Detailed conclusion table per each integral is given by the table below. The elapsed time is in seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2) if the failure was due to an exception being raised, which could indicate a bug in the system. If the failure was due to integral not being evaluated within the time limit, then it is given as F.
In this table, the column N.S.
means normalized size and is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To make the table
fit the page, the name Mathematica
was abbreviated to MMA
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 17 | 17 | 14 | 14 | 30 | 15 | 14 | 14 | 14 |
N.S. |
1 | 1.00 | 1.00 | 0.82 | 0.82 | 1.76 | 0.88 | 0.82 | 0.82 | 0.82 |
time (sec) |
N/A | 0.190 | 0.007 | 0.179 | 0.025 | 0.075 | 0.042 | 0.125 | 0.149 | 0.109 |
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 | 5 | 5 | 5 | 6 | 8 | 19 | 15 | 6 | 5 | 5 |
N.S. |
1 | 1.00 | 1.00 | 1.20 | 1.60 | 3.80 | 3.00 | 1.20 | 1.00 | 1.00 |
time (sec) |
N/A | 0.142 | 0.002 | 0.040 | 0.028 | 0.086 | 0.061 | 0.127 | 0.153 | 0.016 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | B | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 47 | 18 | 27 | 44 | 27 | 54 | 21 | 16 |
N.S. |
1 | 1.00 | 2.94 | 1.12 | 1.69 | 2.75 | 1.69 | 3.38 | 1.31 | 1.00 |
time (sec) |
N/A | 0.189 | 0.008 | 0.159 | 0.032 | 0.074 | 0.055 | 0.122 | 0.148 | 0.022 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 8 | 8 | 19 | 10 | 17 | 21 | 19 | 19 | 9 | 8 |
N.S. |
1 | 1.00 | 2.38 | 1.25 | 2.12 | 2.62 | 2.38 | 2.38 | 1.12 | 1.00 |
time (sec) |
N/A | 0.162 | 0.011 | 0.111 | 0.023 | 0.082 | 0.040 | 0.123 | 0.136 | 0.017 |
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 | 13 | 13 | 17 | 12 | 14 | 25 | 20 | 14 | 16 | 17 |
N.S. |
1 | 1.00 | 1.31 | 0.92 | 1.08 | 1.92 | 1.54 | 1.08 | 1.23 | 1.31 |
time (sec) |
N/A | 0.165 | 0.007 | 0.175 | 0.025 | 0.069 | 0.027 | 0.125 | 0.147 | 0.086 |
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 | 24 | 26 | 13 | 21 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.82 | 0.76 | 1.41 | 1.53 | 0.76 | 1.24 | 0.76 |
time (sec) |
N/A | 0.163 | 0.005 | 0.456 | 0.030 | 0.077 | 0.113 | 0.126 | 0.155 | 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 | 17 | 17 | 17 | 14 | 13 | 13 | 22 | 13 | 17 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.82 | 0.76 | 0.76 | 1.29 | 0.76 | 1.00 | 0.76 |
time (sec) |
N/A | 0.159 | 0.020 | 0.385 | 0.031 | 0.079 | 0.122 | 0.120 | 0.151 | 0.015 |
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 | 15 | 15 | 15 | 12 | 11 | 24 | 26 | 11 | 21 | 11 |
N.S. |
1 | 1.00 | 1.00 | 0.80 | 0.73 | 1.60 | 1.73 | 0.73 | 1.40 | 0.73 |
time (sec) |
N/A | 0.159 | 0.005 | 0.429 | 0.023 | 0.079 | 0.112 | 0.115 | 0.153 | 0.106 |
Optimal | Rubi | MMA | 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 | 9 | 13 | 14 | 24 | 8 | 21 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.53 | 0.76 | 0.82 | 1.41 | 0.47 | 1.24 | 0.76 |
time (sec) |
N/A | 0.163 | 0.020 | 0.416 | 0.029 | 0.080 | 0.112 | 0.120 | 0.157 | 0.106 |
Optimal | Rubi | MMA | 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 | 6 | 19 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 0.75 | 0.75 | 0.88 | 0.75 | 0.75 | 2.38 |
time (sec) |
N/A | 0.152 | 0.001 | 0.919 | 0.031 | 0.072 | 0.018 | 0.115 | 0.152 | 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 | 30 | 30 | 30 | 23 | 22 | 25 | 114 | 22 | 89 | 22 |
