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 | 28 | 20 | 19 | 19 | 19 | 20 | 19 | 25 |
N.S. |
1 | 1.00 | 1.22 | 0.87 | 0.83 | 0.83 | 0.83 | 0.87 | 0.83 | 1.09 |
time (sec) |
N/A | 0.192 | 0.006 | 0.131 | 0.104 | 0.072 | 0.057 | 0.124 | 0.151 | 0.065 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 28 | 24 | 23 | 23 | 29 | 24 | 22 | 55 |
N.S. |
1 | 1.00 | 1.00 | 0.86 | 0.82 | 0.82 | 1.04 | 0.86 | 0.79 | 1.96 |
time (sec) |
N/A | 0.172 | 0.007 | 0.095 | 0.104 | 0.071 | 0.065 | 0.117 | 0.153 | 0.218 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 41 | 46 | 41 | 31 | 32 | 32 | 41 | 33 | 31 | 46 |
N.S. |
1 | 1.12 | 1.00 | 0.76 | 0.78 | 0.78 | 1.00 | 0.80 | 0.76 | 1.12 |
time (sec) |
N/A | 0.183 | 0.004 | 0.099 | 0.119 | 0.091 | 0.055 | 0.124 | 0.147 | 0.039 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 41 | 47 | 42 | 34 | 35 | 35 | 42 | 36 | 34 | 47 |
N.S. |
1 | 1.15 | 1.02 | 0.83 | 0.85 | 0.85 | 1.02 | 0.88 | 0.83 | 1.15 |
time (sec) |
N/A | 0.186 | 0.006 | 0.087 | 0.113 | 0.073 | 0.053 | 0.125 | 0.154 | 0.134 |
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 | 22 | 21 | 20 | 36 | 20 | 47 | 49 | 28 |
N.S. |
1 | 1.00 | 0.92 | 0.88 | 0.83 | 1.50 | 0.83 | 1.96 | 2.04 | 1.17 |
time (sec) |
N/A | 0.188 | 0.010 | 0.129 | 0.106 | 0.070 | 0.055 | 0.114 | 0.154 | 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 | 14 | 14 | 26 | 19 | 18 | 18 | 19 | 20 | 18 | 10 |
N.S. |
1 | 1.00 | 1.86 | 1.36 | 1.29 | 1.29 | 1.36 | 1.43 | 1.29 | 0.71 |
time (sec) |
N/A | 0.134 | 0.004 | 0.121 | 0.105 | 0.069 | 0.052 | 0.119 | 0.155 | 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 | 29 | 29 | 29 | 25 | 24 | 24 | 29 | 24 | 23 | 51 |
N.S. |
1 | 1.00 | 1.00 | 0.86 | 0.83 | 0.83 | 1.00 | 0.83 | 0.79 | 1.76 |
time (sec) |
N/A | 0.273 | 0.011 | 0.139 | 0.102 | 0.069 | 0.082 | 0.116 | 0.153 | 0.116 |
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 | 18 | 17 | 17 | 19 | 17 | 17 | 33 |
N.S. |
1 | 1.00 | 1.00 | 0.78 | 0.74 | 0.74 | 0.83 | 0.74 | 0.74 | 1.43 |
time (sec) |
N/A | 0.188 | 0.009 | 0.059 | 0.109 | 0.084 | 0.079 | 0.113 | 0.155 | 0.033 |
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 | 39 | 44 | 39 | 32 | 32 | 39 | 41 | 32 | 63 | 36 |
N.S. |
1 | 1.13 | 1.00 | 0.82 | 0.82 | 1.00 | 1.05 | 0.82 | 1.62 | 0.92 |
time (sec) |
N/A | 0.160 | 0.016 | 0.213 | 0.103 | 0.070 | 0.048 | 0.120 | 0.148 | 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 | 10 | 18 | 10 | 11 | 14 | 18 | 8 | 14 | 22 | 10 |
N.S. |
1 | 1.80 | 1.00 | 1.10 | 1.40 | 1.80 | 0.80 | 1.40 | 2.20 | 1.00 |
time (sec) |
N/A | 0.162 | 0.004 | 0.092 | 0.027 | 0.064 | 0.038 | 0.122 | 0.147 | 0.090 |
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 | 0.213 | 0.126 | 0.272 | 0.023 | 0.084 | 0.074 | 0.120 | 0.153 | 0.123 |
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 | 0.210 | 0.138 | 0.265 | 0.113 | 0.101 | 0.123 | 0.126 | 0.153 | 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 | 19 | 19 | 19 | 14 | 13 | 13 | 12 | 15 | 13 | 8 |
N.S. |
1 | 1.00 | 1.00 | 0.74 | 0.68 | 0.68 | 0.63 | 0.79 | 0.68 | 0.42 |
time (sec) |
N/A | 0.148 | 0.002 | 0.132 | 0.022 | 0.062 | 0.039 | 0.118 | 0.145 | 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 | 17 | 17 | 17 | 12 | 11 | 11 | 10 | 13 | 11 | 6 |
