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 | F | A | A | A | A | A | A | F | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 18 | 17 | 16 | 16 | 12 | 16 | 49 | 16 |
N.S. |
1 | 0.00 | 0.75 | 0.71 | 0.67 | 0.67 | 0.50 | 0.67 | 2.04 | 0.67 |
time (sec) |
N/A | 0.000 | 0.226 | 0.240 | 0.076 | 0.077 | 0.055 | 0.117 | 35.263 | 2.668 |
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 | 27 | 75 | 23 | 25 | 22 | 25 | 20 | 25 | 28 | 23 |
N.S. |
1 | 2.78 | 0.85 | 0.93 | 0.81 | 0.93 | 0.74 | 0.93 | 1.04 | 0.85 |
time (sec) |
N/A | 0.230 | 0.052 | 0.428 | 0.109 | 0.098 | 0.108 | 0.125 | 0.183 | 2.576 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 32 | 30 | 31 | 33 | 37 | 27 | 0 | 54 | 42 |
N.S. |
1 | 1.19 | 1.11 | 1.15 | 1.22 | 1.37 | 1.00 | 0.00 | 2.00 | 1.56 |
time (sec) |
N/A | 0.688 | 0.053 | 1.046 | 0.147 | 0.088 | 0.119 | 0.000 | 0.194 | 2.618 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | A | A | B | B | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 55 | 49 | 31 | 44 | 53 | 42 | 44 | 24 | 39 |
N.S. |
1 | 2.39 | 2.13 | 1.35 | 1.91 | 2.30 | 1.83 | 1.91 | 1.04 | 1.70 |
time (sec) |
N/A | 0.369 | 0.019 | 0.877 | 0.038 | 0.083 | 0.562 | 0.116 | 0.182 | 2.728 |
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 | 38 | 25 | 25 | 30 | 30 | 19 | 30 | 38 | 20 |
N.S. |
1 | 1.65 | 1.09 | 1.09 | 1.30 | 1.30 | 0.83 | 1.30 | 1.65 | 0.87 |
time (sec) |
N/A | 0.196 | 0.011 | 0.221 | 0.031 | 0.086 | 0.023 | 0.116 | 0.177 | 0.026 |
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 | 26 | 0 | 26 | 27 | 26 | 28 | 27 | 0 | 29 | 26 |
N.S. |
1 | 0.00 | 1.00 | 1.04 | 1.00 | 1.08 | 1.04 | 0.00 | 1.12 | 1.00 |
time (sec) |
N/A | 0.000 | 2.390 | 0.555 | 0.107 | 0.077 | 0.113 | 0.000 | 0.204 | 2.718 |
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 | 22 | 15 | 15 | 20 | 20 | 12 | 20 | 22 | 14 |
N.S. |
1 | 1.22 | 0.83 | 0.83 | 1.11 | 1.11 | 0.67 | 1.11 | 1.22 | 0.78 |
time (sec) |
N/A | 0.157 | 0.009 | 0.109 | 0.035 | 0.093 | 0.043 | 0.109 | 0.163 | 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 | 19 | 15 | 15 | 14 | 14 | 13 | 15 | 14 | 13 | 13 |
N.S. |
1 | 0.79 | 0.79 | 0.74 | 0.74 | 0.68 | 0.79 | 0.74 | 0.68 | 0.68 |
time (sec) |
N/A | 0.150 | 0.004 | 0.078 | 0.026 | 0.067 | 0.036 | 0.113 | 0.174 | 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 | 17 | 17 | 17 | 12 | 11 | 11 | 14 | 11 | 18 | 11 |
N.S. |
1 | 1.00 | 1.00 | 0.71 | 0.65 | 0.65 | 0.82 | 0.65 | 1.06 | 0.65 |
time (sec) |
N/A | 0.177 | 0.012 | 0.079 | 0.031 | 0.074 | 0.051 | 0.110 | 0.174 | 0.036 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | B | A | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 37 | 53 | 55 | 65 | 42 | 56 | 52 | 58 |
N.S. |
1 | 0.00 | 1.16 | 1.66 | 1.72 | 2.03 | 1.31 | 1.75 | 1.62 | 1.81 |
time (sec) |
N/A | 0.000 | 5.231 | 2.082 | 0.105 | 0.092 | 0.106 | 0.189 | 0.177 | 2.967 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | A | B | B | B | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 81 | 43 | 73 | 60 | 58 | 82 | 233 | 126 |
N.S. |
1 | 0.00 | 2.61 | 1.39 | 2.35 | 1.94 | 1.87 | 2.65 | 7.52 | 4.06 |
time (sec) |
N/A | 0.000 | 0.132 | 11.993 | 0.184 | 0.089 | 0.171 | 0.191 | 0.177 | 3.873 |
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 | 16 | 17 | 14 | 25 | 14 | 15 | 14 | 14 | 13 |
N.S. |
1 | 0.84 | 0.89 | 0.74 | 1.32 | 0.74 | 0.79 | 0.74 | 0.74 | 0.68 |
time (sec) |
N/A | 0.264 | 0.066 | 0.378 | 0.155 | 0.081 | 0.081 | 0.117 | 0.171 | 2.751 |
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 | 28 | 22 | 23 | 22 | 29 | 19 | 22 | 66 | 22 |
N.S. |
