 | 0.091 | 0.065 | 0.100 | 0.127 | 0.192 | 1.764 |
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 | 15 | 15 | 15 | 15 | 14 | 14 |
N.S. |
1 | 1.00 | 1.00 | 1.08 | 1.25 | 1.25 | 1.25 | 1.25 | 1.17 | 1.17 |
time (sec) |
N/A | 0.328 | 0.030 | 0.268 | 0.124 | 0.065 | 0.099 | 0.110 | 0.179 | 1.805 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | B | B | B | B | B | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 587 | 92 | 80 | 349 | 114 | 88 | 753 | 181 | 80 |
N.S. |
1 | 17.79 | 2.79 | 2.42 | 10.58 | 3.45 | 2.67 | 22.82 | 5.48 | 2.42 |
time (sec) |
N/A | 13.678 | 5.757 | 3.434 | 0.208 | 0.072 | 0.149 | 0.350 | 0.183 | 2.042 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | F(-1) | F | B | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 28 | 36 | 29 | 28 | 0 | 0 | 37 | 0 |
N.S. |
1 | 0.00 | 1.00 | 1.29 | 1.04 | 1.00 | 0.00 | 0.00 | 1.32 | 0.00 |
time (sec) |
N/A | 0.000 | 0.050 | 28.645 | 0.217 | 0.064 | 0.000 | 0.000 | 0.218 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 31 | 31 | 32 | 29 | 34 | 31 | 34 | 56 | 32 |
N.S. |
1 | 1.19 | 1.19 | 1.23 | 1.12 | 1.31 | 1.19 | 1.31 | 2.15 | 1.23 |
time (sec) |
N/A | 0.701 | 0.210 | 1.875 | 0.172 | 0.071 | 0.135 | 0.134 | 200.029 | 1.904 |
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 | 27 | 23 | 23 | 19 | 20 | 27 | 17 | 20 | 24 | 20 |
N.S. |
1 | 0.85 | 0.85 | 0.70 | 0.74 | 1.00 | 0.63 | 0.74 | 0.89 | 0.74 |
time (sec) |
N/A | 0.326 | 0.007 | 0.421 | 0.028 | 0.057 | 0.060 | 0.105 | 0.189 | 0.062 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | B | B | F(-1) | F(-1) | F | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 0 | 70 | 153 | 260 | 239 | 0 | 0 | 544 | 2084 |
N.S. |
1 | 0.00 | 1.94 | 4.25 | 7.22 | 6.64 | 0.00 | 0.00 | 15.11 | 57.89 |
time (sec) |
N/A | 0.000 | 10.377 | 0.212 | 2.717 | 0.112 | 0.000 | 0.000 | 200.021 | 5.524 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | B | B | F(-2) | B | B | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 55 | 76 | 92 | 71 | 0 | 95 | 82 | 0 |
N.S. |
1 | 0.00 | 1.77 | 2.45 | 2.97 | 2.29 | 0.00 | 3.06 | 2.65 | 0.00 |
time (sec) |
N/A | 0.000 | 0.234 | 34.659 | 0.154 | 0.073 | 0.000 | 2.883 | 0.190 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 0 | 33 | 45 | 44 | 43 | 46 | 41 | 54 | 34 |
N.S. |
1 | 0.00 | 0.94 | 1.29 | 1.26 | 1.23 | 1.31 | 1.17 | 1.54 | 0.97 |
time (sec) |
N/A | 0.000 | 0.028 | 0.649 | 0.029 | 0.067 | 1.119 | 0.125 | 0.175 | 2.107 |
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 | 19 | 19 | 19 | 20 | 19 | 20 | 17 | 19 | 22 | 15 |
N.S. |
1 | 1.00 | 1.00 | 1.05 | 1.00 | 1.05 | 0.89 | 1.00 | 1.16 | 0.79 |
time (sec) |
N/A | 0.201 | 0.002 | 0.302 | 0.037 | 0.061 | 0.033 | 0.110 | 0.204 | 1.848 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 25 | 22 | 22 | 22 | 17 | 22 | 27 | 21 |
N.S. |
1 | 0.00 | 0.96 | 0.85 | 0.85 | 0.85 | 0.65 | 0.85 | 1.04 | 0.81 |
time (sec) |
N/A | 0.000 | 0.217 | 2.703 | 0.149 | 0.065 | 0.083 | 0.121 | 0.193 | 1.972 |
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 | 5 | 5 | 5 | 5 | 4 | 4 | 3 | 4 | 7 | 4 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.80 | 0.80 | 0.60 | 0.80 | 1.40 | 0.80 |
time (sec) |
N/A | 0.187 | 0.010 | 0.077 | 0.025 | 0.060 | 0.041 | 0.114 | 0.180 | 0.016 |
