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 | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 9 | 9 | 9 | 8 | 7 | 12 | 0 | 7 | 21 | 27 |
N.S. |
1 | 1.00 | 1.00 | 0.89 | 0.78 | 1.33 | 0.00 | 0.78 | 2.33 | 3.00 |
time (sec) |
N/A | 0.173 | 0.005 | 0.713 | 0.030 | 0.078 | 0.000 | 0.113 | 0.151 | 1.460 |
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 | 20 | 16 | 16 | 16 | 12 | 16 | 15 | 15 |
N.S. |
1 | 1.00 | 1.00 | 0.80 | 0.80 | 0.80 | 0.60 | 0.80 | 0.75 | 0.75 |
time (sec) |
N/A | 0.134 | 0.000 | 0.027 | 0.029 | 0.071 | 0.019 | 0.127 | 0.144 | 0.014 |
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 | 15 | 13 | 10 | 9 | 9 | 8 | 10 | 10 | 9 |
N.S. |
1 | 1.25 | 1.08 | 0.83 | 0.75 | 0.75 | 0.67 | 0.83 | 0.83 | 0.75 |
time (sec) |
N/A | 0.167 | 0.014 | 0.033 | 0.028 | 0.069 | 0.030 | 0.117 | 0.151 | 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 | 21 | 25 | 21 | 18 | 17 | 17 | 15 | 17 | 17 | 17 |
N.S. |
1 | 1.19 | 1.00 | 0.86 | 0.81 | 0.81 | 0.71 | 0.81 | 0.81 | 0.81 |
time (sec) |
N/A | 0.135 | 0.004 | 0.094 | 0.023 | 0.061 | 0.036 | 0.118 | 0.146 | 0.028 |
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 | 33 | 43 | 22 | 30 | 27 | 20 | 23 | 21 | 11 |
N.S. |
1 | 0.77 | 1.00 | 0.51 | 0.70 | 0.63 | 0.47 | 0.53 | 0.49 | 0.26 |
time (sec) |
N/A | 0.192 | 0.014 | 0.118 | 0.024 | 0.081 | 0.098 | 0.131 | 0.142 | 0.224 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 18 | 15 | 16 | 22 | 144 | 43 | 21 | 14 |
N.S. |
1 | 1.00 | 0.75 | 0.62 | 0.67 | 0.92 | 6.00 | 1.79 | 0.88 | 0.58 |
time (sec) |
N/A | 0.143 | 0.013 | 0.134 | 0.022 | 0.067 | 0.520 | 0.117 | 0.149 | 0.019 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 41 | 24 | 20 | 16 | 16 | 34 | 16 | 17 | 21 |
N.S. |
1 | 1.08 | 0.63 | 0.53 | 0.42 | 0.42 | 0.89 | 0.42 | 0.45 | 0.55 |
time (sec) |
N/A | 0.205 | 0.007 | 0.019 | 0.025 | 0.066 | 0.088 | 0.118 | 0.154 | 0.018 |
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 | 37 | 43 | 37 | 31 | 30 | 32 | 39 | 30 | 27 | 32 |
N.S. |
1 | 1.16 | 1.00 | 0.84 | 0.81 | 0.86 | 1.05 | 0.81 | 0.73 | 0.86 |
time (sec) |
N/A | 0.221 | 0.031 | 0.155 | 0.106 | 0.073 | 0.559 | 0.122 | 0.154 | 0.107 |
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 | 17 | 17 | 17 | 16 | 15 | 21 | 14 | 17 | 21 | 15 |
N.S. |
1 | 1.00 | 1.00 | 0.94 | 0.88 | 1.24 | 0.82 | 1.00 | 1.24 | 0.88 |
time (sec) |
N/A | 0.197 | 0.003 | 0.099 | 0.023 | 0.077 | 0.040 | 0.125 | 0.148 | 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 | 40 | 40 | 29 | 26 | 38 | 26 | 39 | 26 | 34 | 34 |
N.S. |