1 | 1.33 | 1.05 | 1.10 | 1.05 | 1.38 | 0.90 | 1.05 | 3.14 | 1.05 |
time (sec) |
N/A | 0.306 | 0.016 | 0.599 | 0.030 | 0.088 | 0.182 | 0.122 | 0.175 | 2.604 |
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 | 6 | 4 | 4 | 6 | 5 | 5 | 5 | 5 | 4 | 5 |
N.S. |
1 | 0.67 | 0.67 | 1.00 | 0.83 | 0.83 | 0.83 | 0.83 | 0.67 | 0.83 |
time (sec) |
N/A | 0.120 | 0.000 | 0.038 | 0.030 | 0.064 | 0.013 | 0.112 | 0.175 | 0.001 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | B | A | F | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 24 | 19 | 16 | 44 | 19 | 0 | 22 | 16 |
N.S. |
1 | 0.00 | 0.86 | 0.68 | 0.57 | 1.57 | 0.68 | 0.00 | 0.79 | 0.57 |
time (sec) |
N/A | 0.000 | 0.178 | 0.167 | 0.190 | 0.088 | 0.137 | 0.000 | 2.055 | 2.890 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | A | A | B | A | F | B | B |
verified | N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 0 | 35 | 20 | 77 | 36 | 0 | 27 | 21 |
N.S. |
1 | 0.00 | 0.00 | 1.46 | 0.83 | 3.21 | 1.50 | 0.00 | 1.12 | 0.88 |
time (sec) |
N/A | 0.000 | 0.000 | 1.119 | 0.301 | 0.085 | 0.209 | 0.000 | 0.778 | 2.806 |
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 | 9 | 7 | 8 | 5 | 8 | 8 | 8 |
N.S. |
1 | 1.00 | 1.00 | 1.12 | 0.88 | 1.00 | 0.62 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.189 | 0.025 | 0.485 | 0.053 | 0.068 | 0.033 | 0.111 | 0.173 | 2.743 |
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 | 24 | 24 | 21 | 20 | 20 | 17 | 23 | 20 | 18 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 0.83 | 0.83 | 0.71 | 0.96 | 0.83 | 0.75 |
time (sec) |
N/A | 0.226 | 0.008 | 0.078 | 0.026 | 0.069 | 0.050 | 0.110 | 0.172 | 2.860 |
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 | 20 | 60 | 16 | 47 | 45 | 45 | 44 | 45 | 60 | 19 |
N.S. |
1 | 3.00 | 0.80 | 2.35 | 2.25 | 2.25 | 2.20 | 2.25 | 3.00 | 0.95 |
time (sec) |
N/A | 0.290 | 0.115 | 0.551 | 0.033 | 0.081 | 0.061 | 0.108 | 0.177 | 0.067 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | B | B | B | B | B | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 132 | 182 | 190 | 195 | 137 | 226 | 159 | 182 | 0 |
N.S. |
1 | 6.00 | 8.27 | 8.64 | 8.86 | 6.23 | 10.27 | 7.23 | 8.27 | 0.00 |
time (sec) |
N/A | 0.389 | 0.083 | 2.289 | 0.036 | 0.095 | 2.559 | 0.143 | 0.181 | 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 | 24 | 17 | 17 | 16 | 29 | 17 | 15 | 15 | 26 | 15 |
N.S. |
1 | 0.71 | 0.71 | 0.67 | 1.21 | 0.71 | 0.62 | 0.62 | 1.08 | 0.62 |
time (sec) |
N/A | 0.284 | 0.027 | 0.285 | 0.028 | 0.081 | 0.059 | 0.108 | 0.176 | 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 | 14 | 11 | 9 | 8 | 9 | 9 | 5 | 9 | 7 | 7 |
N.S. |
1 | 0.79 | 0.64 | 0.57 | 0.64 | 0.64 | 0.36 | 0.64 | 0.50 | 0.50 |
time (sec) |
N/A | 0.126 | 0.000 | 0.030 | 0.024 | 0.060 | 0.017 | 0.114 | 0.182 | 0.018 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | A | B | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 109 | 50 | 49 | 43 | 47 | 80 | 69 | 39 | 24 |
N.S. |
1 | 3.89 | 1.79 | 1.75 | 1.54 | 1.68 | 2.86 | 2.46 | 1.39 | 0.86 |
time (sec) |
N/A | 1.060 | 5.274 | 0.675 | 0.074 | 0.090 | 0.106 | 0.117 | 0.173 | 0.111 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | A | B | B | B | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 113 | 54 | 24 | 218 | 64 | 85 | 76 | 68 | 62 |
N.S. |
1 | 5.65 | 2.70 | 1.20 | 10.90 | 3.20 | 4.25 | 3.80 | 3.40 | 3.10 |
time (sec) |
N/A | 0.542 | 5.032 | 0.223 | 0.041 | 0.097 | 0.092 | 0.111 | 0.175 | 0.057 |
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 | 23 | 23 | 22 | 19 | 21 | 15 | 21 | 21 | 21 |
N.S. |
1 | 0.92 | 0.92 | 0.88 | 0.76 | 0.84 | 0.60 | 0.84 | 0.84 | 0.84 |
time (sec) |
