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 | 25 | 25 | 16 | 17 | 22 | 29 | 17 | 18 | 36 | 22 |
N.S. |
1 | 1.00 | 0.64 | 0.68 | 0.88 | 1.16 | 0.68 | 0.72 | 1.44 | 0.88 |
time (sec) |
N/A | 0.158 | 0.007 | 0.077 | 0.027 | 0.057 | 0.036 | 0.120 | 0.151 | 0.096 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
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 | 33 | 32 | 39 | 31 | 45 | 43 | 32 |
N.S. |
1 | 1.00 | 1.00 | 0.92 | 0.89 | 1.08 | 0.86 | 1.25 | 1.19 | 0.89 |
time (sec) |
N/A | 0.165 | 0.010 | 0.083 | 0.024 | 0.058 | 0.034 | 0.120 | 0.158 | 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 | 41 | 41 | 37 | 25 | 30 | 45 | 31 | 27 | 64 | 30 |
N.S. |
1 | 1.00 | 0.90 | 0.61 | 0.73 | 1.10 | 0.76 | 0.66 | 1.56 | 0.73 |
time (sec) |
N/A | 0.205 | 0.015 | 0.038 | 0.025 | 0.059 | 0.057 | 0.122 | 0.159 | 0.114 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
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 | 28 | 29 | 45 | 26 | 37 | 62 | 29 |
N.S. |
1 | 1.00 | 1.00 | 1.04 | 1.07 | 1.67 | 0.96 | 1.37 | 2.30 | 1.07 |
time (sec) |
N/A | 0.196 | 0.011 | 0.102 | 0.026 | 0.060 | 0.049 | 0.127 | 0.150 | 0.112 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
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 | 47 | 31 | 29 | 45 | 32 | 35 | 60 | 31 |
N.S. |
1 | 1.13 | 1.21 | 0.79 | 0.74 | 1.15 | 0.82 | 0.90 | 1.54 | 0.79 |
time (sec) |
N/A | 0.208 | 0.012 | 0.117 | 0.023 | 0.068 | 0.062 | 0.120 | 0.156 | 0.024 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 46 | 46 | 40 | 35 | 40 | 65 | 37 | 40 | 69 | 40 |
N.S. |
1 | 1.00 | 0.87 | 0.76 | 0.87 | 1.41 | 0.80 | 0.87 | 1.50 | 0.87 |
time (sec) |
N/A | 0.210 | 0.011 | 0.038 | 0.024 | 0.061 | 0.064 | 0.112 | 0.151 | 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 | 29 | 29 | 29 | 24 | 23 | 23 | 22 | 24 | 23 | 29 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 0.79 | 0.79 | 0.76 | 0.83 | 0.79 | 1.00 |
time (sec) |
N/A | 0.181 | 0.006 | 0.067 | 0.104 | 0.064 | 0.051 | 0.124 | 0.146 | 0.113 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
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 | 22 | 21 | 21 | 22 | 23 | 21 | 27 |
N.S. |
1 | 1.00 | 1.00 | 0.81 | 0.78 | 0.78 | 0.81 | 0.85 | 0.78 | 1.00 |
time (sec) |
N/A | 0.164 | 0.006 | 0.108 | 0.102 | 0.062 | 0.079 | 0.125 | 0.145 | 0.047 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
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 | 32 | 26 | 25 | 25 | 29 | 27 | 24 | 17 |
N.S. |
1 | 1.00 | 1.33 | 1.08 | 1.04 | 1.04 | 1.21 | 1.12 | 1.00 | 0.71 |
time (sec) |
N/A | 0.144 | 0.008 | 0.043 | 0.103 | 0.069 | 0.071 | 0.119 | 0.142 | 0.067 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 41 | 41 | 41 | 33 | 32 | 44 | 39 | 33 | 65 | 49 |
N.S. |
1 | 1.00 | 1.00 | 0.80 | 0.78 | 1.07 | 0.95 | 0.80 | 1.59 | 1.20 |
time (sec) |
N/A | 0.240 | 0.015 | 0.045 | 0.104 | 0.062 | 0.064 | 0.120 | 0.139 | 0.227 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 46 | 46 | 40 | 35 | 36 | 57 | 37 | 62 | 68 | 38 |
N.S. |
1 | 1.00 | 0.87 | 0.76 | 0.78 | 1.24 | 0.80 | 1.35 | 1.48 | 0.83 |
time (sec) |
