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 | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 75 | 75 | 65 | 62 | 64 | 123 | 65 | 86 | 188 | 56 |
N.S. |
1 | 1.00 | 0.87 | 0.83 | 0.85 | 1.64 | 0.87 | 1.15 | 2.51 | 0.75 |
time (sec) |
N/A | 0.255 | 0.044 | 0.242 | 0.029 | 0.085 | 0.116 | 0.126 | 0.160 | 1.007 |
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 | 86 | 86 | 79 | 68 | 74 | 148 | 75 | 97 | 231 | 68 |
N.S. |
1 | 1.00 | 0.92 | 0.79 | 0.86 | 1.72 | 0.87 | 1.13 | 2.69 | 0.79 |
time (sec) |
N/A | 0.245 | 0.075 | 0.250 | 0.027 | 0.119 | 0.130 | 0.124 | 0.164 | 1.023 |
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 | 97 | 97 | 88 | 73 | 84 | 173 | 85 | 106 | 274 | 76 |
N.S. |
1 | 1.00 | 0.91 | 0.75 | 0.87 | 1.78 | 0.88 | 1.09 | 2.82 | 0.78 |
time (sec) |
N/A | 0.286 | 0.062 | 0.243 | 0.032 | 0.123 | 0.124 | 0.123 | 0.162 | 1.110 |
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 | 66 | 66 | 61 | 47 | 51 | 67 | 58 | 47 | 73 | 46 |
N.S. |
1 | 1.00 | 0.92 | 0.71 | 0.77 | 1.02 | 0.88 | 0.71 | 1.11 | 0.70 |
time (sec) |
N/A | 0.231 | 0.014 | 0.235 | 0.025 | 0.084 | 0.069 | 0.126 | 0.159 | 0.021 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 59 | 59 | 56 | 42 | 46 | 62 | 51 | 42 | 68 | 41 |
N.S. |
1 | 1.00 | 0.95 | 0.71 | 0.78 | 1.05 | 0.86 | 0.71 | 1.15 | 0.69 |
time (sec) |
N/A | 0.223 | 0.012 | 0.216 | 0.036 | 0.087 | 0.066 | 0.121 | 0.160 | 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 | 50 | 50 | 51 | 37 | 41 | 57 | 42 | 37 | 63 | 36 |
N.S. |
1 | 1.00 | 1.02 | 0.74 | 0.82 | 1.14 | 0.84 | 0.74 | 1.26 | 0.72 |
time (sec) |
N/A | 0.210 | 0.011 | 0.211 | 0.025 | 0.079 | 0.059 | 0.130 | 0.160 | 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 | 45 | 45 | 46 | 32 | 36 | 52 | 37 | 32 | 58 | 31 |
N.S. |
1 | 1.00 | 1.02 | 0.71 | 0.80 | 1.16 | 0.82 | 0.71 | 1.29 | 0.69 |
time (sec) |
N/A | 0.199 | 0.010 | 0.209 | 0.025 | 0.074 | 0.060 | 0.123 | 0.160 | 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 | 38 | 34 | 27 | 31 | 47 | 31 | 27 | 53 | 26 |
N.S. |
1 | 1.00 | 0.89 | 0.71 | 0.82 | 1.24 | 0.82 | 0.71 | 1.39 | 0.68 |
time (sec) |
N/A | 0.214 | 0.016 | 0.199 | 0.025 | 0.092 | 0.058 | 0.119 | 0.160 | 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 | 33 | 33 | 33 | 24 | 28 | 37 | 26 | 24 | 48 | 23 |
N.S. |
1 | 1.00 | 1.00 | 0.73 | 0.85 | 1.12 | 0.79 | 0.73 | 1.45 | 0.70 |
time (sec) |
N/A | 0.192 | 0.006 | 0.179 | 0.027 | 0.073 | 0.054 | 0.124 | 0.167 | 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 | 18 | 18 | 16 | 15 | 19 | 19 | 17 | 14 | 20 | 14 |
N.S. |
1 | 1.00 | 0.89 | 0.83 | 1.06 | 1.06 | 0.94 | 0.78 | 1.11 | 0.78 |
time (sec) |
N/A | 0.157 | 0.004 | 0.182 | 0.035 | 0.070 | 0.049 | 0.121 | 0.167 | 1.135 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 43 | 43 | 35 | 32 | 36 | 55 | 36 | 33 | 76 | 25 |
N.S. |
1 | 1.00 | 0.81 | 0.74 | 0.84 | 1.28 | 0.84 | 0.77 | 1.77 | 0.58 |
time (sec) |
N/A | 0.203 | 0.015 | 0.204 | 0.030 | 0.099 | 0.061 | 0.124 | 0.165 | 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 | 54 | 54 | 47 | 44 | 46 | 75 | 44 | 51 | 106 | 38 |
N.S. |
1 | 1.00 | 0.87 | 0.81 | 0.85 | 1.39 | 0.81 | 0.94 | 1.96 | 0.70 |
time (sec) |
N/A | 0.199 | 0.026 | 0.204 | 0.036 | 0.070 | 0.076 | 0.126 | 0.166 | 0.027 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 65 | 65 | 48 | 48 | 56 | 95 | 54 | 46 | 138 | 45 |
N.S. |