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 | 29 | 19 | 17 | 42 | 40 | 27 | 16 | 32 | 16 |
N.S. |
1 | 1.45 | 0.95 | 0.85 | 2.10 | 2.00 | 1.35 | 0.80 | 1.60 | 0.80 |
time (sec) |
N/A | 0.331 | 0.010 | 0.220 | 0.025 | 0.062 | 0.274 | 0.105 | 0.186 | 0.105 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | A | B | A | B | F | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 129 | 71 | 40 | 83 | 44 | 76 | 0 | 30 | 39 |
N.S. |
1 | 4.78 | 2.63 | 1.48 | 3.07 | 1.63 | 2.81 | 0.00 | 1.11 | 1.44 |
time (sec) |
N/A | 1.009 | 0.095 | 1.141 | 0.092 | 0.065 | 0.223 | 0.000 | 0.183 | 1.913 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | B | B | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 47 | 47 | 84 | 41 | 44 | 63 | 35 | 31 |
N.S. |
1 | 0.00 | 1.81 | 1.81 | 3.23 | 1.58 | 1.69 | 2.42 | 1.35 | 1.19 |
time (sec) |
N/A | 0.000 | 0.208 | 0.825 | 0.193 | 0.067 | 0.214 | 0.139 | 0.181 | 2.137 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 25 | 21 | 28 | 28 | 17 | 52 | 30 | 18 |
N.S. |
1 | 0.00 | 1.14 | 0.95 | 1.27 | 1.27 | 0.77 | 2.36 | 1.36 | 0.82 |
time (sec) |
N/A | 0.000 | 0.159 | 0.446 | 0.170 | 0.067 | 0.083 | 0.122 | 0.177 | 2.218 |
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 | 22 | 20 | 20 | 19 | 18 | 16 | 15 | 18 | 18 | 18 |
N.S. |
1 | 0.91 | 0.91 | 0.86 | 0.82 | 0.73 | 0.68 | 0.82 | 0.82 | 0.82 |
time (sec) |
N/A | 0.193 | 0.002 | 0.182 | 0.024 | 0.063 | 0.060 | 0.102 | 0.189 | 1.863 |
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 | 29 | 18 | 14 | 18 | 31 | 16 |
N.S. |
1 | 1.00 | 1.00 | 1.06 | 1.61 | 1.00 | 0.78 | 1.00 | 1.72 | 0.89 |
time (sec) |
N/A | 0.480 | 0.016 | 0.493 | 0.155 | 0.063 | 0.081 | 0.106 | 0.178 | 2.334 |
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 | 27 | 29 | 23 | 20 | 26 | 17 | 20 | 24 | 23 |
N.S. |
1 | 0.96 | 1.04 | 0.82 | 0.71 | 0.93 | 0.61 | 0.71 | 0.86 | 0.82 |
time (sec) |
N/A | 0.276 | 0.010 | 0.408 | 0.037 | 0.057 | 0.073 | 0.112 | 0.179 | 0.067 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | B | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 25 | 23 | 21 | 21 | 32 | 21 | 21 | 34 |
N.S. |
1 | 0.00 | 1.09 | 1.00 | 0.91 | 0.91 | 1.39 | 0.91 | 0.91 | 1.48 |
time (sec) |
N/A | 0.000 | 1.147 | 0.109 | 0.075 | 0.071 | 0.132 | 0.120 | 0.190 | 1.930 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | A | F | A | A | B | B | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 63 | 25 | 0 | 22 | 24 | 114 | 25 | 0 |
N.S. |
1 | 0.00 | 2.10 | 0.83 | 0.00 | 0.73 | 0.80 | 3.80 | 0.83 | 0.00 |
time (sec) |
N/A | 0.000 | 0.383 | 0.684 | 0.000 | 0.070 | 2.265 | 0.146 | 0.197 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | F(-1) | A | F | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 29 | 24 | 23 | 20 | 0 | 20 | 133 | 20 |
N.S. |
1 | 0.00 | 1.16 | 0.96 | 0.92 | 0.80 | 0.00 | 0.80 | 5.32 | 0.80 |
time (sec) |
N/A | 0.000 | 0.928 | 0.062 | 0.285 | 0.079 | 0.000 | 1.205 | 200.017 | 5.893 |
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 | 21 | 22 | 22 | 20 | 18 | 25 | 27 | 25 | 21 | 19 |
N.S. |
1 | 1.05 | 1.05 | 0.95 | 0.86 | 1.19 | 1.29 | 1.19 | 1.00 | 0.90 |
time (sec) |
