Detailed conclusion table per each integral is given by the table below. The elapsed time is in seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2) if the failure was due to an exception being raised, which could indicate a bug in the system. If the failure was due to integral not being evaluated within the time limit, then it is given as F.
In this table, the column N.S.
means normalized size and is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To make the table
fit the page, the name Mathematica
was abbreviated to MMA
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 37 | 37 | 26 | 24 | 26 | 29 | 32 | 23 | 26 | 25 |
N.S. |
1 | 1.00 | 0.70 | 0.65 | 0.70 | 0.78 | 0.86 | 0.62 | 0.70 | 0.68 |
time (sec) |
N/A | 0.174 | 0.022 | 0.206 | 0.035 | 0.071 | 0.187 | 0.132 | 0.160 | 0.028 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | B | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 12 | 129 | 49 | 176 | 8 | 39 | 236 | 37 | 10 | 49 |
N.S. |
1 | 10.75 | 4.08 | 14.67 | 0.67 | 3.25 | 19.67 | 3.08 | 0.83 | 4.08 |
time (sec) |
N/A | 0.466 | 0.094 | 0.100 | 0.034 | 0.099 | 0.032 | 0.161 | 0.149 | 16.710 |
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 | 9 | 9 | 9 | 8 | 7 | 13 | 19 | 8 | 23 | 19 |
N.S. |
1 | 1.00 | 1.00 | 0.89 | 0.78 | 1.44 | 2.11 | 0.89 | 2.56 | 2.11 |
time (sec) |
N/A | 0.189 | 0.006 | 0.113 | 0.027 | 0.072 | 0.073 | 0.147 | 0.200 | 17.377 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 8 | 8 | 8 | 7 | 35 | 12 | 0 | 6 | 12 | 14 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 4.38 | 1.50 | 0.00 | 0.75 | 1.50 | 1.75 |
time (sec) |
N/A | 0.208 | 0.014 | 0.111 | 0.028 | 0.062 | 0.000 | 0.150 | 0.157 | 0.113 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 15 | 12 | 0 | 13 | 0 | 11 | 17 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.80 | 0.00 | 0.87 | 0.00 | 0.73 | 1.13 | 0.87 |
time (sec) |
N/A | 0.204 | 0.012 | 15.041 | 0.000 | 0.075 | 0.000 | 0.137 | 0.160 | 17.339 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 20 | 16 | 15 | 15 | 19 | 15 | 15 | 15 |
N.S. |
1 | 1.00 | 0.87 | 0.70 | 0.65 | 0.65 | 0.83 | 0.65 | 0.65 | 0.65 |
time (sec) |
N/A | 0.187 | 0.012 | 0.129 | 0.106 | 0.075 | 0.096 | 0.156 | 0.170 | 0.084 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 37 | 37 | 37 | 30 | 29 | 29 | 42 | 29 | 40 | 33 |
N.S. |
1 | 1.00 | 1.00 | 0.81 | 0.78 | 0.78 | 1.14 | 0.78 | 1.08 | 0.89 |
time (sec) |
N/A | 0.201 | 0.036 | 0.887 | 0.031 | 0.071 | 0.122 | 0.151 | 0.165 | 16.813 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 10 | 10 | 12 | 9 | 8 | 10 | 8 | 10 | 8 | 8 |
N.S. |
1 | 1.00 | 1.20 | 0.90 | 0.80 | 1.00 | 0.80 | 1.00 | 0.80 | 0.80 |
time (sec) |
N/A | 0.220 | 0.014 | 0.100 | 0.022 | 0.070 | 0.072 | 0.147 | 0.166 | 16.167 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 8 | 8 | 8 | 7 | 6 | 6 | 5 | 6 | 6 | 6 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 0.75 | 0.75 | 0.62 | 0.75 | 0.75 | 0.75 |
time (sec) |
N/A | 0.179 | 0.002 | 0.197 | 0.027 | 0.072 | 0.061 | 0.142 | 0.160 | 0.063 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 10 | 10 | 10 | 9 | 8 | 8 | 7 | 8 | 8 | 8 |
N.S. |
1 | 1.00 | 1.00 | 0.90 | 0.80 | 0.80 | 0.70 | 0.80 | 0.80 | 0.80 |
time (sec) |
N/A | 0.188 | 0.004 | 0.174 | 0.023 | 0.069 | 0.082 | 0.134 | 0.147 | 0.063 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 8 | 8 | 8 | 7 | 6 | 6 | 5 | 6 | 6 | 6 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 0.75 | 0.75 | 0.62 | 0.75 | 0.75 | 0.75 |
time (sec) |