1 | 1.00 | 0.74 | 0.74 | 0.86 | 1.46 | 0.83 | 0.71 | 2.12 | 0.69 |
time (sec) |
N/A | 0.221 | 0.018 | 0.211 | 0.027 | 0.077 | 0.087 | 0.120 | 0.173 | 1.030 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 76 | 76 | 57 | 53 | 66 | 115 | 65 | 55 | 170 | 53 |
N.S. |
1 | 1.00 | 0.75 | 0.70 | 0.87 | 1.51 | 0.86 | 0.72 | 2.24 | 0.70 |
time (sec) |
N/A | 0.237 | 0.025 | 0.205 | 0.035 | 0.077 | 0.083 | 0.123 | 0.165 | 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 | 66 | 66 | 61 | 47 | 51 | 67 | 58 | 47 | 73 | 46 |
N.S. |
1 | 1.00 | 0.92 | 0.71 | 0.77 | 1.02 | 0.88 | 0.71 | 1.11 | 0.70 |
time (sec) |
N/A | 0.218 | 0.015 | 0.233 | 0.033 | 0.080 | 0.068 | 0.128 | 0.153 | 1.016 |
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 | 59 | 59 | 56 | 42 | 46 | 62 | 51 | 42 | 68 | 41 |
N.S. |
1 | 1.00 | 0.95 | 0.71 | 0.78 | 1.05 | 0.86 | 0.71 | 1.15 | 0.69 |
time (sec) |
N/A | 0.228 | 0.014 | 0.240 | 0.025 | 0.072 | 0.063 | 0.121 | 0.159 | 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 | 52 | 52 | 47 | 37 | 41 | 57 | 44 | 37 | 63 | 36 |
N.S. |
1 | 1.00 | 0.90 | 0.71 | 0.79 | 1.10 | 0.85 | 0.71 | 1.21 | 0.69 |
time (sec) |
N/A | 0.206 | 0.014 | 0.238 | 0.027 | 0.087 | 0.073 | 0.115 | 0.158 | 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 | 45 | 45 | 46 | 32 | 36 | 52 | 37 | 32 | 58 | 31 |
N.S. |
1 | 1.00 | 1.02 | 0.71 | 0.80 | 1.16 | 0.82 | 0.71 | 1.29 | 0.69 |
time (sec) |
N/A | 0.209 | 0.011 | 0.224 | 0.030 | 0.086 | 0.062 | 0.120 | 0.155 | 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 | 38 | 34 | 27 | 31 | 47 | 31 | 27 | 53 | 26 |
N.S. |
1 | 1.00 | 0.89 | 0.71 | 0.82 | 1.24 | 0.82 | 0.71 | 1.39 | 0.68 |
time (sec) |
N/A | 0.186 | 0.016 | 0.219 | 0.024 | 0.070 | 0.056 | 0.129 | 0.158 | 0.994 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 33 | 33 | 24 | 28 | 37 | 26 | 24 | 48 | 23 |
N.S. |
1 | 1.00 | 1.00 | 0.73 | 0.85 | 1.12 | 0.79 | 0.73 | 1.45 | 0.70 |
time (sec) |
N/A | 0.177 | 0.007 | 0.191 | 0.031 | 0.087 | 0.063 | 0.118 | 0.161 | 1.001 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 43 | 43 | 35 | 32 | 36 | 55 | 32 | 33 | 76 | 25 |
N.S. |
1 | 1.00 | 0.81 | 0.74 | 0.84 | 1.28 | 0.74 | 0.77 | 1.77 | 0.58 |
time (sec) |
N/A | 0.198 | 0.016 | 0.227 | 0.031 | 0.081 | 0.070 | 0.125 | 0.158 | 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 | 54 | 54 | 47 | 44 | 46 | 75 | 46 | 51 | 106 | 38 |
N.S. |
1 | 1.00 | 0.87 | 0.81 | 0.85 | 1.39 | 0.85 | 0.94 | 1.96 | 0.70 |
time (sec) |
N/A | 0.221 | 0.026 | 0.241 | 0.025 | 0.083 | 0.075 | 0.126 | 0.154 | 0.027 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 65 | 65 | 48 | 48 | 56 | 95 | 54 | 46 | 138 | 45 |
N.S. |
1 | 1.00 | 0.74 | 0.74 | 0.86 | 1.46 | 0.83 | 0.71 | 2.12 | 0.69 |
time (sec) |
N/A | 0.231 | 0.022 | 0.223 | 0.029 | 0.082 | 0.079 | 0.119 | 0.162 | 1.018 |
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 | 76 | 76 | 57 | 53 | 66 | 115 | 65 | 55 | 170 | 53 |
N.S. |
1 | 1.00 | 0.75 | 0.70 | 0.87 | 1.51 | 0.86 | 0.72 | 2.24 | 0.70 |
time (sec) |
N/A | 0.237 | 0.033 | 0.230 | 0.025 | 0.083 | 0.083 | 0.119 | 0.167 | 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 | 73 | 73 | 66 | 52 | 56 | 72 | 65 | 52 | 78 | 51 |
N.S. |
1 | 1.00 | 0.90 | 0.71 | 0.77 | 0.99 | 0.89 | 0.71 | 1.07 | 0.70 |
time (sec) |
N/A | 0.261 | 0.015 | 0.243 | 0.032 | 0.091 | 0.069 | 0.122 | 0.161 | 0.023 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 64 | 64 | 61 | 47 | 51 | 67 | 56 | 47 | 73 | 46 |