N/A | 0.601 | 0.022 | 0.342 | 0.100 | 0.063 | 0.124 | 0.111 | 0.217 | 1.899 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 16 | 16 | 16 | 22 | 16 | 14 | 17 | 20 | 14 |
N.S. |
1 | 0.80 | 0.80 | 0.80 | 1.10 | 0.80 | 0.70 | 0.85 | 1.00 | 0.70 |
time (sec) |
N/A | 0.335 | 0.074 | 0.370 | 0.063 | 0.063 | 0.061 | 0.116 | 0.194 | 0.062 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | B | B | B | B | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 75 | 55 | 51 | 86 | 54 | 49 | 57 | 35 | 21 |
N.S. |
1 | 3.75 | 2.75 | 2.55 | 4.30 | 2.70 | 2.45 | 2.85 | 1.75 | 1.05 |
time (sec) |
N/A | 0.296 | 0.015 | 0.454 | 0.034 | 0.066 | 0.087 | 0.116 | 0.221 | 1.864 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | B | F | B | B | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 83 | 27 | 63 | 0 | 62 | 73 | 66 | 78 | 66 |
N.S. |
1 | 3.07 | 1.00 | 2.33 | 0.00 | 2.30 | 2.70 | 2.44 | 2.89 | 2.44 |
time (sec) |
N/A | 0.606 | 0.103 | 25.327 | 0.000 | 0.069 | 0.252 | 0.118 | 0.203 | 1.976 |
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 | 26 | 27 | 25 | 27 | 26 | 28 | 20 | 28 | 31 | 28 |
N.S. |
1 | 1.04 | 0.96 | 1.04 | 1.00 | 1.08 | 0.77 | 1.08 | 1.19 | 1.08 |
time (sec) |
N/A | 0.207 | 0.021 | 0.242 | 0.032 | 0.064 | 0.064 | 0.123 | 0.180 | 1.824 |
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 | 26 | 32 | 25 | 27 | 29 | 26 | 26 | 32 | 26 | 32 |
N.S. |
1 | 1.23 | 0.96 | 1.04 | 1.12 | 1.00 | 1.00 | 1.23 | 1.00 | 1.23 |
time (sec) |
N/A | 0.284 | 0.019 | 1.592 | 0.026 | 0.059 | 0.155 | 0.109 | 0.188 | 0.164 |
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 | 13 | 15 | 13 | 12 | 11 | 11 | 12 | 11 | 15 | 9 |
N.S. |
1 | 1.15 | 1.00 | 0.92 | 0.85 | 0.85 | 0.92 | 0.85 | 1.15 | 0.69 |
time (sec) |
N/A | 0.152 | 0.027 | 0.122 | 0.035 | 0.063 | 0.062 | 0.120 | 0.229 | 1.827 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 18 | 34 | 37 | 33 | 29 | 33 | 31 | 31 |
N.S. |
1 | 1.00 | 1.00 | 1.89 | 2.06 | 1.83 | 1.61 | 1.83 | 1.72 | 1.72 |
time (sec) |
N/A | 0.476 | 0.019 | 9.141 | 0.159 | 0.074 | 0.518 | 0.166 | 0.209 | 2.055 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | F | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 16 | 22 | 14 | 25 | 15 | 0 | 24 | 16 |
N.S. |
1 | 0.00 | 0.73 | 1.00 | 0.64 | 1.14 | 0.68 | 0.00 | 1.09 | 0.73 |
time (sec) |
N/A | 0.000 | 0.317 | 0.497 | 0.150 | 0.066 | 0.125 | 0.000 | 2.949 | 1.900 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 35 | 22 | 31 | 30 | 32 | 27 | 54 | 67 | 34 |
N.S. |
1 | 1.13 | 0.71 | 1.00 | 0.97 | 1.03 | 0.87 | 1.74 | 2.16 | 1.10 |
time (sec) |
N/A | 0.580 | 0.033 | 0.713 | 0.243 | 0.074 | 0.116 | 0.137 | 0.210 | 0.234 |
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 | 16 | 16 | 26 | 15 | 16 | 15 | 27 | 19 | 55 | 12 |
N.S. |
1 | 1.00 | 1.62 | 0.94 | 1.00 | 0.94 | 1.69 | 1.19 | 3.44 | 0.75 |
time (sec) |
N/A | 0.186 | 0.008 | 0.542 | 0.023 | 0.061 | 0.162 | 0.125 | 0.194 | 0.138 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 18 | 18 | 18 | 46 | 17 | 19 | 17 | 116 | 17 |
N.S. |
1 | 0.78 | 0.78 | 0.78 | 2.00 | 0.74 | 0.83 | 0.74 | 5.04 | 0.74 |
time (sec) |
N/A | 0.403 | 0.059 | 0.690 | 0.201 | 0.066 | 0.092 | 0.137 | 0.221 | 1.943 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 21 | 22 | 25 | 26 | 22 | 57 | 47 | 60 |
N.S. |