1 | 1.00 | 0.72 | 0.65 | 0.95 | 0.65 | 0.98 | 0.65 | 0.85 | 0.85 |
time (sec) |
N/A | 0.242 | 0.058 | 0.287 | 0.035 | 0.078 | 0.083 | 0.122 | 0.147 | 0.105 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 5 | 5 | 5 | 6 | 5 | 20 | 5 | 5 | 5 | 5 |
N.S. |
1 | 1.00 | 1.00 | 1.20 | 1.00 | 4.00 | 1.00 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.176 | 2.619 | 0.167 | 0.029 | 0.079 | 0.128 | 0.119 | 0.155 | 0.046 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 6 | 6 | 20 | 5 | 4 | 18 | 3 | 19 | 4 | 4 |
N.S. |
1 | 1.00 | 3.33 | 0.83 | 0.67 | 3.00 | 0.50 | 3.17 | 0.67 | 0.67 |
time (sec) |
N/A | 0.119 | 0.021 | 0.306 | 0.100 | 0.072 | 0.057 | 0.128 | 0.144 | 0.004 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 37 | 37 | 24 | 22 | 62 | 62 | 61 | 22 | 63 | 29 |
N.S. |
1 | 1.00 | 0.65 | 0.59 | 1.68 | 1.68 | 1.65 | 0.59 | 1.70 | 0.78 |
time (sec) |
N/A | 0.153 | 0.005 | 0.093 | 0.024 | 0.058 | 0.049 | 0.120 | 0.166 | 0.053 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 25 | 21 | 18 | 18 | 36 | 19 | 18 | 18 | 18 |
N.S. |
1 | 1.19 | 1.00 | 0.86 | 0.86 | 1.71 | 0.90 | 0.86 | 0.86 | 0.86 |
time (sec) |
N/A | 0.203 | 0.017 | 0.128 | 0.029 | 0.071 | 0.041 | 0.132 | 0.168 | 0.187 |
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 | 30 | 25 | 24 | 22 | 41 | 24 | 24 | 24 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 0.80 | 0.73 | 1.37 | 0.80 | 0.80 | 0.80 |
time (sec) |
N/A | 0.197 | 0.040 | 8.827 | 0.025 | 0.073 | 0.061 | 0.128 | 0.158 | 0.101 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 4 | 4 | 27 | 4 | 3 | 3 | 3 | 3 | 4 | 3 |
N.S. |
1 | 1.00 | 6.75 | 1.00 | 0.75 | 0.75 | 0.75 | 0.75 | 1.00 | 0.75 |
time (sec) |
N/A | 0.170 | 0.005 | 0.117 | 0.029 | 0.073 | 0.168 | 0.123 | 0.149 | 0.048 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 13 | 17 | 13 | 12 | 15 | 11 | 10 | 15 | 28 | 11 |
N.S. |
1 | 1.31 | 1.00 | 0.92 | 1.15 | 0.85 | 0.77 | 1.15 | 2.15 | 0.85 |
time (sec) |
N/A | 0.137 | 0.003 | 0.090 | 0.024 | 0.064 | 0.040 | 0.122 | 0.144 | 0.024 |
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 | 49 | 24 | 21 | 21 | 21 | 22 | 21 | 24 | 21 |
N.S. |
1 | 1.11 | 0.55 | 0.48 | 0.48 | 0.48 | 0.50 | 0.48 | 0.55 | 0.48 |
time (sec) |
N/A | 0.232 | 0.014 | 0.039 | 0.023 | 0.071 | 0.030 | 0.117 | 0.160 | 0.014 |
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 | 45 | 42 | 28 | 27 | 25 | 37 | 27 | 26 | 27 |
N.S. |
1 | 1.10 | 1.02 | 0.68 | 0.66 | 0.61 | 0.90 | 0.66 | 0.63 | 0.66 |
time (sec) |
N/A | 0.158 | 0.025 | 0.074 | 0.114 | 0.067 | 1.518 | 0.122 | 0.148 | 0.016 |