N.S. |
1 | 1.00 | 0.95 | 0.73 | 0.80 | 1.05 | 0.88 | 0.73 | 1.14 | 0.72 |
time (sec) |
N/A | 0.218 | 0.018 | 0.225 | 0.039 | 0.077 | 0.067 | 0.121 | 0.156 | 0.020 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 59 | 59 | 56 | 42 | 46 | 62 | 51 | 42 | 68 | 41 |
N.S. |
1 | 1.00 | 0.95 | 0.71 | 0.78 | 1.05 | 0.86 | 0.71 | 1.15 | 0.69 |
time (sec) |
N/A | 0.222 | 0.014 | 0.236 | 0.026 | 0.077 | 0.074 | 0.122 | 0.151 | 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 | 52 | 52 | 47 | 37 | 41 | 57 | 44 | 37 | 63 | 36 |
N.S. |
1 | 1.00 | 0.90 | 0.71 | 0.79 | 1.10 | 0.85 | 0.71 | 1.21 | 0.69 |
time (sec) |
N/A | 0.207 | 0.014 | 0.223 | 0.025 | 0.083 | 0.065 | 0.108 | 0.159 | 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 | 45 | 45 | 46 | 32 | 36 | 52 | 37 | 32 | 58 | 31 |
N.S. |
1 | 1.00 | 1.02 | 0.71 | 0.80 | 1.16 | 0.82 | 0.71 | 1.29 | 0.69 |
time (sec) |
N/A | 0.206 | 0.012 | 0.213 | 0.031 | 0.085 | 0.058 | 0.122 | 0.160 | 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 | 38 | 34 | 27 | 31 | 47 | 31 | 27 | 53 | 26 |
N.S. |
1 | 1.00 | 0.89 | 0.71 | 0.82 | 1.24 | 0.82 | 0.71 | 1.39 | 0.68 |
time (sec) |
N/A | 0.185 | 0.015 | 0.199 | 0.053 | 0.073 | 0.054 | 0.111 | 0.163 | 1.019 |
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 | 43 | 43 | 35 | 32 | 36 | 55 | 34 | 33 | 76 | 29 |
N.S. |
1 | 1.00 | 0.81 | 0.74 | 0.84 | 1.28 | 0.79 | 0.77 | 1.77 | 0.67 |
time (sec) |
N/A | 0.201 | 0.016 | 0.253 | 0.052 | 0.070 | 0.075 | 0.120 | 0.159 | 0.034 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 54 | 54 | 47 | 44 | 46 | 75 | 44 | 51 | 106 | 38 |
N.S. |
1 | 1.00 | 0.87 | 0.81 | 0.85 | 1.39 | 0.81 | 0.94 | 1.96 | 0.70 |
time (sec) |
N/A | 0.213 | 0.025 | 0.223 | 0.040 | 0.082 | 0.086 | 0.124 | 0.162 | 1.028 |
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 | 65 | 65 | 48 | 48 | 56 | 95 | 56 | 46 | 138 | 45 |
N.S. |
1 | 1.00 | 0.74 | 0.74 | 0.86 | 1.46 | 0.86 | 0.71 | 2.12 | 0.69 |
time (sec) |
N/A | 0.227 | 0.021 | 0.234 | 0.038 | 0.075 | 0.096 | 0.125 | 0.161 | 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 | 76 | 76 | 57 | 53 | 66 | 115 | 65 | 55 | 170 | 53 |
N.S. |
1 | 1.00 | 0.75 | 0.70 | 0.87 | 1.51 | 0.86 | 0.72 | 2.24 | 0.70 |
time (sec) |
N/A | 0.228 | 0.034 | 0.227 | 0.026 | 0.088 | 0.094 | 0.121 | 0.161 | 1.019 |
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 | 87 | 87 | 64 | 58 | 76 | 135 | 75 | 78 | 202 | 65 |
N.S. |
1 | 1.00 | 0.74 | 0.67 | 0.87 | 1.55 | 0.86 | 0.90 | 2.32 | 0.75 |
time (sec) |
N/A | 0.252 | 0.036 | 0.229 | 0.031 | 0.100 | 0.096 | 0.123 | 0.164 | 1.101 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 69 | 69 | 60 | 50 | 54 | 80 | 58 | 51 | 96 | 47 |
N.S. |
1 | 1.00 | 0.87 | 0.72 | 0.78 | 1.16 | 0.84 | 0.74 | 1.39 | 0.68 |
time (sec) |
N/A | 0.229 | 0.028 | 0.236 | 0.033 | 0.091 | 0.091 | 0.122 | 0.158 | 0.027 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 62 | 62 | 55 | 45 | 49 | 75 | 51 | 46 | 91 | 42 |
N.S. |
1 | 1.00 | 0.89 | 0.73 | 0.79 | 1.21 | 0.82 | 0.74 | 1.47 | 0.68 |
time (sec) |
N/A | 0.224 | 0.020 | 0.231 | 0.026 | 0.081 | 0.081 | 0.118 | 0.152 | 1.011 |
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 | 55 | 55 | 55 | 40 | 44 | 70 | 44 | 41 | 86 | 37 |
N.S. |
1 | 1.00 | 1.00 | 0.73 | 0.80 | 1.27 | 0.80 | 0.75 | 1.56 | 0.67 |
time (sec) |