N.S. |
1 | 1.00 | 1.00 | 0.71 | 0.65 | 0.65 | 0.59 | 0.76 | 0.65 | 0.35 |
time (sec) |
N/A | 0.146 | 0.002 | 0.089 | 0.025 | 0.077 | 0.039 | 0.122 | 0.148 | 0.055 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 23 | 21 | 14 | 17 | 17 | 17 | 19 | 17 | 13 |
N.S. |
1 | 1.10 | 1.00 | 0.67 | 0.81 | 0.81 | 0.81 | 0.90 | 0.81 | 0.62 |
time (sec) |
N/A | 0.158 | 0.004 | 0.141 | 0.022 | 0.067 | 0.043 | 0.118 | 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 | 49 | 49 | 44 | 27 | 37 | 44 | 46 | 40 | 49 | 36 |
N.S. |
1 | 1.00 | 0.90 | 0.55 | 0.76 | 0.90 | 0.94 | 0.82 | 1.00 | 0.73 |
time (sec) |
N/A | 0.190 | 0.012 | 0.142 | 0.098 | 0.070 | 0.040 | 0.123 | 0.155 | 0.082 |
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 | 63 | 63 | 57 | 51 | 50 | 50 | 68 | 53 | 49 | 58 |
N.S. |
1 | 1.00 | 0.90 | 0.81 | 0.79 | 0.79 | 1.08 | 0.84 | 0.78 | 0.92 |
time (sec) |
N/A | 0.250 | 0.017 | 0.053 | 0.102 | 0.076 | 0.159 | 0.119 | 0.152 | 0.154 |
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 | 86 | 67 | 54 | 59 | 103 | 65 | 59 | 169 | 71 |
N.S. |
1 | 1.00 | 0.78 | 0.63 | 0.69 | 1.20 | 0.76 | 0.69 | 1.97 | 0.83 |
time (sec) |
N/A | 0.266 | 0.028 | 0.059 | 0.107 | 0.073 | 0.099 | 0.120 | 0.151 | 0.141 |
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 | 24 | 24 | 24 | 28 | 28 | 28 | 42 | 29 | 25 | 18 |
N.S. |
1 | 1.00 | 1.00 | 1.17 | 1.17 | 1.17 | 1.75 | 1.21 | 1.04 | 0.75 |
time (sec) |
N/A | 0.138 | 0.013 | 0.102 | 0.023 | 0.070 | 0.452 | 0.120 | 0.154 | 0.021 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | B | A | F | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 200 | 205 | 126 | 124 | 272 | 147 | 0 | 139 | 26 | 223 |
N.S. |
1 | 1.02 | 0.63 | 0.62 | 1.36 | 0.74 | 0.00 | 0.70 | 0.13 | 1.12 |
time (sec) |
N/A | 0.397 | 0.044 | 0.092 | 0.110 | 0.113 | 0.000 | 0.184 | 0.155 | 0.145 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | B | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 41 | 22 | 30 | 27 | 20 | 23 | 21 | 11 |
N.S. |
1 | 1.00 | 2.28 | 1.22 | 1.67 | 1.50 | 1.11 | 1.28 | 1.17 | 0.61 |
time (sec) |
N/A | 0.174 | 0.019 | 0.198 | 0.030 | 0.080 | 0.118 | 0.128 | 0.153 | 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 | 18 | 18 | 18 | 15 | 15 | 14 | 15 | 14 | 12 | 14 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 0.83 | 0.78 | 0.83 | 0.78 | 0.67 | 0.78 |
time (sec) |
N/A | 0.145 | 0.009 | 0.066 | 0.028 | 0.063 | 0.046 | 0.117 | 0.154 | 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 | 32 | 32 | 28 | 21 | 28 | 20 | 26 | 20 | 20 | 20 |
N.S. |
1 | 1.00 | 0.88 | 0.66 | 0.88 | 0.62 | 0.81 | 0.62 | 0.62 | 0.62 |
time (sec) |
N/A | 0.163 | 0.012 | 0.114 | 0.022 | 0.062 | 0.048 | 0.116 | 0.150 | 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 | 16 | 16 | 16 | 13 | 12 | 12 | 14 | 12 | 10 | 12 |
N.S. |
1 | 1.00 | 1.00 | 0.81 | 0.75 | 0.75 | 0.88 | 0.75 | 0.62 | 0.75 |
time (sec) |
N/A | 0.136 | 0.011 | 0.144 | 0.114 | 0.079 | 0.063 | 0.120 | 0.155 | 0.018 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 10 | 10 | 10 | 9 | 19 | 19 | 26 | 20 | 17 | 8 |
N.S. |
1 | 1.00 | 1.00 | 0.90 | 1.90 | 1.90 | 2.60 | 2.00 | 1.70 | 0.80 |
time (sec) |
N/A | 0.130 | 0.010 | 0.080 | 0.023 | 0.067 | 0.293 | 0.118 | 0.154 | 0.023 |
