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 | 23 | 23 | 23 | 20 | 19 | 19 | 19 | 19 | 20 | 20 |
N.S. |
1 | 1.00 | 1.00 | 0.87 | 0.83 | 0.83 | 0.83 | 0.83 | 0.87 | 0.87 |
time (sec) |
N/A | 0.141 | 0.002 | 0.039 | 0.027 | 0.068 | 0.018 | 0.134 | 0.169 | 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 | 23 | 23 | 23 | 20 | 19 | 19 | 19 | 19 | 20 | 20 |
N.S. |
1 | 1.00 | 1.00 | 0.87 | 0.83 | 0.83 | 0.83 | 0.83 | 0.87 | 0.87 |
time (sec) |
N/A | 0.146 | 0.002 | 0.038 | 0.031 | 0.060 | 0.018 | 0.117 | 0.161 | 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 | 23 | 23 | 23 | 20 | 19 | 19 | 19 | 19 | 20 | 20 |
N.S. |
1 | 1.00 | 1.00 | 0.87 | 0.83 | 0.83 | 0.83 | 0.83 | 0.87 | 0.87 |
time (sec) |
N/A | 0.146 | 0.002 | 0.033 | 0.028 | 0.067 | 0.018 | 0.126 | 0.157 | 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 | 18 | 18 | 18 | 17 | 16 | 16 | 15 | 16 | 18 | 18 |
N.S. |
1 | 1.00 | 1.00 | 0.94 | 0.89 | 0.89 | 0.83 | 0.89 | 1.00 | 1.00 |
time (sec) |
N/A | 0.143 | 0.001 | 0.025 | 0.032 | 0.064 | 0.018 | 0.126 | 0.146 | 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 | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 19 | 18 | 17 | 17 | 17 | 20 | 19 | 19 |
N.S. |
1 | 1.00 | 1.00 | 0.95 | 0.89 | 0.89 | 0.89 | 1.05 | 1.00 | 1.00 |
time (sec) |
N/A | 0.146 | 0.003 | 0.038 | 0.036 | 0.089 | 0.037 | 0.126 | 0.148 | 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 | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 17 | 17 | 18 | 17 | 19 | 14 | 17 | 17 | 17 |
N.S. |
1 | 1.00 | 1.00 | 1.06 | 1.00 | 1.12 | 0.82 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.145 | 0.002 | 0.040 | 0.026 | 0.066 | 0.041 | 0.121 | 0.144 | 0.244 |
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 | 20 | 20 | 20 | 19 | 18 | 22 | 19 | 31 | 22 | 18 |
N.S. |
1 | 1.00 | 1.00 | 0.95 | 0.90 | 1.10 | 0.95 | 1.55 | 1.10 | 0.90 |
time (sec) |
N/A | 0.149 | 0.003 | 0.039 | 0.034 | 0.087 | 0.066 | 0.126 | 0.160 | 0.030 |
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 | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 20 | 19 | 21 | 21 | 20 | 21 | 20 | 18 |
N.S. |
1 | 1.00 | 1.00 | 0.95 | 1.05 | 1.05 | 1.00 | 1.05 | 1.00 | 0.90 |
time (sec) |
N/A | 0.149 | 0.003 | 0.041 | 0.029 | 0.064 | 0.066 | 0.120 | 0.156 | 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 | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 23 | 19 | 21 | 21 | 20 | 21 | 20 | 18 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 0.91 | 0.91 | 0.87 | 0.91 | 0.87 | 0.78 |
time (sec) |
N/A | 0.150 | 0.003 | 0.042 | 0.048 | 0.069 | 0.071 | 0.114 | 0.158 | 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 | 43 | 41 | 43 | 34 | 37 | 37 | 37 | 37 | 33 | 33 |
N.S. |
1 | 0.95 | 1.00 | 0.79 | 0.86 | 0.86 | 0.86 | 0.86 | 0.77 | 0.77 |
time (sec) |
N/A | 0.171 | 0.002 | 0.112 | 0.038 | 0.072 | 0.021 | 0.118 | 0.146 | 0.032 |
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 | 43 | 34 | 37 | 37 | 39 | 37 | 33 | 33 |
N.S. |
1 | 1.00 | 1.00 | 0.79 | 0.86 | 0.86 | 0.91 | 0.86 | 0.77 | 0.77 |
time (sec) |
N/A | 0.168 | 0.001 | 0.112 | 0.033 | 0.074 | 0.022 | 0.121 | 0.178 | 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 | 24 | 24 | 43 | 33 | 37 | 37 | 37 | 37 | 32 | 32 |
N.S. |
1 | 1.00 | 1.79 | 1.38 | 1.54 | 1.54 | 1.54 | 1.54 | 1.33 | 1.33 |
time (sec) |
N/A | 0.140 | 0.001 | 0.109 | 0.027 | 0.074 | 0.024 | 0.120 | 0.164 | 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 | 38 | 38 | 38 | 32 | 34 | 34 | 36 | 34 | 31 | 31 |