N/A | 0.608 | 0.088 | 0.568 | 0.073 | 0.083 | 0.075 | 0.130 | 0.170 | 2.574 |
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 | 14 | 90 | 12 | 12 | 19 | 11 | 10 | 11 | 12 | 11 |
N.S. |
1 | 6.43 | 0.86 | 0.86 | 1.36 | 0.79 | 0.71 | 0.79 | 0.86 | 0.79 |
time (sec) |
N/A | 0.540 | 0.100 | 0.128 | 0.034 | 0.077 | 0.048 | 0.117 | 0.174 | 0.082 |
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 | 25 | 27 | 27 | 25 | 30 | 24 | 29 | 49 | 33 | 29 |
N.S. |
1 | 1.08 | 1.08 | 1.00 | 1.20 | 0.96 | 1.16 | 1.96 | 1.32 | 1.16 |
time (sec) |
N/A | 0.555 | 0.031 | 0.268 | 0.099 | 0.081 | 0.071 | 0.119 | 0.173 | 0.099 |
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 | 22 | 17 | 20 | 18 | 19 | 17 | 18 | 24 | 13 |
N.S. |
1 | 1.22 | 0.94 | 1.11 | 1.00 | 1.06 | 0.94 | 1.00 | 1.33 | 0.72 |
time (sec) |
N/A | 0.298 | 0.067 | 0.135 | 0.024 | 0.083 | 0.038 | 0.113 | 0.172 | 0.033 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | B | B | B | B | B | B | B |
verified | N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 0 | 109 | 65 | 120 | 112 | 215 | 145 | 56 |
N.S. |
1 | 0.00 | 0.00 | 3.52 | 2.10 | 3.87 | 3.61 | 6.94 | 4.68 | 1.81 |
time (sec) |
N/A | 0.000 | 0.000 | 38.689 | 0.108 | 0.101 | 0.759 | 3.302 | 0.201 | 3.076 |
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 | 32 | 33 | 33 | 29 | 33 | 34 | 33 |
N.S. |
1 | 0.00 | 1.03 | 1.03 | 1.06 | 1.06 | 0.94 | 1.06 | 1.10 | 1.06 |
time (sec) |
N/A | 0.000 | 0.027 | 39.562 | 0.036 | 0.085 | 0.115 | 0.178 | 0.184 | 3.040 |
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 | 26 | 24 | 23 | 23 | 17 | 23 | 26 | 140 |
N.S. |
1 | 0.00 | 1.00 | 0.92 | 0.88 | 0.88 | 0.65 | 0.88 | 1.00 | 5.38 |
time (sec) |
N/A | 0.000 | 0.044 | 7.289 | 0.080 | 0.088 | 0.424 | 0.172 | 0.175 | 2.821 |
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 | 25 | 19 | 22 | 25 | 21 | 17 | 25 | 18 | 14 |
N.S. |
1 | 1.00 | 0.76 | 0.88 | 1.00 | 0.84 | 0.68 | 1.00 | 0.72 | 0.56 |
time (sec) |
N/A | 0.147 | 0.002 | 0.096 | 0.025 | 0.075 | 0.019 | 0.108 | 0.174 | 2.594 |
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 | 9 | 7 | 8 | 7 | 7 | 5 | 7 | 8 | 7 |
N.S. |
1 | 0.38 | 0.29 | 0.33 | 0.29 | 0.29 | 0.21 | 0.29 | 0.33 | 0.29 |
time (sec) |
N/A | 0.139 | 0.001 | 0.177 | 0.025 | 0.077 | 0.033 | 0.114 | 0.173 | 0.025 |
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 | 13 | 13 | 11 | 12 | 12 | 10 | 12 | 19 | 12 |
N.S. |
1 | 1.00 | 1.00 | 0.85 | 0.92 | 0.92 | 0.77 | 0.92 | 1.46 | 0.92 |
time (sec) |
N/A | 0.156 | 0.002 | 0.122 | 0.034 | 0.076 | 0.057 | 0.118 | 0.169 | 0.033 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | F | B | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 35 | 28 | 29 | 25 | 27 | 0 | 27 | 0 |
N.S. |
1 | 0.00 | 1.21 | 0.97 | 1.00 | 0.86 | 0.93 | 0.00 | 0.93 | 0.00 |
time (sec) |
N/A | 0.000 | 0.107 | 24.204 | 0.174 | 0.091 | 17.108 | 0.000 | 0.197 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 37 | 34 | 35 | 37 | 31 | 37 | 31 | 34 | 22 |
N.S. |
1 | 1.76 | 1.62 | 1.67 | 1.76 | 1.48 | 1.76 | 1.48 | 1.62 | 1.05 |
time (sec) |
N/A | 0.219 | 0.010 | 0.306 | 0.034 | 0.082 | 0.085 | 0.115 | 0.179 | 2.923 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | B | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 28 | 47 | 28 | 65 | 32 | 45 | 54 | 48 |
N.S. |
1 | 0.00 | 0.97 | 1.62 | 0.97 | 2.24 | 1.10 | 1.55 | 1.86 | 1.66 |
time (sec) |
N/A | 0.000 | 0.113 | 46.942 | 0.352 | 0.093 | 0.523 | 0.502 | 0.199 | 3.213 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | C | A | B | A | A | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 85 | 188 | 29 | 88 | 27 | 26 | 88 | 28 | 27 |