N.S. |
1 | 1.00 | 1.00 | 0.77 | 0.73 | 0.83 | 3.80 | 0.73 | 2.97 | 0.73 |
time (sec) |
N/A | 0.196 | 0.006 | 1.678 | 0.029 | 0.079 | 0.730 | 0.120 | 0.155 | 0.176 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | B | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 5 | 11 | 8 | 6 | 11 | 5 | 7 | 9 | 5 | 6 |
N.S. |
1 | 2.20 | 1.60 | 1.20 | 2.20 | 1.00 | 1.40 | 1.80 | 1.00 | 1.20 |
time (sec) |
N/A | 0.179 | 0.001 | 0.571 | 0.033 | 0.075 | 0.158 | 0.117 | 0.156 | 0.098 |
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 | 23 | 24 |
N.S. |
1 | 1.00 | 1.00 | 1.20 | 4.60 | 2.33 | 2.13 | 1.93 | 1.53 | 1.60 |
time (sec) |
N/A | 0.207 | 0.007 | 0.449 | 0.115 | 0.078 | 0.472 | 0.127 | 0.155 | 0.229 |
Optimal | Rubi | MMA | 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 | 0.174 | 0.001 | 0.260 | 0.030 | 0.091 | 0.031 | 0.119 | 0.154 | 0.112 |
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 | 0.196 | 0.001 | 0.812 | 0.027 | 0.089 | 0.037 | 0.121 | 0.151 | 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 | 8 | 8 | 8 | 7 | 6 | 6 | 7 | 6 | 6 | 6 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 0.75 | 0.75 | 0.88 | 0.75 | 0.75 | 0.75 |
time (sec) |
N/A | 0.155 | 0.001 | 0.292 | 0.029 | 0.071 | 0.021 | 0.122 | 0.145 | 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 | 0.185 | 0.005 | 0.659 | 0.025 | 0.073 | 0.038 | 0.121 | 0.143 | 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 | 25 | 25 | 37 | 26 | 21 | 35 | 15 | 39 | 22 | 21 |
N.S. |
1 | 1.00 | 1.48 | 1.04 | 0.84 | 1.40 | 0.60 | 1.56 | 0.88 | 0.84 |
time (sec) |
N/A | 0.133 | 0.034 | 0.316 | 0.107 | 0.068 | 0.084 | 0.125 | 0.162 | 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 | 16 | 16 | 16 | 13 | 12 | 14 | 12 | 19 | 17 | 12 |
N.S. |
1 | 1.00 | 1.00 | 0.81 | 0.75 | 0.88 | 0.75 | 1.19 | 1.06 | 0.75 |
time (sec) |
N/A | 0.126 | 0.019 | 0.099 | 0.102 | 0.072 | 0.341 | 0.124 | 0.154 | 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 | 9 | 9 | 9 | 8 | 7 | 7 | 7 | 7 | 6 | 7 |
N.S. |
1 | 1.00 | 1.00 | 0.89 | 0.78 | 0.78 | 0.78 | 0.78 | 0.67 | 0.78 |
time (sec) |
N/A | 0.120 | 0.001 | 0.086 | 0.027 | 0.078 | 0.057 | 0.123 | 0.154 | 0.016 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | A | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 46 | 15 | 18 | 18 | 19 | 37 | 17 | 14 |
N.S. |
1 | 1.00 | 2.88 | 0.94 | 1.12 | 1.12 | 1.19 | 2.31 | 1.06 | 0.88 |
time (sec) |
N/A | 0.129 | 0.002 | 0.121 | 0.029 | 0.072 | 0.460 | 0.126 | 0.153 | 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 | 31 | 35 | 22 | 19 | 26 | 18 | 27 | 23 | 25 | 24 |
N.S. |
1 | 1.13 | 0.71 | 0.61 | 0.84 | 0.58 | 0.87 | 0.74 | 0.81 | 0.77 |
time (sec) |
N/A | 0.152 | 0.016 | 0.102 | 0.102 | 0.068 | 0.178 | 0.117 | 0.149 | 0.110 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 40 | 24 | 21 | 42 | 20 | 23 | 22 | 38 |
N.S. |
1 | 1.00 | 1.48 | 0.89 | 0.78 | 1.56 | 0.74 | 0.85 | 0.81 | 1.41 |
time (sec) |
N/A | 0.151 | 0.052 | 0.185 | 0.100 | 0.076 | 0.260 | 0.127 | 0.153 | 0.047 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 16 | 15 | 14 | 14 | 27 | 33 | 13 | 14 |
N.S. |
1 | 1.00 | 1.00 | 0.94 | 0.88 | 0.88 | 1.69 | 2.06 | 0.81 | 0.88 |
time (sec) |
N/A | 0.130 | 0.020 | 0.114 | 0.104 | 0.069 | 0.351 | 0.124 | 0.151 | 0.146 |
Optimal | Rubi | MMA | 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 | 35 | 27 | 19 | 26 | 23 | 39 | 30 | 22 | 23 |