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 | 25 | 25 | 25 | 20 | 19 | 17 | 116 | 13 | 89 | 14 |
N.S. |
1 | 1.00 | 1.00 | 0.80 | 0.76 | 0.68 | 4.64 | 0.52 | 3.56 | 0.56 |
time (sec) |
N/A | 0.198 | 0.007 | 1.605 | 0.024 | 0.082 | 0.710 | 0.120 | 0.156 | 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 | 12 | 12 | 12 | 11 | 10 | 10 | 7 | 10 | 8 | 8 |
N.S. |
1 | 1.00 | 1.00 | 0.92 | 0.83 | 0.83 | 0.58 | 0.83 | 0.67 | 0.67 |
time (sec) |
N/A | 0.134 | 0.002 | 0.041 | 0.026 | 0.064 | 0.029 | 0.124 | 0.149 | 0.098 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 41 | 57 | 65 | 41 | 43 | 32 | 0 | 30 | 29 | 43 |
N.S. |
1 | 1.39 | 1.59 | 1.00 | 1.05 | 0.78 | 0.00 | 0.73 | 0.71 | 1.05 |
time (sec) |
N/A | 0.155 | 0.058 | 0.154 | 0.106 | 0.070 | 0.000 | 0.120 | 0.156 | 0.101 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 41 | 27 | 119 | 27 | 27 | 29 | 28 | 29 | 0 |
N.S. |
1 | 1.21 | 0.79 | 3.50 | 0.79 | 0.79 | 0.85 | 0.82 | 0.85 | 0.00 |
time (sec) |
N/A | 0.184 | 0.010 | 0.106 | 0.106 | 0.079 | 1.053 | 0.126 | 0.156 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 19 | 18 | 17 | 17 | 42 | 17 | 17 | 17 |
N.S. |
1 | 1.00 | 1.00 | 0.95 | 0.89 | 0.89 | 2.21 | 0.89 | 0.89 | 0.89 |
time (sec) |
N/A | 0.135 | 0.004 | 0.106 | 0.107 | 0.073 | 0.041 | 0.123 | 0.157 | 0.024 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 38 | 45 | 30 | 39 | 37 | 34 | 31 | 37 | 28 |
N.S. |
1 | 1.00 | 1.18 | 0.79 | 1.03 | 0.97 | 0.89 | 0.82 | 0.97 | 0.74 |
time (sec) |
N/A | 0.157 | 0.066 | 0.214 | 0.105 | 0.074 | 0.210 | 0.120 | 0.147 | 0.027 |
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 | 12 | 12 | 12 | 9 | 8 | 8 | 7 | 8 | 13 | 8 |
N.S. |
1 | 1.00 | 1.00 | 0.75 | 0.67 | 0.67 | 0.58 | 0.67 | 1.08 | 0.67 |
time (sec) |
N/A | 0.130 | 0.004 | 0.131 | 0.104 | 0.063 | 0.047 | 0.119 | 0.155 | 0.105 |
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 | 27 | 26 | 26 | 36 | 26 | 25 | 28 |
N.S. |
1 | 1.00 | 1.00 | 0.87 | 0.84 | 0.84 | 1.16 | 0.84 | 0.81 | 0.90 |
time (sec) |
N/A | 0.156 | 0.008 | 0.214 | 0.108 | 0.065 | 0.045 | 0.120 | 0.155 | 0.098 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | B | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 10 | 10 | 37 | 16 | 121 | 29 | 12 | 150 | 28 | 19 |
N.S. |
1 | 1.00 | 3.70 | 1.60 | 12.10 | 2.90 | 1.20 | 15.00 | 2.80 | 1.90 |
time (sec) |
N/A | 0.176 | 0.009 | 0.092 | 0.107 | 0.079 | 0.409 | 0.161 | 0.153 | 0.136 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 15 | 27 | 29 | 26 | 22 | 30 | 26 | 13 |
N.S. |