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 | 14 | 14 | 25 | 11 | 17 | 8 | 22 | 18 | 17 | 8 |
N.S. |
1 | 1.00 | 1.79 | 0.79 | 1.21 | 0.57 | 1.57 | 1.29 | 1.21 | 0.57 |
time (sec) |
N/A | 0.142 | 0.010 | 0.135 | 0.023 | 0.071 | 0.064 | 0.129 | 0.154 | 0.179 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 33 | 29 | 22 | 21 | 21 | 36 | 22 | 19 | 25 |
N.S. |
1 | 1.06 | 0.94 | 0.71 | 0.68 | 0.68 | 1.16 | 0.71 | 0.61 | 0.81 |
time (sec) |
N/A | 0.203 | 0.015 | 0.089 | 0.028 | 0.065 | 0.644 | 0.124 | 0.154 | 0.038 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 32 | 21 | 17 | 22 | 17 | 76 | 22 | 16 | 19 |
N.S. |
1 | 1.00 | 0.66 | 0.53 | 0.69 | 0.53 | 2.38 | 0.69 | 0.50 | 0.59 |
time (sec) |
N/A | 0.143 | 0.011 | 0.096 | 0.024 | 0.063 | 0.613 | 0.120 | 0.150 | 0.021 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 31 | 31 | 25 | 24 | 24 | 75 | 24 | 21 | 24 |
N.S. |
1 | 1.00 | 1.00 | 0.81 | 0.77 | 0.77 | 2.42 | 0.77 | 0.68 | 0.77 |
time (sec) |
N/A | 0.141 | 0.022 | 0.142 | 0.109 | 0.066 | 0.669 | 0.124 | 0.151 | 0.119 |
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 | 31 | 22 | 20 | 19 | 14 | 117 | 19 | 11 | 12 |
N.S. |
1 | 1.07 | 0.76 | 0.69 | 0.66 | 0.48 | 4.03 | 0.66 | 0.38 | 0.41 |
time (sec) |
N/A | 0.145 | 0.011 | 0.081 | 0.026 | 0.072 | 0.441 | 0.117 | 0.145 | 0.150 |
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 | 0.127 | 0.009 | 0.132 | 0.101 | 0.073 | 0.089 | 0.122 | 0.150 | 0.152 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 27 | 19 | 16 | 15 | 15 | 17 | 16 | 13 | 15 |
N.S. |
1 | 1.29 | 0.90 | 0.76 | 0.71 | 0.71 | 0.81 | 0.76 | 0.62 | 0.71 |
time (sec) |
N/A | 0.159 | 0.010 | 0.084 | 0.027 | 0.069 | 0.054 | 0.120 | 0.148 | 0.115 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 34 | 28 | 23 | 22 | 22 | 26 | 23 | 22 | 22 |
N.S. |
1 | 1.13 | 0.93 | 0.77 | 0.73 | 0.73 | 0.87 | 0.77 | 0.73 | 0.73 |
time (sec) |
N/A | 0.169 | 0.015 | 0.118 | 0.023 | 0.071 | 0.058 | 0.118 | 0.155 | 0.023 |
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 | 27 | 31 | 20 | 16 | 19 | 16 | 26 | 19 | 13 | 16 |
N.S. |
1 | 1.15 | 0.74 | 0.59 | 0.70 | 0.59 | 0.96 | 0.70 | 0.48 | 0.59 |
time (sec) |
N/A | 0.149 | 0.013 | 0.105 | 0.029 | 0.065 | 0.453 | 0.118 | 0.158 | 0.158 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | B | A | F | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 201 | 208 | 127 | 132 | 293 | 156 | 0 | 140 | 43 | 208 |
N.S. |
1 | 1.03 | 0.63 | 0.66 | 1.46 | 0.78 | 0.00 | 0.70 | 0.21 | 1.03 |
time (sec) |
N/A | 0.405 | 0.044 | 0.077 | 0.119 | 0.084 | 0.000 | 0.194 | 0.164 | 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 | 71 | 62 | 46 | 45 | 47 | 68 | 45 | 42 | 73 |
N.S. |
1 | 1.15 | 1.00 | 0.74 | 0.73 | 0.76 | 1.10 | 0.73 | 0.68 | 1.18 |
time (sec) |
N/A | 0.219 | 0.038 | 0.064 | 0.104 | 0.076 | 0.165 | 0.126 | 0.155 | 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 | 130 | 140 | 117 | 83 | 82 | 76 | 121 | 82 | 81 | 82 |
N.S. |
1 | 1.08 | 0.90 | 0.64 | 0.63 | 0.58 | 0.93 | 0.63 | 0.62 | 0.63 |
time (sec) |
N/A | 0.224 | 0.038 | 0.103 | 0.034 | 0.075 | 1.038 | 0.127 | 0.156 | 0.090 |
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 | 24 | 24 | 24 | 40 | 37 | 26 | 0 | 28 | 25 | 20 |
N.S. |