N.S. |
1 | 1.13 | 0.87 | 0.61 | 0.84 | 0.74 | 1.26 | 0.97 | 0.71 | 0.74 |
time (sec) |
N/A | 0.159 | 0.014 | 0.106 | 0.105 | 0.068 | 0.121 | 0.118 | 0.149 | 0.021 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 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 | 0.127 | 0.001 | 0.096 | 0.022 | 0.068 | 0.053 | 0.126 | 0.156 | 0.018 |
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 | 15 | 15 | 15 | 12 | 11 | 16 | 24 | 11 | 15 | 11 |
N.S. |
1 | 1.00 | 1.00 | 0.80 | 0.73 | 1.07 | 1.60 | 0.73 | 1.00 | 0.73 |
time (sec) |
N/A | 0.123 | 0.002 | 0.103 | 0.023 | 0.063 | 0.067 | 0.125 | 0.159 | 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 | 25 | 25 | 41 | 20 | 19 | 32 | 19 | 19 | 18 | 18 |
N.S. |
1 | 1.00 | 1.64 | 0.80 | 0.76 | 1.28 | 0.76 | 0.76 | 0.72 | 0.72 |
time (sec) |
N/A | 0.132 | 0.036 | 0.371 | 0.107 | 0.066 | 0.069 | 0.114 | 0.148 | 0.021 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 29 | 18 | 15 | 22 | 14 | 24 | 19 | 13 | 14 |
N.S. |
1 | 1.16 | 0.72 | 0.60 | 0.88 | 0.56 | 0.96 | 0.76 | 0.52 | 0.56 |
time (sec) |
N/A | 0.146 | 0.011 | 0.097 | 0.101 | 0.062 | 0.099 | 0.118 | 0.144 | 0.013 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 6 | 6 | 16 | 5 | 4 | 14 | 3 | 25 | 13 | 4 |
N.S. |
1 | 1.00 | 2.67 | 0.83 | 0.67 | 2.33 | 0.50 | 4.17 | 2.17 | 0.67 |
time (sec) |
N/A | 0.117 | 0.011 | 0.126 | 0.102 | 0.069 | 0.054 | 0.123 | 0.148 | 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 | 21 | 21 | 33 | 16 | 15 | 25 | 15 | 25 | 21 | 15 |
N.S. |
1 | 1.00 | 1.57 | 0.76 | 0.71 | 1.19 | 0.71 | 1.19 | 1.00 | 0.71 |
time (sec) |
N/A | 0.131 | 0.018 | 0.140 | 0.126 | 0.075 | 0.064 | 0.117 | 0.157 | 0.017 |
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 | 35 | 39 | 35 | 26 | 22 | 33 | 66 | 25 | 31 | 25 |
N.S. |
1 | 1.11 | 1.00 | 0.74 | 0.63 | 0.94 | 1.89 | 0.71 | 0.89 | 0.71 |
time (sec) |
N/A | 0.142 | 0.023 | 0.250 | 0.110 | 0.070 | 0.997 | 0.125 | 0.155 | 0.196 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 23 | 20 | 19 | 23 | 76 | 48 | 41 | 19 |
N.S. |
1 | 1.00 | 1.00 | 0.87 | 0.83 | 1.00 | 3.30 | 2.09 | 1.78 | 0.83 |
time (sec) |
N/A | 0.134 | 0.032 | 0.127 | 0.112 | 0.072 | 0.370 | 0.123 | 0.159 | 0.199 |
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 | 19 | 28 | 92 | 24 | 26 | 24 |
N.S. |
1 | 1.20 | 1.00 | 0.83 | 0.63 | 0.93 | 3.07 | 0.80 | 0.87 | 0.80 |
time (sec) |
N/A | 0.146 | 0.018 | 0.230 | 0.104 | 0.069 | 0.686 | 0.121 | 0.152 | 0.204 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 18 | 15 | 14 | 18 | 37 | 23 | 17 | 14 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 0.78 | 1.00 | 2.06 | 1.28 | 0.94 | 0.78 |
time (sec) |
N/A | 0.128 | 0.020 | 0.134 | 0.115 | 0.071 | 0.368 | 0.118 | 0.146 | 0.177 |
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 | 34 | 34 | 34 | 31 | 22 | 58 | 49 | 24 | 33 | 34 |
N.S. |
1 | 1.00 | 1.00 | 0.91 | 0.65 | 1.71 | 1.44 | 0.71 | 0.97 | 1.00 |
time (sec) |
N/A | 0.144 | 0.076 | 0.165 | 0.103 | 0.070 | 0.731 | 0.124 | 0.151 | 0.148 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 43 | 23 | 22 | 34 | 24 | 22 | 21 | 22 |
N.S. |
1 | 1.00 | 1.48 | 0.79 | 0.76 | 1.17 | 0.83 | 0.76 | 0.72 | 0.76 |
time (sec) |
N/A | 0.138 | 0.048 | 0.356 | 0.102 | 0.071 | 0.074 | 0.125 | 0.151 | 0.022 |
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 | 23 | 18 | 14 | 24 | 15 | 37 | 41 | 18 |