N.S. |
1 | 2.74 | 6.06 | 0.94 | 2.84 | 0.87 | 0.84 | 2.84 | 0.90 | 0.87 |
time (sec) |
N/A | 0.698 | 0.284 | 1.124 | 0.264 | 0.080 | 0.096 | 0.118 | 0.180 | 2.700 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-2) | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 37 | 37 | 28 | 0 | 27 | 0 | 34 | 33 | 31 |
N.S. |
1 | 1.95 | 1.95 | 1.47 | 0.00 | 1.42 | 0.00 | 1.79 | 1.74 | 1.63 |
time (sec) |
N/A | 1.469 | 0.414 | 0.644 | 0.000 | 0.081 | 0.000 | 0.123 | 0.207 | 2.795 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | A | B | B | B | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 51 | 80 | 46 | 50 | 73 | 46 | 44 | 72 | 47 |
N.S. |
1 | 2.12 | 3.33 | 1.92 | 2.08 | 3.04 | 1.92 | 1.83 | 3.00 | 1.96 |
time (sec) |
N/A | 0.296 | 0.024 | 0.270 | 0.029 | 0.080 | 0.167 | 0.111 | 0.188 | 2.767 |
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 | 22 | 22 | 22 | 22 | 22 | 17 | 22 | 22 | 24 |
N.S. |
1 | 0.81 | 0.81 | 0.81 | 0.81 | 0.81 | 0.63 | 0.81 | 0.81 | 0.89 |
time (sec) |
N/A | 0.657 | 0.069 | 0.448 | 0.059 | 0.084 | 0.077 | 0.113 | 0.178 | 2.680 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 35 | 25 | 0 | 25 | 22 | 26 | 27 | 27 |
N.S. |
1 | 0.00 | 1.17 | 0.83 | 0.00 | 0.83 | 0.73 | 0.87 | 0.90 | 0.90 |
time (sec) |
N/A | 0.000 | 0.060 | 20.778 | 0.000 | 0.093 | 0.399 | 0.181 | 0.193 | 2.892 |
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 | 21 | 51 | 20 | 19 | 151 | 36 | 27 | 25 | 34 | 29 |
N.S. |
1 | 2.43 | 0.95 | 0.90 | 7.19 | 1.71 | 1.29 | 1.19 | 1.62 | 1.38 |
time (sec) |
N/A | 0.374 | 0.043 | 0.181 | 0.047 | 0.080 | 0.155 | 0.111 | 0.176 | 0.077 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | F(-1) | F | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 25 | 25 | 30 | 24 | 0 | 0 | 30 | 24 |
N.S. |
1 | 0.00 | 1.00 | 1.00 | 1.20 | 0.96 | 0.00 | 0.00 | 1.20 | 0.96 |
time (sec) |
N/A | 0.000 | 5.090 | 4.602 | 0.108 | 0.093 | 0.000 | 0.000 | 0.178 | 2.910 |
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 | 24 | 21 | 21 | 26 | 22 | 20 | 22 | 24 | 22 |
N.S. |
1 | 1.00 | 0.88 | 0.88 | 1.08 | 0.92 | 0.83 | 0.92 | 1.00 | 0.92 |
time (sec) |
N/A | 0.334 | 0.195 | 3.623 | 0.168 | 0.091 | 0.227 | 0.136 | 0.181 | 3.257 |
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 | 30 | 31 | 30 | 30 | 34 | 30 | 30 | 30 |
N.S. |
1 | 0.00 | 1.30 | 1.35 | 1.30 | 1.30 | 1.48 | 1.30 | 1.30 | 1.30 |
time (sec) |
N/A | 0.000 | 0.108 | 7.335 | 0.097 | 0.093 | 0.930 | 0.133 | 0.177 | 3.071 |
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 | 33 | 54 | 39 | 41 | 45 | 54 | 29 | 54 | 58 | 0 |
N.S. |
1 | 1.64 | 1.18 | 1.24 | 1.36 | 1.64 | 0.88 | 1.64 | 1.76 | 0.00 |
time (sec) |
N/A | 2.391 | 5.067 | 1.046 | 0.152 | 0.084 | 0.168 | 0.114 | 0.178 | 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 | 24 | 23 | 23 | 29 | 31 | 33 | 32 | 29 | 28 | 33 |
N.S. |
1 | 0.96 | 0.96 | 1.21 | 1.29 | 1.38 | 1.33 | 1.21 | 1.17 | 1.38 |
time (sec) |
N/A | 0.557 | 0.038 | 1.641 | 0.156 | 0.089 | 0.366 | 0.150 | 0.175 | 3.178 |
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 | 20 | 20 | 19 | 16 | 18 | 17 | 18 | 18 | 18 |
N.S. |
1 | 0.83 | 0.83 | 0.79 | 0.67 | 0.75 | 0.71 | 0.75 | 0.75 | 0.75 |
time (sec) |
N/A | 0.571 | 0.075 | 0.548 | 0.144 | 0.083 | 0.064 | 0.128 | 0.166 | 2.753 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | F(-1) | B | B | B | F | B | B |
verified | N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 27 | 0 | 296 | 83 | 76 | 0 | 134 | 234 |
N.S. |
1 | 0.00 | 1.12 | 0.00 | 12.33 | 3.46 | 3.17 | 0.00 | 5.58 | 9.75 |
time (sec) |