1 | 1.00 | 1.00 | 1.67 | 1.54 | 1.08 | 0.00 | 1.17 | 1.04 | 0.83 |
time (sec) |
N/A | 0.161 | 0.019 | 0.143 | 0.106 | 0.071 | 0.000 | 0.127 | 0.159 | 0.090 |
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 | 0.197 | 0.007 | 0.161 | 0.023 | 0.079 | 0.068 | 0.124 | 0.148 | 0.083 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 17 | 17 | 16 | 15 | 15 | 14 | 15 | 17 | 15 |
N.S. |
1 | 1.00 | 1.00 | 0.94 | 0.88 | 0.88 | 0.82 | 0.88 | 1.00 | 0.88 |
time (sec) |
N/A | 0.189 | 0.027 | 0.052 | 0.033 | 0.070 | 0.051 | 0.115 | 0.152 | 0.044 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | A | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 12 | 10 | 21 | 21 | 22 | 21 | 16 | 9 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 1.75 | 1.75 | 1.83 | 1.75 | 1.33 | 0.75 |
time (sec) |
N/A | 0.148 | 0.016 | 0.049 | 0.027 | 0.083 | 0.213 | 0.118 | 0.153 | 0.017 |
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 | 28 | 28 | 28 | 27 | 35 | 35 | 32 | 37 | 31 | 40 |
N.S. |
1 | 1.00 | 1.00 | 0.96 | 1.25 | 1.25 | 1.14 | 1.32 | 1.11 | 1.43 |
time (sec) |
N/A | 0.161 | 0.021 | 0.054 | 0.026 | 0.066 | 0.381 | 0.124 | 0.153 | 0.119 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 43 | 33 | 43 | 22 | 30 | 27 | 20 | 23 | 21 | 11 |
N.S. |
1 | 0.77 | 1.00 | 0.51 | 0.70 | 0.63 | 0.47 | 0.53 | 0.49 | 0.26 |
time (sec) |
N/A | 0.196 | 0.014 | 0.129 | 0.023 | 0.080 | 0.099 | 0.129 | 0.151 | 0.230 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | B | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 24 | 19 | 39 | 38 | 39 | 37 | 27 | 21 |
N.S. |
1 | 1.00 | 1.14 | 0.90 | 1.86 | 1.81 | 1.86 | 1.76 | 1.29 | 1.00 |
time (sec) |
N/A | 0.171 | 0.011 | 0.105 | 0.104 | 0.074 | 0.202 | 0.140 | 0.158 | 0.217 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | B | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 11 | 11 | 24 | 16 | 25 | 17 | 14 | 17 | 15 | 11 |
N.S. |
1 | 1.00 | 2.18 | 1.45 | 2.27 | 1.55 | 1.27 | 1.55 | 1.36 | 1.00 |
time (sec) |
N/A | 0.165 | 0.018 | 0.198 | 0.024 | 0.077 | 0.103 | 0.131 | 0.151 | 0.114 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | B | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 43 | 22 | 30 | 27 | 20 | 23 | 21 | 11 |
N.S. |
1 | 1.00 | 2.39 | 1.22 | 1.67 | 1.50 | 1.11 | 1.28 | 1.17 | 0.61 |
time (sec) |
N/A | 0.175 | 0.019 | 0.182 | 0.025 | 0.079 | 0.109 | 0.128 | 0.154 | 0.276 |
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 | 24 | 24 | 35 | 24 | 25 | 35 | 0 | 28 | 16 | 16 |
N.S. |
1 | 1.00 | 1.46 | 1.00 | 1.04 | 1.46 | 0.00 | 1.17 | 0.67 | 0.67 |
time (sec) |
N/A | 0.351 | 0.021 | 0.153 | 0.025 | 0.081 | 0.000 | 0.124 | 0.158 | 0.164 |
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 | 0.194 | 0.022 | 0.247 | 0.036 | 0.084 | 0.000 | 0.121 | 0.160 | 0.183 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 18 | 24 | 23 | 33 | 0 | 25 | 48 | 22 |
N.S. |
1 | 1.00 | 1.00 | 1.33 | 1.28 | 1.83 | 0.00 | 1.39 | 2.67 | 1.22 |
time (sec) |
N/A | 0.195 | 0.014 | 0.201 | 0.027 | 0.088 | 0.000 | 0.122 | 0.158 | 0.074 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 36 | 38 | 35 | 61 | 98 | 121 | 61 | 44 | 31 |
N.S. |
1 | 1.00 | 1.06 | 0.97 | 1.69 | 2.72 | 3.36 | 1.69 | 1.22 | 0.86 |
time (sec) |