N.S. |
1 | 1.00 | 1.00 | 0.78 | 0.61 | 1.04 | 0.65 | 1.61 | 1.78 | 0.78 |
time (sec) |
N/A | 0.142 | 0.028 | 0.158 | 0.102 | 0.067 | 0.451 | 0.115 | 0.161 | 0.035 |
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 | 13 | 13 | 13 | 10 | 9 | 21 | 26 | 9 | 22 | 9 |
N.S. |
1 | 1.00 | 1.00 | 0.77 | 0.69 | 1.62 | 2.00 | 0.69 | 1.69 | 0.69 |
time (sec) |
N/A | 0.120 | 0.002 | 0.105 | 0.024 | 0.064 | 0.333 | 0.121 | 0.151 | 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 | 31 | 35 | 22 | 19 | 26 | 23 | 44 | 32 | 22 | 23 |
N.S. |
1 | 1.13 | 0.71 | 0.61 | 0.84 | 0.74 | 1.42 | 1.03 | 0.71 | 0.74 |
time (sec) |
N/A | 0.151 | 0.014 | 0.102 | 0.107 | 0.069 | 0.127 | 0.118 | 0.145 | 0.117 |
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 | 45 | 50 | 46 | 32 | 31 | 39 | 110 | 26 | 31 | 27 |
N.S. |
1 | 1.11 | 1.02 | 0.71 | 0.69 | 0.87 | 2.44 | 0.58 | 0.69 | 0.60 |
time (sec) |
N/A | 0.147 | 0.061 | 0.187 | 0.104 | 0.068 | 1.588 | 0.118 | 0.157 | 0.021 |
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 | 13 | 13 | 13 | 10 | 9 | 9 | 26 | 9 | 13 | 9 |
N.S. |
1 | 1.00 | 1.00 | 0.77 | 0.69 | 0.69 | 2.00 | 0.69 | 1.00 | 0.69 |
time (sec) |
N/A | 0.123 | 0.001 | 0.102 | 0.023 | 0.065 | 0.066 | 0.121 | 0.159 | 0.016 |
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 | 16 | 16 | 16 | 13 | 12 | 30 | 34 | 12 | 28 | 12 |
N.S. |
1 | 1.00 | 1.00 | 0.81 | 0.75 | 1.88 | 2.12 | 0.75 | 1.75 | 0.75 |
time (sec) |
N/A | 0.121 | 0.022 | 0.138 | 0.029 | 0.064 | 0.371 | 0.129 | 0.150 | 0.146 |
Optimal | Rubi | MMA | 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 | 37 | 47 | 25 | 36 | 37 | 22 | 23 | 42 | 24 |
N.S. |
1 | 1.12 | 1.42 | 0.76 | 1.09 | 1.12 | 0.67 | 0.70 | 1.27 | 0.73 |
time (sec) |
N/A | 0.153 | 0.042 | 0.162 | 0.114 | 0.068 | 0.207 | 0.128 | 0.146 | 0.025 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 8 | 10 | 20 | 7 | 6 | 18 | 5 | 34 | 17 | 14 |
N.S. |
1 | 1.25 | 2.50 | 0.88 | 0.75 | 2.25 | 0.62 | 4.25 | 2.12 | 1.75 |
time (sec) |
N/A | 0.132 | 0.040 | 0.179 | 0.102 | 0.067 | 0.232 | 0.124 | 0.168 | 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 | 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 | 0.139 | 0.043 | 0.155 | 0.102 | 0.066 | 0.246 | 0.121 | 0.152 | 0.180 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 44 | 49 | 55 | 27 | 36 | 37 | 24 | 25 | 40 | 0 |
N.S. |
1 | 1.11 | 1.25 | 0.61 | 0.82 | 0.84 | 0.55 | 0.57 | 0.91 | 0.00 |
time (sec) |
N/A | 0.175 | 0.046 | 0.329 | 0.103 | 0.070 | 0.231 | 0.131 | 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 | 26 | 26 | 23 | 24 | 22 | 28 | 19 | 22 | 41 | 23 |
N.S. |
1 | 1.00 | 0.88 | 0.92 | 0.85 | 1.08 | 0.73 | 0.85 | 1.58 | 0.88 |
time (sec) |
N/A | 0.146 | 0.006 | 0.142 | 0.106 | 0.068 | 0.048 | 0.120 | 0.146 | 0.019 |
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 | 43 | 43 | 43 | 36 | 59 | 49 | 0 | 36 | 40 | 29 |
N.S. |
1 | 1.00 | 1.00 | 0.84 | 1.37 | 1.14 | 0.00 | 0.84 | 0.93 | 0.67 |
time (sec) |
N/A | 0.147 | 0.153 | 0.127 | 0.028 | 0.073 | 0.000 | 0.132 | 0.148 | 0.034 |
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 | 33 | 33 | 45 | 23 | 22 | 35 | 24 | 22 | 43 | 22 |
N.S. |
1 | 1.00 | 1.36 | 0.70 | 0.67 | 1.06 | 0.73 | 0.67 | 1.30 | 0.67 |
time (sec) |
N/A | 0.158 | 0.058 | 0.040 | 0.112 | 0.076 | 0.299 | 0.129 | 0.149 | 0.049 |