N/A | 0.237 | 0.013 | 0.142 | 0.103 | 0.063 | 0.092 | 0.119 | 0.142 | 0.159 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 47 | 47 | 37 | 31 | 36 | 59 | 36 | 32 | 86 | 42 |
N.S. |
1 | 1.00 | 0.79 | 0.66 | 0.77 | 1.26 | 0.77 | 0.68 | 1.83 | 0.89 |
time (sec) |
N/A | 0.207 | 0.018 | 0.129 | 0.103 | 0.063 | 0.072 | 0.122 | 0.157 | 0.023 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 67 | 71 | 73 | 54 | 53 | 53 | 70 | 53 | 51 | 47 |
N.S. |
1 | 1.06 | 1.09 | 0.81 | 0.79 | 0.79 | 1.04 | 0.79 | 0.76 | 0.70 |
time (sec) |
N/A | 0.212 | 0.041 | 0.026 | 0.104 | 0.065 | 0.079 | 0.123 | 0.155 | 0.049 |
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 | 48 | 48 | 67 | 46 | 54 | 58 | 306 | 64 | 60 | 73 |
N.S. |
1 | 1.00 | 1.40 | 0.96 | 1.12 | 1.21 | 6.38 | 1.33 | 1.25 | 1.52 |
time (sec) |
N/A | 0.233 | 0.013 | 0.120 | 0.109 | 0.069 | 0.298 | 0.123 | 0.160 | 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 | 58 | 58 | 46 | 38 | 43 | 66 | 46 | 39 | 107 | 44 |
N.S. |
1 | 1.00 | 0.79 | 0.66 | 0.74 | 1.14 | 0.79 | 0.67 | 1.84 | 0.76 |
time (sec) |
N/A | 0.222 | 0.017 | 0.217 | 0.104 | 0.064 | 0.080 | 0.117 | 0.158 | 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 | 51 | 51 | 47 | 36 | 35 | 35 | 44 | 35 | 33 | 35 |
N.S. |
1 | 1.00 | 0.92 | 0.71 | 0.69 | 0.69 | 0.86 | 0.69 | 0.65 | 0.69 |
time (sec) |
N/A | 0.411 | 0.018 | 0.207 | 0.105 | 0.065 | 0.193 | 0.120 | 0.153 | 0.139 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
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 | 45 | 41 | 34 | 33 | 33 | 32 | 33 | 33 | 33 |
N.S. |
1 | 1.10 | 1.00 | 0.83 | 0.80 | 0.80 | 0.78 | 0.80 | 0.80 | 0.80 |
time (sec) |
N/A | 0.407 | 0.006 | 0.124 | 0.030 | 0.066 | 0.070 | 0.122 | 0.149 | 0.059 |
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 | 56 | 58 | 52 | 51 | 49 | 45 | 73 | 50 | 44 | 64 |
N.S. |
1 | 1.04 | 0.93 | 0.91 | 0.88 | 0.80 | 1.30 | 0.89 | 0.79 | 1.14 |
time (sec) |
N/A | 0.197 | 0.010 | 0.111 | 0.103 | 0.069 | 0.052 | 0.127 | 0.151 | 0.340 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 56 | 58 | 50 | 43 | 49 | 43 | 71 | 50 | 42 | 68 |
N.S. |
1 | 1.04 | 0.89 | 0.77 | 0.88 | 0.77 | 1.27 | 0.89 | 0.75 | 1.21 |
time (sec) |
N/A | 0.194 | 0.006 | 0.121 | 0.104 | 0.068 | 0.046 | 0.116 | 0.141 | 0.071 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
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 | 21 | 10 |
N.S. |
1 | 1.00 | 1.00 | 0.92 | 0.83 | 0.83 | 0.67 | 0.92 | 1.75 | 0.83 |
time (sec) |
N/A | 0.127 | 0.002 | 0.099 | 0.028 | 0.058 | 0.039 | 0.114 | 0.157 | 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 | 22 | 26 | 22 | 21 | 23 | 18 | 19 | 22 | 30 | 18 |
N.S. |
1 | 1.18 | 1.00 | 0.95 | 1.05 | 0.82 | 0.86 | 1.00 | 1.36 | 0.82 |
time (sec) |
N/A | 0.143 | 0.004 | 0.125 | 0.029 | 0.059 | 0.100 | 0.118 | 0.149 | 0.150 |
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 | 63 | 72 | 60 | 60 | 57 | 53 | 83 | 58 | 53 | 88 |
N.S. |
1 | 1.14 | 0.95 | 0.95 | 0.90 | 0.84 | 1.32 | 0.92 | 0.84 | 1.40 |
time (sec) |
N/A | 0.216 | 0.012 | 0.148 | 0.104 | 0.068 | 0.080 | 0.124 | 0.144 | 0.065 |
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 | 65 | 74 | 68 | 60 | 57 | 62 | 80 | 58 | 60 | 86 |