N.S. |
1 | 1.00 | 1.00 | 0.84 | 0.89 | 0.89 | 0.95 | 0.89 | 0.82 | 0.82 |
time (sec) |
N/A | 0.166 | 0.001 | 0.104 | 0.028 | 0.064 | 0.021 | 0.125 | 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 | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 37 | 37 | 37 | 31 | 35 | 35 | 34 | 38 | 31 | 31 |
N.S. |
1 | 1.00 | 1.00 | 0.84 | 0.95 | 0.95 | 0.92 | 1.03 | 0.84 | 0.84 |
time (sec) |
N/A | 0.167 | 0.001 | 0.128 | 0.028 | 0.066 | 0.053 | 0.124 | 0.159 | 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 | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 37 | 37 | 37 | 31 | 35 | 38 | 32 | 35 | 32 | 31 |
N.S. |
1 | 1.00 | 1.00 | 0.84 | 0.95 | 1.03 | 0.86 | 0.95 | 0.86 | 0.84 |
time (sec) |
N/A | 0.166 | 0.001 | 0.112 | 0.035 | 0.064 | 0.057 | 0.128 | 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 | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 40 | 35 | 40 | 32 | 36 | 40 | 37 | 55 | 34 | 33 |
N.S. |
1 | 0.88 | 1.00 | 0.80 | 0.90 | 1.00 | 0.92 | 1.38 | 0.85 | 0.82 |
time (sec) |
N/A | 0.172 | 0.001 | 0.118 | 0.032 | 0.064 | 0.067 | 0.121 | 0.159 | 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 | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 36 | 36 | 30 | 37 | 39 | 34 | 37 | 33 | 33 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 1.03 | 1.08 | 0.94 | 1.03 | 0.92 | 0.92 |
time (sec) |
N/A | 0.172 | 0.001 | 0.114 | 0.027 | 0.063 | 0.074 | 0.117 | 0.160 | 0.222 |
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 | 36 | 37 | 36 | 30 | 38 | 41 | 36 | 51 | 35 | 38 |
N.S. |
1 | 1.03 | 1.00 | 0.83 | 1.06 | 1.14 | 1.00 | 1.42 | 0.97 | 1.06 |
time (sec) |
N/A | 0.173 | 0.001 | 0.115 | 0.026 | 0.070 | 0.101 | 0.142 | 0.159 | 0.029 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 43 | 43 | 43 | 49 | 59 | 48 | 46 | 70 | 50 | 41 |
N.S. |
1 | 1.00 | 1.00 | 1.14 | 1.37 | 1.12 | 1.07 | 1.63 | 1.16 | 0.95 |
time (sec) |
N/A | 0.182 | 0.008 | 0.200 | 0.031 | 0.089 | 0.100 | 0.129 | 0.153 | 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 | 40 | 37 | 40 | 37 | 48 | 34 | 32 | 38 | 43 | 34 |
N.S. |
1 | 0.92 | 1.00 | 0.92 | 1.20 | 0.85 | 0.80 | 0.95 | 1.08 | 0.85 |
time (sec) |
N/A | 0.178 | 0.006 | 0.184 | 0.035 | 0.075 | 0.081 | 0.121 | 0.152 | 0.237 |
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 | 25 | 33 | 42 | 32 | 31 | 44 | 34 | 21 |
N.S. |
1 | 1.00 | 1.00 | 1.32 | 1.68 | 1.28 | 1.24 | 1.76 | 1.36 | 0.84 |
time (sec) |
N/A | 0.149 | 0.005 | 0.185 | 0.038 | 0.096 | 0.090 | 0.151 | 0.153 | 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 | 23 | 23 | 23 | 22 | 31 | 22 | 19 | 23 | 29 | 22 |
N.S. |
1 | 1.00 | 1.00 | 0.96 | 1.35 | 0.96 | 0.83 | 1.00 | 1.26 | 0.96 |
time (sec) |
N/A | 0.137 | 0.003 | 0.190 | 0.036 | 0.078 | 0.065 | 0.129 | 0.157 | 0.031 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 17 | 17 | 29 | 37 | 28 | 22 | 39 | 30 | 17 |
N.S. |
1 | 1.00 | 1.00 | 1.71 | 2.18 | 1.65 | 1.29 | 2.29 | 1.76 | 1.00 |
time (sec) |
N/A | 0.136 | 0.004 | 0.184 | 0.043 | 0.073 | 0.074 | 0.128 | 0.157 | 0.235 |
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 | 34 | 33 | 32 | 40 | 27 | 26 | 36 | 33 | 32 |
N.S. |
1 | 1.03 | 1.00 | 0.97 | 1.21 | 0.82 | 0.79 | 1.09 | 1.00 | 0.97 |
time (sec) |
N/A | 0.154 | 0.006 | 0.189 | 0.033 | 0.069 | 0.121 | 0.130 | 0.155 | 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 | 27 | 27 | 27 | 37 | 44 | 36 | 32 | 46 | 38 | 24 |