1 | 0.00 | 0.95 | 1.00 | 1.14 | 1.18 | 1.00 | 2.59 | 2.14 | 2.73 |
time (sec) |
N/A | 0.000 | 0.330 | 0.221 | 0.154 | 0.058 | 0.100 | 0.109 | 0.211 | 0.171 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 50 | 33 | 22 | 64 | 30 | 22 | 34 | 31 | 22 |
N.S. |
1 | 1.92 | 1.27 | 0.85 | 2.46 | 1.15 | 0.85 | 1.31 | 1.19 | 0.85 |
time (sec) |
N/A | 0.842 | 0.060 | 0.602 | 0.067 | 0.072 | 0.093 | 0.121 | 0.210 | 0.158 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 16 | 16 | 16 | 34 | 15 | 10 | 15 | 23 | 15 |
N.S. |
1 | 0.84 | 0.84 | 0.84 | 1.79 | 0.79 | 0.53 | 0.79 | 1.21 | 0.79 |
time (sec) |
N/A | 0.342 | 0.132 | 0.178 | 0.067 | 0.064 | 0.041 | 0.116 | 0.199 | 1.828 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 25 | 23 | 25 | 26 | 22 | 27 | 27 | 24 |
N.S. |
1 | 0.00 | 1.09 | 1.00 | 1.09 | 1.13 | 0.96 | 1.17 | 1.17 | 1.04 |
time (sec) |
N/A | 0.000 | 0.420 | 0.861 | 0.099 | 0.073 | 0.159 | 0.142 | 0.215 | 2.009 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | B | B | B | B | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 123 | 69 | 87 | 150 | 163 | 99 | 150 | 63 | 66 |
N.S. |
1 | 6.47 | 3.63 | 4.58 | 7.89 | 8.58 | 5.21 | 7.89 | 3.32 | 3.47 |
time (sec) |
N/A | 0.324 | 0.201 | 0.528 | 0.027 | 0.072 | 1.929 | 0.114 | 0.195 | 0.934 |
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 | 26 | 14 | 19 | 16 | 15 | 22 | 10 | 15 | 29 | 15 |
N.S. |
1 | 0.54 | 0.73 | 0.62 | 0.58 | 0.85 | 0.38 | 0.58 | 1.12 | 0.58 |
time (sec) |
N/A | 0.191 | 0.015 | 0.372 | 0.025 | 0.060 | 0.060 | 0.110 | 0.210 | 0.072 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 29 | 22 | 26 | 21 | 25 | 24 | 21 | 48 | 24 |
N.S. |
1 | 0.97 | 0.73 | 0.87 | 0.70 | 0.83 | 0.80 | 0.70 | 1.60 | 0.80 |
time (sec) |
N/A | 0.397 | 0.051 | 0.217 | 0.111 | 0.073 | 0.082 | 0.123 | 35.283 | 1.819 |
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 | 22 | 27 | 24 | 27 | 38 | 29 | 26 | 29 | 29 | 25 |
N.S. |
1 | 1.23 | 1.09 | 1.23 | 1.73 | 1.32 | 1.18 | 1.32 | 1.32 | 1.14 |
time (sec) |
N/A | 0.239 | 0.101 | 0.302 | 0.038 | 0.063 | 0.067 | 0.110 | 0.220 | 1.769 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | A | B | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 84 | 38 | 36 | 45 | 42 | 42 | 36 | 53 | 27 |
N.S. |
1 | 2.62 | 1.19 | 1.12 | 1.41 | 1.31 | 1.31 | 1.12 | 1.66 | 0.84 |
time (sec) |
N/A | 0.362 | 0.023 | 0.255 | 0.028 | 0.055 | 0.476 | 0.108 | 0.249 | 0.202 |
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 | 23 | 34 | 25 | 23 | 32 | 29 | 42 | 27 | 22 | 41 |
N.S. |
1 | 1.48 | 1.09 | 1.00 | 1.39 | 1.26 | 1.83 | 1.17 | 0.96 | 1.78 |
time (sec) |
N/A | 0.272 | 0.009 | 0.128 | 0.026 | 0.057 | 0.109 | 0.118 | 0.206 | 1.820 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 54 | 41 | 45 | 178 | 33 | 36 | 45 | 80 | 49 |
N.S. |
1 | 1.64 | 1.24 | 1.36 | 5.39 | 1.00 | 1.09 | 1.36 | 2.42 | 1.48 |
time (sec) |
N/A | 0.599 | 0.067 | 1.132 | 0.168 | 0.071 | 0.249 | 0.115 | 0.203 | 2.411 |
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 | 18 | 18 | 17 | 16 | 16 | 10 | 16 | 26 | 17 |
N.S. |
1 | 0.55 | 0.55 | 0.52 | 0.48 | 0.48 | 0.30 | 0.48 | 0.79 | 0.52 |
time (sec) |
N/A | 0.195 | 0.016 | 0.092 | 0.031 | 0.060 | 0.073 | 0.111 | 0.200 | 0.071 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 30 | 28 | 35 | 37 | 33 | 32 | 40 | 40 | 34 |