N.S. |
1 | 1.14 | 1.05 | 0.92 | 0.88 | 0.95 | 1.23 | 0.89 | 0.92 | 1.32 |
time (sec) |
N/A | 0.221 | 0.013 | 0.113 | 0.103 | 0.069 | 0.080 | 0.118 | 0.148 | 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 | 33 | 34 | 33 | 34 | 31 | 33 | 29 | 40 | 45 | 29 |
N.S. |
1 | 1.03 | 1.00 | 1.03 | 0.94 | 1.00 | 0.88 | 1.21 | 1.36 | 0.88 |
time (sec) |
N/A | 0.157 | 0.005 | 0.102 | 0.024 | 0.058 | 0.123 | 0.120 | 0.142 | 0.042 |
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 | 73 | 88 | 74 | 66 | 66 | 68 | 90 | 67 | 67 | 99 |
N.S. |
1 | 1.21 | 1.01 | 0.90 | 0.90 | 0.93 | 1.23 | 0.92 | 0.92 | 1.36 |
time (sec) |
N/A | 0.238 | 0.011 | 0.117 | 0.108 | 0.068 | 0.094 | 0.126 | 0.154 | 0.103 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 46 | 46 | 45 | 0 | 0 | 0 | 92 | 0 | 19 | 0 |
N.S. |
1 | 1.00 | 0.98 | 0.00 | 0.00 | 0.00 | 2.00 | 0.00 | 0.41 | 0.00 |
time (sec) |
N/A | 0.151 | 0.093 | 0.000 | 0.000 | 0.000 | 1.163 | 0.000 | 0.141 | 0.000 |
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 | 27 | 27 | 38 | 33 | 32 | 26 | 37 | 34 | 26 | 18 |
N.S. |
1 | 1.00 | 1.41 | 1.22 | 1.19 | 0.96 | 1.37 | 1.26 | 0.96 | 0.67 |
time (sec) |
N/A | 0.147 | 0.007 | 0.135 | 0.103 | 0.069 | 0.061 | 0.121 | 0.138 | 0.039 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 15 | 27 | 29 | 26 | 24 | 30 | 28 | 13 |
N.S. |
1 | 1.00 | 1.00 | 1.80 | 1.93 | 1.73 | 1.60 | 2.00 | 1.87 | 0.87 |
time (sec) |
N/A | 0.134 | 0.004 | 0.106 | 0.028 | 0.060 | 0.071 | 0.121 | 0.142 | 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 | 24 | 28 | 24 | 23 | 25 | 20 | 19 | 26 | 34 | 20 |
N.S. |
1 | 1.17 | 1.00 | 0.96 | 1.04 | 0.83 | 0.79 | 1.08 | 1.42 | 0.83 |
time (sec) |
N/A | 0.142 | 0.005 | 0.099 | 0.023 | 0.060 | 0.111 | 0.115 | 0.150 | 0.156 |
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 | 40 | 46 | 41 | 40 | 36 | 44 | 42 | 36 | 31 |
N.S. |
1 | 1.14 | 1.31 | 1.17 | 1.14 | 1.03 | 1.26 | 1.20 | 1.03 | 0.89 |
time (sec) |
N/A | 0.158 | 0.010 | 0.136 | 0.102 | 0.067 | 0.085 | 0.119 | 0.146 | 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 | 26 | 25 | 50 | 42 | 37 | 41 | 34 | 38 | 46 | 22 |
N.S. |
1 | 0.96 | 1.92 | 1.62 | 1.42 | 1.58 | 1.31 | 1.46 | 1.77 | 0.85 |
time (sec) |
N/A | 0.147 | 0.006 | 0.118 | 0.025 | 0.060 | 0.097 | 0.125 | 0.147 | 0.111 |
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 | 37 | 42 | 48 | 41 | 40 | 45 | 48 | 42 | 45 | 31 |
N.S. |
1 | 1.14 | 1.30 | 1.11 | 1.08 | 1.22 | 1.30 | 1.14 | 1.22 | 0.84 |
time (sec) |
N/A | 0.156 | 0.009 | 0.134 | 0.106 | 0.067 | 0.104 | 0.114 | 0.145 | 0.135 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 45 | 45 | 44 | 0 | 0 | 0 | 95 | 0 | 20 | 0 |
N.S. |
1 | 1.00 | 0.98 | 0.00 | 0.00 | 0.00 | 2.11 | 0.00 | 0.44 | 0.00 |
time (sec) |
N/A | 0.148 | 0.149 | 0.000 | 0.000 | 0.000 | 0.445 | 0.000 | 0.152 | 0.000 |
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 | 15 | 15 | 15 | 14 | 13 | 13 | 29 | 13 | 44 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 0.87 | 0.87 | 1.93 | 0.87 | 2.93 | 0.87 |
time (sec) |