1 | 1.00 | 1.00 | 1.80 | 1.93 | 1.73 | 1.47 | 2.00 | 1.73 | 0.87 |
time (sec) |
N/A | 0.138 | 0.004 | 0.112 | 0.031 | 0.067 | 0.061 | 0.125 | 0.152 | 0.106 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 21 | 14 | 0 | 13 | 63 | 13 | 19 | 21 |
N.S. |
1 | 1.00 | 1.00 | 0.67 | 0.00 | 0.62 | 3.00 | 0.62 | 0.90 | 1.00 |
time (sec) |
N/A | 0.135 | 0.059 | 0.020 | 0.000 | 0.064 | 0.146 | 0.119 | 0.153 | 0.110 |
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 | 18 | 16 | 19 | 17 | 17 | 18 | 19 | 17 |
N.S. |
1 | 1.09 | 0.78 | 0.70 | 0.83 | 0.74 | 0.74 | 0.78 | 0.83 | 0.74 |
time (sec) |
N/A | 0.176 | 0.030 | 0.053 | 0.028 | 0.067 | 0.061 | 0.118 | 0.145 | 0.148 |
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 | 20 | 17 | 16 | 16 | 17 | 16 | 14 | 16 |
N.S. |
1 | 1.00 | 1.00 | 0.85 | 0.80 | 0.80 | 0.85 | 0.80 | 0.70 | 0.80 |
time (sec) |
N/A | 0.158 | 0.006 | 0.043 | 0.029 | 0.078 | 0.114 | 0.121 | 0.148 | 0.144 |
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 | 19 | 14 | 20 | 22 | 18 |
N.S. |
1 | 1.00 | 1.00 | 0.89 | 1.00 | 1.06 | 0.78 | 1.11 | 1.22 | 1.00 |
time (sec) |
N/A | 0.146 | 0.004 | 0.065 | 0.023 | 0.079 | 0.053 | 0.120 | 0.142 | 0.103 |
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 | 12 | 12 | 12 | 20 | 19 | 25 | 20 | 20 | 30 | 19 |
N.S. |
1 | 1.00 | 1.00 | 1.67 | 1.58 | 2.08 | 1.67 | 1.67 | 2.50 | 1.58 |
time (sec) |
N/A | 0.150 | 0.028 | 0.037 | 0.025 | 0.084 | 0.060 | 0.130 | 0.153 | 0.131 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 8 | 8 | 23 | 13 | 10 | 15 | 12 | 16 | 15 | 8 |
N.S. |
1 | 1.00 | 2.88 | 1.62 | 1.25 | 1.88 | 1.50 | 2.00 | 1.88 | 1.00 |
time (sec) |
N/A | 0.261 | 0.004 | 0.138 | 0.106 | 0.086 | 0.299 | 0.121 | 0.153 | 0.124 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 18 | 13 | 12 | 12 | 44 | 12 | 11 | 12 |
N.S. |
1 | 1.00 | 1.00 | 0.72 | 0.67 | 0.67 | 2.44 | 0.67 | 0.61 | 0.67 |
time (sec) |
N/A | 0.128 | 0.012 | 0.216 | 0.107 | 0.073 | 0.471 | 0.120 | 0.147 | 0.158 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F(-1) | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 11 | 15 | 11 | 10 | 0 | 24 | 0 | 9 | 26 | 18 |
N.S. |
1 | 1.36 | 1.00 | 0.91 | 0.00 | 2.18 | 0.00 | 0.82 | 2.36 | 1.64 |
time (sec) |
N/A | 0.221 | 0.012 | 0.322 | 0.000 | 0.160 | 0.000 | 0.130 | 0.151 | 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 | 30 | 30 | 46 | 23 | 22 | 37 | 27 | 22 | 22 | 22 |
N.S. |
1 | 1.00 | 1.53 | 0.77 | 0.73 | 1.23 | 0.90 | 0.73 | 0.73 | 0.73 |
time (sec) |