N.S. |
1 | 1.00 | 1.00 | 1.37 | 1.63 | 1.33 | 1.19 | 1.70 | 1.41 | 0.89 |
time (sec) |
N/A | 0.159 | 0.006 | 0.195 | 0.034 | 0.077 | 0.106 | 0.124 | 0.151 | 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 | 52 | 48 | 52 | 49 | 60 | 46 | 44 | 64 | 59 | 48 |
N.S. |
1 | 0.92 | 1.00 | 0.94 | 1.15 | 0.88 | 0.85 | 1.23 | 1.13 | 0.92 |
time (sec) |
N/A | 0.194 | 0.007 | 0.190 | 0.036 | 0.076 | 0.155 | 0.120 | 0.148 | 0.256 |
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 | 64 | 57 | 65 | 62 | 75 | 82 | 60 | 168 | 106 | 65 |
N.S. |
1 | 0.89 | 1.02 | 0.97 | 1.17 | 1.28 | 0.94 | 2.62 | 1.66 | 1.02 |
time (sec) |
N/A | 0.199 | 0.032 | 0.184 | 0.046 | 0.071 | 0.147 | 0.129 | 0.149 | 0.249 |
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 | 57 | 86 | 67 | 71 | 88 | 65 | 104 | 98 | 55 |
N.S. |
1 | 1.04 | 1.56 | 1.22 | 1.29 | 1.60 | 1.18 | 1.89 | 1.78 | 1.00 |
time (sec) |
N/A | 0.177 | 0.023 | 0.185 | 0.051 | 0.078 | 0.159 | 0.125 | 0.147 | 0.247 |
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 | 51 | 46 | 72 | 49 | 60 | 59 | 46 | 114 | 86 | 52 |
N.S. |
1 | 0.90 | 1.41 | 0.96 | 1.18 | 1.16 | 0.90 | 2.24 | 1.69 | 1.02 |
time (sec) |
N/A | 0.183 | 0.016 | 0.182 | 0.046 | 0.084 | 0.151 | 0.129 | 0.147 | 0.241 |
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 | 46 | 76 | 60 | 64 | 76 | 49 | 80 | 87 | 46 |
N.S. |
1 | 1.00 | 1.65 | 1.30 | 1.39 | 1.65 | 1.07 | 1.74 | 1.89 | 1.00 |
time (sec) |
N/A | 0.162 | 0.020 | 0.182 | 1.132 | 0.111 | 0.133 | 0.122 | 0.151 | 0.254 |
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 | 24 | 24 | 25 | 24 | 26 | 26 | 26 | 57 | 25 | 25 |
N.S. |
1 | 1.00 | 1.04 | 1.00 | 1.08 | 1.08 | 1.08 | 2.38 | 1.04 | 1.04 |
time (sec) |
N/A | 0.145 | 0.009 | 0.181 | 0.051 | 0.077 | 0.091 | 0.125 | 0.157 | 0.243 |
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 | 46 | 74 | 61 | 64 | 76 | 49 | 83 | 87 | 46 |
N.S. |
1 | 1.00 | 1.61 | 1.33 | 1.39 | 1.65 | 1.07 | 1.80 | 1.89 | 1.00 |
time (sec) |
N/A | 0.156 | 0.015 | 0.173 | 0.044 | 0.085 | 0.149 | 0.118 | 0.154 | 0.044 |
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 | 57 | 52 | 51 | 55 | 66 | 75 | 54 | 116 | 103 | 56 |
N.S. |
1 | 0.91 | 0.89 | 0.96 | 1.16 | 1.32 | 0.95 | 2.04 | 1.81 | 0.98 |
time (sec) |
N/A | 0.187 | 0.025 | 0.194 | 0.044 | 0.076 | 0.185 | 0.120 | 0.153 | 0.260 |
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 | 58 | 59 | 85 | 66 | 74 | 90 | 66 | 114 | 102 | 56 |
N.S. |
1 | 1.02 | 1.47 | 1.14 | 1.28 | 1.55 | 1.14 | 1.97 | 1.76 | 0.97 |
time (sec) |
N/A | 0.176 | 0.025 | 0.197 | 0.063 | 0.079 | 0.201 | 0.134 | 0.156 | 0.259 |
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 | 78 | 70 | 74 | 77 | 93 | 104 | 75 | 174 | 132 | 81 |
N.S. |
1 | 0.90 | 0.95 | 0.99 | 1.19 | 1.33 | 0.96 | 2.23 | 1.69 | 1.04 |
time (sec) |
N/A | 0.208 | 0.038 | 0.200 | 0.056 | 0.070 | 0.243 | 0.130 | 0.153 | 0.266 |
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 | 89 | 99 | 90 | 99 | 130 | 95 | 85 | 157 | 83 |
N.S. |
1 | 1.06 | 1.18 | 1.07 | 1.18 | 1.55 | 1.13 | 1.01 | 1.87 | 0.99 |
time (sec) |
N/A | 0.196 | 0.027 | 0.194 | 0.029 | 0.072 | 0.255 | 0.121 | 0.157 | 0.049 |
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 | 72 | 87 | 61 | 87 | 94 | 76 | 64 | 142 | 79 |
N.S. |
1 | 0.95 | 1.14 | 0.80 | 1.14 | 1.24 | 1.00 | 0.84 | 1.87 | 1.04 |
time (sec) |