N.S. |
1 | 0.97 | 0.90 | 1.13 | 1.19 | 1.06 | 1.03 | 1.29 | 1.29 | 1.10 |
time (sec) |
N/A | 0.609 | 0.021 | 1.952 | 0.152 | 0.063 | 0.153 | 0.201 | 0.236 | 2.738 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 31 | 31 | 28 | 45 | 27 | 24 | 30 | 29 | 0 |
N.S. |
1 | 1.29 | 1.29 | 1.17 | 1.88 | 1.12 | 1.00 | 1.25 | 1.21 | 0.00 |
time (sec) |
N/A | 1.032 | 0.135 | 0.685 | 0.151 | 0.068 | 0.173 | 0.152 | 0.212 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 0 | 21 | 20 | 24 | 25 | 22 | 25 | 27 | 0 |
N.S. |
1 | 0.00 | 1.00 | 0.95 | 1.14 | 1.19 | 1.05 | 1.19 | 1.29 | 0.00 |
time (sec) |
N/A | 0.000 | 5.047 | 0.490 | 0.179 | 0.063 | 0.127 | 0.168 | 0.207 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | A | B | B | A | F | B | B |
verified | N/A | Yes | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 29 | 0 | 34 | 84 | 96 | 41 | 0 | 89 | 30 |
N.S. |
1 | 0.91 | 0.00 | 1.06 | 2.62 | 3.00 | 1.28 | 0.00 | 2.78 | 0.94 |
time (sec) |
N/A | 2.218 | 0.000 | 64.142 | 0.227 | 0.074 | 1.172 | 0.000 | 8.453 | 2.122 |
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 | 21 | 21 | 21 | 19 | 18 | 20 | 19 | 20 | 21 | 20 |
N.S. |
1 | 1.00 | 1.00 | 0.90 | 0.86 | 0.95 | 0.90 | 0.95 | 1.00 | 0.95 |
time (sec) |
N/A | 0.574 | 0.063 | 2.014 | 0.161 | 0.067 | 0.277 | 0.141 | 0.191 | 112.898 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 61 | 32 | 40 | 45 | 29 | 26 | 42 | 33 | 29 |
N.S. |
1 | 2.35 | 1.23 | 1.54 | 1.73 | 1.12 | 1.00 | 1.62 | 1.27 | 1.12 |
time (sec) |
N/A | 0.672 | 0.796 | 0.690 | 0.093 | 0.061 | 4.471 | 0.117 | 1.512 | 1.721 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 77 | 49 | 32 | 35 | 30 | 31 | 53 | 64 | 50 |
N.S. |
1 | 2.03 | 1.29 | 0.84 | 0.92 | 0.79 | 0.82 | 1.39 | 1.68 | 1.32 |
time (sec) |
N/A | 2.335 | 3.002 | 0.522 | 0.106 | 0.072 | 0.085 | 0.215 | 0.223 | 1.809 |
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 | 20 | 20 | 20 | 19 | 18 | 18 | 0 | 18 | 20 | 18 |
N.S. |
1 | 1.00 | 1.00 | 0.95 | 0.90 | 0.90 | 0.00 | 0.90 | 1.00 | 0.90 |
time (sec) |
N/A | 1.007 | 0.143 | 4.494 | 0.145 | 0.066 | 0.000 | 0.210 | 0.228 | 0.342 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | B | F(-2) | A | B | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 40 | 43 | 56 | 61 | 0 | 48 | 119 | 0 |
N.S. |
1 | 0.00 | 1.33 | 1.43 | 1.87 | 2.03 | 0.00 | 1.60 | 3.97 | 0.00 |
time (sec) |
N/A | 0.000 | 0.058 | 20.361 | 0.212 | 0.075 | 0.000 | 0.150 | 0.219 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | A | A | A | A | A | B | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 121 | 33 | 35 | 32 | 31 | 39 | 35 | 0 |
N.S. |
1 | 0.00 | 3.78 | 1.03 | 1.09 | 1.00 | 0.97 | 1.22 | 1.09 | 0.00 |
time (sec) |
N/A | 0.000 | 5.052 | 0.992 | 0.166 | 0.072 | 99.782 | 0.130 | 0.214 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 47 | 39 | 38 | 105 | 37 | 41 | 37 | 676 | 76 |
N.S. |
1 | 1.74 | 1.44 | 1.41 | 3.89 | 1.37 | 1.52 | 1.37 | 25.04 | 2.81 |
time (sec) |
N/A | 4.791 | 0.240 | 6.810 | 0.458 | 0.070 | 15.745 | 1.425 | 0.561 | 1.934 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | B | A | A | A | B | B |