N/A | 0.184 | 0.002 | 0.151 | 0.024 | 0.075 | 0.120 | 0.109 | 0.152 | 0.080 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 10 | 10 | 10 | 9 | 8 | 8 | 7 | 8 | 8 | 8 |
N.S. |
1 | 1.00 | 1.00 | 0.90 | 0.80 | 0.80 | 0.70 | 0.80 | 0.80 | 0.80 |
time (sec) |
N/A | 0.184 | 0.023 | 0.201 | 0.027 | 0.069 | 0.065 | 0.147 | 0.153 | 16.057 |
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 | 8 | 8 | 8 | 7 | 56 | 8 | 5 | 8 | 6 | 8 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 7.00 | 1.00 | 0.62 | 1.00 | 0.75 | 1.00 |
time (sec) |
N/A | 0.251 | 0.005 | 0.069 | 0.030 | 0.066 | 0.102 | 0.139 | 0.160 | 0.079 |
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 | 10 | 10 | 12 | 13 | 67 | 13 | 7 | 10 | 13 | 10 |
N.S. |
1 | 1.00 | 1.20 | 1.30 | 6.70 | 1.30 | 0.70 | 1.00 | 1.30 | 1.00 |
time (sec) |
N/A | 0.203 | 0.018 | 0.046 | 0.026 | 0.068 | 0.092 | 0.127 | 0.209 | 15.912 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 11 | 11 | 11 | 10 | 9 | 15 | 12 | 10 | 13 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.91 | 0.82 | 1.36 | 1.09 | 0.91 | 1.18 | 1.18 |
time (sec) |
N/A | 0.193 | 0.014 | 0.088 | 0.024 | 0.071 | 0.060 | 0.154 | 0.159 | 0.302 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
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 | 12 | 12 | 10 | 10 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.92 | 0.83 | 1.00 | 1.00 | 0.83 | 0.83 | 1.08 |
time (sec) |
N/A | 0.164 | 0.008 | 0.115 | 0.029 | 0.073 | 0.509 | 0.135 | 0.167 | 0.057 |
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 | 21 | 21 | 25 | 18 | 18 | 29 | 0 | 18 | 29 | 16 |
N.S. |
1 | 1.00 | 1.19 | 0.86 | 0.86 | 1.38 | 0.00 | 0.86 | 1.38 | 0.76 |
time (sec) |
N/A | 0.245 | 0.014 | 0.334 | 0.025 | 0.068 | 0.000 | 0.127 | 0.165 | 15.635 |
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 | 19 | 19 | 19 | 16 | 15 | 40 | 32 | 39 | 29 | 15 |
N.S. |
1 | 1.00 | 1.00 | 0.84 | 0.79 | 2.11 | 1.68 | 2.05 | 1.53 | 0.79 |
time (sec) |
N/A | 0.199 | 0.009 | 0.787 | 0.028 | 0.080 | 0.569 | 0.113 | 0.156 | 16.925 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 47 | 52 | 35 | 33 | 32 | 32 | 48 | 32 | 43 | 43 |
N.S. |
1 | 1.11 | 0.74 | 0.70 | 0.68 | 0.68 | 1.02 | 0.68 | 0.91 | 0.91 |
time (sec) |
N/A | 0.450 | 0.028 | 0.201 | 0.030 | 0.073 | 3.653 | 0.108 | 0.158 | 16.891 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 39 | 28 | 26 | 25 | 29 | 32 | 25 | 28 | 25 |
N.S. |
1 | 1.11 | 0.80 | 0.74 | 0.71 | 0.83 | 0.91 | 0.71 | 0.80 | 0.71 |
time (sec) |
N/A | 0.327 | 0.044 | 0.243 | 0.034 | 0.071 | 0.385 | 0.150 | 0.157 | 16.855 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 4 | 4 | 4 | 5 | 4 | 4 | 3 | 4 | 4 | 4 |
N.S. |
1 | 1.00 | 1.00 | 1.25 | 1.00 | 1.00 | 0.75 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.186 | 0.001 | 0.148 | 0.022 | 0.076 | 0.065 | 0.108 | 0.171 | 0.058 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
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 | 6 | 6 | 7 | 6 | 6 | 5 | 6 | 6 | 6 |
N.S. |
1 | 1.00 | 1.00 | 1.17 | 1.00 | 1.00 | 0.83 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.192 | 0.004 | 0.191 | 0.036 | 0.071 | 0.090 | 0.166 | 0.165 | 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 | 7 | 7 | 7 | 8 | 7 | 7 | 5 | 7 | 7 | 7 |
N.S. |
1 | 1.00 | 1.00 | 1.14 | 1.00 | 1.00 | 0.71 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.140 | 0.006 | 0.422 | 0.107 | 0.073 | 0.041 | 0.126 | 0.176 | 0.059 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 10 | 10 | 21 | 9 | 8 | 8 | 8 | 8 | 8 | 8 |
N.S. |