N/A | 0.138 | 0.048 | 0.353 | 0.104 | 0.087 | 0.086 | 0.129 | 0.153 | 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 | 24 | 27 | 20 | 23 | 21 | 21 | 26 | 21 | 24 | 23 |
N.S. |
1 | 1.12 | 0.83 | 0.96 | 0.88 | 0.88 | 1.08 | 0.88 | 1.00 | 0.96 |
time (sec) |
N/A | 0.302 | 0.006 | 0.158 | 0.030 | 0.079 | 0.118 | 0.113 | 0.144 | 0.017 |
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 | 55 | 47 | 33 | 49 | 39 | 37 | 40 | 58 | 39 |
N.S. |
1 | 1.10 | 0.94 | 0.66 | 0.98 | 0.78 | 0.74 | 0.80 | 1.16 | 0.78 |
time (sec) |
N/A | 0.174 | 0.052 | 0.215 | 0.101 | 0.078 | 0.254 | 0.129 | 0.166 | 0.122 |
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 | 11 | 11 | 11 | 10 | 9 | 46 | 51 | 9 | 45 | 9 |
N.S. |
1 | 1.00 | 1.00 | 0.91 | 0.82 | 4.18 | 4.64 | 0.82 | 4.09 | 0.82 |
time (sec) |
N/A | 0.126 | 0.001 | 0.091 | 0.022 | 0.074 | 0.018 | 0.123 | 0.158 | 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 | 25 | 25 | 31 | 20 | 19 | 19 | 20 | 19 | 30 | 19 |
N.S. |
1 | 1.00 | 1.24 | 0.80 | 0.76 | 0.76 | 0.80 | 0.76 | 1.20 | 0.76 |
time (sec) |
N/A | 0.192 | 0.008 | 1.574 | 0.022 | 0.082 | 0.023 | 0.123 | 0.152 | 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 | 27 | 27 | 22 | 20 | 19 | 21 | 26 | 19 | 22 | 19 |
N.S. |
1 | 1.00 | 0.81 | 0.74 | 0.70 | 0.78 | 0.96 | 0.70 | 0.81 | 0.70 |
time (sec) |
N/A | 0.155 | 0.033 | 0.198 | 0.026 | 0.093 | 0.162 | 0.118 | 0.149 | 0.016 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 41 | 23 | 34 | 56 | 36 | 70 | 26 | 18 |
N.S. |
1 | 1.00 | 1.71 | 0.96 | 1.42 | 2.33 | 1.50 | 2.92 | 1.08 | 0.75 |
time (sec) |
N/A | 0.205 | 0.027 | 0.172 | 0.025 | 0.088 | 0.052 | 0.125 | 0.156 | 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 | 34 | 34 | 35 | 32 | 33 | 35 | 27 | 44 | 34 | 32 |
N.S. |
1 | 1.00 | 1.03 | 0.94 | 0.97 | 1.03 | 0.79 | 1.29 | 1.00 | 0.94 |
time (sec) |
N/A | 0.150 | 0.026 | 0.168 | 0.102 | 0.081 | 0.091 | 0.120 | 0.151 | 0.258 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 36 | 30 | 25 | 35 | 28 | 73 | 38 | 22 | 37 |
N.S. |
1 | 1.20 | 1.00 | 0.83 | 1.17 | 0.93 | 2.43 | 1.27 | 0.73 | 1.23 |
time (sec) |
N/A | 0.152 | 0.018 | 0.135 | 0.105 | 0.072 | 0.739 | 0.121 | 0.155 | 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 | 32 | 37 | 19 | 16 | 16 | 16 | 15 | 16 | 17 | 16 |
N.S. |
1 | 1.16 | 0.59 | 0.50 | 0.50 | 0.50 | 0.47 | 0.50 | 0.53 | 0.50 |
time (sec) |
N/A | 0.192 | 0.013 | 0.039 | 0.028 | 0.077 | 0.031 | 0.122 | 0.153 | 0.019 |
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 | 23 | 23 | 31 | 18 | 17 | 12 | 26 | 42 | 11 | 12 |
N.S. |
1 | 1.00 | 1.35 | 0.78 | 0.74 | 0.52 | 1.13 | 1.83 | 0.48 | 0.52 |