N/A | 0.215 | 0.023 | 0.226 | 0.034 | 0.085 | 0.092 | 0.120 | 0.157 | 0.023 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 48 | 48 | 46 | 35 | 39 | 65 | 37 | 36 | 81 | 32 |
N.S. |
1 | 1.00 | 0.96 | 0.73 | 0.81 | 1.35 | 0.77 | 0.75 | 1.69 | 0.67 |
time (sec) |
N/A | 0.208 | 0.022 | 0.227 | 0.040 | 0.087 | 0.084 | 0.117 | 0.158 | 0.023 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 43 | 43 | 35 | 32 | 36 | 55 | 32 | 33 | 76 | 29 |
N.S. |
1 | 1.00 | 0.81 | 0.74 | 0.84 | 1.28 | 0.74 | 0.77 | 1.77 | 0.67 |
time (sec) |
N/A | 0.218 | 0.017 | 0.230 | 0.033 | 0.088 | 0.076 | 0.113 | 0.161 | 0.052 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 43 | 43 | 35 | 32 | 36 | 55 | 32 | 33 | 76 | 25 |
N.S. |
1 | 1.00 | 0.81 | 0.74 | 0.84 | 1.28 | 0.74 | 0.77 | 1.77 | 0.58 |
time (sec) |
N/A | 0.209 | 0.015 | 0.234 | 0.037 | 0.081 | 0.067 | 0.120 | 0.162 | 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 | 43 | 43 | 46 | 32 | 36 | 55 | 34 | 33 | 76 | 26 |
N.S. |
1 | 1.00 | 1.07 | 0.74 | 0.84 | 1.28 | 0.79 | 0.77 | 1.77 | 0.60 |
time (sec) |
N/A | 0.201 | 0.012 | 0.209 | 0.028 | 0.096 | 0.072 | 0.114 | 0.166 | 1.025 |
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 | 43 | 43 | 46 | 32 | 36 | 55 | 34 | 33 | 76 | 26 |
N.S. |
1 | 1.00 | 1.07 | 0.74 | 0.84 | 1.28 | 0.79 | 0.77 | 1.77 | 0.60 |
time (sec) |
N/A | 0.203 | 0.010 | 0.194 | 0.027 | 0.080 | 0.075 | 0.120 | 0.161 | 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 | 53 | 53 | 52 | 40 | 44 | 73 | 44 | 42 | 104 | 36 |
N.S. |
1 | 1.00 | 0.98 | 0.75 | 0.83 | 1.38 | 0.83 | 0.79 | 1.96 | 0.68 |
time (sec) |
N/A | 0.212 | 0.018 | 0.233 | 0.031 | 0.110 | 0.090 | 0.119 | 0.152 | 0.027 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 64 | 64 | 57 | 52 | 54 | 98 | 54 | 66 | 145 | 48 |
N.S. |
1 | 1.00 | 0.89 | 0.81 | 0.84 | 1.53 | 0.84 | 1.03 | 2.27 | 0.75 |
time (sec) |
N/A | 0.218 | 0.038 | 0.240 | 0.032 | 0.120 | 0.103 | 0.120 | 0.149 | 0.026 |
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 | 75 | 75 | 58 | 56 | 64 | 123 | 65 | 59 | 188 | 56 |
N.S. |
1 | 1.00 | 0.77 | 0.75 | 0.85 | 1.64 | 0.87 | 0.79 | 2.51 | 0.75 |
time (sec) |
N/A | 0.256 | 0.040 | 0.227 | 0.027 | 0.099 | 0.115 | 0.118 | 0.149 | 1.049 |
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 | 86 | 86 | 69 | 61 | 74 | 148 | 75 | 64 | 231 | 63 |
N.S. |
1 | 1.00 | 0.80 | 0.71 | 0.86 | 1.72 | 0.87 | 0.74 | 2.69 | 0.73 |
time (sec) |
N/A | 0.258 | 0.059 | 0.236 | 0.037 | 0.083 | 0.114 | 0.124 | 0.146 | 1.028 |
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 | 80 | 80 | 98 | 62 | 64 | 100 | 70 | 112 | 126 | 60 |
N.S. |
1 | 1.00 | 1.22 | 0.78 | 0.80 | 1.25 | 0.88 | 1.40 | 1.58 | 0.75 |
time (sec) |
N/A | 0.232 | 0.033 | 0.257 | 0.026 | 0.078 | 0.099 | 0.121 | 0.151 | 1.038 |
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 | 73 | 73 | 67 | 57 | 59 | 95 | 63 | 103 | 121 | 55 |
N.S. |
1 | 1.00 | 0.92 | 0.78 | 0.81 | 1.30 | 0.86 | 1.41 | 1.66 | 0.75 |
time (sec) |
N/A | 0.234 | 0.031 | 0.233 | 0.026 | 0.072 | 0.096 | 0.126 | 0.150 | 1.008 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 66 | 66 | 74 | 52 | 54 | 90 | 56 | 94 | 116 | 50 |
N.S. |
1 | 1.00 | 1.12 | 0.79 | 0.82 | 1.36 | 0.85 | 1.42 | 1.76 | 0.76 |
time (sec) |
N/A | 0.230 | 0.026 | 0.233 | 0.029 | 0.067 | 0.092 | 0.123 | 0.155 | 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 | 59 | 59 | 55 | 47 | 49 | 85 | 49 | 83 | 111 | 45 |
N.S. |
1 | 1.00 | 0.93 | 0.80 | 0.83 | 1.44 | 0.83 | 1.41 | 1.88 | 0.76 |