1 | 1.00 | 2.10 | 0.90 | 0.80 | 0.80 | 0.80 | 0.80 | 0.80 | 0.80 |
time (sec) |
N/A | 0.190 | 0.015 | 0.214 | 0.030 | 0.078 | 0.067 | 0.125 | 0.167 | 0.045 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 10 | 10 | 10 | 9 | 8 | 8 | 7 | 8 | 8 | 8 |
N.S. |
1 | 1.00 | 1.00 | 0.90 | 0.80 | 0.80 | 0.70 | 0.80 | 0.80 | 0.80 |
time (sec) |
N/A | 0.186 | 0.003 | 0.168 | 0.024 | 0.069 | 0.065 | 0.143 | 0.172 | 16.038 |
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 | 10 | 10 | 10 | 9 | 8 | 8 | 7 | 8 | 8 | 8 |
N.S. |
1 | 1.00 | 1.00 | 0.90 | 0.80 | 0.80 | 0.70 | 0.80 | 0.80 | 0.80 |
time (sec) |
N/A | 0.146 | 0.001 | 0.288 | 0.027 | 0.074 | 0.083 | 0.106 | 0.209 | 0.050 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 10 | 10 | 21 | 9 | 8 | 8 | 8 | 8 | 8 | 8 |
N.S. |
1 | 1.00 | 2.10 | 0.90 | 0.80 | 0.80 | 0.80 | 0.80 | 0.80 | 0.80 |
time (sec) |
N/A | 0.191 | 0.012 | 0.155 | 0.027 | 0.071 | 0.090 | 0.122 | 0.155 | 15.489 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
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 | 6 | 6 | 7 | 6 | 6 | 5 | 6 | 6 | 6 |
N.S. |
1 | 1.00 | 1.00 | 1.17 | 1.00 | 1.00 | 0.83 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.190 | 0.001 | 0.118 | 0.033 | 0.073 | 0.090 | 0.102 | 0.151 | 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 | 14 | 14 | 14 | 15 | 14 | 14 | 15 | 14 | 18 | 14 |
N.S. |
1 | 1.00 | 1.00 | 1.07 | 1.00 | 1.00 | 1.07 | 1.00 | 1.29 | 1.00 |
time (sec) |
N/A | 0.203 | 0.022 | 0.209 | 0.034 | 0.065 | 0.068 | 0.106 | 0.151 | 15.925 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
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 | 17 | 20 | 17 | 16 | 16 | 15 | 16 | 16 | 16 |
N.S. |
1 | 0.85 | 1.00 | 0.85 | 0.80 | 0.80 | 0.75 | 0.80 | 0.80 | 0.80 |
time (sec) |
N/A | 0.237 | 0.013 | 0.165 | 0.035 | 0.068 | 0.241 | 0.132 | 0.168 | 15.390 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 16 | 14 | 15 | 17 | 20 | 15 | 16 | 15 |
N.S. |
1 | 1.00 | 0.70 | 0.61 | 0.65 | 0.74 | 0.87 | 0.65 | 0.70 | 0.65 |
time (sec) |
N/A | 0.162 | 0.011 | 0.132 | 0.032 | 0.068 | 0.175 | 0.101 | 0.166 | 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 | 20 | 18 | 20 | 17 | 16 | 16 | 15 | 16 | 16 | 16 |
N.S. |
1 | 0.90 | 1.00 | 0.85 | 0.80 | 0.80 | 0.75 | 0.80 | 0.80 | 0.80 |
time (sec) |
N/A | 0.235 | 0.003 | 0.198 | 0.033 | 0.068 | 0.117 | 0.130 | 0.165 | 15.710 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
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 | 17 | 20 | 17 | 16 | 16 | 15 | 16 | 16 | 16 |
N.S. |
1 | 0.85 | 1.00 | 0.85 | 0.80 | 0.80 | 0.75 | 0.80 | 0.80 | 0.80 |
time (sec) |
N/A | 0.241 | 0.008 | 0.178 | 0.035 | 0.069 | 0.115 | 0.126 | 0.163 | 0.054 |
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 | 9 | 9 | 9 | 8 | 7 | 19 | 7 | 7 | 7 | 7 |
N.S. |
1 | 1.00 | 1.00 | 0.89 | 0.78 | 2.11 | 0.78 | 0.78 | 0.78 | 0.78 |
time (sec) |
N/A | 0.195 | 0.949 | 0.150 | 0.032 | 0.067 | 0.147 | 0.107 | 0.164 | 0.084 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 11 | 11 | 11 | 10 | 9 | 11 | 10 | 9 | 9 | 17 |
N.S. |
1 | 1.00 | 1.00 | 0.91 | 0.82 | 1.00 | 0.91 | 0.82 | 0.82 | 1.55 |
time (sec) |
N/A | 0.200 | 0.070 | 0.085 | 0.026 | 0.076 | 0.073 | 0.154 | 0.168 | 16.441 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 10 | 10 | 10 | 65 | 8 | 45 | 36 | 61 | 33 | 8 |
N.S. |
1 | 1.00 | 1.00 | 6.50 | 0.80 | 4.50 | 3.60 | 6.10 | 3.30 | 0.80 |
time (sec) |
N/A | 0.180 | 0.014 | 0.090 | 0.022 | 0.071 | 0.123 | 0.139 | 0.155 | 17.202 |