N/A | 0.135 | 0.004 | 0.122 | 0.102 | 0.059 | 0.058 | 0.119 | 0.154 | 0.106 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 109 | 114 | 79 | 24 | 98 | 80 | 19 | 114 | 75 | 33 |
N.S. |
1 | 1.05 | 0.72 | 0.22 | 0.90 | 0.73 | 0.17 | 1.05 | 0.69 | 0.30 |
time (sec) |
N/A | 0.276 | 0.021 | 0.108 | 0.104 | 0.064 | 0.053 | 0.123 | 0.154 | 0.057 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | C | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 201 | 202 | 204 | 55 | 180 | 11094 | 39 | 177 | 11 | 174 |
N.S. |
1 | 1.00 | 1.01 | 0.27 | 0.90 | 55.19 | 0.19 | 0.88 | 0.05 | 0.87 |
time (sec) |
N/A | 0.418 | 0.101 | 0.121 | 0.109 | 0.723 | 0.056 | 0.122 | 0.154 | 0.327 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | C | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 201 | 203 | 204 | 60 | 160 | 18781 | 41 | 177 | 13 | 182 |
N.S. |
1 | 1.01 | 1.01 | 0.30 | 0.80 | 93.44 | 0.20 | 0.88 | 0.06 | 0.91 |
time (sec) |
N/A | 0.386 | 0.037 | 0.108 | 0.107 | 0.739 | 0.054 | 0.125 | 0.154 | 0.332 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | C | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 201 | 220 | 204 | 58 | 160 | 12656 | 41 | 177 | 15 | 202 |
N.S. |
1 | 1.09 | 1.01 | 0.29 | 0.80 | 62.97 | 0.20 | 0.88 | 0.07 | 1.00 |
time (sec) |
N/A | 0.371 | 0.040 | 0.115 | 0.104 | 0.735 | 0.064 | 0.132 | 0.153 | 0.441 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | C | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 201 | 202 | 204 | 73 | 180 | 17865 | 39 | 177 | 15 | 202 |
N.S. |
1 | 1.00 | 1.01 | 0.36 | 0.90 | 88.88 | 0.19 | 0.88 | 0.07 | 1.00 |
time (sec) |
N/A | 0.373 | 0.025 | 0.111 | 0.106 | 0.739 | 0.057 | 0.135 | 0.154 | 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 | 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 | 0.129 | 0.002 | 0.102 | 0.027 | 0.055 | 0.042 | 0.126 | 0.153 | 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 | 22 | 26 | 22 | 21 | 23 | 18 | 19 | 22 | 20 | 18 |
N.S. |
1 | 1.18 | 1.00 | 0.95 | 1.05 | 0.82 | 0.86 | 1.00 | 0.91 | 0.82 |
time (sec) |
N/A | 0.143 | 0.005 | 0.099 | 0.027 | 0.060 | 0.116 | 0.131 | 0.151 | 0.169 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | C | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 209 | 216 | 172 | 76 | 192 | 15275 | 48 | 185 | 27 | 210 |
N.S. |
1 | 1.03 | 0.82 | 0.36 | 0.92 | 73.09 | 0.23 | 0.89 | 0.13 | 1.00 |
time (sec) |
N/A | 0.388 | 0.100 | 0.108 | 0.106 | 0.747 | 0.079 | 0.138 | 0.151 | 0.313 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | C | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 211 | 236 | 174 | 78 | 173 | 15499 | 51 | 185 | 30 | 210 |
N.S. |
1 | 1.12 | 0.82 | 0.37 | 0.82 | 73.45 | 0.24 | 0.88 | 0.14 | 1.00 |
time (sec) |
N/A | 0.381 | 0.095 | 0.110 | 0.105 | 0.734 | 0.098 | 0.136 | 0.153 | 0.443 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | C | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 211 | 219 | 175 | 81 | 172 | 15501 | 51 | 185 | 28 | 214 |
N.S. |
1 | 1.04 | 0.83 | 0.38 | 0.82 | 73.46 | 0.24 | 0.88 | 0.13 | 1.01 |
time (sec) |
N/A | 0.387 | 0.074 | 0.106 | 0.109 | 0.765 | 0.088 | 0.140 | 0.156 | 0.396 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 46 | 46 | 45 | 0 | 0 | 0 | 92 | 0 | 19 | 0 |