verified | N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 33 | 55 | 16 | 36 | 15 | 15 | 15 | 136 | 15 |
N.S. |
1 | 1.83 | 3.06 | 0.89 | 2.00 | 0.83 | 0.83 | 0.83 | 7.56 | 0.83 |
time (sec) |
N/A | 4.893 | 0.301 | 1.355 | 0.105 | 0.068 | 0.272 | 0.134 | 0.254 | 1.915 |
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 | 36 | 36 | 25 | 30 | 44 | 24 | 29 | 46 | 29 |
N.S. |
1 | 1.24 | 1.24 | 0.86 | 1.03 | 1.52 | 0.83 | 1.00 | 1.59 | 1.00 |
time (sec) |
N/A | 1.673 | 0.143 | 0.253 | 0.247 | 0.062 | 0.120 | 0.118 | 0.215 | 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 | 34 | 42 | 41 | 40 | 40 | 39 | 36 | 43 | 40 | 39 |
N.S. |
1 | 1.24 | 1.21 | 1.18 | 1.18 | 1.15 | 1.06 | 1.26 | 1.18 | 1.15 |
time (sec) |
N/A | 0.419 | 0.021 | 0.112 | 0.041 | 0.061 | 0.098 | 0.113 | 0.190 | 0.176 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 43 | 17 | 15 | 14 | 14 | 15 | 14 | 15 | 14 |
N.S. |
1 | 2.53 | 1.00 | 0.88 | 0.82 | 0.82 | 0.88 | 0.82 | 0.88 | 0.82 |
time (sec) |
N/A | 0.561 | 0.012 | 0.280 | 0.143 | 0.062 | 0.102 | 0.115 | 0.203 | 1.901 |
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 | 27 | 25 | 23 | 20 | 21 | 21 | 22 | 25 | 37 | 19 |
N.S. |
1 | 0.93 | 0.85 | 0.74 | 0.78 | 0.78 | 0.81 | 0.93 | 1.37 | 0.70 |
time (sec) |
N/A | 0.255 | 3.846 | 0.196 | 0.033 | 0.062 | 0.090 | 0.114 | 0.207 | 0.142 |
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 | 21 | 19 | 17 | 12 | 11 | 11 | 12 | 11 | 14 | 11 |
N.S. |
1 | 0.90 | 0.81 | 0.57 | 0.52 | 0.52 | 0.57 | 0.52 | 0.67 | 0.52 |
time (sec) |
N/A | 0.155 | 0.010 | 0.094 | 0.031 | 0.064 | 0.042 | 0.114 | 0.183 | 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 | 18 | 18 | 18 | 15 | 16 | 16 | 14 | 16 | 18 | 16 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 0.89 | 0.89 | 0.78 | 0.89 | 1.00 | 0.89 |
time (sec) |
N/A | 0.154 | 0.018 | 0.229 | 0.030 | 0.061 | 0.048 | 0.108 | 0.211 | 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 | 34 | 33 | 33 | 36 | 35 | 35 | 36 | 35 | 47 | 35 |
N.S. |
1 | 0.97 | 0.97 | 1.06 | 1.03 | 1.03 | 1.06 | 1.03 | 1.38 | 1.03 |
time (sec) |
N/A | 0.814 | 0.149 | 1.658 | 0.151 | 0.068 | 0.145 | 0.124 | 0.213 | 1.804 |
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 | 25 | 33 | 32 | 24 | 30 | 30 | 20 | 30 | 31 | 23 |
N.S. |
1 | 1.32 | 1.28 | 0.96 | 1.20 | 1.20 | 0.80 | 1.20 | 1.24 | 0.92 |
time (sec) |
N/A | 0.244 | 0.021 | 0.441 | 0.027 | 0.076 | 0.095 | 0.112 | 0.203 | 1.740 |
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 | 19 | 35 | 22 | 24 | 23 | 19 | 20 | 23 | 40 | 22 |
N.S. |
1 | 1.84 | 1.16 | 1.26 | 1.21 | 1.00 | 1.05 | 1.21 | 2.11 | 1.16 |
time (sec) |
N/A | 0.529 | 0.014 | 0.219 | 0.026 | 0.071 | 0.373 | 0.124 | 0.188 | 1.809 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | A | B | A | B | B | B | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 59 | 51 | 81 | 48 | 51 | 78 | 71 | 0 |
N.S. |
1 | 0.00 | 2.03 | 1.76 | 2.79 | 1.66 | 1.76 | 2.69 | 2.45 | 0.00 |
time (sec) |
N/A | 0.000 | 1.322 | 1.098 | 0.168 | 0.070 | 17.018 | 0.126 | 0.202 | 0.000 |
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 | 8 | 8 | 8 | 8 | 7 | 7 | 7 | 7 | 8 | 7 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.88 | 0.88 | 0.88 | 0.88 | 1.00 | 0.88 |
time (sec) |