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 | 9 | 9 | 9 | 7 | 13 | 10 | 8 | 8 | 22 | 6 |
N.S. |
1 | 1.00 | 1.00 | 0.78 | 1.44 | 1.11 | 0.89 | 0.89 | 2.44 | 0.67 |
time (sec) |
N/A | 0.217 | 0.003 | 0.134 | 0.031 | 0.062 | 0.829 | 0.108 | 0.158 | 16.778 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 5 | 5 | 5 | 20 | 7 | 11 | 7 | 7 | 17 | 7 |
N.S. |
1 | 1.00 | 1.00 | 4.00 | 1.40 | 2.20 | 1.40 | 1.40 | 3.40 | 1.40 |
time (sec) |
N/A | 0.184 | 0.013 | 0.181 | 0.027 | 0.068 | 0.032 | 0.140 | 0.201 | 16.906 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | A | F(-1) | B | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 13 | 0 | 13 | 15 | 88 | 14 | 0 | 794 | 32 | 14 |
N.S. |
1 | 0.00 | 1.00 | 1.15 | 6.77 | 1.08 | 0.00 | 61.08 | 2.46 | 1.08 |
time (sec) |
N/A | 0.000 | 0.550 | 1.104 | 0.357 | 0.072 | 0.000 | 0.149 | 0.190 | 15.947 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 9 | 9 | 9 | 10 | 104 | 20 | 8 | 52 | 32 | 9 |
N.S. |
1 | 1.00 | 1.00 | 1.11 | 11.56 | 2.22 | 0.89 | 5.78 | 3.56 | 1.00 |
time (sec) |
N/A | 0.221 | 0.014 | 0.078 | 0.033 | 0.078 | 0.282 | 0.165 | 0.164 | 15.380 |
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 | 20 | 20 | 20 | 15 | 14 | 31 | 37 | 14 | 33 | 18 |
N.S. |
1 | 1.00 | 1.00 | 0.75 | 0.70 | 1.55 | 1.85 | 0.70 | 1.65 | 0.90 |
time (sec) |
N/A | 0.180 | 0.012 | 0.300 | 0.028 | 0.071 | 0.146 | 0.148 | 0.166 | 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 | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 18 | 19 | 15 | 15 | 15 | 22 | 15 | 20 | 14 |
N.S. |
1 | 0.95 | 1.00 | 0.79 | 0.79 | 0.79 | 1.16 | 0.79 | 1.05 | 0.74 |
time (sec) |
N/A | 0.204 | 0.011 | 0.477 | 0.025 | 0.070 | 0.134 | 0.127 | 0.185 | 15.640 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
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 | 14 | 14 | 13 | 16 | 14 | 10 | 18 | 34 | 16 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 1.14 | 1.00 | 0.71 | 1.29 | 2.43 | 1.14 |
time (sec) |
N/A | 0.191 | 0.006 | 0.208 | 0.027 | 0.074 | 0.036 | 0.120 | 0.173 | 15.763 |
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 | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 18 | 20 | 29 | 20 | 37 | 20 | 28 | 42 | 32 |
N.S. |
1 | 0.82 | 0.91 | 1.32 | 0.91 | 1.68 | 0.91 | 1.27 | 1.91 | 1.45 |
time (sec) |
N/A | 0.212 | 0.019 | 0.819 | 0.024 | 0.076 | 0.050 | 0.107 | 0.175 | 16.456 |
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 | 5 | 5 | 7 | 6 | 5 | 5 | 12 | 5 | 21 | 5 |
N.S. |
1 | 1.00 | 1.40 | 1.20 | 1.00 | 1.00 | 2.40 | 1.00 | 4.20 | 1.00 |
time (sec) |
N/A | 0.176 | 0.006 | 0.076 | 0.022 | 0.068 | 0.841 | 0.145 | 0.161 | 15.526 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 7 | 7 | 9 | 13 | 5 | 7 | 12 | 7 | 13 | 5 |
N.S. |
1 | 1.00 | 1.29 | 1.86 | 0.71 | 1.00 | 1.71 | 1.00 | 1.86 | 0.71 |
time (sec) |
N/A | 0.177 | 0.002 | 0.095 | 0.025 | 0.072 | 0.761 | 0.110 | 0.162 | 16.482 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | B | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 5 | 11 | 8 | 6 | 11 | 5 | 14 | 9 | 5 | 6 |
N.S. |
1 | 2.20 | 1.60 | 1.20 | 2.20 | 1.00 | 2.80 | 1.80 | 1.00 | 1.20 |
time (sec) |
N/A | 0.185 | 0.002 | 0.495 | 0.028 | 0.070 | 1.529 | 0.133 | 0.160 | 15.822 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | B | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 15 | 18 | 69 | 35 | 32 | 29 | 19 | 24 |
N.S. |
1 | 1.00 | 1.00 | 1.20 | 4.60 | 2.33 | 2.13 | 1.93 | 1.27 | 1.60 |
time (sec) |