time (sec) |
N/A | 0.209 | 0.024 | 0.226 | 0.031 | 0.089 | 0.095 | 0.120 | 0.157 | 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 | 54 | 54 | 48 | 44 | 46 | 75 | 44 | 69 | 106 | 42 |
N.S. |
1 | 1.00 | 0.89 | 0.81 | 0.85 | 1.39 | 0.81 | 1.28 | 1.96 | 0.78 |
time (sec) |
N/A | 0.214 | 0.021 | 0.232 | 0.026 | 0.072 | 0.099 | 0.121 | 0.153 | 0.067 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 54 | 54 | 47 | 44 | 46 | 75 | 46 | 51 | 106 | 38 |
N.S. |
1 | 1.00 | 0.87 | 0.81 | 0.85 | 1.39 | 0.85 | 0.94 | 1.96 | 0.70 |
time (sec) |
N/A | 0.218 | 0.024 | 0.224 | 0.030 | 0.079 | 0.075 | 0.123 | 0.158 | 0.990 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 54 | 54 | 48 | 44 | 46 | 75 | 44 | 51 | 106 | 38 |
N.S. |
1 | 1.00 | 0.89 | 0.81 | 0.85 | 1.39 | 0.81 | 0.94 | 1.96 | 0.70 |
time (sec) |
N/A | 0.210 | 0.022 | 0.222 | 0.033 | 0.084 | 0.077 | 0.118 | 0.154 | 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 | 54 | 54 | 62 | 44 | 46 | 75 | 44 | 51 | 106 | 38 |
N.S. |
1 | 1.00 | 1.15 | 0.81 | 0.85 | 1.39 | 0.81 | 0.94 | 1.96 | 0.70 |
time (sec) |
N/A | 0.204 | 0.015 | 0.204 | 0.031 | 0.083 | 0.068 | 0.125 | 0.154 | 1.010 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 54 | 54 | 62 | 44 | 46 | 75 | 44 | 51 | 106 | 38 |
N.S. |
1 | 1.00 | 1.15 | 0.81 | 0.85 | 1.39 | 0.81 | 0.94 | 1.96 | 0.70 |
time (sec) |
N/A | 0.208 | 0.013 | 0.201 | 0.030 | 0.084 | 0.074 | 0.116 | 0.156 | 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 | 64 | 64 | 60 | 52 | 54 | 98 | 54 | 66 | 145 | 47 |
N.S. |
1 | 1.00 | 0.94 | 0.81 | 0.84 | 1.53 | 0.84 | 1.03 | 2.27 | 0.73 |
time (sec) |
N/A | 0.234 | 0.021 | 0.230 | 0.024 | 0.072 | 0.103 | 0.120 | 0.156 | 0.028 |
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 | 75 | 75 | 68 | 62 | 64 | 123 | 65 | 86 | 188 | 55 |
N.S. |
1 | 1.00 | 0.91 | 0.83 | 0.85 | 1.64 | 0.87 | 1.15 | 2.51 | 0.73 |
time (sec) |
N/A | 0.230 | 0.046 | 0.276 | 0.026 | 0.087 | 0.118 | 0.127 | 0.152 | 0.026 |
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 | 86 | 86 | 74 | 68 | 74 | 148 | 75 | 95 | 231 | 66 |
N.S. |
1 | 1.00 | 0.86 | 0.79 | 0.86 | 1.72 | 0.87 | 1.10 | 2.69 | 0.77 |
time (sec) |
N/A | 0.258 | 0.041 | 0.234 | 0.026 | 0.068 | 0.114 | 0.123 | 0.153 | 1.050 |
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 | 97 | 97 | 88 | 73 | 84 | 173 | 85 | 104 | 274 | 76 |
N.S. |
1 | 1.00 | 0.91 | 0.75 | 0.87 | 1.78 | 0.88 | 1.07 | 2.82 | 0.78 |
time (sec) |
N/A | 0.273 | 0.090 | 0.231 | 0.030 | 0.077 | 0.120 | 0.122 | 0.157 | 1.007 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 91 | 91 | 75 | 67 | 74 | 120 | 80 | 68 | 158 | 68 |
N.S. |
1 | 1.00 | 0.82 | 0.74 | 0.81 | 1.32 | 0.88 | 0.75 | 1.74 | 0.75 |
time (sec) |
N/A | 0.283 | 0.030 | 0.247 | 0.041 | 0.087 | 0.105 | 0.128 | 0.162 | 0.027 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 84 | 84 | 70 | 62 | 69 | 115 | 73 | 63 | 153 | 63 |
N.S. |
1 | 1.00 | 0.83 | 0.74 | 0.82 | 1.37 | 0.87 | 0.75 | 1.82 | 0.75 |
time (sec) |
N/A | 0.257 | 0.029 | 0.240 | 0.033 | 0.078 | 0.102 | 0.120 | 0.163 | 1.028 |
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 | 77 | 77 | 65 | 57 | 64 | 110 | 66 | 58 | 148 | 58 |
N.S. |
1 | 1.00 | 0.84 | 0.74 | 0.83 | 1.43 | 0.86 | 0.75 | 1.92 | 0.75 |
time (sec) |
N/A | 0.233 | 0.023 | 0.238 | 0.031 | 0.079 | 0.096 | 0.126 | 0.155 | 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 | 70 | 70 | 60 | 52 | 59 | 105 | 60 | 53 | 143 | 52 |