N/A | 0.217 | 0.000 | 0.099 | 0.030 | 0.054 | 0.017 | 0.117 | 0.226 | 0.023 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 31 | 31 | 29 | 35 | 37 | 22 | 28 | 32 | 26 |
N.S. |
1 | 1.41 | 1.41 | 1.32 | 1.59 | 1.68 | 1.00 | 1.27 | 1.45 | 1.18 |
time (sec) |
N/A | 0.546 | 0.063 | 0.643 | 0.059 | 0.065 | 0.057 | 0.112 | 0.200 | 1.680 |
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 | 21 | 29 | 32 | 26 | 30 | 30 | 27 | 30 | 26 | 28 |
N.S. |
1 | 1.38 | 1.52 | 1.24 | 1.43 | 1.43 | 1.29 | 1.43 | 1.24 | 1.33 |
time (sec) |
N/A | 0.267 | 0.002 | 0.113 | 0.027 | 0.060 | 0.022 | 0.112 | 0.184 | 1.634 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 32 | 24 | 31 | 31 | 22 | 23 | 36 | 31 |
N.S. |
1 | 0.00 | 1.03 | 0.77 | 1.00 | 1.00 | 0.71 | 0.74 | 1.16 | 1.00 |
time (sec) |
N/A | 0.000 | 5.042 | 0.684 | 0.148 | 0.076 | 0.182 | 0.263 | 0.209 | 1.902 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | F | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 31 | 27 | 26 | 26 | 36 | 26 | 698 | 26 |
N.S. |
1 | 0.00 | 1.11 | 0.96 | 0.93 | 0.93 | 1.29 | 0.93 | 24.93 | 0.93 |
time (sec) |
N/A | 0.000 | 0.156 | 6.594 | 0.176 | 0.081 | 5.095 | 7.631 | 0.393 | 1.862 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 20 | 16 | 15 | 17 | 19 | 17 | 18 | 17 |
N.S. |
1 | 0.00 | 0.83 | 0.67 | 0.62 | 0.71 | 0.79 | 0.71 | 0.75 | 0.71 |
time (sec) |
N/A | 0.000 | 0.153 | 0.132 | 0.069 | 0.080 | 0.134 | 0.112 | 0.189 | 1.801 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 19 | 20 | 22 | 22 | 27 | 31 | 24 | 19 |
N.S. |
1 | 0.00 | 0.86 | 0.91 | 1.00 | 1.00 | 1.23 | 1.41 | 1.09 | 0.86 |
time (sec) |
N/A | 0.000 | 0.104 | 0.487 | 0.078 | 0.063 | 0.094 | 0.124 | 0.208 | 2.064 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 24 | 25 | 31 | 24 | 17 | 24 | 21 | 20 |
N.S. |
1 | 0.00 | 1.09 | 1.14 | 1.41 | 1.09 | 0.77 | 1.09 | 0.95 | 0.91 |
time (sec) |
N/A | 0.000 | 0.043 | 4.196 | 0.159 | 0.068 | 0.361 | 0.170 | 0.236 | 1.864 |
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 | 21 | 20 | 18 | 20 | 19 | 16 | 17 | 19 | 21 | 17 |
N.S. |
1 | 0.95 | 0.86 | 0.95 | 0.90 | 0.76 | 0.81 | 0.90 | 1.00 | 0.81 |
time (sec) |
N/A | 0.168 | 0.004 | 0.172 | 0.030 | 0.058 | 0.071 | 0.109 | 0.212 | 0.053 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 12 | 12 | 12 | 18 | 11 | 8 | 11 | 15 | 11 |
N.S. |
1 | 0.86 | 0.86 | 0.86 | 1.29 | 0.79 | 0.57 | 0.79 | 1.07 | 0.79 |
time (sec) |
N/A | 0.174 | 0.051 | 0.152 | 0.061 | 0.060 | 0.052 | 0.114 | 0.197 | 1.704 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | B | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 52 | 34 | 31 | 99 | 32 | 26 | 32 | 34 | 30 |
N.S. |
1 | 2.08 | 1.36 | 1.24 | 3.96 | 1.28 | 1.04 | 1.28 | 1.36 | 1.20 |
time (sec) |
N/A | 0.285 | 0.013 | 1.020 | 0.033 | 0.066 | 0.081 | 0.114 | 0.198 | 1.700 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | F(-1) | A | A | F(-1) | F | F | B |
verified | N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 54 | 0 | 46 | 41 | 0 | 0 | 192 | 53 |
N.S. |
1 | 0.00 | 1.74 | 0.00 | 1.48 | 1.32 | 0.00 | 0.00 | 6.19 | 1.71 |
time (sec) |
N/A | 0.000 | 0.249 | 0.000 | 0.282 | 0.071 | 0.000 | 0.000 | 247.675 | 2.093 |
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 | 21 | 17 | 13 | 16 | 15 | 15 | 14 | 15 | 15 | 13 |