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 | 30 | 36 | 30 | 23 | 22 | 22 | 24 | 22 | 31 | 34 |
N.S. |
1 | 1.20 | 1.00 | 0.77 | 0.73 | 0.73 | 0.80 | 0.73 | 1.03 | 1.13 |
time (sec) |
N/A | 0.154 | 0.022 | 0.072 | 0.119 | 0.067 | 0.274 | 0.123 | 0.147 | 0.157 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 42 | 13 | 6 | 16 | 3 | 32 | 15 | 12 |
N.S. |
1 | 1.00 | 3.00 | 0.93 | 0.43 | 1.14 | 0.21 | 2.29 | 1.07 | 0.86 |
time (sec) |
N/A | 0.126 | 0.002 | 0.119 | 0.024 | 0.065 | 0.443 | 0.119 | 0.143 | 0.128 |
Optimal | Rubi | MMA | 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 | 15 | 15 | 15 | 14 | 13 | 13 | 10 | 15 | 13 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 0.87 | 0.87 | 0.67 | 1.00 | 0.87 | 0.87 |
time (sec) |
N/A | 0.146 | 0.003 | 0.117 | 0.026 | 0.066 | 0.038 | 0.121 | 0.148 | 0.122 |
Optimal | Rubi | MMA | 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 | 26 | 26 | 25 | 21 | 20 | 20 | 19 | 21 | 20 | 20 |
N.S. |
1 | 1.00 | 0.96 | 0.81 | 0.77 | 0.77 | 0.73 | 0.81 | 0.77 | 0.77 |
time (sec) |
N/A | 0.159 | 0.004 | 0.085 | 0.027 | 0.063 | 0.026 | 0.123 | 0.153 | 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 | 25 | 25 | 25 | 18 | 19 | 19 | 19 | 22 | 19 | 19 |
N.S. |
1 | 1.00 | 1.00 | 0.72 | 0.76 | 0.76 | 0.76 | 0.88 | 0.76 | 0.76 |
time (sec) |
N/A | 0.206 | 0.004 | 0.034 | 0.024 | 0.068 | 0.059 | 0.124 | 0.150 | 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 | 30 | 30 | 29 | 25 | 24 | 36 | 20 | 26 | 44 | 22 |
N.S. |
1 | 1.00 | 0.97 | 0.83 | 0.80 | 1.20 | 0.67 | 0.87 | 1.47 | 0.73 |
time (sec) |
N/A | 0.184 | 0.010 | 0.039 | 0.022 | 0.066 | 0.038 | 0.122 | 0.152 | 0.027 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 23 | 18 | 17 | 17 | 17 | 18 | 17 | 21 |
N.S. |
1 | 1.00 | 1.00 | 0.78 | 0.74 | 0.74 | 0.74 | 0.78 | 0.74 | 0.91 |
time (sec) |
N/A | 0.201 | 0.003 | 0.111 | 0.101 | 0.069 | 0.066 | 0.125 | 0.154 | 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 | 38 | 38 | 38 | 32 | 31 | 31 | 34 | 31 | 30 | 30 |
N.S. |
1 | 1.00 | 1.00 | 0.84 | 0.82 | 0.82 | 0.89 | 0.82 | 0.79 | 0.79 |
time (sec) |
N/A | 0.191 | 0.008 | 0.227 | 0.103 | 0.067 | 0.051 | 0.121 | 0.176 | 0.101 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 103 | 103 | 93 | 72 | 77 | 136 | 88 | 74 | 204 | 96 |
N.S. |
1 | 1.00 | 0.90 | 0.70 | 0.75 | 1.32 | 0.85 | 0.72 | 1.98 | 0.93 |
time (sec) |
N/A | 0.540 | 0.031 | 0.299 | 0.104 | 0.079 | 0.237 | 0.125 | 0.150 | 0.146 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 33 | 33 | 28 | 29 | 44 | 27 | 30 | 58 | 33 |
N.S. |
1 | 1.00 | 1.00 | 0.85 | 0.88 | 1.33 | 0.82 | 0.91 | 1.76 | 1.00 |
time (sec) |
N/A | 0.205 | 0.014 | 0.127 | 0.118 | 0.079 | 0.057 | 0.115 | 0.147 | 0.022 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 16 | 16 | 15 | 19 | 12 | 15 | 20 | 16 |
N.S. |
1 | 1.00 | 0.84 | 0.84 | 0.79 | 1.00 | 0.63 | 0.79 | 1.05 | 0.84 |
time (sec) |
N/A | 0.135 | 0.004 | 0.083 | 0.109 | 0.075 | 0.041 | 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 | 19 | 19 | 19 | 14 | 13 | 13 | 12 | 15 | 13 | 12 |
N.S. |
1 | 1.00 | 1.00 | 0.74 | 0.68 | 0.68 | 0.63 | 0.79 | 0.68 | 0.63 |
time (sec) |
N/A | 0.132 | 0.002 | 0.101 | 0.034 | 0.062 | 0.040 | 0.119 | 0.165 | 0.141 |
Optimal | Rubi | MMA | 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 | 21 | 21 | 14 | 15 | 15 | 17 | 17 | 15 | 8 |
N.S. |
1 | 1.11 | 1.11 | 0.74 | 0.79 | 0.79 | 0.89 | 0.89 | 0.79 | 0.42 |