N/A | 0.217 | 0.007 | 0.253 | 0.107 | 0.072 | 0.756 | 0.130 | 0.165 | 16.227 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 11 | 11 | 17 | 12 | 11 | 15 | 12 | 15 | 11 | 11 |
N.S. |
1 | 1.00 | 1.55 | 1.09 | 1.00 | 1.36 | 1.09 | 1.36 | 1.00 | 1.00 |
time (sec) |
N/A | 0.240 | 0.140 | 0.212 | 0.025 | 0.074 | 0.087 | 0.154 | 0.227 | 0.098 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 82 | 18 | 17 | 17 | 19 | 17 | 16 | 17 |
N.S. |
1 | 1.00 | 4.10 | 0.90 | 0.85 | 0.85 | 0.95 | 0.85 | 0.80 | 0.85 |
time (sec) |
N/A | 0.226 | 0.155 | 0.202 | 0.106 | 0.077 | 0.164 | 0.140 | 0.181 | 15.918 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 11 | 11 | 11 | 12 | 11 | 13 | 10 | 12 | 11 | 9 |
N.S. |
1 | 1.00 | 1.00 | 1.09 | 1.00 | 1.18 | 0.91 | 1.09 | 1.00 | 0.82 |
time (sec) |
N/A | 0.204 | 0.008 | 0.132 | 0.023 | 0.071 | 0.077 | 0.133 | 0.173 | 0.159 |
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 | 35 | 26 | 31 | 34 | 27 | 37 | 0 | 36 | 29 |
N.S. |
1 | 1.35 | 1.00 | 1.19 | 1.31 | 1.04 | 1.42 | 0.00 | 1.38 | 1.12 |
time (sec) |
N/A | 0.233 | 0.032 | 0.685 | 0.105 | 0.075 | 0.412 | 0.000 | 0.175 | 16.655 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 39 | 24 | 220 | 35 | 0 | 28 | 13 | 16 |
N.S. |
1 | 1.00 | 1.62 | 1.00 | 9.17 | 1.46 | 0.00 | 1.17 | 0.54 | 0.67 |
time (sec) |
N/A | 0.202 | 0.023 | 0.199 | 0.033 | 0.074 | 0.000 | 0.143 | 0.166 | 16.420 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
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 | 0.261 | 0.070 | 0.232 | 0.037 | 0.067 | 0.103 | 0.127 | 0.160 | 0.060 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 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 | 0.177 | 0.034 | 0.158 | 0.036 | 0.067 | 0.181 | 0.127 | 0.159 | 0.031 |
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 | 0.222 | 0.016 | 0.185 | 0.030 | 0.066 | 0.125 | 0.142 | 0.157 | 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 | 30 | 30 | 46 | 25 | 24 | 36 | 27 | 24 | 24 | 24 |
N.S. |
1 | 1.00 | 1.53 | 0.83 | 0.80 | 1.20 | 0.90 | 0.80 | 0.80 | 0.80 |
time (sec) |
N/A | 0.179 | 0.077 | 0.011 | 0.024 | 0.076 | 0.025 | 0.142 | 0.157 | 16.887 |
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 | 6 | 6 | 6 | 7 | 6 | 6 | 3 | 14 | 7 | 6 |
N.S. |
1 | 1.00 | 1.00 | 1.17 | 1.00 | 1.00 | 0.50 | 2.33 | 1.17 | 1.00 |
time (sec) |
N/A | 0.175 | 0.001 | 0.183 | 0.036 | 0.067 | 0.513 | 0.128 | 0.170 | 17.673 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 7 | 7 | 7 | 8 | 7 | 15 | 8 | 30 | 15 | 12 |
N.S. |
1 | 1.00 | 1.00 | 1.14 | 1.00 | 2.14 | 1.14 | 4.29 | 2.14 | 1.71 |
time (sec) |
N/A | 0.212 | 0.002 | 1.346 | 0.033 | 0.070 | 2.920 | 0.149 | 0.165 | 17.353 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
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 | 11 | 10 | 10 | 13 | 10 | 14 | 13 | 6 | 6 |
N.S. |
1 | 0.85 | 0.77 | 0.77 | 1.00 | 0.77 | 1.08 | 1.00 | 0.46 | 0.46 |
time (sec) |
N/A | 0.156 | 0.004 | 0.162 | 0.034 | 0.061 | 0.029 | 0.122 | 0.166 | 16.177 |
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 | 11 | 11 | 11 | 10 | 11 | 22 | 12 | 11 | 19 | 14 |
N.S. |
1 | 1.00 | 1.00 | 0.91 | 1.00 | 2.00 | 1.09 | 1.00 | 1.73 | 1.27 |
time (sec) |
N/A | 0.149 | 0.021 | 0.240 | 0.028 | 0.072 | 0.031 | 0.108 | 0.200 | 15.858 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 10 | 10 | 10 | 17 | 10 | 18 | 10 | 11 | 17 | 24 |
N.S. |
1 | 1.00 | 1.00 | 1.70 | 1.00 | 1.80 | 1.00 | 1.10 | 1.70 | 2.40 |
time (sec) |
N/A | 0.149 | 0.037 | 0.188 | 0.030 | 0.079 | 0.027 | 0.120 | 0.180 | 15.684 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 10 | 10 | 10 | 9 | 8 | 8 | 8 | 8 | 8 | 8 |