N.S. |
1 | 1.00 | 0.98 | 0.00 | 0.00 | 0.00 | 2.00 | 0.00 | 0.41 | 0.00 |
time (sec) |
N/A | 0.153 | 0.170 | 0.000 | 0.000 | 0.000 | 7.894 | 0.000 | 0.150 | 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 | 35 | 35 | 21 | 10 | 27 | 9 | 8 | 27 | 23 | 9 |
N.S. |
1 | 1.00 | 0.60 | 0.29 | 0.77 | 0.26 | 0.23 | 0.77 | 0.66 | 0.26 |
time (sec) |
N/A | 0.489 | 0.005 | 0.137 | 0.105 | 0.059 | 0.060 | 0.117 | 0.149 | 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 | 60 | 65 | 51 | 44 | 54 | 71 | 63 | 44 | 123 | 45 |
N.S. |
1 | 1.08 | 0.85 | 0.73 | 0.90 | 1.18 | 1.05 | 0.73 | 2.05 | 0.75 |
time (sec) |
N/A | 0.183 | 0.020 | 0.395 | 0.104 | 0.060 | 0.068 | 0.118 | 0.152 | 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 | 43 | 53 | 30 | 28 | 38 | 52 | 36 | 28 | 59 | 27 |
N.S. |
1 | 1.23 | 0.70 | 0.65 | 0.88 | 1.21 | 0.84 | 0.65 | 1.37 | 0.63 |
time (sec) |
N/A | 0.168 | 0.009 | 0.125 | 0.101 | 0.058 | 0.058 | 0.114 | 0.153 | 0.022 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 90 | 96 | 88 | 103 | 0 | 448 | 323 | 92 | 18 | 159 |
N.S. |
1 | 1.07 | 0.98 | 1.14 | 0.00 | 4.98 | 3.59 | 1.02 | 0.20 | 1.77 |
time (sec) |
N/A | 0.229 | 0.051 | 0.336 | 0.000 | 0.072 | 0.489 | 0.123 | 0.147 | 0.165 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
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 | 42 | 38 | 35 | 33 | 50 | 31 | 33 | 79 | 41 |
N.S. |
1 | 1.11 | 1.00 | 0.92 | 0.87 | 1.32 | 0.82 | 0.87 | 2.08 | 1.08 |
time (sec) |
N/A | 0.216 | 0.011 | 0.190 | 0.101 | 0.057 | 0.054 | 0.121 | 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 | 57 | 65 | 49 | 47 | 42 | 58 | 53 | 43 | 82 | 60 |
N.S. |
1 | 1.14 | 0.86 | 0.82 | 0.74 | 1.02 | 0.93 | 0.75 | 1.44 | 1.05 |
time (sec) |
N/A | 0.206 | 0.016 | 0.112 | 0.101 | 0.063 | 0.068 | 0.116 | 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 | 36 | 44 | 33 | 29 | 31 | 40 | 32 | 28 | 48 | 29 |
N.S. |
1 | 1.22 | 0.92 | 0.81 | 0.86 | 1.11 | 0.89 | 0.78 | 1.33 | 0.81 |
time (sec) |
N/A | 0.178 | 0.011 | 0.122 | 0.102 | 0.059 | 0.056 | 0.125 | 0.152 | 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 | 49 | 55 | 78 | 39 | 40 | 40 | 46 | 40 | 56 | 52 |
N.S. |
1 | 1.12 | 1.59 | 0.80 | 0.82 | 0.82 | 0.94 | 0.82 | 1.14 | 1.06 |
time (sec) |
N/A | 0.211 | 0.010 | 0.121 | 0.103 | 0.062 | 0.059 | 0.118 | 0.148 | 0.058 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 13 | 39 | 13 | 14 | 14 | 13 | 14 | 0 | 13 | 14 |
N.S. |
1 | 3.00 | 1.00 | 1.08 | 1.08 | 1.00 | 1.08 | 0.00 | 1.00 | 1.08 |
time (sec) |
N/A | 0.212 | 0.018 | 0.175 | 0.028 | 0.064 | 0.755 | 0.000 | 0.154 | 0.192 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
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 | 48 | 38 | 35 | 34 | 34 | 42 | 34 | 120 | 34 |
N.S. |
1 | 1.17 | 0.93 | 0.85 | 0.83 | 0.83 | 1.02 | 0.83 | 2.93 | 0.83 |
time (sec) |
N/A | 0.198 | 0.009 | 0.043 | 0.103 | 0.058 | 0.046 | 0.261 | 0.151 | 0.123 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
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 | 36 | 32 | 25 | 24 | 24 | 24 | 25 | 28 | 22 |
N.S. |