time (sec) |
N/A | 0.203 | 0.016 | 0.171 | 0.024 | 0.084 | 0.103 | 0.129 | 0.154 | 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 | 27 | 24 | 24 | 22 | 21 | 21 | 19 | 21 | 20 | 21 |
N.S. |
1 | 0.89 | 0.89 | 0.81 | 0.78 | 0.78 | 0.70 | 0.78 | 0.74 | 0.78 |
time (sec) |
N/A | 0.195 | 0.005 | 0.084 | 0.108 | 0.084 | 0.067 | 0.128 | 0.150 | 0.160 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 43 | 32 | 31 | 53 | 28 | 29 | 32 | 29 | 28 |
N.S. |
1 | 1.13 | 0.84 | 0.82 | 1.39 | 0.74 | 0.76 | 0.84 | 0.76 | 0.74 |
time (sec) |
N/A | 0.189 | 0.009 | 0.064 | 0.106 | 0.083 | 0.129 | 0.127 | 0.156 | 0.126 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 5 | 5 | 7 | 5 | 4 | 16 | 8 | 6 | 8 | 6 |
N.S. |
1 | 1.00 | 1.40 | 1.00 | 0.80 | 3.20 | 1.60 | 1.20 | 1.60 | 1.20 |
time (sec) |
N/A | 0.178 | 0.005 | 0.228 | 0.025 | 0.083 | 0.293 | 0.119 | 0.156 | 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 | 29 | 34 | 25 | 22 | 21 | 21 | 27 | 21 | 23 | 23 |
N.S. |
1 | 1.17 | 0.86 | 0.76 | 0.72 | 0.72 | 0.93 | 0.72 | 0.79 | 0.79 |
time (sec) |
N/A | 0.261 | 0.010 | 0.224 | 0.025 | 0.079 | 0.080 | 0.119 | 0.145 | 0.109 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 36 | 45 | 29 | 36 | 47 | 27 | 26 | 34 | 27 |
N.S. |
1 | 1.00 | 1.25 | 0.81 | 1.00 | 1.31 | 0.75 | 0.72 | 0.94 | 0.75 |
time (sec) |
N/A | 0.157 | 0.055 | 0.159 | 0.105 | 0.076 | 0.257 | 0.124 | 0.145 | 0.104 |
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 | 34 | 31 | 23 | 22 | 22 | 24 | 22 | 20 | 22 |
N.S. |
1 | 1.21 | 1.11 | 0.82 | 0.79 | 0.79 | 0.86 | 0.79 | 0.71 | 0.79 |
time (sec) |
N/A | 0.164 | 0.008 | 0.132 | 0.100 | 0.075 | 0.063 | 0.120 | 0.168 | 0.030 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 31 | 26 | 25 | 42 | 43 | 46 | 38 | 98 | 29 |
N.S. |
1 | 1.19 | 1.00 | 0.96 | 1.62 | 1.65 | 1.77 | 1.46 | 3.77 | 1.12 |
time (sec) |
N/A | 0.263 | 0.004 | 0.302 | 0.024 | 0.091 | 0.081 | 0.121 | 0.151 | 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 | 46 | 56 | 30 | 23 | 24 | 33 | 46 | 22 | 38 | 22 |
N.S. |
1 | 1.22 | 0.65 | 0.50 | 0.52 | 0.72 | 1.00 | 0.48 | 0.83 | 0.48 |
time (sec) |
N/A | 0.256 | 0.025 | 1.123 | 0.032 | 0.095 | 0.026 | 0.118 | 0.149 | 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 | 20 | 20 | 15 | 17 | 16 | 24 | 17 | 16 | 13 | 11 |
N.S. |
1 | 1.00 | 0.75 | 0.85 | 0.80 | 1.20 | 0.85 | 0.80 | 0.65 | 0.55 |
time (sec) |
N/A | 0.208 | 0.011 | 0.374 | 0.030 | 0.083 | 0.603 | 0.117 | 0.151 | 0.147 |
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 | 24 | 24 | 18 | 16 | 24 | 17 | 19 | 27 | 19 |