N.S. |
1 | 1.00 | 0.86 | 0.74 | 0.84 | 1.50 | 0.86 | 0.76 | 2.04 | 0.74 |
time (sec) |
N/A | 0.230 | 0.023 | 0.231 | 0.033 | 0.075 | 0.102 | 0.124 | 0.157 | 1.023 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 65 | 65 | 50 | 48 | 56 | 95 | 54 | 50 | 138 | 49 |
N.S. |
1 | 1.00 | 0.77 | 0.74 | 0.86 | 1.46 | 0.83 | 0.77 | 2.12 | 0.75 |
time (sec) |
N/A | 0.237 | 0.019 | 0.221 | 0.035 | 0.077 | 0.100 | 0.125 | 0.153 | 0.062 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 65 | 65 | 48 | 48 | 56 | 95 | 56 | 46 | 138 | 45 |
N.S. |
1 | 1.00 | 0.74 | 0.74 | 0.86 | 1.46 | 0.86 | 0.71 | 2.12 | 0.69 |
time (sec) |
N/A | 0.228 | 0.020 | 0.225 | 0.027 | 0.085 | 0.081 | 0.116 | 0.180 | 1.013 |
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 | 65 | 65 | 48 | 48 | 56 | 95 | 54 | 46 | 138 | 45 |
N.S. |
1 | 1.00 | 0.74 | 0.74 | 0.86 | 1.46 | 0.83 | 0.71 | 2.12 | 0.69 |
time (sec) |
N/A | 0.236 | 0.021 | 0.223 | 0.026 | 0.094 | 0.089 | 0.121 | 0.183 | 1.052 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 65 | 65 | 48 | 48 | 56 | 95 | 54 | 46 | 138 | 45 |
N.S. |
1 | 1.00 | 0.74 | 0.74 | 0.86 | 1.46 | 0.83 | 0.71 | 2.12 | 0.69 |
time (sec) |
N/A | 0.232 | 0.020 | 0.227 | 0.033 | 0.068 | 0.082 | 0.125 | 0.168 | 0.027 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 65 | 65 | 48 | 48 | 56 | 95 | 54 | 46 | 138 | 45 |
N.S. |
1 | 1.00 | 0.74 | 0.74 | 0.86 | 1.46 | 0.83 | 0.71 | 2.12 | 0.69 |
time (sec) |
N/A | 0.235 | 0.015 | 0.201 | 0.032 | 0.081 | 0.080 | 0.122 | 0.191 | 1.008 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 65 | 65 | 48 | 48 | 56 | 95 | 54 | 46 | 138 | 45 |
N.S. |
1 | 1.00 | 0.74 | 0.74 | 0.86 | 1.46 | 0.83 | 0.71 | 2.12 | 0.69 |
time (sec) |
N/A | 0.228 | 0.015 | 0.199 | 0.026 | 0.099 | 0.080 | 0.120 | 0.154 | 1.039 |
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 | 75 | 75 | 60 | 56 | 64 | 123 | 65 | 59 | 188 | 56 |
N.S. |
1 | 1.00 | 0.80 | 0.75 | 0.85 | 1.64 | 0.87 | 0.79 | 2.51 | 0.75 |
time (sec) |
N/A | 0.240 | 0.043 | 0.232 | 0.033 | 0.100 | 0.110 | 0.122 | 0.153 | 0.028 |
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 | 86 | 86 | 76 | 68 | 74 | 148 | 75 | 95 | 231 | 65 |
N.S. |
1 | 1.00 | 0.88 | 0.79 | 0.86 | 1.72 | 0.87 | 1.10 | 2.69 | 0.76 |
time (sec) |
N/A | 0.255 | 0.047 | 0.243 | 0.026 | 0.094 | 0.120 | 0.120 | 0.164 | 0.028 |
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 | 97 | 97 | 88 | 73 | 84 | 173 | 85 | 72 | 274 | 75 |
N.S. |
1 | 1.00 | 0.91 | 0.75 | 0.87 | 1.78 | 0.88 | 0.74 | 2.82 | 0.77 |
time (sec) |
N/A | 0.273 | 0.093 | 0.245 | 0.038 | 0.081 | 0.116 | 0.122 | 0.155 | 1.058 |
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 | 108 | 108 | 82 | 78 | 94 | 198 | 95 | 81 | 317 | 85 |
N.S. |
1 | 1.00 | 0.76 | 0.72 | 0.87 | 1.83 | 0.88 | 0.75 | 2.94 | 0.79 |
time (sec) |
N/A | 0.267 | 0.069 | 0.244 | 0.035 | 0.072 | 0.126 | 0.121 | 0.151 | 1.039 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 361 | 361 | 653 | 767 | 727 | 727 | 1018 | 987 | 987 | 787 |
N.S. |
1 | 1.00 | 1.81 | 2.12 | 2.01 | 2.01 | 2.82 | 2.73 | 2.73 | 2.18 |
time (sec) |
N/A | 1.035 | 0.145 | 0.230 | 0.039 | 0.101 | 0.067 | 0.123 | 0.157 | 0.137 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 193 | 193 | 241 | 286 | 269 | 269 | 345 | 346 | 346 | 270 |
N.S. |
1 | 1.00 | 1.25 | 1.48 | 1.39 | 1.39 | 1.79 | 1.79 | 1.79 | 1.40 |
time (sec) |