N/A | 0.218 | 0.021 | 0.189 | 0.039 | 0.080 | 0.201 | 0.121 | 0.158 | 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 | 73 | 78 | 90 | 74 | 91 | 119 | 83 | 77 | 148 | 72 |
N.S. |
1 | 1.07 | 1.23 | 1.01 | 1.25 | 1.63 | 1.14 | 1.05 | 2.03 | 0.99 |
time (sec) |
N/A | 0.181 | 0.019 | 0.191 | 0.029 | 0.090 | 0.207 | 0.124 | 0.163 | 0.251 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 37 | 36 | 53 | 53 | 51 | 37 | 35 | 53 |
N.S. |
1 | 1.00 | 1.37 | 1.33 | 1.96 | 1.96 | 1.89 | 1.37 | 1.30 | 1.96 |
time (sec) |
N/A | 0.140 | 0.017 | 0.188 | 0.032 | 0.072 | 0.159 | 0.124 | 0.158 | 0.262 |
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 | 74 | 82 | 89 | 75 | 92 | 120 | 83 | 78 | 146 | 69 |
N.S. |
1 | 1.11 | 1.20 | 1.01 | 1.24 | 1.62 | 1.12 | 1.05 | 1.97 | 0.93 |
time (sec) |
N/A | 0.179 | 0.020 | 0.199 | 0.034 | 0.085 | 0.192 | 0.124 | 0.149 | 0.046 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 25 | 24 | 39 | 39 | 39 | 23 | 32 | 39 |
N.S. |
1 | 1.00 | 1.04 | 1.00 | 1.62 | 1.62 | 1.62 | 0.96 | 1.33 | 1.62 |
time (sec) |
N/A | 0.137 | 0.010 | 0.194 | 0.031 | 0.068 | 0.127 | 0.126 | 0.159 | 0.247 |
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 | 71 | 82 | 90 | 74 | 91 | 119 | 83 | 77 | 148 | 72 |
N.S. |
1 | 1.15 | 1.27 | 1.04 | 1.28 | 1.68 | 1.17 | 1.08 | 2.08 | 1.01 |
time (sec) |
N/A | 0.173 | 0.020 | 0.200 | 0.030 | 0.077 | 0.187 | 0.126 | 0.155 | 0.254 |
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 | 81 | 73 | 115 | 68 | 93 | 120 | 82 | 84 | 172 | 83 |
N.S. |
1 | 0.90 | 1.42 | 0.84 | 1.15 | 1.48 | 1.01 | 1.04 | 2.12 | 1.02 |
time (sec) |
N/A | 0.207 | 0.021 | 0.213 | 0.033 | 0.074 | 0.257 | 0.111 | 0.158 | 0.044 |
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 | 86 | 91 | 103 | 84 | 98 | 134 | 95 | 87 | 161 | 80 |
N.S. |
1 | 1.06 | 1.20 | 0.98 | 1.14 | 1.56 | 1.10 | 1.01 | 1.87 | 0.93 |
time (sec) |
N/A | 0.193 | 0.021 | 0.214 | 0.034 | 0.074 | 0.266 | 0.133 | 0.160 | 0.054 |
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 | 104 | 95 | 150 | 89 | 117 | 148 | 107 | 116 | 204 | 105 |
N.S. |
1 | 0.91 | 1.44 | 0.86 | 1.12 | 1.42 | 1.03 | 1.12 | 1.96 | 1.01 |
time (sec) |
N/A | 0.229 | 0.037 | 0.220 | 0.030 | 0.071 | 0.302 | 0.121 | 0.158 | 0.268 |
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 | 27 | 24 | 31 | 28 | 34 | 32 | 25 | 29 |
N.S. |
1 | 1.00 | 0.73 | 0.65 | 0.84 | 0.76 | 0.92 | 0.86 | 0.68 | 0.78 |
time (sec) |
N/A | 0.159 | 0.014 | 0.263 | 0.058 | 0.077 | 0.168 | 0.131 | 0.158 | 0.031 |
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 | 27 | 22 | 31 | 24 | 34 | 27 | 22 | 29 |
N.S. |
1 | 1.00 | 0.73 | 0.59 | 0.84 | 0.65 | 0.92 | 0.73 | 0.59 | 0.78 |
time (sec) |
N/A | 0.162 | 0.012 | 0.237 | 0.035 | 0.071 | 0.102 | 0.121 | 0.159 | 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 | 35 | 35 | 26 | 24 | 30 | 25 | 32 | 30 | 24 | 29 |
N.S. |
1 | 1.00 | 0.74 | 0.69 | 0.86 | 0.71 | 0.91 | 0.86 | 0.69 | 0.83 |
time (sec) |
N/A | 0.168 | 0.013 | 0.232 | 0.039 | 0.072 | 0.217 | 0.130 | 0.158 | 0.228 |
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 | 35 | 26 | 23 | 30 | 28 | 34 | 31 | 26 | 26 |
N.S. |
1 | 1.00 | 0.74 | 0.66 | 0.86 | 0.80 | 0.97 | 0.89 | 0.74 | 0.74 |
time (sec) |
N/A | 0.175 | 0.015 | 0.088 | 1.655 | 0.071 | 0.226 | 0.126 | 0.154 | 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 | 35 | 35 | 25 | 22 | 30 | 28 | 34 | 36 | 29 | 29 |
N.S. |
1 | 1.00 | 0.71 | 0.63 | 0.86 | 0.80 | 0.97 | 1.03 | 0.83 | 0.83 |