N.S. |
1 | 1.14 | 1.14 | 0.86 | 0.76 | 1.14 | 0.81 | 0.90 | 1.29 | 0.90 |
time (sec) |
N/A | 0.174 | 0.019 | 0.032 | 0.029 | 0.072 | 0.046 | 0.124 | 0.147 | 0.037 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 37 | 37 | 33 | 77 | 47 | 58 | 0 | 50 | 12 | 0 |
N.S. |
1 | 1.00 | 0.89 | 2.08 | 1.27 | 1.57 | 0.00 | 1.35 | 0.32 | 0.00 |
time (sec) |
N/A | 0.206 | 0.015 | 0.258 | 0.129 | 0.127 | 0.000 | 0.123 | 0.150 | 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 | 28 | 28 | 46 | 26 | 29 | 27 | 29 | 28 | 22 | 23 |
N.S. |
1 | 1.00 | 1.64 | 0.93 | 1.04 | 0.96 | 1.04 | 1.00 | 0.79 | 0.82 |
time (sec) |
N/A | 0.152 | 0.036 | 0.148 | 0.023 | 0.069 | 0.225 | 0.116 | 0.148 | 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 | 19 | 19 | 19 | 17 | 15 | 18 | 17 | 15 | 18 | 21 |
N.S. |
1 | 1.00 | 1.00 | 0.89 | 0.79 | 0.95 | 0.89 | 0.79 | 0.95 | 1.11 |
time (sec) |
N/A | 0.169 | 0.006 | 0.680 | 0.022 | 0.089 | 0.021 | 0.119 | 0.148 | 0.019 |
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 | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 46 | 55 | 26 | 25 | 24 | 24 | 22 | 24 | 26 | 24 |
N.S. |
1 | 1.20 | 0.57 | 0.54 | 0.52 | 0.52 | 0.48 | 0.52 | 0.57 | 0.52 |
time (sec) |
N/A | 0.258 | 0.013 | 0.031 | 0.025 | 0.064 | 0.033 | 0.121 | 0.165 | 0.016 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | C | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 18 | 15 | 33 | 16 | 32 | 30 | 29 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 1.83 | 0.89 | 1.78 | 1.67 | 1.61 | 0.00 |
time (sec) |
N/A | 0.136 | 0.182 | 0.199 | 0.032 | 0.069 | 0.504 | 0.123 | 0.157 | 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 | 27 | 27 | 22 | 20 | 19 | 21 | 24 | 19 | 20 | 19 |
N.S. |
1 | 1.00 | 0.81 | 0.74 | 0.70 | 0.78 | 0.89 | 0.70 | 0.74 | 0.70 |
time (sec) |
N/A | 0.160 | 0.047 | 0.259 | 0.032 | 0.077 | 0.095 | 0.122 | 0.154 | 0.040 |
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 | 18 | 22 | 18 | 17 | 16 | 15 | 0 | 16 | 22 | 18 |
N.S. |
1 | 1.22 | 1.00 | 0.94 | 0.89 | 0.83 | 0.00 | 0.89 | 1.22 | 1.00 |
time (sec) |
N/A | 0.199 | 0.006 | 0.029 | 0.029 | 0.071 | 0.000 | 0.116 | 0.151 | 0.157 |
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 | 26 | 23 | 22 | 21 | 21 | 20 | 21 | 21 | 21 |
N.S. |
1 | 0.96 | 0.85 | 0.81 | 0.78 | 0.78 | 0.74 | 0.78 | 0.78 | 0.78 |
time (sec) |
N/A | 0.172 | 0.001 | 0.044 | 0.027 | 0.079 | 0.090 | 0.121 | 0.156 | 0.001 |
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 | 32 | 26 | 21 | 20 | 20 | 20 | 20 | 31 | 31 |
N.S. |