N/A | 0.000 | 0.810 | 0.000 | 0.280 | 0.112 | 0.515 | 0.000 | 0.271 | 0.473 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | B | B | B | B | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 12 | 0 | 12 | 13 | 39 | 39 | 36 | 63 | 28 | 0 |
N.S. |
1 | 0.00 | 1.00 | 1.08 | 3.25 | 3.25 | 3.00 | 5.25 | 2.33 | 0.00 |
time (sec) |
N/A | 0.000 | 0.130 | 0.460 | 0.069 | 0.083 | 0.070 | 0.121 | 0.179 | 0.000 |
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 | 20 | 17 | 17 | 18 | 40 | 17 | 14 | 17 | 42 | 17 |
N.S. |
1 | 0.85 | 0.85 | 0.90 | 2.00 | 0.85 | 0.70 | 0.85 | 2.10 | 0.85 |
time (sec) |
N/A | 0.258 | 0.025 | 0.535 | 0.142 | 0.083 | 0.066 | 0.121 | 0.175 | 3.134 |
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 | 25 | 25 | 24 | 25 | 27 | 24 | 28 | 25 | 25 |
N.S. |
1 | 1.09 | 1.09 | 1.04 | 1.09 | 1.17 | 1.04 | 1.22 | 1.09 | 1.09 |
time (sec) |
N/A | 0.313 | 0.008 | 0.086 | 0.032 | 0.076 | 0.065 | 0.122 | 0.179 | 0.093 |
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 | 18 | 35 | 26 | 26 | 23 | 23 | 22 | 25 | 28 | 25 |
N.S. |
1 | 1.94 | 1.44 | 1.44 | 1.28 | 1.28 | 1.22 | 1.39 | 1.56 | 1.39 |
time (sec) |
N/A | 0.473 | 0.017 | 0.923 | 0.080 | 0.078 | 0.110 | 0.126 | 0.175 | 3.213 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 39 | 41 | 59 | 48 | 36 | 39 | 39 | 39 |
N.S. |
1 | 0.00 | 1.34 | 1.41 | 2.03 | 1.66 | 1.24 | 1.34 | 1.34 | 1.34 |
time (sec) |
N/A | 0.000 | 0.139 | 0.542 | 0.145 | 0.080 | 0.259 | 0.119 | 0.179 | 3.253 |
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 | 13 | 13 | 13 | 12 | 12 | 14 | 13 | 13 | 12 |
N.S. |
1 | 0.68 | 0.68 | 0.68 | 0.63 | 0.63 | 0.74 | 0.68 | 0.68 | 0.63 |
time (sec) |
N/A | 0.132 | 0.002 | 0.174 | 0.043 | 0.069 | 0.029 | 0.109 | 0.181 | 2.723 |
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 | 20 | 25 | 11 | 9 | 11 | 19 | 9 | 11 | 11 |
N.S. |
1 | 0.65 | 0.81 | 0.35 | 0.29 | 0.35 | 0.61 | 0.29 | 0.35 | 0.35 |
time (sec) |
N/A | 0.134 | 0.000 | 0.096 | 0.025 | 0.070 | 0.017 | 0.115 | 0.185 | 0.002 |
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 | 24 | 93 | 24 | 82 | 98 | 74 | 82 | 90 | 90 | 39 |
N.S. |
1 | 3.88 | 1.00 | 3.42 | 4.08 | 3.08 | 3.42 | 3.75 | 3.75 | 1.62 |
time (sec) |
N/A | 0.300 | 0.022 | 3.569 | 0.032 | 0.084 | 0.096 | 0.123 | 0.189 | 2.992 |
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 | 17 | 0 | 17 | 16 | 15 | 15 | 14 | 15 | 17 | 15 |
N.S. |
1 | 0.00 | 1.00 | 0.94 | 0.88 | 0.88 | 0.82 | 0.88 | 1.00 | 0.88 |
time (sec) |
N/A | 0.000 | 0.164 | 0.217 | 0.068 | 0.079 | 0.086 | 0.127 | 0.180 | 2.925 |
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 | 29 | 261 | 29 | 32 | 28 | 29 | 88 | 49 | 38 | 29 |
N.S. |
1 | 9.00 | 1.00 | 1.10 | 0.97 | 1.00 | 3.03 | 1.69 | 1.31 | 1.00 |
time (sec) |
N/A | 6.236 | 0.102 | 8.650 | 0.144 | 0.105 | 1.425 | 36.089 | 0.249 | 3.444 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | B | B | B | F(-2) | B | F | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 70 | 69 | 102 | 68 | 0 | 90 | 811 | 173 |
N.S. |
1 | 0.00 | 2.50 | 2.46 | 3.64 | 2.43 | 0.00 | 3.21 | 28.96 | 6.18 |
time (sec) |
N/A | 0.000 | 0.057 | 1.547 | 0.150 | 0.113 | 0.000 | 0.259 | 0.186 | 3.416 |
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 | 17 | 16 | 16 | 16 | 21 | 15 | 14 | 17 | 17 | 15 |
N.S. |
1 | 0.94 | 0.94 | 0.94 | 1.24 | 0.88 | 0.82 | 1.00 | 1.00 | 0.88 |
time (sec) |
N/A | 0.334 | 0.044 | 4.004 | 0.142 | 0.079 | 0.107 | 0.117 | 0.184 | 3.135 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | A | A | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 81 | 25 | 24 | 23 | 23 | 24 | 75 | 37 | 24 |
N.S. |
1 | 2.53 | 0.78 | 0.75 | 0.72 | 0.72 | 0.75 | 2.34 | 1.16 | 0.75 |