time (sec) |
N/A | 0.165 | 0.017 | 0.091 | 0.037 | 0.067 | 0.290 | 0.124 | 0.155 | 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 | 40 | 37 | 54 | 47 | 61 | 55 | 38 | 54 |
N.S. |
1 | 1.00 | 0.62 | 0.58 | 0.84 | 0.73 | 0.95 | 0.86 | 0.59 | 0.84 |
time (sec) |
N/A | 0.186 | 0.022 | 0.282 | 0.026 | 0.077 | 0.220 | 0.120 | 0.153 | 0.259 |
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 | 40 | 37 | 54 | 42 | 61 | 50 | 35 | 54 |
N.S. |
1 | 1.00 | 0.62 | 0.58 | 0.84 | 0.66 | 0.95 | 0.78 | 0.55 | 0.84 |
time (sec) |
N/A | 0.185 | 0.023 | 0.268 | 0.041 | 0.069 | 0.131 | 0.121 | 0.152 | 0.234 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 62 | 62 | 40 | 37 | 54 | 44 | 60 | 54 | 37 | 54 |
N.S. |
1 | 1.00 | 0.65 | 0.60 | 0.87 | 0.71 | 0.97 | 0.87 | 0.60 | 0.87 |
time (sec) |
N/A | 0.184 | 0.022 | 0.272 | 0.036 | 0.068 | 0.254 | 0.111 | 0.156 | 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 | 62 | 62 | 40 | 37 | 57 | 47 | 60 | 64 | 39 | 44 |
N.S. |
1 | 1.00 | 0.65 | 0.60 | 0.92 | 0.76 | 0.97 | 1.03 | 0.63 | 0.71 |
time (sec) |
N/A | 0.184 | 0.024 | 0.171 | 0.047 | 0.082 | 0.265 | 0.124 | 0.151 | 0.035 |
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 | 40 | 37 | 56 | 47 | 60 | 68 | 42 | 47 |
N.S. |
1 | 1.00 | 0.65 | 0.60 | 0.90 | 0.76 | 0.97 | 1.10 | 0.68 | 0.76 |
time (sec) |
N/A | 0.197 | 0.023 | 0.158 | 0.029 | 0.074 | 0.310 | 0.125 | 0.149 | 0.035 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 106 | 120 | 85 | 70 | 0 | 216 | 211 | 86 | 76 | 74 |
N.S. |
1 | 1.13 | 0.80 | 0.66 | 0.00 | 2.04 | 1.99 | 0.81 | 0.72 | 0.70 |
time (sec) |
N/A | 0.223 | 0.059 | 0.519 | 0.000 | 0.112 | 2.504 | 0.127 | 0.155 | 0.101 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 103 | 116 | 80 | 63 | 0 | 195 | 207 | 86 | 67 | 73 |
N.S. |
1 | 1.13 | 0.78 | 0.61 | 0.00 | 1.89 | 2.01 | 0.83 | 0.65 | 0.71 |
time (sec) |
N/A | 0.229 | 0.045 | 0.263 | 0.000 | 0.119 | 1.653 | 0.129 | 0.149 | 0.289 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 88 | 93 | 63 | 46 | 0 | 188 | 170 | 68 | 55 | 53 |
N.S. |
1 | 1.06 | 0.72 | 0.52 | 0.00 | 2.14 | 1.93 | 0.77 | 0.62 | 0.60 |
time (sec) |
N/A | 0.197 | 0.041 | 0.236 | 0.000 | 0.111 | 1.016 | 0.132 | 0.154 | 0.074 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 87 | 98 | 61 | 43 | 0 | 173 | 291 | 58 | 58 | 46 |
N.S. |
1 | 1.13 | 0.70 | 0.49 | 0.00 | 1.99 | 3.34 | 0.67 | 0.67 | 0.53 |
time (sec) |
N/A | 0.193 | 0.041 | 0.244 | 0.000 | 0.099 | 1.088 | 0.129 | 0.154 | 0.278 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 106 | 120 | 82 | 64 | 0 | 207 | 369 | 77 | 77 | 76 |
N.S. |
1 | 1.13 | 0.77 | 0.60 | 0.00 | 1.95 | 3.48 | 0.73 | 0.73 | 0.72 |
time (sec) |
N/A | 0.222 | 0.048 | 0.291 | 0.000 | 0.132 | 1.622 | 0.130 | 0.161 | 0.077 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 107 | 122 | 86 | 81 | 0 | 221 | 371 | 89 | 89 | 75 |
N.S. |
1 | 1.14 | 0.80 | 0.76 | 0.00 | 2.07 | 3.47 | 0.83 | 0.83 | 0.70 |
time (sec) |
N/A | 0.214 | 0.052 | 0.302 | 0.000 | 0.142 | 2.590 | 0.130 | 0.157 | 0.291 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 145 | 156 | 141 | 114 | 0 | 342 | 0 | 128 | 175 | 123 |
N.S. |
1 | 1.08 | 0.97 | 0.79 | 0.00 | 2.36 | 0.00 | 0.88 | 1.21 | 0.85 |
time (sec) |
N/A | 0.236 | 0.137 | 0.612 | 0.000 | 0.129 | 0.000 | 0.124 | 0.166 | 0.309 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 125 | 133 | 124 | 91 | 0 | 324 | 0 | 104 | 169 | 101 |