N.S. |
1 | 1.00 | 1.00 | 0.90 | 0.80 | 0.80 | 0.80 | 0.80 | 0.80 | 0.80 |
time (sec) |
N/A | 0.184 | 0.009 | 0.213 | 0.042 | 0.067 | 0.066 | 0.121 | 0.152 | 0.055 |
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 | 18 | 18 | 18 | 13 | 12 | 14 | 32 | 12 | 19 | 12 |
N.S. |
1 | 1.00 | 1.00 | 0.72 | 0.67 | 0.78 | 1.78 | 0.67 | 1.06 | 0.67 |
time (sec) |
N/A | 0.220 | 0.024 | 0.128 | 0.024 | 0.073 | 0.162 | 0.127 | 0.155 | 16.001 |
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 | 10 | 10 | 10 | 9 | 8 | 8 | 31 | 8 | 8 | 8 |
N.S. |
1 | 1.00 | 1.00 | 0.90 | 0.80 | 0.80 | 3.10 | 0.80 | 0.80 | 0.80 |
time (sec) |
N/A | 0.155 | 0.004 | 0.205 | 0.028 | 0.061 | 0.513 | 0.132 | 0.152 | 15.919 |
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 | 16 | 16 | 25 | 11 | 10 | 21 | 12 | 10 | 10 | 14 |
N.S. |
1 | 1.00 | 1.56 | 0.69 | 0.62 | 1.31 | 0.75 | 0.62 | 0.62 | 0.88 |
time (sec) |
N/A | 0.181 | 0.020 | 0.740 | 0.023 | 0.067 | 0.122 | 0.166 | 0.154 | 16.010 |
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 | 7 | 7 | 7 | 8 | 7 | 13 | 8 | 9 | 9 | 9 |
N.S. |
1 | 1.00 | 1.00 | 1.14 | 1.00 | 1.86 | 1.14 | 1.29 | 1.29 | 1.29 |
time (sec) |
N/A | 0.190 | 0.006 | 0.079 | 0.025 | 0.069 | 0.051 | 0.136 | 0.154 | 15.882 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 13 | 13 | 13 | 17 | 16 | 25 | 15 | 41 | 27 | 15 |
N.S. |
1 | 1.00 | 1.00 | 1.31 | 1.23 | 1.92 | 1.15 | 3.15 | 2.08 | 1.15 |
time (sec) |
N/A | 0.208 | 0.014 | 0.098 | 0.037 | 0.071 | 7.773 | 0.131 | 0.156 | 16.773 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 5 | 5 | 5 | 10 | 10 | 23 | 10 | 43 | 9 | 31 |
N.S. |
1 | 1.00 | 1.00 | 2.00 | 2.00 | 4.60 | 2.00 | 8.60 | 1.80 | 6.20 |
time (sec) |
N/A | 0.195 | 0.008 | 0.059 | 0.030 | 0.068 | 0.558 | 0.113 | 0.162 | 17.666 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | B | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 7 | 19 | 7 | 8 | 15 | 7 | 8 | 16 | 31 | 26 |
N.S. |
1 | 2.71 | 1.00 | 1.14 | 2.14 | 1.00 | 1.14 | 2.29 | 4.43 | 3.71 |
time (sec) |
N/A | 0.227 | 0.002 | 0.317 | 0.025 | 0.072 | 1.101 | 0.127 | 0.167 | 15.955 |
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 | 4 | 4 | 4 | 5 | 4 | 4 | 20 | 4 | 21 | 4 |
N.S. |
1 | 1.00 | 1.00 | 1.25 | 1.00 | 1.00 | 5.00 | 1.00 | 5.25 | 1.00 |
time (sec) |
N/A | 0.147 | 0.001 | 0.480 | 0.026 | 0.070 | 0.148 | 0.128 | 0.160 | 15.597 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 13 | 21 | 21 | 14 | 74 | 27 | 0 | 81 | 48 | 13 |
N.S. |
1 | 1.62 | 1.62 | 1.08 | 5.69 | 2.08 | 0.00 | 6.23 | 3.69 | 1.00 |
time (sec) |
N/A | 0.231 | 0.006 | 0.143 | 0.103 | 0.075 | 0.000 | 0.139 | 0.153 | 15.505 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 31 | 18 | 28 | 20 | 22 | 20 | 20 | 22 | 18 |
N.S. |
1 | 1.94 | 1.12 | 1.75 | 1.25 | 1.38 | 1.25 | 1.25 | 1.38 | 1.12 |
time (sec) |
N/A | 0.198 | 0.009 | 0.279 | 0.102 | 0.069 | 0.021 | 0.127 | 0.219 | 15.861 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
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 | 50 | 26 | 34 | 35 | 28 | 36 | 31 | 32 | 26 |
N.S. |
1 | 1.56 | 0.81 | 1.06 | 1.09 | 0.88 | 1.12 | 0.97 | 1.00 | 0.81 |
time (sec) |
N/A | 0.220 | 0.026 | 5.190 | 0.106 | 0.070 | 0.023 | 0.124 | 0.149 | 16.028 |
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 | 18 | 31 | 16 | 11 | 10 | 19 | 12 | 10 | 18 | 18 |
N.S. |
1 | 1.72 | 0.89 | 0.61 | 0.56 | 1.06 | 0.67 | 0.56 | 1.00 | 1.00 |
time (sec) |