N/A | 0.529 | 0.053 | 0.207 | 0.028 | 0.072 | 0.034 | 0.117 | 0.148 | 1.086 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 56 | 56 | 53 | 53 | 52 | 62 | 63 | 62 | 59 | 54 |
N.S. |
1 | 1.00 | 0.95 | 0.95 | 0.93 | 1.11 | 1.12 | 1.11 | 1.05 | 0.96 |
time (sec) |
N/A | 0.222 | 0.012 | 0.045 | 0.034 | 0.042 | 0.022 | 0.120 | 0.152 | 0.026 |
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 | 86 | 86 | 80 | 87 | 112 | 112 | 0 | 131 | 125 | 106 |
N.S. |
1 | 1.00 | 0.93 | 1.01 | 1.30 | 1.30 | 0.00 | 1.52 | 1.45 | 1.23 |
time (sec) |
N/A | 0.273 | 0.031 | 0.396 | 0.033 | 2.807 | 0.000 | 0.126 | 0.153 | 0.218 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | F(-1) | F(-1) | C | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 234 | 234 | 232 | 235 | 2096 | 0 | 0 | 1635 | 8516 | 1940 |
N.S. |
1 | 1.00 | 0.99 | 1.00 | 8.96 | 0.00 | 0.00 | 6.99 | 36.39 | 8.29 |
time (sec) |
N/A | 0.669 | 0.295 | 0.642 | 0.107 | 0.000 | 0.000 | 0.163 | 0.178 | 4.823 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | F(-1) | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 495 | 495 | 490 | 514 | 11005 | 0 | 0 | 7111 | 42188 | 82532 |
N.S. |
1 | 1.00 | 0.99 | 1.04 | 22.23 | 0.00 | 0.00 | 14.37 | 85.23 | 166.73 |
time (sec) |
N/A | 1.778 | 0.667 | 1.829 | 0.561 | 0.000 | 0.000 | 0.211 | 0.855 | 12.814 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 164 | 154 | 190 | 192 | 0 | 591 | 258 | 371 | 561 | 330 |
N.S. |
1 | 0.94 | 1.16 | 1.17 | 0.00 | 3.60 | 1.57 | 2.26 | 3.42 | 2.01 |
time (sec) |
N/A | 0.266 | 0.247 | 0.752 | 0.000 | 0.128 | 4.127 | 0.134 | 0.161 | 0.080 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 130 | 125 | 129 | 138 | 0 | 373 | 175 | 226 | 323 | 236 |
N.S. |
1 | 0.96 | 0.99 | 1.06 | 0.00 | 2.87 | 1.35 | 1.74 | 2.48 | 1.82 |
time (sec) |
N/A | 0.233 | 0.183 | 0.425 | 0.000 | 0.127 | 3.889 | 0.127 | 0.159 | 1.110 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 98 | 96 | 94 | 101 | 0 | 211 | 124 | 122 | 139 | 107 |
N.S. |
1 | 0.98 | 0.96 | 1.03 | 0.00 | 2.15 | 1.27 | 1.24 | 1.42 | 1.09 |
time (sec) |
N/A | 0.215 | 0.194 | 0.398 | 0.000 | 0.109 | 3.674 | 0.127 | 0.159 | 0.085 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 74 | 74 | 74 | 63 | 0 | 209 | 92 | 66 | 122 | 62 |
N.S. |
1 | 1.00 | 1.00 | 0.85 | 0.00 | 2.82 | 1.24 | 0.89 | 1.65 | 0.84 |
time (sec) |
N/A | 0.188 | 0.115 | 0.395 | 0.000 | 0.104 | 1.647 | 0.127 | 0.168 | 0.051 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 88 | 88 | 88 | 79 | 0 | 363 | 110 | 87 | 161 | 96 |
N.S. |
1 | 1.00 | 1.00 | 0.90 | 0.00 | 4.12 | 1.25 | 0.99 | 1.83 | 1.09 |
time (sec) |
N/A | 0.207 | 0.181 | 0.375 | 0.000 | 0.096 | 3.808 | 0.117 | 0.173 | 0.075 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 119 | 124 | 117 | 116 | 0 | 486 | 138 | 153 | 383 | 128 |
N.S. |
1 | 1.04 | 0.98 | 0.97 | 0.00 | 4.08 | 1.16 | 1.29 | 3.22 | 1.08 |
time (sec) |
N/A | 0.229 | 0.222 | 0.507 | 0.000 | 0.092 | 4.883 | 0.134 | 0.162 | 1.184 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 151 | 160 | 183 | 149 | 0 | 882 | 170 | 276 | 719 | 173 |
N.S. |
1 | 1.06 | 1.21 | 0.99 | 0.00 | 5.84 | 1.13 | 1.83 | 4.76 | 1.15 |
time (sec) |
N/A | 0.252 | 0.307 | 0.438 | 0.000 | 0.125 | 5.430 | 0.133 | 0.165 | 0.137 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 185 | 196 | 265 | 178 | 0 | 1376 | 204 | 439 | 1131 | 218 |
N.S. |
1 | 1.06 | 1.43 | 0.96 | 0.00 | 7.44 | 1.10 | 2.37 | 6.11 | 1.18 |