N.S. |
1 | 1.06 | 0.99 | 0.73 | 0.00 | 2.59 | 0.00 | 0.83 | 1.35 | 0.81 |
time (sec) |
N/A | 0.220 | 0.144 | 0.532 | 0.000 | 0.099 | 0.000 | 0.136 | 0.152 | 0.098 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 125 | 131 | 122 | 92 | 0 | 304 | 0 | 112 | 164 | 101 |
N.S. |
1 | 1.05 | 0.98 | 0.74 | 0.00 | 2.43 | 0.00 | 0.90 | 1.31 | 0.81 |
time (sec) |
N/A | 0.210 | 0.125 | 0.328 | 0.000 | 0.095 | 0.000 | 0.129 | 0.164 | 0.291 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 127 | 133 | 125 | 86 | 0 | 296 | 2740 | 112 | 164 | 99 |
N.S. |
1 | 1.05 | 0.98 | 0.68 | 0.00 | 2.33 | 21.57 | 0.88 | 1.29 | 0.78 |
time (sec) |
N/A | 0.222 | 0.103 | 0.309 | 0.000 | 0.113 | 3.725 | 0.129 | 0.156 | 0.273 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 127 | 135 | 125 | 87 | 0 | 278 | 2395 | 94 | 168 | 99 |
N.S. |
1 | 1.06 | 0.98 | 0.69 | 0.00 | 2.19 | 18.86 | 0.74 | 1.32 | 0.78 |
time (sec) |
N/A | 0.213 | 0.123 | 0.322 | 0.000 | 0.089 | 120.674 | 0.126 | 0.161 | 0.293 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 147 | 159 | 114 | 113 | 0 | 329 | 1239 | 125 | 187 | 112 |
N.S. |
1 | 1.08 | 0.78 | 0.77 | 0.00 | 2.24 | 8.43 | 0.85 | 1.27 | 0.76 |
time (sec) |
N/A | 0.242 | 0.146 | 0.386 | 0.000 | 0.104 | 2.824 | 0.132 | 0.161 | 0.084 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 147 | 161 | 114 | 126 | 0 | 347 | 0 | 130 | 198 | 112 |
N.S. |
1 | 1.10 | 0.78 | 0.86 | 0.00 | 2.36 | 0.00 | 0.88 | 1.35 | 0.76 |
time (sec) |
N/A | 0.243 | 0.200 | 0.394 | 0.000 | 0.093 | 0.000 | 0.124 | 0.156 | 0.289 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 179 | 196 | 155 | 138 | 0 | 448 | 0 | 150 | 276 | 158 |
N.S. |
1 | 1.09 | 0.87 | 0.77 | 0.00 | 2.50 | 0.00 | 0.84 | 1.54 | 0.88 |
time (sec) |
N/A | 0.263 | 0.238 | 1.771 | 0.000 | 0.093 | 0.000 | 0.133 | 0.156 | 0.116 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 159 | 173 | 144 | 125 | 0 | 436 | 0 | 126 | 270 | 135 |
N.S. |
1 | 1.09 | 0.91 | 0.79 | 0.00 | 2.74 | 0.00 | 0.79 | 1.70 | 0.85 |
time (sec) |
N/A | 0.248 | 0.230 | 1.666 | 0.000 | 0.112 | 0.000 | 0.137 | 0.153 | 0.313 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 159 | 171 | 144 | 142 | 0 | 436 | 0 | 135 | 269 | 135 |
N.S. |
1 | 1.08 | 0.91 | 0.89 | 0.00 | 2.74 | 0.00 | 0.85 | 1.69 | 0.85 |
time (sec) |
N/A | 0.238 | 0.209 | 1.625 | 0.000 | 0.103 | 0.000 | 0.136 | 0.157 | 0.316 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 160 | 173 | 139 | 152 | 0 | 440 | 0 | 134 | 270 | 132 |
N.S. |
1 | 1.08 | 0.87 | 0.95 | 0.00 | 2.75 | 0.00 | 0.84 | 1.69 | 0.82 |
time (sec) |
N/A | 0.247 | 0.204 | 1.586 | 0.000 | 0.134 | 0.000 | 0.134 | 0.159 | 0.081 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 160 | 175 | 140 | 146 | 0 | 406 | 0 | 137 | 267 | 132 |
N.S. |
1 | 1.09 | 0.88 | 0.91 | 0.00 | 2.54 | 0.00 | 0.86 | 1.67 | 0.82 |
time (sec) |
N/A | 0.238 | 0.219 | 0.359 | 0.000 | 0.124 | 0.000 | 0.127 | 0.160 | 0.313 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 161 | 172 | 139 | 146 | 0 | 386 | 5715 | 136 | 267 | 133 |
N.S. |
1 | 1.07 | 0.86 | 0.91 | 0.00 | 2.40 | 35.50 | 0.84 | 1.66 | 0.83 |
time (sec) |
N/A | 0.251 | 0.223 | 0.357 | 0.000 | 0.118 | 8.042 | 0.131 | 0.163 | 0.077 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 161 | 174 | 139 | 131 | 0 | 370 | 0 | 118 | 269 | 133 |
N.S. |
1 | 1.08 | 0.86 | 0.81 | 0.00 | 2.30 | 0.00 | 0.73 | 1.67 | 0.83 |
time (sec) |