time (sec) |
N/A | 0.226 | 0.148 | 0.407 | 0.032 | 0.085 | 0.108 | 0.109 | 0.181 | 2.870 |
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 | 15 | 15 | 14 | 13 | 13 | 14 | 13 | 12 | 10 |
N.S. |
1 | 0.68 | 0.68 | 0.64 | 0.59 | 0.59 | 0.64 | 0.59 | 0.55 | 0.45 |
time (sec) |
N/A | 0.155 | 0.008 | 0.095 | 0.038 | 0.073 | 0.080 | 0.113 | 0.177 | 0.032 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | B | F(-1) | F | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 0 | 31 | 24 | 21 | 198 | 0 | 0 | 28 | 21 |
N.S. |
1 | 0.00 | 0.94 | 0.73 | 0.64 | 6.00 | 0.00 | 0.00 | 0.85 | 0.64 |
time (sec) |
N/A | 0.000 | 0.063 | 0.247 | 1.173 | 0.117 | 0.000 | 0.000 | 0.297 | 3.004 |
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 | 46 | 42 | 41 | 47 | 47 | 39 | 47 | 48 | 33 |
N.S. |
1 | 1.64 | 1.50 | 1.46 | 1.68 | 1.68 | 1.39 | 1.68 | 1.71 | 1.18 |
time (sec) |
N/A | 0.208 | 0.004 | 0.153 | 0.025 | 0.078 | 0.023 | 0.113 | 0.171 | 2.982 |
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 | 38 | 29 | 25 | 24 | 24 | 27 | 24 | 23 | 22 |
N.S. |
1 | 1.65 | 1.26 | 1.09 | 1.04 | 1.04 | 1.17 | 1.04 | 1.00 | 0.96 |
time (sec) |
N/A | 0.166 | 0.011 | 0.294 | 0.037 | 0.078 | 0.050 | 0.108 | 0.176 | 0.029 |
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 | 24 | 24 | 22 | 23 | 26 | 20 | 26 | 52 | 24 |
N.S. |
1 | 1.26 | 1.26 | 1.16 | 1.21 | 1.37 | 1.05 | 1.37 | 2.74 | 1.26 |
time (sec) |
N/A | 0.404 | 0.014 | 0.383 | 0.048 | 0.095 | 0.635 | 0.137 | 0.183 | 2.950 |
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 | 31 | 61 | 31 | 40 | 0 | 69 | 0 | 65 | 44 | 36 |
N.S. |
1 | 1.97 | 1.00 | 1.29 | 0.00 | 2.23 | 0.00 | 2.10 | 1.42 | 1.16 |
time (sec) |
N/A | 0.301 | 0.315 | 0.430 | 0.000 | 0.087 | 0.000 | 0.110 | 0.183 | 3.026 |
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 | 54 | 29 | 34 | 42 | 37 | 34 | 45 | 43 | 51 |
N.S. |
1 | 1.74 | 0.94 | 1.10 | 1.35 | 1.19 | 1.10 | 1.45 | 1.39 | 1.65 |
time (sec) |
N/A | 0.225 | 0.034 | 0.762 | 0.035 | 0.089 | 0.271 | 0.116 | 0.183 | 2.995 |
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 | 22 | 24 | 22 | 20 | 25 | 19 | 21 | 25 | 21 |
N.S. |
1 | 1.10 | 1.20 | 1.10 | 1.00 | 1.25 | 0.95 | 1.05 | 1.25 | 1.05 |
time (sec) |
N/A | 0.185 | 0.004 | 0.099 | 0.022 | 0.074 | 0.044 | 0.105 | 0.181 | 2.863 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | C | B | B | A | B | B | B |
verified | N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 525 | 37 | 142 | 105 | 72 | 31 | 91 | 120 | 89 |
N.S. |
1 | 14.58 | 1.03 | 3.94 | 2.92 | 2.00 | 0.86 | 2.53 | 3.33 | 2.47 |
time (sec) |
N/A | 5.117 | 0.107 | 0.471 | 0.115 | 0.095 | 0.316 | 0.433 | 0.184 | 3.271 |
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 | 10 | 10 | 7 | 6 | 6 | 10 | 7 | 6 | 6 |
N.S. |
1 | 0.83 | 0.83 | 0.58 | 0.50 | 0.50 | 0.83 | 0.58 | 0.50 | 0.50 |
time (sec) |
N/A | 0.127 | 0.001 | 0.097 | 0.023 | 0.074 | 0.025 | 0.116 | 0.186 | 0.025 |
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 | 23 | 23 | 26 | 25 | 24 | 27 | 23 | 25 |
N.S. |
1 | 0.00 | 1.05 | 1.05 | 1.18 | 1.14 | 1.09 | 1.23 | 1.05 | 1.14 |
time (sec) |
N/A | 0.000 | 0.098 | 1.119 | 0.068 | 0.094 | 0.155 | 0.126 | 0.186 | 2.966 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | C | A | A | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 12 | 29 | 12 | 13 | 182 | 14 | 14 | 38 | 14 | 14 |
N.S. |
1 | 2.42 | 1.00 | 1.08 | 15.17 | 1.17 | 1.17 | 3.17 | 1.17 | 1.17 |
time (sec) |
N/A | 0.182 | 0.031 | 0.192 | 0.158 | 0.087 | 0.059 | 0.118 | 0.193 | 0.062 |
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 | 29 | 400 | 29 | 37 | 703 | 44 | 31 | 45 | 59 | 28 |