N/A | 0.233 | 0.029 | 0.301 | 0.022 | 0.068 | 0.024 | 0.145 | 0.144 | 0.051 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 48 | 32 | 23 | 18 | 25 | 32 | 22 | 26 | 24 |
N.S. |
1 | 1.41 | 0.94 | 0.68 | 0.53 | 0.74 | 0.94 | 0.65 | 0.76 | 0.71 |
time (sec) |
N/A | 0.296 | 0.022 | 0.931 | 0.028 | 0.069 | 0.020 | 0.130 | 0.162 | 0.053 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 13 | 19 | 33 | 14 | 13 | 21 | 12 | 13 | 13 | 13 |
N.S. |
1 | 1.46 | 2.54 | 1.08 | 1.00 | 1.62 | 0.92 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.194 | 0.007 | 1.541 | 0.027 | 0.067 | 0.022 | 0.152 | 0.166 | 0.042 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 46 | 63 | 24 | 17 | 16 | 31 | 31 | 16 | 34 | 33 |
N.S. |
1 | 1.37 | 0.52 | 0.37 | 0.35 | 0.67 | 0.67 | 0.35 | 0.74 | 0.72 |
time (sec) |
N/A | 0.353 | 0.020 | 2.190 | 0.023 | 0.070 | 0.028 | 0.126 | 0.164 | 0.043 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | C | B | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 9 | 21 | 9 | 20 | 20 | 19 | 20 | 18 | 20 | 13 |
N.S. |
1 | 2.33 | 1.00 | 2.22 | 2.22 | 2.11 | 2.22 | 2.00 | 2.22 | 1.44 |
time (sec) |
N/A | 0.204 | 0.007 | 0.126 | 0.024 | 0.071 | 0.115 | 0.105 | 0.171 | 15.853 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
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 | 14 | 17 | 13 | 13 | 12 | 12 | 13 | 27 | 11 |
N.S. |
1 | 1.00 | 1.21 | 0.93 | 0.93 | 0.86 | 0.86 | 0.93 | 1.93 | 0.79 |
time (sec) |
N/A | 0.160 | 0.019 | 0.227 | 0.025 | 0.065 | 0.024 | 0.108 | 0.148 | 15.726 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 1 | 1 | 1 | 2 | 1 | 1 | 0 | 1 | 11 | 1 |
N.S. |
1 | 1.00 | 1.00 | 2.00 | 1.00 | 1.00 | 0.00 | 1.00 | 11.00 | 1.00 |
time (sec) |
N/A | 0.151 | 0.000 | 0.066 | 0.023 | 0.048 | 0.025 | 0.115 | 0.149 | 15.644 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
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 | 6 | 8 | 7 | 6 | 6 | 7 | 6 | 6 | 6 |
N.S. |
1 | 1.00 | 1.33 | 1.17 | 1.00 | 1.00 | 1.17 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.143 | 0.002 | 0.175 | 0.028 | 0.063 | 0.023 | 0.133 | 0.148 | 15.311 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 9 | 9 | 9 | 10 | 9 | 9 | 7 | 9 | 9 | 9 |
N.S. |
1 | 1.00 | 1.00 | 1.11 | 1.00 | 1.00 | 0.78 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.170 | 0.006 | 0.205 | 0.022 | 0.064 | 0.150 | 0.105 | 0.150 | 0.079 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 8 | 8 | 8 | 7 | 35 | 6 | 22 | 6 | 6 | 6 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 4.38 | 0.75 | 2.75 | 0.75 | 0.75 | 0.75 |
time (sec) |
N/A | 0.160 | 0.003 | 0.059 | 0.030 | 0.059 | 0.066 | 0.121 | 0.151 | 16.473 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | B | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 6 | 6 | 51 | 9 | 51 | 8 | 5 | 26 | 6 | 8 |
N.S. |
1 | 1.00 | 8.50 | 1.50 | 8.50 | 1.33 | 0.83 | 4.33 | 1.00 | 1.33 |
time (sec) |
N/A | 0.338 | 0.030 | 0.117 | 0.171 | 0.065 | 0.135 | 0.159 | 0.165 | 0.098 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 8 | 8 | 8 | 7 | 8 | 8 | 8 | 8 | 5 | 8 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 1.00 | 1.00 | 1.00 | 1.00 | 0.62 | 1.00 |
time (sec) |
N/A | 0.374 | 0.014 | 0.069 | 0.034 | 0.068 | 0.131 | 0.115 | 0.169 | 16.356 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
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 | 12 | 9 | 8 | 8 | 7 | 6 | 5 | 8 |
N.S. |
1 | 1.00 | 1.50 | 1.12 | 1.00 | 1.00 | 0.88 | 0.75 | 0.62 | 1.00 |
time (sec) |
N/A | 0.157 | 0.011 | 0.046 | 0.031 | 0.068 | 0.106 | 0.118 | 0.157 | 17.311 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