N/A | 0.191 | 0.040 | 0.215 | 0.101 | 0.087 | 1.398 | 0.131 | 0.151 | 0.439 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 15 | 16 | 15 | 43 | 71839 | 26 | 21 | 15 |
N.S. |
1 | 1.00 | 1.00 | 1.07 | 1.00 | 2.87 | 4789.27 | 1.73 | 1.40 | 1.00 |
time (sec) |
N/A | 0.193 | 0.023 | 0.336 | 0.112 | 0.092 | 14.477 | 0.122 | 0.146 | 0.289 |
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 | 10 | 9 | 8 | 8 | 7 | 9 | 13 | 8 |
N.S. |
1 | 1.00 | 0.83 | 0.75 | 0.67 | 0.67 | 0.58 | 0.75 | 1.08 | 0.67 |
time (sec) |
N/A | 0.121 | 0.002 | 0.094 | 0.025 | 0.065 | 0.025 | 0.129 | 0.145 | 0.024 |
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 | 17 | 17 | 17 | 12 | 26 | 11 | 12 | 11 | 11 | 11 |
N.S. |
1 | 1.00 | 1.00 | 0.71 | 1.53 | 0.65 | 0.71 | 0.65 | 0.65 | 0.65 |
time (sec) |
N/A | 0.138 | 0.002 | 0.045 | 0.031 | 0.075 | 0.047 | 0.118 | 0.142 | 0.014 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 8 | 7 | 10 | 10 | 7 | 8 | 8 | 6 |
N.S. |
1 | 1.00 | 0.67 | 0.58 | 0.83 | 0.83 | 0.58 | 0.67 | 0.67 | 0.50 |
time (sec) |
N/A | 0.157 | 0.003 | 0.058 | 0.029 | 0.064 | 0.153 | 0.123 | 0.149 | 0.115 |
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 | 16 | 16 | 16 | 24 | 27 | 34 | 27 | 29 | 57 | 30 |
N.S. |
1 | 1.00 | 1.00 | 1.50 | 1.69 | 2.12 | 1.69 | 1.81 | 3.56 | 1.88 |
time (sec) |
N/A | 0.192 | 0.001 | 0.084 | 0.029 | 0.084 | 0.052 | 0.123 | 0.140 | 0.001 |
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 | 17 | 17 | 17 | 14 | 14 | 14 | 14 | 14 | 14 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.82 | 0.82 | 0.82 | 0.82 | 0.82 | 0.82 | 0.76 |
time (sec) |
N/A | 0.181 | 0.005 | 0.635 | 0.029 | 0.073 | 0.037 | 0.121 | 0.142 | 0.001 |
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 | 24 | 25 | 16 | 16 | 11 | 11 | 20 | 11 | 10 | 11 |
N.S. |
1 | 1.04 | 0.67 | 0.67 | 0.46 | 0.46 | 0.83 | 0.46 | 0.42 | 0.46 |
time (sec) |
N/A | 0.169 | 0.002 | 0.016 | 0.031 | 0.069 | 0.066 | 0.120 | 0.152 | 0.011 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 42 | 42 | 42 | 31 | 30 | 30 | 36 | 33 | 30 | 30 |
N.S. |
1 | 1.00 | 1.00 | 0.74 | 0.71 | 0.71 | 0.86 | 0.79 | 0.71 | 0.71 |
time (sec) |
N/A | 0.213 | 0.005 | 0.047 | 0.025 | 0.070 | 0.064 | 0.126 | 0.149 | 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 | 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 | 0.146 | 0.003 | 0.044 | 0.023 | 0.062 | 0.100 | 0.116 | 0.156 | 0.036 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 12 | 11 | 10 | 10 | 8 | 11 | 10 | 10 |
N.S. |
1 | 1.00 | 1.00 | 0.92 | 0.83 | 0.83 | 0.67 | 0.92 | 0.83 | 0.83 |
time (sec) |
N/A | 0.140 | 0.002 | 0.106 | 0.026 | 0.070 | 0.026 | 0.124 | 0.156 | 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 | 5 | 5 | 5 | 4 | 3 | 3 | 3 | 3 | 5 | 3 |
N.S. |
1 | 1.00 | 1.00 | 0.80 | 0.60 | 0.60 | 0.60 | 0.60 | 1.00 | 0.60 |
time (sec) |
N/A | 0.151 | 0.004 | 0.032 | 0.030 | 0.066 | 0.230 | 0.123 | 0.152 | 0.091 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 29 | 14 | 11 | 10 | 19 | 14 | 10 | 18 | 18 |
N.S. |
1 | 1.21 | 0.58 | 0.46 | 0.42 | 0.79 | 0.58 | 0.42 | 0.75 | 0.75 |
time (sec) |
N/A | 0.212 | 0.001 | 0.327 | 0.030 | 0.080 | 0.024 | 0.127 | 0.157 | 0.014 |
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 | 8 | 8 | 8 | 9 | 8 | 11 | 8 | 18 | 8 | 32 |
N.S. |