N.S. |
1 | 13.79 | 1.00 | 1.28 | 24.24 | 1.52 | 1.07 | 1.55 | 2.03 | 0.97 |
time (sec) |
N/A | 1.484 | 4.103 | 2.988 | 0.098 | 0.082 | 0.335 | 0.130 | 0.222 | 3.602 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 29 | 29 | 27 | 42 | 26 | 26 | 0 | 30 | 28 |
N.S. |
1 | 1.12 | 1.12 | 1.04 | 1.62 | 1.00 | 1.00 | 0.00 | 1.15 | 1.08 |
time (sec) |
N/A | 1.359 | 0.089 | 157.205 | 0.171 | 0.091 | 27.458 | 0.000 | 0.172 | 3.193 |
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 | 21 | 19 | 19 | 19 | 19 | 20 | 19 | 23 | 18 |
N.S. |
1 | 1.11 | 1.00 | 1.00 | 1.00 | 1.00 | 1.05 | 1.00 | 1.21 | 0.95 |
time (sec) |
N/A | 0.178 | 0.015 | 0.225 | 0.024 | 0.079 | 0.068 | 0.115 | 0.198 | 0.039 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 24 | 22 | 28 | 0 | 42 | 29 | 40 | 27 | 27 |
N.S. |
1 | 0.96 | 0.88 | 1.12 | 0.00 | 1.68 | 1.16 | 1.60 | 1.08 | 1.08 |
time (sec) |
N/A | 0.498 | 0.014 | 0.417 | 0.000 | 0.103 | 0.215 | 0.121 | 0.175 | 0.084 |
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 | 20 | 19 | 32 | 32 | 17 | 22 | 30 | 18 |
N.S. |
1 | 0.00 | 0.74 | 0.70 | 1.19 | 1.19 | 0.63 | 0.81 | 1.11 | 0.67 |
time (sec) |
N/A | 0.000 | 1.678 | 3.449 | 0.063 | 0.081 | 0.078 | 0.116 | 0.180 | 3.034 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | B | A | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 25 | 28 | 56 | 56 | 27 | 68 | 63 | 57 |
N.S. |
1 | 0.00 | 1.00 | 1.12 | 2.24 | 2.24 | 1.08 | 2.72 | 2.52 | 2.28 |
time (sec) |
N/A | 0.000 | 0.184 | 7.732 | 0.186 | 0.091 | 0.168 | 0.163 | 43.402 | 3.158 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | A | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 40 | 142 | 60 | 43 | 37 | 48 | 304 | 43 |
N.S. |
1 | 0.00 | 1.29 | 4.58 | 1.94 | 1.39 | 1.19 | 1.55 | 9.81 | 1.39 |
time (sec) |
N/A | 0.000 | 0.079 | 9.061 | 0.178 | 0.096 | 0.682 | 0.355 | 0.213 | 3.338 |
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 | 21 | 81 | 23 | 26 | 18 | 25 | 24 | 25 | 24 | 18 |
N.S. |
1 | 3.86 | 1.10 | 1.24 | 0.86 | 1.19 | 1.14 | 1.19 | 1.14 | 0.86 |
time (sec) |
N/A | 0.275 | 0.017 | 0.222 | 0.099 | 0.069 | 0.069 | 0.117 | 0.205 | 2.956 |
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 | 27 | 0 | 33 | 30 | 48 | 43 | 44 | 0 | 41 | 42 |
N.S. |
1 | 0.00 | 1.22 | 1.11 | 1.78 | 1.59 | 1.63 | 0.00 | 1.52 | 1.56 |
time (sec) |
N/A | 0.000 | 0.043 | 4.694 | 0.139 | 0.087 | 0.303 | 0.000 | 9.545 | 3.216 |
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 | 23 | 19 | 18 | 20 | 24 | 20 | 21 | 18 |
N.S. |
1 | 0.00 | 0.85 | 0.70 | 0.67 | 0.74 | 0.89 | 0.74 | 0.78 | 0.67 |
time (sec) |
N/A | 0.000 | 0.346 | 0.328 | 0.084 | 0.092 | 0.156 | 0.125 | 0.209 | 3.359 |
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 | 19 | 0 | 17 | 18 | 21 | 17 | 14 | 17 | 17 | 17 |
N.S. |
1 | 0.00 | 0.89 | 0.95 | 1.11 | 0.89 | 0.74 | 0.89 | 0.89 | 0.89 |
time (sec) |
N/A | 0.000 | 1.100 | 0.616 | 0.151 | 0.071 | 0.069 | 0.124 | 0.192 | 3.420 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | A | A | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 23 | 42 | 114 | 40 | 20 | 1412 | 36 | 254 |
N.S. |
1 | 0.00 | 1.00 | 1.83 | 4.96 | 1.74 | 0.87 | 61.39 | 1.57 | 11.04 |
time (sec) |
N/A | 0.000 | 0.334 | 2.020 | 0.192 | 0.086 | 0.178 | 2.126 | 0.195 | 3.315 |
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 | 17 | 16 | 12 | 10 | 13 | 15 | 7 | 15 | 16 | 9 |
N.S. |
1 | 0.94 | 0.71 | 0.59 | 0.76 | 0.88 | 0.41 | 0.88 | 0.94 | 0.53 |
time (sec) |
N/A | 0.187 | 0.008 | 0.198 | 0.052 | 0.073 | 0.052 | 0.109 | 0.187 | 0.031 |