time (sec) |
N/A | 0.154 | 0.003 | 0.108 | 0.034 | 0.062 | 0.041 | 0.127 | 0.154 | 0.072 |
Optimal | Rubi | MMA | 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 | 32 | 25 | 26 | 37 | 26 | 43 | 46 | 22 |
N.S. |
1 | 1.00 | 1.00 | 0.78 | 0.81 | 1.16 | 0.81 | 1.34 | 1.44 | 0.69 |
time (sec) |
N/A | 0.171 | 0.011 | 0.120 | 0.028 | 0.062 | 0.054 | 0.125 | 0.165 | 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 | 43 | 43 | 33 | 30 | 34 | 53 | 32 | 31 | 70 | 29 |
N.S. |
1 | 1.00 | 0.77 | 0.70 | 0.79 | 1.23 | 0.74 | 0.72 | 1.63 | 0.67 |
time (sec) |
N/A | 0.196 | 0.016 | 0.109 | 0.024 | 0.067 | 0.065 | 0.121 | 0.156 | 0.061 |
Optimal | Rubi | MMA | 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 | 21 | 21 | 17 | 19 | 26 | 17 | 21 | 26 | 16 |
N.S. |
1 | 1.00 | 1.00 | 0.81 | 0.90 | 1.24 | 0.81 | 1.00 | 1.24 | 0.76 |
time (sec) |
N/A | 0.163 | 0.002 | 0.122 | 0.029 | 0.066 | 0.040 | 0.119 | 0.153 | 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 | 25 | 25 | 25 | 20 | 23 | 19 | 17 | 26 | 23 | 19 |
N.S. |
1 | 1.00 | 1.00 | 0.80 | 0.92 | 0.76 | 0.68 | 1.04 | 0.92 | 0.76 |
time (sec) |
N/A | 0.212 | 0.004 | 0.128 | 0.023 | 0.063 | 0.035 | 0.127 | 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 | 11 | 19 | 11 | 12 | 13 | 11 | 8 | 13 | 11 | 11 |
N.S. |
1 | 1.73 | 1.00 | 1.09 | 1.18 | 1.00 | 0.73 | 1.18 | 1.00 | 1.00 |
time (sec) |
N/A | 0.156 | 0.003 | 0.094 | 0.028 | 0.061 | 0.036 | 0.118 | 0.147 | 0.131 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 36 | 36 | 32 | 31 | 31 | 36 | 31 | 30 | 56 |
N.S. |
1 | 1.00 | 1.00 | 0.89 | 0.86 | 0.86 | 1.00 | 0.86 | 0.83 | 1.56 |
time (sec) |
N/A | 0.279 | 0.010 | 0.110 | 0.101 | 0.071 | 0.085 | 0.120 | 0.145 | 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 | 29 | 29 | 29 | 22 | 21 | 33 | 22 | 21 | 40 | 23 |
N.S. |
1 | 1.00 | 1.00 | 0.76 | 0.72 | 1.14 | 0.76 | 0.72 | 1.38 | 0.79 |
time (sec) |
N/A | 0.269 | 0.011 | 0.119 | 0.108 | 0.069 | 0.075 | 0.125 | 0.158 | 0.097 |
Optimal | Rubi | MMA | 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 | 60 | 60 | 54 | 48 | 47 | 60 | 63 | 60 | 92 | 61 |
N.S. |
1 | 1.00 | 0.90 | 0.80 | 0.78 | 1.00 | 1.05 | 1.00 | 1.53 | 1.02 |
time (sec) |
N/A | 0.250 | 0.036 | 0.240 | 0.103 | 0.070 | 0.112 | 0.124 | 0.154 | 0.069 |
Optimal | Rubi | MMA | 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 | 42 | 28 | 25 | 30 | 39 | 27 | 25 | 47 | 30 |
N.S. |
1 | 1.14 | 0.76 | 0.68 | 0.81 | 1.05 | 0.73 | 0.68 | 1.27 | 0.81 |
time (sec) |
N/A | 0.150 | 0.009 | 0.097 | 0.100 | 0.064 | 0.048 | 0.115 | 0.150 | 0.089 |
Optimal | Rubi | MMA | 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 | 97 | 104 | 78 | 68 | 75 | 134 | 88 | 71 | 239 | 84 |
N.S. |
1 | 1.07 | 0.80 | 0.70 | 0.77 | 1.38 | 0.91 | 0.73 | 2.46 | 0.87 |
time (sec) |
N/A | 0.260 | 0.027 | 0.411 | 0.118 | 0.072 | 0.091 | 0.121 | 0.152 | 0.068 |
Optimal | Rubi | MMA | 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 | 46 | 34 | 35 | 39 | 46 | 36 | 38 | 49 |
N.S. |
1 | 1.00 | 1.00 | 0.74 | 0.76 | 0.85 | 1.00 | 0.78 | 0.83 | 1.07 |
time (sec) |
N/A | 0.232 | 0.018 | 0.041 | 0.106 | 0.073 | 0.067 | 0.125 | 0.160 | 0.128 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 48 | 53 | 48 | 36 | 37 | 46 | 48 | 38 | 46 | 51 |
N.S. |
1 | 1.10 | 1.00 | 0.75 | 0.77 | 0.96 | 1.00 | 0.79 | 0.96 | 1.06 |
time (sec) |
N/A | 0.205 | 0.009 | 0.102 | 0.112 | 0.072 | 0.063 | 0.116 | 0.153 | 0.050 |