1 | 1.00 | 1.00 | 1.12 | 1.00 | 1.38 | 1.00 | 2.25 | 1.00 | 4.00 |
time (sec) |
N/A | 0.171 | 0.032 | 0.253 | 0.030 | 0.079 | 0.048 | 0.121 | 0.161 | 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 | 13 | 13 | 13 | 12 | 11 | 11 | 8 | 11 | 10 | 11 |
N.S. |
1 | 1.00 | 1.00 | 0.92 | 0.85 | 0.85 | 0.62 | 0.85 | 0.77 | 0.85 |
time (sec) |
N/A | 0.125 | 0.001 | 0.102 | 0.023 | 0.069 | 0.052 | 0.124 | 0.152 | 0.001 |
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 | 17 | 17 | 17 | 14 | 13 | 13 | 12 | 13 | 11 | 9 |
N.S. |
1 | 1.00 | 1.00 | 0.82 | 0.76 | 0.76 | 0.71 | 0.76 | 0.65 | 0.53 |
time (sec) |
N/A | 0.142 | 0.002 | 0.036 | 0.022 | 0.067 | 0.032 | 0.117 | 0.150 | 0.094 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 24 | 19 | 18 | 18 | 109 | 18 | 16 | 18 |
N.S. |
1 | 1.00 | 1.00 | 0.79 | 0.75 | 0.75 | 4.54 | 0.75 | 0.67 | 0.75 |
time (sec) |
N/A | 0.135 | 0.014 | 0.154 | 0.109 | 0.066 | 0.643 | 0.122 | 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 | 12 | 12 | 12 | 13 | 12 | 16 | 8 | 13 | 22 | 12 |
N.S. |
1 | 1.00 | 1.00 | 1.08 | 1.00 | 1.33 | 0.67 | 1.08 | 1.83 | 1.00 |
time (sec) |
N/A | 0.136 | 0.002 | 0.076 | 0.023 | 0.068 | 0.025 | 0.119 | 0.157 | 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 | 16 | 17 | 16 | 17 | 16 | 16 | 15 | 16 | 16 | 16 |
N.S. |
1 | 1.06 | 1.00 | 1.06 | 1.00 | 1.00 | 0.94 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.146 | 0.002 | 0.089 | 0.103 | 0.072 | 0.046 | 0.126 | 0.151 | 0.026 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 22 | 30 | 29 | 29 | 32 | 268 | 29 | 18 |
N.S. |
1 | 1.00 | 1.00 | 1.36 | 1.32 | 1.32 | 1.45 | 12.18 | 1.32 | 0.82 |
time (sec) |
N/A | 0.190 | 0.026 | 0.041 | 0.032 | 0.069 | 0.524 | 0.307 | 0.154 | 0.141 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 29 | 56 | 43 | 19 | 46 | 54 | 42 | 46 | 42 |
N.S. |
1 | 1.07 | 2.07 | 1.59 | 0.70 | 1.70 | 2.00 | 1.56 | 1.70 | 1.56 |
time (sec) |
N/A | 0.148 | 0.011 | 1.251 | 0.023 | 0.067 | 0.112 | 0.114 | 0.156 | 0.019 |
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 | 17 | 17 | 17 | 14 | 30 | 14 | 14 | 14 | 14 | 14 |
N.S. |
1 | 1.00 | 1.00 | 0.82 | 1.76 | 0.82 | 0.82 | 0.82 | 0.82 | 0.82 |
time (sec) |
N/A | 0.183 | 0.009 | 1.711 | 0.024 | 0.075 | 0.042 | 0.121 | 0.154 | 0.104 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 22 | 17 | 16 | 16 | 15 | 16 | 16 | 16 |
N.S. |
1 | 1.00 | 1.00 | 0.77 | 0.73 | 0.73 | 0.68 | 0.73 | 0.73 | 0.73 |
time (sec) |
N/A | 0.161 | 0.003 | 0.273 | 0.103 | 0.070 | 0.039 | 0.117 | 0.142 | 0.092 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 37 | 28 | 25 | 24 | 24 | 24 | 26 | 23 | 24 |
N.S. |
1 | 1.16 | 0.88 | 0.78 | 0.75 | 0.75 | 0.75 | 0.81 | 0.72 | 0.75 |
time (sec) |
N/A | 0.159 | 0.006 | 0.059 | 0.101 | 0.079 | 0.072 | 0.117 | 0.153 | 0.016 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 36 | 30 | 25 | 35 | 28 | 66 | 40 | 20 | 30 |
N.S. |
1 | 1.20 | 1.00 | 0.83 | 1.17 | 0.93 | 2.20 | 1.33 | 0.67 | 1.00 |
time (sec) |
N/A | 0.146 | 0.017 | 0.123 | 0.107 | 0.078 | 0.672 | 0.118 | 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 | 13 | 13 | 13 | 14 | 13 | 13 | 10 | 15 | 13 | 13 |
N.S. |
1 | 1.00 | 1.00 | 1.08 | 1.00 | 1.00 | 0.77 | 1.15 | 1.00 | 1.00 |
time (sec) |