1 | 1.12 | 1.00 | 0.78 | 0.75 | 0.75 | 0.75 | 0.78 | 0.88 | 0.69 |
time (sec) |
N/A | 0.179 | 0.005 | 0.045 | 0.024 | 0.059 | 0.049 | 0.124 | 0.145 | 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 | 25 | 29 | 25 | 18 | 17 | 17 | 15 | 19 | 43 | 16 |
N.S. |
1 | 1.16 | 1.00 | 0.72 | 0.68 | 0.68 | 0.60 | 0.76 | 1.72 | 0.64 |
time (sec) |
N/A | 0.177 | 0.004 | 0.038 | 0.027 | 0.060 | 0.049 | 0.112 | 0.149 | 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 | 36 | 36 | 24 | 22 | 32 | 46 | 29 | 23 | 59 | 22 |
N.S. |
1 | 1.00 | 0.67 | 0.61 | 0.89 | 1.28 | 0.81 | 0.64 | 1.64 | 0.61 |
time (sec) |
N/A | 0.186 | 0.009 | 0.080 | 0.029 | 0.056 | 0.043 | 0.124 | 0.145 | 0.104 |
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 | 45 | 45 | 24 | 22 | 72 | 72 | 70 | 22 | 73 | 29 |
N.S. |
1 | 1.00 | 0.53 | 0.49 | 1.60 | 1.60 | 1.56 | 0.49 | 1.62 | 0.64 |
time (sec) |
N/A | 0.164 | 0.005 | 0.108 | 0.028 | 0.053 | 0.059 | 0.121 | 0.146 | 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 | 55 | 55 | 41 | 34 | 48 | 67 | 42 | 55 | 88 | 43 |
N.S. |
1 | 1.00 | 0.75 | 0.62 | 0.87 | 1.22 | 0.76 | 1.00 | 1.60 | 0.78 |
time (sec) |
N/A | 0.226 | 0.009 | 0.090 | 0.029 | 0.056 | 0.051 | 0.120 | 0.144 | 0.110 |
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 | 36 | 36 | 38 | 35 | 38 | 59 | 41 | 43 | 90 | 31 |
N.S. |
1 | 1.00 | 1.06 | 0.97 | 1.06 | 1.64 | 1.14 | 1.19 | 2.50 | 0.86 |
time (sec) |
N/A | 0.162 | 0.016 | 0.086 | 0.030 | 0.058 | 0.056 | 0.125 | 0.144 | 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 | 35 | 35 | 31 | 28 | 31 | 48 | 29 | 40 | 51 | 34 |
N.S. |
1 | 1.00 | 0.89 | 0.80 | 0.89 | 1.37 | 0.83 | 1.14 | 1.46 | 0.97 |
time (sec) |
N/A | 0.159 | 0.012 | 0.120 | 0.027 | 0.057 | 0.050 | 0.122 | 0.148 | 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 | 61 | 59 | 46 | 40 | 50 | 85 | 51 | 42 | 118 | 45 |
N.S. |
1 | 0.97 | 0.75 | 0.66 | 0.82 | 1.39 | 0.84 | 0.69 | 1.93 | 0.74 |
time (sec) |
N/A | 0.188 | 0.016 | 0.125 | 0.028 | 0.058 | 0.066 | 0.117 | 0.150 | 0.160 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 51 | 58 | 36 | 36 | 44 | 62 | 42 | 34 | 88 | 39 |
N.S. |
1 | 1.14 | 0.71 | 0.71 | 0.86 | 1.22 | 0.82 | 0.67 | 1.73 | 0.76 |
time (sec) |
N/A | 0.179 | 0.012 | 0.355 | 0.101 | 0.056 | 0.066 | 0.117 | 0.145 | 0.035 |
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 | 54 | 54 | 54 | 45 | 60 | 105 | 58 | 47 | 146 | 55 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 1.11 | 1.94 | 1.07 | 0.87 | 2.70 | 1.02 |
time (sec) |
N/A | 0.182 | 0.011 | 0.108 | 0.025 | 0.057 | 0.072 | 0.119 | 0.143 | 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 | 36 | 47 | 53 | 32 | 40 | 53 | 49 | 48 | 70 | 33 |
N.S. |
1 | 1.31 | 1.47 | 0.89 | 1.11 | 1.47 | 1.36 | 1.33 | 1.94 | 0.92 |
time (sec) |
N/A | 0.169 | 0.024 | 0.105 | 0.103 | 0.058 | 0.036 | 0.119 | 0.144 | 0.143 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 67 | 40 | 31 | 41 | 59 | 39 | 31 | 72 | 40 |
N.S. |
1 | 1.16 | 0.69 | 0.53 | 0.71 | 1.02 | 0.67 | 0.53 | 1.24 | 0.69 |
time (sec) |
N/A | 0.166 | 0.013 | 0.110 | 0.103 | 0.061 | 0.052 | 0.118 | 0.143 | 0.040 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