Optimal | Rubi | MMA | 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 | 15 | 15 | 19 | 14 | 13 | 13 | 10 | 14 | 13 | 13 |
N.S. |
1 | 1.00 | 1.27 | 0.93 | 0.87 | 0.87 | 0.67 | 0.93 | 0.87 | 0.87 |
time (sec) |
N/A | 0.137 | 0.003 | 0.086 | 0.031 | 0.069 | 0.024 | 0.116 | 0.145 | 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 | 10 | 10 | 8 | 9 | 8 | 8 | 7 | 9 | 8 | 8 |
N.S. |
1 | 1.00 | 0.80 | 0.90 | 0.80 | 0.80 | 0.70 | 0.90 | 0.80 | 0.80 |
time (sec) |
N/A | 0.136 | 0.002 | 0.081 | 0.027 | 0.064 | 0.025 | 0.129 | 0.162 | 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 | 13 | 13 | 13 | 12 | 11 | 11 | 10 | 13 | 11 | 11 |
N.S. |
1 | 1.00 | 1.00 | 0.92 | 0.85 | 0.85 | 0.77 | 1.00 | 0.85 | 0.85 |
time (sec) |
N/A | 0.142 | 0.003 | 0.105 | 0.026 | 0.074 | 0.046 | 0.118 | 0.147 | 0.022 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 11 | 11 | 11 | 12 | 11 | 11 | 8 | 13 | 11 | 10 |
N.S. |
1 | 1.00 | 1.00 | 1.09 | 1.00 | 1.00 | 0.73 | 1.18 | 1.00 | 0.91 |
time (sec) |
N/A | 0.129 | 0.003 | 0.092 | 0.023 | 0.066 | 0.039 | 0.121 | 0.142 | 0.037 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 15 | 11 | 12 | 12 | 10 | 13 | 12 | 10 |
N.S. |
1 | 1.00 | 1.25 | 0.92 | 1.00 | 1.00 | 0.83 | 1.08 | 1.00 | 0.83 |
time (sec) |
N/A | 0.142 | 0.002 | 0.071 | 0.022 | 0.062 | 0.029 | 0.117 | 0.142 | 0.090 |
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 | 26 | 26 | 19 | 21 | 26 | 20 | 80 | 28 | 19 | 18 |
N.S. |
1 | 1.00 | 0.73 | 0.81 | 1.00 | 0.77 | 3.08 | 1.08 | 0.73 | 0.69 |
time (sec) |
N/A | 0.137 | 0.005 | 0.125 | 0.023 | 0.068 | 0.093 | 0.120 | 0.145 | 0.124 |
Optimal | Rubi | MMA | 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 | 12 | 12 | 10 | 14 | 12 | 12 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 0.86 | 0.86 | 0.71 | 1.00 | 0.86 | 0.86 |
time (sec) |
N/A | 0.162 | 0.003 | 0.082 | 0.023 | 0.065 | 0.044 | 0.119 | 0.153 | 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 | 26 | 26 | 26 | 19 | 18 | 18 | 17 | 20 | 18 | 14 |
N.S. |
1 | 1.00 | 1.00 | 0.73 | 0.69 | 0.69 | 0.65 | 0.77 | 0.69 | 0.54 |
time (sec) |
N/A | 0.170 | 0.003 | 0.130 | 0.022 | 0.069 | 0.037 | 0.121 | 0.153 | 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 | 14 | 14 | 14 | 15 | 14 | 17 | 10 | 15 | 21 | 14 |
N.S. |
1 | 1.00 | 1.00 | 1.07 | 1.00 | 1.21 | 0.71 | 1.07 | 1.50 | 1.00 |
time (sec) |
N/A | 0.138 | 0.003 | 0.078 | 0.025 | 0.063 | 0.031 | 0.121 | 0.149 | 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 | 23 | 23 | 23 | 18 | 19 | 19 | 19 | 22 | 19 | 17 |
N.S. |
1 | 1.00 | 1.00 | 0.78 | 0.83 | 0.83 | 0.83 | 0.96 | 0.83 | 0.74 |
time (sec) |
N/A | 0.146 | 0.004 | 0.092 | 0.028 | 0.075 | 0.060 | 0.125 | 0.154 | 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 | 17 | 17 | 17 | 16 | 15 | 15 | 15 | 18 | 15 | 15 |
N.S. |
1 | 1.00 | 1.00 | 0.94 | 0.88 | 0.88 | 0.88 | 1.06 | 0.88 | 0.88 |
time (sec) |
N/A | 0.205 | 0.004 | 0.033 | 0.029 | 0.069 | 0.055 | 0.121 | 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 | 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 | 0.147 | 0.003 | 0.108 | 0.022 | 0.061 | 0.030 | 0.119 | 0.155 | 0.094 |
Optimal | Rubi | MMA | 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 | 22 | 21 | 20 | 26 | 19 | 21 | 35 | 22 |
N.S. |
1 | 1.00 | 0.73 | 0.70 | 0.67 | 0.87 | 0.63 | 0.70 | 1.17 | 0.73 |
time (sec) |