N/A | 0.147 | 0.003 | 0.103 | 0.028 | 0.065 | 0.035 | 0.123 | 0.160 | 0.029 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | B | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 25 | 14 | 17 | 44 | 14 | 17 | 27 | 16 | 16 |
N.S. |
1 | 1.56 | 0.88 | 1.06 | 2.75 | 0.88 | 1.06 | 1.69 | 1.00 | 1.00 |
time (sec) |
N/A | 0.242 | 0.011 | 0.112 | 0.027 | 0.066 | 0.084 | 0.118 | 0.156 | 0.103 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 17 | 20 | 14 | 15 | 15 | 14 | 18 | 16 | 13 |
N.S. |
1 | 1.00 | 1.18 | 0.82 | 0.88 | 0.88 | 0.82 | 1.06 | 0.94 | 0.76 |
time (sec) |
N/A | 0.137 | 0.005 | 0.033 | 0.027 | 0.064 | 0.036 | 0.124 | 0.155 | 0.041 |
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 | 3 | 3 | 3 | 4 | 3 | 3 | 3 | 3 | 3 | 3 |
N.S. |
1 | 1.00 | 1.00 | 1.33 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.162 | 0.004 | 0.356 | 0.106 | 0.076 | 0.071 | 0.122 | 0.156 | 0.119 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 21 | 22 | 17 | 16 | 16 | 20 | 16 | 13 | 16 |
N.S. |
1 | 0.95 | 1.00 | 0.77 | 0.73 | 0.73 | 0.91 | 0.73 | 0.59 | 0.73 |
time (sec) |
N/A | 0.207 | 0.004 | 0.088 | 0.026 | 0.078 | 0.083 | 0.119 | 0.151 | 0.129 |
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 | 0.143 | 0.007 | 0.125 | 0.030 | 0.071 | 0.040 | 0.120 | 0.158 | 0.010 |
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 | 12 | 12 | 12 | 11 | 10 | 10 | 8 | 10 | 12 | 10 |
N.S. |
1 | 1.00 | 1.00 | 0.92 | 0.83 | 0.83 | 0.67 | 0.83 | 1.00 | 0.83 |
time (sec) |
N/A | 0.161 | 0.002 | 0.026 | 0.025 | 0.082 | 0.031 | 0.114 | 0.156 | 0.025 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 22 | 20 | 19 | 21 | 26 | 19 | 20 | 19 |
N.S. |
1 | 1.00 | 0.81 | 0.74 | 0.70 | 0.78 | 0.96 | 0.70 | 0.74 | 0.70 |
time (sec) |
N/A | 0.159 | 0.031 | 0.197 | 0.030 | 0.073 | 0.081 | 0.122 | 0.158 | 0.016 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 17 | 17 | 14 | 13 | 22 | 26 | 13 | 21 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.82 | 0.76 | 1.29 | 1.53 | 0.76 | 1.24 | 0.76 |
time (sec) |
N/A | 0.163 | 0.005 | 0.493 | 0.027 | 0.078 | 0.114 | 0.126 | 0.149 | 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 | 25 | 25 | 25 | 20 | 19 | 19 | 19 | 20 | 19 | 25 |
N.S. |
1 | 1.00 | 1.00 | 0.80 | 0.76 | 0.76 | 0.76 | 0.80 | 0.76 | 1.00 |
time (sec) |
N/A | 0.165 | 0.004 | 0.052 | 0.103 | 0.066 | 0.051 | 0.115 | 0.150 | 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 | 39 | 38 | 28 | 28 | 29 | 25 | 29 | 49 | 29 | 25 |
N.S. |
1 | 0.97 | 0.72 | 0.72 | 0.74 | 0.64 | 0.74 | 1.26 | 0.74 | 0.64 |
time (sec) |
N/A | 0.169 | 0.008 | 0.078 | 0.029 | 0.068 | 0.041 | 0.122 | 0.154 | 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 | 26 | 26 | 16 | 14 | 13 | 13 | 12 | 13 | 16 | 13 |
N.S. |
1 | 1.00 | 0.62 | 0.54 | 0.50 | 0.50 | 0.46 | 0.50 | 0.62 | 0.50 |
time (sec) |
N/A | 0.173 | 0.018 | 0.043 | 0.029 | 0.073 | 0.034 | 0.119 | 0.153 | 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 | 12 | 12 | 18 | 11 | 10 | 10 | 12 | 10 | 10 | 10 |
N.S. |
1 | 1.00 | 1.50 | 0.92 | 0.83 | 0.83 | 1.00 | 0.83 | 0.83 | 0.83 |
time (sec) |
N/A | 0.152 | 0.007 | 0.046 | 0.101 | 0.073 | 0.022 | 0.150 | 0.152 | 0.105 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 24 | 21 | 22 | 20 | 22 | 41 | 19 | 20 |
N.S. |