N/A | 0.241 | 0.206 | 0.359 | 0.000 | 0.112 | 0.000 | 0.123 | 0.154 | 0.090 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 181 | 198 | 150 | 123 | 0 | 427 | 6196 | 142 | 292 | 149 |
N.S. |
1 | 1.09 | 0.83 | 0.68 | 0.00 | 2.36 | 34.23 | 0.78 | 1.61 | 0.82 |
time (sec) |
N/A | 0.273 | 0.219 | 0.442 | 0.000 | 0.136 | 5.077 | 0.124 | 0.146 | 0.310 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 181 | 200 | 125 | 149 | 0 | 445 | 0 | 155 | 303 | 149 |
N.S. |
1 | 1.10 | 0.69 | 0.82 | 0.00 | 2.46 | 0.00 | 0.86 | 1.67 | 0.82 |
time (sec) |
N/A | 0.268 | 0.235 | 0.441 | 0.000 | 0.104 | 0.000 | 0.122 | 0.145 | 0.364 |
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 | 88 | 92 | 85 | 99 | 59 | 72 | 0 | 138 | 69 | 369 |
N.S. |
1 | 1.05 | 0.97 | 1.12 | 0.67 | 0.82 | 0.00 | 1.57 | 0.78 | 4.19 |
time (sec) |
N/A | 0.185 | 0.124 | 0.227 | 0.169 | 0.083 | 0.000 | 0.191 | 0.147 | 4.920 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 147 | 163 | 67 | 66 | 119 | 70 | 0 | 329 | 67 | 95 |
N.S. |
1 | 1.11 | 0.46 | 0.45 | 0.81 | 0.48 | 0.00 | 2.24 | 0.46 | 0.65 |
time (sec) |
N/A | 0.231 | 0.171 | 0.215 | 0.134 | 0.086 | 0.000 | 0.308 | 0.159 | 0.350 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 109 | 117 | 56 | 55 | 88 | 59 | 0 | 277 | 56 | 77 |
N.S. |
1 | 1.07 | 0.51 | 0.50 | 0.81 | 0.54 | 0.00 | 2.54 | 0.51 | 0.71 |
time (sec) |
N/A | 0.201 | 0.135 | 0.210 | 0.154 | 0.105 | 0.000 | 0.309 | 0.160 | 0.330 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 71 | 71 | 45 | 44 | 57 | 48 | 0 | 225 | 45 | 59 |
N.S. |
1 | 1.00 | 0.63 | 0.62 | 0.80 | 0.68 | 0.00 | 3.17 | 0.63 | 0.83 |
time (sec) |
N/A | 0.165 | 0.105 | 0.205 | 0.113 | 0.078 | 0.000 | 0.304 | 0.155 | 0.339 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 32 | 31 | 30 | 25 | 36 | 0 | 170 | 33 | 35 |
N.S. |
1 | 1.00 | 0.97 | 0.94 | 0.78 | 1.12 | 0.00 | 5.31 | 1.03 | 1.09 |
time (sec) |
N/A | 0.137 | 0.077 | 0.199 | 0.137 | 0.076 | 0.000 | 0.297 | 0.150 | 0.325 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 64 | 64 | 68 | 109 | 63 | 143 | 0 | 82 | 132 | 225 |
N.S. |
1 | 1.00 | 1.06 | 1.70 | 0.98 | 2.23 | 0.00 | 1.28 | 2.06 | 3.52 |
time (sec) |
N/A | 0.187 | 0.070 | 0.204 | 0.119 | 0.089 | 0.000 | 0.151 | 0.156 | 1.772 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 114 | 70 | 116 | 104 | 171 | 0 | 198 | 161 | 395 |
N.S. |
1 | 1.48 | 0.91 | 1.51 | 1.35 | 2.22 | 0.00 | 2.57 | 2.09 | 5.13 |
time (sec) |
N/A | 0.199 | 0.100 | 0.217 | 0.114 | 0.084 | 0.000 | 0.167 | 0.157 | 2.747 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 112 | 121 | 96 | 140 | 135 | 196 | 0 | 300 | 184 | 685 |
N.S. |
1 | 1.08 | 0.86 | 1.25 | 1.21 | 1.75 | 0.00 | 2.68 | 1.64 | 6.12 |
time (sec) |
N/A | 0.216 | 0.121 | 0.217 | 0.115 | 0.100 | 0.000 | 0.173 | 0.180 | 6.729 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 147 | 167 | 108 | 151 | 166 | 222 | 0 | 400 | 211 | 922 |
N.S. |
1 | 1.14 | 0.73 | 1.03 | 1.13 | 1.51 | 0.00 | 2.72 | 1.44 | 6.27 |
time (sec) |
N/A | 0.257 | 0.145 | 0.215 | 0.112 | 0.102 | 0.000 | 0.189 | 0.183 | 9.756 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 142 | 159 | 103 | 138 | 102 | 211 | 0 | 251 | 95 | 1110 |
N.S. |
1 | 1.12 | 0.73 | 0.97 | 0.72 | 1.49 | 0.00 | 1.77 | 0.67 | 7.82 |
time (sec) |
N/A | 0.227 | 0.147 | 0.207 | 0.161 | 0.099 | 0.000 | 0.309 | 0.163 | 9.354 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 107 | 113 | 92 | 125 | 71 | 187 | 0 | 198 | 71 | 760 |