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 | 46 | 43 | 34 | 36 | 45 | 42 | 36 | 69 | 36 |
N.S. |
1 | 1.07 | 1.00 | 0.79 | 0.84 | 1.05 | 0.98 | 0.84 | 1.60 | 0.84 |
time (sec) |
N/A | 0.167 | 0.022 | 0.451 | 0.106 | 0.057 | 0.062 | 0.123 | 0.143 | 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 | 43 | 69 | 62 | 37 | 47 | 68 | 58 | 51 | 106 | 34 |
N.S. |
1 | 1.60 | 1.44 | 0.86 | 1.09 | 1.58 | 1.35 | 1.19 | 2.47 | 0.79 |
time (sec) |
N/A | 0.215 | 0.025 | 0.171 | 0.103 | 0.061 | 0.060 | 0.119 | 0.145 | 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 | 37 | 46 | 25 | 27 | 30 | 38 | 24 | 40 | 120 | 32 |
N.S. |
1 | 1.24 | 0.68 | 0.73 | 0.81 | 1.03 | 0.65 | 1.08 | 3.24 | 0.86 |
time (sec) |
N/A | 0.155 | 0.008 | 0.131 | 0.099 | 0.058 | 0.059 | 0.123 | 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 | 32 | 43 | 26 | 29 | 28 | 38 | 26 | 32 | 138 | 28 |
N.S. |
1 | 1.34 | 0.81 | 0.91 | 0.88 | 1.19 | 0.81 | 1.00 | 4.31 | 0.88 |
time (sec) |
N/A | 0.177 | 0.010 | 0.080 | 0.023 | 0.057 | 0.053 | 0.211 | 0.154 | 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 | 13 | 13 | 13 | 12 | 11 | 19 | 20 | 11 | 23 | 11 |
N.S. |
1 | 1.00 | 1.00 | 0.92 | 0.85 | 1.46 | 1.54 | 0.85 | 1.77 | 0.85 |
time (sec) |
N/A | 0.130 | 0.003 | 0.107 | 0.024 | 0.056 | 0.111 | 0.126 | 0.150 | 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 | 54 | 55 | 46 | 45 | 57 | 81 | 51 | 56 | 174 | 52 |
N.S. |
1 | 1.02 | 0.85 | 0.83 | 1.06 | 1.50 | 0.94 | 1.04 | 3.22 | 0.96 |
time (sec) |
N/A | 0.182 | 0.018 | 0.119 | 0.023 | 0.065 | 0.215 | 0.126 | 0.144 | 0.058 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 157 | 182 | 134 | 75 | 147 | 188 | 66 | 150 | 328 | 76 |
N.S. |
1 | 1.16 | 0.85 | 0.48 | 0.94 | 1.20 | 0.42 | 0.96 | 2.09 | 0.48 |
time (sec) |
N/A | 0.367 | 0.071 | 0.120 | 0.106 | 0.070 | 0.197 | 0.129 | 0.157 | 0.064 |
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 | 64 | 80 | 75 | 53 | 60 | 78 | 78 | 50 | 191 | 53 |
N.S. |
1 | 1.25 | 1.17 | 0.83 | 0.94 | 1.22 | 1.22 | 0.78 | 2.98 | 0.83 |
time (sec) |
N/A | 0.181 | 0.032 | 0.148 | 0.105 | 0.062 | 0.204 | 0.124 | 0.156 | 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 | 39 | 43 | 33 | 29 | 34 | 45 | 27 | 30 | 58 | 29 |
N.S. |
1 | 1.10 | 0.85 | 0.74 | 0.87 | 1.15 | 0.69 | 0.77 | 1.49 | 0.74 |
time (sec) |
N/A | 0.165 | 0.011 | 0.079 | 0.022 | 0.066 | 0.068 | 0.150 | 0.154 | 0.027 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 319 | 347 | 293 | 47 | 335 | 324 | 37 | 250 | 25 | 285 |
N.S. |
1 | 1.09 | 0.92 | 0.15 | 1.05 | 1.02 | 0.12 | 0.78 | 0.08 | 0.89 |
time (sec) |
N/A | 0.577 | 0.205 | 0.173 | 0.109 | 0.080 | 0.110 | 0.383 | 0.153 | 0.911 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 59 | 75 | 65 | 39 | 56 | 73 | 58 | 55 | 117 | 41 |
N.S. |
1 | 1.27 | 1.10 | 0.66 | 0.95 | 1.24 | 0.98 | 0.93 | 1.98 | 0.69 |
time (sec) |
N/A | 0.169 | 0.049 | 0.104 | 0.102 | 0.058 | 0.068 | 0.123 | 0.145 | 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 | 36 | 44 | 33 | 29 | 31 | 40 | 32 | 28 | 48 | 29 |
N.S. |
1 | 1.22 | 0.92 | 0.81 | 0.86 | 1.11 | 0.89 | 0.78 | 1.33 | 0.81 |
time (sec) |