1 | 1.23 | 1.00 | 0.81 | 0.77 | 0.77 | 0.77 | 0.77 | 1.19 | 1.19 |
time (sec) |
N/A | 0.150 | 0.020 | 0.052 | 0.107 | 0.072 | 0.259 | 0.123 | 0.150 | 0.129 |
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 | 15 | 16 | 11 | 14 | 9 | 9 | 15 | 9 | 11 | 9 |
N.S. |
1 | 1.07 | 0.73 | 0.93 | 0.60 | 0.60 | 1.00 | 0.60 | 0.73 | 0.60 |
time (sec) |
N/A | 0.186 | 0.022 | 1.133 | 0.024 | 0.079 | 0.772 | 0.124 | 0.148 | 0.151 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 47 | 52 | 50 | 35 | 34 | 42 | 121 | 29 | 34 | 30 |
N.S. |
1 | 1.11 | 1.06 | 0.74 | 0.72 | 0.89 | 2.57 | 0.62 | 0.72 | 0.64 |
time (sec) |
N/A | 0.144 | 0.083 | 0.158 | 0.105 | 0.071 | 1.753 | 0.131 | 0.153 | 0.021 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 11 | 11 | 36 | 10 | 9 | 26 | 27 | 9 | 25 | 26 |
N.S. |
1 | 1.00 | 3.27 | 0.91 | 0.82 | 2.36 | 2.45 | 0.82 | 2.27 | 2.36 |
time (sec) |
N/A | 0.122 | 0.002 | 0.079 | 0.022 | 0.065 | 0.019 | 0.121 | 0.166 | 0.013 |
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 | 14 | 13 | 13 | 12 | 13 | 14 | 14 |
N.S. |
1 | 1.00 | 1.00 | 0.82 | 0.76 | 0.76 | 0.71 | 0.76 | 0.82 | 0.82 |
time (sec) |
N/A | 0.179 | 0.005 | 0.810 | 0.034 | 0.078 | 0.021 | 0.123 | 0.161 | 0.102 |
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 | 17 | 17 | 27 | 14 | 13 | 20 | 29 | 13 | 32 | 13 |
N.S. |
1 | 1.00 | 1.59 | 0.82 | 0.76 | 1.18 | 1.71 | 0.76 | 1.88 | 0.76 |
time (sec) |
N/A | 0.173 | 0.008 | 1.132 | 0.044 | 0.072 | 0.022 | 0.123 | 0.157 | 0.105 |
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 | 27 | 18 | 15 | 19 | 17 | 36 | 19 | 16 | 14 |
N.S. |
1 | 1.00 | 0.67 | 0.56 | 0.70 | 0.63 | 1.33 | 0.70 | 0.59 | 0.52 |
time (sec) |
N/A | 0.147 | 0.008 | 0.107 | 0.028 | 0.068 | 0.497 | 0.127 | 0.147 | 0.019 |
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 | 29 | 22 | 17 | 16 | 19 | 24 | 16 | 18 | 16 |
N.S. |
1 | 1.21 | 0.92 | 0.71 | 0.67 | 0.79 | 1.00 | 0.67 | 0.75 | 0.67 |
time (sec) |
N/A | 0.198 | 0.001 | 0.438 | 0.029 | 0.077 | 0.018 | 0.122 | 0.152 | 0.017 |
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 | 17 | 20 | 18 | 12 | 16 | 16 | 16 |
N.S. |
1 | 1.00 | 1.00 | 1.42 | 1.67 | 1.50 | 1.00 | 1.33 | 1.33 | 1.33 |
time (sec) |
N/A | 0.191 | 0.007 | 0.032 | 0.033 | 0.089 | 0.034 | 0.121 | 0.151 | 0.011 |
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 | 40 | 44 | 30 | 22 | 34 | 26 | 53 | 28 | 25 | 25 |
N.S. |
1 | 1.10 | 0.75 | 0.55 | 0.85 | 0.65 | 1.32 | 0.70 | 0.62 | 0.62 |
time (sec) |
N/A | 0.148 | 0.015 | 0.089 | 0.102 | 0.066 | 0.238 | 0.120 | 0.151 | 0.013 |