time (sec) |
N/A | 0.267 | 0.462 | 0.490 | 0.000 | 0.193 | 6.121 | 0.128 | 0.171 | 0.157 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 208 | 208 | 295 | 294 | 0 | 1068 | 442 | 647 | 1068 | 602 |
N.S. |
1 | 1.00 | 1.42 | 1.41 | 0.00 | 5.13 | 2.12 | 3.11 | 5.13 | 2.89 |
time (sec) |
N/A | 0.394 | 0.365 | 0.631 | 0.000 | 0.102 | 4.190 | 0.130 | 0.164 | 1.154 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 172 | 172 | 204 | 211 | 0 | 694 | 299 | 404 | 650 | 438 |
N.S. |
1 | 1.00 | 1.19 | 1.23 | 0.00 | 4.03 | 1.74 | 2.35 | 3.78 | 2.55 |
time (sec) |
N/A | 0.319 | 0.267 | 0.857 | 0.000 | 0.097 | 3.776 | 0.138 | 0.164 | 0.076 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 138 | 138 | 152 | 154 | 0 | 402 | 211 | 236 | 318 | 281 |
N.S. |
1 | 1.00 | 1.10 | 1.12 | 0.00 | 2.91 | 1.53 | 1.71 | 2.30 | 2.04 |
time (sec) |
N/A | 0.281 | 0.203 | 0.457 | 0.000 | 0.080 | 3.491 | 0.133 | 0.162 | 1.155 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 112 | 112 | 99 | 99 | 0 | 375 | 162 | 142 | 273 | 152 |
N.S. |
1 | 1.00 | 0.88 | 0.88 | 0.00 | 3.35 | 1.45 | 1.27 | 2.44 | 1.36 |
time (sec) |
N/A | 0.269 | 0.151 | 0.446 | 0.000 | 0.115 | 2.745 | 0.130 | 0.164 | 0.066 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 112 | 112 | 126 | 134 | 0 | 600 | 156 | 136 | 314 | 162 |
N.S. |
1 | 1.00 | 1.12 | 1.20 | 0.00 | 5.36 | 1.39 | 1.21 | 2.80 | 1.45 |
time (sec) |
N/A | 0.295 | 0.184 | 0.458 | 0.000 | 0.115 | 6.311 | 0.131 | 0.165 | 1.116 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 140 | 140 | 135 | 146 | 0 | 975 | 185 | 229 | 623 | 203 |
N.S. |
1 | 1.00 | 0.96 | 1.04 | 0.00 | 6.96 | 1.32 | 1.64 | 4.45 | 1.45 |
time (sec) |
N/A | 0.335 | 0.244 | 0.559 | 0.000 | 0.148 | 8.506 | 0.130 | 0.171 | 0.142 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 173 | 173 | 253 | 214 | 0 | 1155 | 214 | 423 | 1069 | 264 |
N.S. |
1 | 1.00 | 1.46 | 1.24 | 0.00 | 6.68 | 1.24 | 2.45 | 6.18 | 1.53 |
time (sec) |
N/A | 0.396 | 0.372 | 0.523 | 0.000 | 0.135 | 13.294 | 0.138 | 0.176 | 1.212 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 207 | 207 | 378 | 258 | 0 | 1781 | 248 | 682 | 1649 | 327 |
N.S. |
1 | 1.00 | 1.83 | 1.25 | 0.00 | 8.60 | 1.20 | 3.29 | 7.97 | 1.58 |
time (sec) |
N/A | 0.452 | 0.565 | 0.569 | 0.000 | 0.198 | 13.094 | 0.140 | 0.170 | 0.206 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 280 | 280 | 435 | 553 | 0 | 1741 | 690 | 989 | 1725 | 897 |
N.S. |
1 | 1.00 | 1.55 | 1.98 | 0.00 | 6.22 | 2.46 | 3.53 | 6.16 | 3.20 |
time (sec) |
N/A | 0.475 | 0.542 | 1.155 | 0.000 | 0.116 | 6.234 | 0.156 | 0.169 | 0.104 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 244 | 244 | 313 | 316 | 0 | 1165 | 488 | 652 | 1098 | 672 |
N.S. |
1 | 1.00 | 1.28 | 1.30 | 0.00 | 4.77 | 2.00 | 2.67 | 4.50 | 2.75 |
time (sec) |
N/A | 0.387 | 0.379 | 0.625 | 0.000 | 0.115 | 5.805 | 0.145 | 0.160 | 1.115 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 210 | 210 | 249 | 239 | 0 | 705 | 362 | 413 | 589 | 451 |
N.S. |
1 | 1.00 | 1.19 | 1.14 | 0.00 | 3.36 | 1.72 | 1.97 | 2.80 | 2.15 |
time (sec) |
N/A | 0.367 | 0.300 | 0.564 | 0.000 | 0.115 | 5.386 | 0.135 | 0.157 | 1.100 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 184 | 184 | 157 | 158 | 0 | 653 | 296 | 283 | 521 | 264 |
N.S. |
1 | 1.00 | 0.85 | 0.86 | 0.00 | 3.55 | 1.61 | 1.54 | 2.83 | 1.43 |
time (sec) |
N/A | 0.340 | 0.220 | 0.500 | 0.000 | 0.100 | 4.790 | 0.133 | 0.161 | 1.126 |