1 | 1.00 | 0.96 | 0.84 | 0.88 | 0.80 | 0.88 | 1.64 | 0.76 | 0.80 |
time (sec) |
N/A | 0.138 | 0.040 | 0.150 | 0.103 | 0.067 | 0.240 | 0.120 | 0.145 | 0.151 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 26 | 23 | 22 | 21 | 21 | 20 | 21 | 21 | 21 |
N.S. |
1 | 0.96 | 0.85 | 0.81 | 0.78 | 0.78 | 0.74 | 0.78 | 0.78 | 0.78 |
time (sec) |
N/A | 0.174 | 0.005 | 0.086 | 0.028 | 0.075 | 0.086 | 0.124 | 0.149 | 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 | 19 | 19 | 19 | 12 | 11 | 11 | 15 | 11 | 11 | 12 |
N.S. |
1 | 1.00 | 1.00 | 0.63 | 0.58 | 0.58 | 0.79 | 0.58 | 0.58 | 0.63 |
time (sec) |
N/A | 0.138 | 0.002 | 0.070 | 0.029 | 0.062 | 0.324 | 0.123 | 0.154 | 0.014 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 6 | 6 | 6 | 6 | 19 | 15 | 15 | 16 | 17 | 15 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 3.17 | 2.50 | 2.50 | 2.67 | 2.83 | 2.50 |
time (sec) |
N/A | 0.144 | 0.023 | 0.028 | 0.037 | 0.075 | 0.043 | 0.123 | 0.158 | 0.057 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 16 | 14 | 11 | 10 | 10 | 10 | 10 | 63 | 10 |
N.S. |
1 | 1.14 | 1.00 | 0.79 | 0.71 | 0.71 | 0.71 | 0.71 | 4.50 | 0.71 |
time (sec) |
N/A | 0.151 | 0.004 | 0.048 | 0.107 | 0.065 | 0.037 | 0.209 | 0.173 | 0.110 |
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 | 12 | 12 | 12 | 9 | 8 | 8 | 10 | 32 | 30 | 8 |
N.S. |
1 | 1.00 | 1.00 | 0.75 | 0.67 | 0.67 | 0.83 | 2.67 | 2.50 | 0.67 |
time (sec) |
N/A | 0.132 | 0.011 | 0.159 | 0.110 | 0.064 | 0.073 | 0.119 | 0.158 | 0.121 |
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 | 44 | 30 | 23 | 18 | 25 | 31 | 22 | 26 | 26 |
N.S. |
1 | 1.29 | 0.88 | 0.68 | 0.53 | 0.74 | 0.91 | 0.65 | 0.76 | 0.76 |
time (sec) |
N/A | 0.260 | 0.006 | 1.201 | 0.024 | 0.079 | 0.020 | 0.120 | 0.141 | 0.022 |
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 | 12 | 12 | 23 | 7 | 8 | 29 | 7 | 26 | 6 | 6 |
N.S. |
1 | 1.00 | 1.92 | 0.58 | 0.67 | 2.42 | 0.58 | 2.17 | 0.50 | 0.50 |
time (sec) |
N/A | 0.130 | 0.047 | 0.157 | 0.101 | 0.074 | 0.238 | 0.124 | 0.144 | 0.091 |
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 | 16 | 16 | 16 | 15 | 14 | 21 | 48 | 14 | 13 | 21 |
N.S. |
1 | 1.00 | 1.00 | 0.94 | 0.88 | 1.31 | 3.00 | 0.88 | 0.81 | 1.31 |
time (sec) |
N/A | 0.222 | 0.012 | 0.072 | 0.025 | 0.068 | 1.213 | 0.124 | 0.142 | 0.070 |
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 | 0.165 | 0.001 | 0.142 | 0.029 | 0.079 | 0.672 | 0.119 | 0.157 | 0.102 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 6 | 6 | 6 | 6 | 15 | 15 | 15 | 16 | 17 | 15 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 2.50 | 2.50 | 2.50 | 2.67 | 2.83 | 2.50 |
time (sec) |
N/A | 0.147 | 0.001 | 0.035 | 0.022 | 0.074 | 0.048 | 0.121 | 0.152 | 0.015 |
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 | 51 | 43 | 33 | 32 | 32 | 41 | 33 | 31 | 46 |
N.S. |
1 | 1.19 | 1.00 | 0.77 | 0.74 | 0.74 | 0.95 | 0.77 | 0.72 | 1.07 |
time (sec) |
N/A | 0.182 | 0.006 | 0.100 | 0.108 | 0.072 | 0.052 | 0.122 | 0.157 | 0.049 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 37 | 59 | 29 | 33 | 74 | 30 | 42 | 57 | 37 | 37 |
N.S. |
1 | 1.59 | 0.78 | 0.89 | 2.00 | 0.81 | 1.14 | 1.54 | 1.00 | 1.00 |
time (sec) |
N/A | 0.453 | 0.013 | 0.141 | 0.025 | 0.069 | 0.212 | 0.126 | 0.155 | 0.124 |