N.S. |
1 | 0.81 | 0.62 | 0.76 | 0.71 | 0.71 | 0.67 | 0.71 | 0.71 | 0.62 |
time (sec) |
N/A | 0.235 | 0.001 | 0.080 | 0.036 | 0.052 | 0.021 | 0.117 | 0.246 | 0.026 |
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 | 24 | 48 | 20 | 21 | 20 | 27 | 26 | 22 | 22 | 20 |
N.S. |
1 | 2.00 | 0.83 | 0.88 | 0.83 | 1.12 | 1.08 | 0.92 | 0.92 | 0.83 |
time (sec) |
N/A | 0.461 | 0.038 | 0.439 | 0.198 | 0.065 | 0.083 | 0.124 | 3.086 | 1.749 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 29 | 26 | 23 | 28 | 28 | 24 | 28 | 473 | 29 |
N.S. |
1 | 1.21 | 1.08 | 0.96 | 1.17 | 1.17 | 1.00 | 1.17 | 19.71 | 1.21 |
time (sec) |
N/A | 0.909 | 1.994 | 0.563 | 0.193 | 0.066 | 0.148 | 0.114 | 0.471 | 1.929 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | F | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 0 | 42 | 64 | 41 | 40 | 34 | 36 | 1252 | 49 |
N.S. |
1 | 0.00 | 1.17 | 1.78 | 1.14 | 1.11 | 0.94 | 1.00 | 34.78 | 1.36 |
time (sec) |
N/A | 0.000 | 0.242 | 16.675 | 0.133 | 0.072 | 0.599 | 1.030 | 0.506 | 2.295 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | C | A | B | F(-1) | F | B | B |
verified | N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 25 | 113 | 44 | 47 | 0 | 0 | 42 | 52 |
N.S. |
1 | 0.00 | 1.00 | 4.52 | 1.76 | 1.88 | 0.00 | 0.00 | 1.68 | 2.08 |
time (sec) |
N/A | 0.000 | 0.151 | 0.233 | 0.268 | 0.076 | 0.000 | 0.000 | 0.262 | 2.572 |
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 | 20 | 20 | 16 | 18 | 18 | 26 | 18 | 15 | 15 |
N.S. |
1 | 0.71 | 0.71 | 0.57 | 0.64 | 0.64 | 0.93 | 0.64 | 0.54 | 0.54 |
time (sec) |
N/A | 0.158 | 0.001 | 0.091 | 0.037 | 0.057 | 0.024 | 0.114 | 0.250 | 0.041 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 28 | 33 | 28 | 31 | 32 | 36 | 28 | 25 |
N.S. |
1 | 0.00 | 1.04 | 1.22 | 1.04 | 1.15 | 1.19 | 1.33 | 1.04 | 0.93 |
time (sec) |
N/A | 0.000 | 7.914 | 0.440 | 0.086 | 0.070 | 0.162 | 0.115 | 0.231 | 1.765 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | A | A | B | A | A | F | F(-1) |
verified | N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 0 | 34 | 33 | 56 | 34 | 35 | 170 | 0 |
N.S. |
1 | 0.00 | 0.00 | 1.17 | 1.14 | 1.93 | 1.17 | 1.21 | 5.86 | 0.00 |
time (sec) |
N/A | 0.000 | 0.000 | 0.118 | 0.397 | 0.080 | 14.433 | 0.140 | 200.022 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 24 | 25 | 28 | 26 | 22 | 28 | 26 | 27 |
N.S. |
1 | 0.00 | 0.92 | 0.96 | 1.08 | 1.00 | 0.85 | 1.08 | 1.00 | 1.04 |
time (sec) |
N/A | 0.000 | 0.437 | 1.518 | 0.192 | 0.072 | 0.240 | 0.157 | 0.175 | 0.666 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | B | B |
verified | N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 23 | 18 | 20 | 43 | 19 | 19 | 19 | 25 | 14 |
N.S. |
1 | 1.28 | 1.00 | 1.11 | 2.39 | 1.06 | 1.06 | 1.06 | 1.39 | 0.78 |
time (sec) |
N/A | 0.355 | 0.399 | 0.240 | 0.027 | 0.063 | 0.101 | 0.112 | 0.189 | 1.748 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | B | B | B | B | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 109 | 20 | 51 | 221 | 46 | 58 | 63 | 53 | 19 |
N.S. |
1 | 7.27 | 1.33 | 3.40 | 14.73 | 3.07 | 3.87 | 4.20 | 3.53 | 1.27 |
time (sec) |
N/A | 0.540 | 5.509 | 0.295 | 0.042 | 0.064 | 0.077 | 0.117 | 0.180 | 1.778 |