N/A | 0.152 | 0.007 | 0.092 | 0.034 | 0.067 | 0.045 | 0.125 | 0.156 | 0.037 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 26 | 21 | 20 | 27 | 22 | 26 | 38 | 22 |
N.S. |
1 | 1.00 | 0.93 | 0.75 | 0.71 | 0.96 | 0.79 | 0.93 | 1.36 | 0.79 |
time (sec) |
N/A | 0.151 | 0.012 | 0.095 | 0.026 | 0.064 | 0.049 | 0.117 | 0.151 | 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 | 14 | 14 | 14 | 15 | 14 | 18 | 14 | 16 | 18 | 14 |
N.S. |
1 | 1.00 | 1.00 | 1.07 | 1.00 | 1.29 | 1.00 | 1.14 | 1.29 | 1.00 |
time (sec) |
N/A | 0.178 | 0.003 | 0.098 | 0.027 | 0.067 | 0.044 | 0.121 | 0.151 | 0.094 |
Optimal | Rubi | MMA | 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 | 25 | 18 | 17 | 17 | 17 | 20 | 17 | 17 |
N.S. |
1 | 1.00 | 1.32 | 0.95 | 0.89 | 0.89 | 0.89 | 1.05 | 0.89 | 0.89 |
time (sec) |
N/A | 0.184 | 0.005 | 0.041 | 0.029 | 0.068 | 0.052 | 0.113 | 0.151 | 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 | 15 | 15 | 15 | 14 | 13 | 13 | 12 | 14 | 13 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 0.87 | 0.87 | 0.80 | 0.93 | 0.87 | 0.87 |
time (sec) |
N/A | 0.147 | 0.004 | 0.030 | 0.031 | 0.062 | 0.040 | 0.115 | 0.150 | 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 | 25 | 25 | 25 | 24 | 27 | 40 | 20 | 30 | 44 | 27 |
N.S. |
1 | 1.00 | 1.00 | 0.96 | 1.08 | 1.60 | 0.80 | 1.20 | 1.76 | 1.08 |
time (sec) |
N/A | 0.152 | 0.008 | 0.112 | 0.026 | 0.093 | 0.041 | 0.115 | 0.155 | 0.100 |
Optimal | Rubi | MMA | 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 | 21 | 21 | 17 | 22 | 31 | 19 | 18 | 42 | 21 |
N.S. |
1 | 1.00 | 1.00 | 0.81 | 1.05 | 1.48 | 0.90 | 0.86 | 2.00 | 1.00 |
time (sec) |
N/A | 0.146 | 0.007 | 0.085 | 0.025 | 0.063 | 0.034 | 0.121 | 0.155 | 0.015 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | C | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 8 | 8 | 22 | 16 | 16 | 20 | 15 | 18 | 20 | 8 |
N.S. |
1 | 1.00 | 2.75 | 2.00 | 2.00 | 2.50 | 1.88 | 2.25 | 2.50 | 1.00 |
time (sec) |
N/A | 0.134 | 0.003 | 0.096 | 0.028 | 0.065 | 0.038 | 0.116 | 0.147 | 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 | 15 | 15 | 15 | 14 | 13 | 13 | 10 | 13 | 26 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 0.87 | 0.87 | 0.67 | 0.87 | 1.73 | 0.87 |
time (sec) |
N/A | 0.143 | 0.004 | 0.040 | 0.022 | 0.064 | 0.034 | 0.124 | 0.144 | 0.024 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 16 | 18 | 15 | 14 | 14 | 12 | 14 | 14 | 14 |
N.S. |
1 | 0.89 | 1.00 | 0.83 | 0.78 | 0.78 | 0.67 | 0.78 | 0.78 | 0.78 |
time (sec) |
N/A | 0.141 | 0.003 | 0.094 | 0.023 | 0.067 | 0.026 | 0.122 | 0.147 | 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 | 20 | 20 | 20 | 19 | 18 | 18 | 17 | 18 | 18 | 18 |
N.S. |
1 | 1.00 | 1.00 | 0.95 | 0.90 | 0.90 | 0.85 | 0.90 | 0.90 | 0.90 |
time (sec) |
N/A | 0.161 | 0.003 | 0.156 | 0.105 | 0.069 | 0.041 | 0.114 | 0.141 | 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 | 31 | 31 | 31 | 27 | 26 | 26 | 34 | 26 | 25 | 28 |
N.S. |
1 | 1.00 | 1.00 | 0.87 | 0.84 | 0.84 | 1.10 | 0.84 | 0.81 | 0.90 |
time (sec) |
N/A | 0.161 | 0.006 | 0.195 | 0.106 | 0.072 | 0.041 | 0.122 | 0.168 | 0.095 |
Optimal | Rubi | MMA | 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 | 31 | 22 | 21 | 21 | 22 | 21 | 21 | 17 |
N.S. |
1 | 1.00 | 1.15 | 0.81 | 0.78 | 0.78 | 0.81 | 0.78 | 0.78 | 0.63 |
time (sec) |
N/A | 0.180 | 0.004 | 0.156 | 0.105 | 0.062 | 0.049 | 0.124 | 0.155 | 0.033 |