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 | 7 | 8 | 8 | 7 | 8 | 5 | 8 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 1.00 | 1.00 | 0.88 | 1.00 | 0.62 | 1.00 |
time (sec) |
N/A | 0.369 | 0.013 | 0.064 | 0.035 | 0.067 | 0.112 | 0.164 | 0.155 | 16.777 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 55 | 91 | 55 | 80 | 0 | 320 | 124 | 77 | 17 | 1108 |
N.S. |
1 | 1.65 | 1.00 | 1.45 | 0.00 | 5.82 | 2.25 | 1.40 | 0.31 | 20.15 |
time (sec) |
N/A | 0.424 | 0.089 | 1.651 | 0.000 | 0.113 | 2.451 | 0.158 | 0.155 | 18.535 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 55 | 83 | 54 | 72 | 0 | 322 | 124 | 77 | 17 | 1374 |
N.S. |
1 | 1.51 | 0.98 | 1.31 | 0.00 | 5.85 | 2.25 | 1.40 | 0.31 | 24.98 |
time (sec) |
N/A | 0.348 | 0.061 | 1.655 | 0.000 | 0.110 | 2.462 | 0.136 | 0.230 | 17.078 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 52 | 66 | 48 | 49 | 0 | 225 | 432 | 141 | 17 | 108 |
N.S. |
1 | 1.27 | 0.92 | 0.94 | 0.00 | 4.33 | 8.31 | 2.71 | 0.33 | 2.08 |
time (sec) |
N/A | 0.319 | 0.104 | 1.734 | 0.000 | 0.100 | 15.305 | 0.163 | 0.157 | 16.010 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 52 | 54 | 50 | 51 | 0 | 224 | 432 | 159 | 17 | 684 |
N.S. |
1 | 1.04 | 0.96 | 0.98 | 0.00 | 4.31 | 8.31 | 3.06 | 0.33 | 13.15 |
time (sec) |
N/A | 0.289 | 0.064 | 1.732 | 0.000 | 0.099 | 15.571 | 0.116 | 0.151 | 15.918 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 30 | 31 | 30 | 76 | 91 | 0 | 0 | 36 | 0 |
N.S. |
1 | 1.00 | 1.03 | 1.00 | 2.53 | 3.03 | 0.00 | 0.00 | 1.20 | 0.00 |
time (sec) |
N/A | 0.223 | 0.029 | 0.218 | 0.114 | 0.081 | 0.000 | 0.000 | 0.147 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 31 | 32 | 31 | 51 | 84 | 0 | 59 | 19 | 0 |
N.S. |
1 | 1.00 | 1.03 | 1.00 | 1.65 | 2.71 | 0.00 | 1.90 | 0.61 | 0.00 |
time (sec) |
N/A | 0.225 | 0.027 | 0.223 | 0.030 | 0.087 | 0.000 | 0.143 | 0.154 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 8 | 8 | 8 | 7 | 6 | 6 | 7 | 6 | 5 | 6 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 0.75 | 0.75 | 0.88 | 0.75 | 0.62 | 0.75 |
time (sec) |
N/A | 0.155 | 0.002 | 0.101 | 0.022 | 0.069 | 0.114 | 0.150 | 0.161 | 16.485 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 18 | 25 | 41 | 21 | 0 | 14 | 24 | 0 |
N.S. |
1 | 1.00 | 0.95 | 1.32 | 2.16 | 1.11 | 0.00 | 0.74 | 1.26 | 0.00 |
time (sec) |
N/A | 0.202 | 0.012 | 0.160 | 0.113 | 0.080 | 0.000 | 0.140 | 0.161 | 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 | 29 | 34 | 16 | 13 | 12 | 23 | 476 | 12 | 23 | 12 |
N.S. |
1 | 1.17 | 0.55 | 0.45 | 0.41 | 0.79 | 16.41 | 0.41 | 0.79 | 0.41 |
time (sec) |
N/A | 0.269 | 0.014 | 0.188 | 0.024 | 0.073 | 5.859 | 0.121 | 0.154 | 17.455 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 43 | 29 | 36 | 103 | 26 | 32 | 34 | 18 | 45 |
N.S. |
1 | 1.48 | 1.00 | 1.24 | 3.55 | 0.90 | 1.10 | 1.17 | 0.62 | 1.55 |
time (sec) |
N/A | 0.324 | 5.020 | 0.307 | 0.105 | 0.077 | 0.114 | 0.156 | 0.230 | 17.053 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 43 | 29 | 36 | 103 | 26 | 32 | 34 | 18 | 45 |
N.S. |
1 | 1.48 | 1.00 | 1.24 | 3.55 | 0.90 | 1.10 | 1.17 | 0.62 | 1.55 |
time (sec) |
N/A | 0.291 | 3.301 | 0.262 | 0.106 | 0.078 | 0.121 | 0.151 | 0.162 | 16.772 |
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 | 44 | 44 | 38 | 31 | 30 | 46 | 0 | 34 | 87 | 32 |
N.S. |
1 | 1.00 | 0.86 | 0.70 | 0.68 | 1.05 | 0.00 | 0.77 | 1.98 | 0.73 |
time (sec) |
N/A | 0.246 | 0.051 | 0.275 | 0.029 | 0.078 | 0.000 | 0.133 | 0.156 | 0.070 |