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 | 25 | 0 | 24 | 22 | 37 | 37 | 37 | 37 | 47 | 37 |
N.S. |
1 | 0.00 | 0.96 | 0.88 | 1.48 | 1.48 | 1.48 | 1.48 | 1.88 | 1.48 |
time (sec) |
N/A | 0.000 | 0.114 | 3.592 | 0.106 | 0.078 | 0.197 | 0.174 | 0.230 | 0.101 |
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 | 25 | 0 | 37 | 36 | 41 | 35 | 31 | 85 | 41 | 88 |
N.S. |
1 | 0.00 | 1.48 | 1.44 | 1.64 | 1.40 | 1.24 | 3.40 | 1.64 | 3.52 |
time (sec) |
N/A | 0.000 | 0.813 | 0.537 | 0.235 | 0.069 | 0.160 | 0.120 | 0.200 | 2.942 |
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 | 29 | 0 | 26 | 48 | 39 | 37 | 24 | 64 | 32 | 32 |
N.S. |
1 | 0.00 | 0.90 | 1.66 | 1.34 | 1.28 | 0.83 | 2.21 | 1.10 | 1.10 |
time (sec) |
N/A | 0.000 | 0.415 | 1.206 | 0.150 | 0.096 | 0.090 | 0.231 | 0.198 | 3.534 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | A | B | B | B | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 263 | 94 | 34 | 588 | 55 | 71 | 65 | 190 | 135 |
N.S. |
1 | 12.52 | 4.48 | 1.62 | 28.00 | 2.62 | 3.38 | 3.10 | 9.05 | 6.43 |
time (sec) |
N/A | 1.110 | 0.055 | 2.579 | 0.047 | 0.084 | 0.131 | 0.146 | 0.192 | 3.406 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | C | A | A | A | F(-2) | B | B |
verified | N/A | Yes | N/A | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 23 | 0 | 55 | 23 | 34 | 24 | 0 | 24 | 21 |
N.S. |
1 | 0.96 | 0.00 | 2.29 | 0.96 | 1.42 | 1.00 | 0.00 | 1.00 | 0.88 |
time (sec) |
N/A | 1.532 | 0.000 | 0.535 | 0.164 | 0.087 | 1.167 | 0.000 | 0.209 | 3.766 |
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 | 24 | 22 | 20 | 28 | 21 | 27 | 19 | 41 | 19 |
N.S. |
1 | 1.09 | 1.00 | 0.91 | 1.27 | 0.95 | 1.23 | 0.86 | 1.86 | 0.86 |
time (sec) |
N/A | 0.194 | 0.004 | 0.616 | 0.027 | 0.075 | 0.159 | 0.108 | 0.196 | 0.072 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | A | A | A | A | A | B | B |
verified | N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 0 | 0 | 17 | 16 | 16 | 17 | 23 | 18 | 23 |
N.S. |
1 | 0.00 | 0.00 | 1.00 | 0.94 | 0.94 | 1.00 | 1.35 | 1.06 | 1.35 |
time (sec) |
N/A | 0.000 | 0.000 | 0.328 | 0.161 | 0.075 | 0.100 | 0.137 | 0.198 | 3.082 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | B | A | B | B | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 22 | 21 | 42 | 42 | 37 | 94 | 66 | 0 |
N.S. |
1 | 0.00 | 0.96 | 0.91 | 1.83 | 1.83 | 1.61 | 4.09 | 2.87 | 0.00 |
time (sec) |
N/A | 0.000 | 0.096 | 0.277 | 0.074 | 0.079 | 0.128 | 0.121 | 0.198 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | B | A | F | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 26 | 22 | 41 | 46 | 20 | 0 | 37 | 41 |
N.S. |
1 | 0.00 | 1.00 | 0.85 | 1.58 | 1.77 | 0.77 | 0.00 | 1.42 | 1.58 |
time (sec) |
N/A | 0.000 | 5.103 | 38.193 | 0.266 | 0.091 | 0.502 | 0.000 | 0.196 | 2.885 |
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 | 9 | 9 | 10 | 9 | 14 | 5 | 9 | 14 | 9 |
N.S. |
1 | 0.41 | 0.41 | 0.45 | 0.41 | 0.64 | 0.23 | 0.41 | 0.64 | 0.41 |
time (sec) |
N/A | 0.160 | 0.004 | 0.201 | 0.027 | 0.072 | 0.042 | 0.102 | 0.211 | 0.020 |
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 | 22 | 22 | 38 | 38 | 15 | 38 | 40 | 38 |
N.S. |
1 | 0.00 | 0.85 | 0.85 | 1.46 | 1.46 | 0.58 | 1.46 | 1.54 | 1.46 |
time (sec) |
N/A | 0.000 | 0.234 | 2.571 | 0.146 | 0.111 | 0.112 | 0.134 | 0.204 | 3.407 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | F | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 29 | 26 | 27 | 28 | 28 | 0 | 0 | 109 | 21 |
N.S. |
1 | 1.16 | 1.04 | 1.08 | 1.12 | 1.12 | 0.00 | 0.00 | 4.36 | 0.84 |
time (sec) |
N/A | 1.339 | 0.065 | 5.387 | 0.226 | 0.091 | 0.000 | 0.000 | 200.018 | 3.263 |