N.S. |
1 | 1.06 | 0.86 | 1.17 | 0.66 | 1.75 | 0.00 | 1.85 | 0.66 | 7.10 |
time (sec) |
N/A | 0.195 | 0.032 | 0.204 | 0.115 | 0.146 | 0.000 | 0.301 | 0.170 | 7.060 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 69 | 69 | 67 | 107 | 39 | 159 | 0 | 148 | 46 | 72 |
N.S. |
1 | 1.00 | 0.97 | 1.55 | 0.57 | 2.30 | 0.00 | 2.14 | 0.67 | 1.04 |
time (sec) |
N/A | 0.161 | 0.020 | 0.189 | 0.119 | 0.094 | 0.000 | 0.283 | 0.160 | 0.125 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 65 | 65 | 73 | 104 | 36 | 152 | 0 | 109 | 43 | 211 |
N.S. |
1 | 1.00 | 1.12 | 1.60 | 0.55 | 2.34 | 0.00 | 1.68 | 0.66 | 3.25 |
time (sec) |
N/A | 0.173 | 0.062 | 0.207 | 0.121 | 0.086 | 0.000 | 0.166 | 0.164 | 1.344 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 35 | 34 | 33 | 28 | 39 | 0 | 112 | 36 | 44 |
N.S. |
1 | 1.00 | 0.97 | 0.94 | 0.80 | 1.11 | 0.00 | 3.20 | 1.03 | 1.26 |
time (sec) |
N/A | 0.141 | 0.060 | 0.202 | 0.107 | 0.077 | 0.000 | 0.175 | 0.162 | 0.463 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 74 | 112 | 48 | 47 | 60 | 50 | 0 | 210 | 47 | 61 |
N.S. |
1 | 1.51 | 0.65 | 0.64 | 0.81 | 0.68 | 0.00 | 2.84 | 0.64 | 0.82 |
time (sec) |
N/A | 0.202 | 0.078 | 0.204 | 0.121 | 0.080 | 0.000 | 0.178 | 0.168 | 0.498 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 112 | 158 | 59 | 58 | 91 | 62 | 0 | 259 | 59 | 79 |
N.S. |
1 | 1.41 | 0.53 | 0.52 | 0.81 | 0.55 | 0.00 | 2.31 | 0.53 | 0.71 |
time (sec) |
N/A | 0.231 | 0.088 | 0.207 | 0.143 | 0.090 | 0.000 | 0.173 | 0.178 | 0.483 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 147 | 163 | 67 | 66 | 119 | 87 | 0 | 718 | 79 | 119 |
N.S. |
1 | 1.11 | 0.46 | 0.45 | 0.81 | 0.59 | 0.00 | 4.88 | 0.54 | 0.81 |
time (sec) |
N/A | 0.222 | 0.225 | 0.221 | 0.122 | 0.082 | 0.000 | 0.524 | 0.162 | 0.506 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 109 | 117 | 56 | 55 | 88 | 75 | 0 | 614 | 68 | 100 |
N.S. |
1 | 1.07 | 0.51 | 0.50 | 0.81 | 0.69 | 0.00 | 5.63 | 0.62 | 0.92 |
time (sec) |
N/A | 0.208 | 0.179 | 0.204 | 0.120 | 0.112 | 0.000 | 0.512 | 0.172 | 0.497 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 71 | 71 | 45 | 44 | 57 | 62 | 0 | 510 | 57 | 81 |
N.S. |
1 | 1.00 | 0.63 | 0.62 | 0.80 | 0.87 | 0.00 | 7.18 | 0.80 | 1.14 |
time (sec) |
N/A | 0.176 | 0.146 | 0.206 | 0.120 | 0.074 | 0.000 | 0.507 | 0.163 | 0.464 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 32 | 35 | 30 | 25 | 49 | 0 | 403 | 46 | 62 |
N.S. |
1 | 1.00 | 1.09 | 0.94 | 0.78 | 1.53 | 0.00 | 12.59 | 1.44 | 1.94 |
time (sec) |
N/A | 0.142 | 0.109 | 0.209 | 0.125 | 0.086 | 0.000 | 0.477 | 0.158 | 0.469 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 96 | 96 | 86 | 145 | 89 | 180 | 0 | 113 | 169 | 0 |
N.S. |
1 | 1.00 | 0.90 | 1.51 | 0.93 | 1.88 | 0.00 | 1.18 | 1.76 | 0.00 |
time (sec) |
N/A | 0.212 | 0.131 | 0.237 | 0.107 | 0.093 | 0.000 | 0.197 | 0.171 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 105 | 102 | 81 | 155 | 125 | 198 | 0 | 231 | 188 | 0 |
N.S. |
1 | 0.97 | 0.77 | 1.48 | 1.19 | 1.89 | 0.00 | 2.20 | 1.79 | 0.00 |
time (sec) |
N/A | 0.208 | 0.140 | 0.237 | 0.114 | 0.089 | 0.000 | 0.225 | 0.175 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 110 | 194 | 131 | 138 | 161 | 206 | 0 | 302 | 188 | 0 |
N.S. |
1 | 1.76 | 1.19 | 1.25 | 1.46 | 1.87 | 0.00 | 2.75 | 1.71 | 0.00 |
time (sec) |
N/A | 0.253 | 0.147 | 0.237 | 0.111 | 0.095 | 0.000 | 0.223 | 0.182 | 0.000 |