N/A | 0.194 | 0.008 | 0.138 | 0.102 | 0.058 | 0.054 | 0.122 | 0.151 | 0.001 |
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 | 38 | 38 | 32 | 31 | 38 | 65 | 36 | 35 | 90 | 33 |
N.S. |
1 | 1.00 | 0.84 | 0.82 | 1.00 | 1.71 | 0.95 | 0.92 | 2.37 | 0.87 |
time (sec) |
N/A | 0.230 | 0.015 | 0.044 | 0.023 | 0.060 | 0.054 | 0.123 | 0.151 | 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 | 64 | 69 | 65 | 50 | 50 | 73 | 60 | 60 | 105 | 63 |
N.S. |
1 | 1.08 | 1.02 | 0.78 | 0.78 | 1.14 | 0.94 | 0.94 | 1.64 | 0.98 |
time (sec) |
N/A | 0.273 | 0.020 | 0.112 | 0.103 | 0.066 | 0.102 | 0.117 | 0.156 | 0.064 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
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 | 66 | 63 | 54 | 59 | 97 | 68 | 72 | 169 | 73 |
N.S. |
1 | 1.05 | 1.00 | 0.86 | 0.94 | 1.54 | 1.08 | 1.14 | 2.68 | 1.16 |
time (sec) |
N/A | 0.288 | 0.025 | 0.242 | 0.103 | 0.063 | 0.082 | 0.125 | 0.149 | 0.144 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 43 | 43 | 46 | 32 | 36 | 55 | 34 | 33 | 76 | 25 |
N.S. |
1 | 1.00 | 1.07 | 0.74 | 0.84 | 1.28 | 0.79 | 0.77 | 1.77 | 0.58 |
time (sec) |
N/A | 0.169 | 0.012 | 0.110 | 0.024 | 0.058 | 0.064 | 0.121 | 0.151 | 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 | 27 | 31 | 20 | 18 | 43 | 43 | 39 | 18 | 42 | 18 |
N.S. |
1 | 1.15 | 0.74 | 0.67 | 1.59 | 1.59 | 1.44 | 0.67 | 1.56 | 0.67 |
time (sec) |
N/A | 0.160 | 0.007 | 0.095 | 0.029 | 0.054 | 0.070 | 0.121 | 0.156 | 0.066 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 46 | 50 | 44 | 34 | 39 | 55 | 36 | 40 | 99 | 34 |
N.S. |
1 | 1.09 | 0.96 | 0.74 | 0.85 | 1.20 | 0.78 | 0.87 | 2.15 | 0.74 |
time (sec) |
N/A | 0.174 | 0.012 | 0.092 | 0.024 | 0.054 | 0.046 | 0.116 | 0.151 | 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 | 44 | 50 | 39 | 35 | 37 | 56 | 34 | 43 | 73 | 33 |
N.S. |
1 | 1.14 | 0.89 | 0.80 | 0.84 | 1.27 | 0.77 | 0.98 | 1.66 | 0.75 |
time (sec) |
N/A | 0.171 | 0.015 | 0.112 | 0.029 | 0.056 | 0.065 | 0.118 | 0.156 | 0.028 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 54 | 54 | 54 | 45 | 60 | 105 | 58 | 47 | 146 | 55 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 1.11 | 1.94 | 1.07 | 0.87 | 2.70 | 1.02 |
time (sec) |
N/A | 0.177 | 0.006 | 0.086 | 0.028 | 0.057 | 0.070 | 0.122 | 0.147 | 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 | 36 | 36 | 36 | 33 | 32 | 39 | 31 | 45 | 43 | 32 |
N.S. |
1 | 1.00 | 1.00 | 0.92 | 0.89 | 1.08 | 0.86 | 1.25 | 1.19 | 0.89 |
time (sec) |
N/A | 0.162 | 0.009 | 0.066 | 0.023 | 0.056 | 0.027 | 0.121 | 0.147 | 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 | 44 | 44 | 41 | 38 | 38 | 38 | 39 | 39 | 39 | 37 |
N.S. |
1 | 1.00 | 0.93 | 0.86 | 0.86 | 0.86 | 0.89 | 0.89 | 0.89 | 0.84 |
time (sec) |
N/A | 0.189 | 0.009 | 0.057 | 0.031 | 0.055 | 0.017 | 0.113 | 0.151 | 0.026 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 96 | 96 | 91 | 89 | 91 | 91 | 100 | 98 | 99 | 88 |
N.S. |
1 | 1.00 | 0.95 | 0.93 | 0.95 | 0.95 | 1.04 | 1.02 | 1.03 | 0.92 |
time (sec) |
N/A | 0.268 | 0.019 | 0.204 | 0.030 | 0.054 | 0.023 | 0.120 | 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 | 167 | 167 | 167 | 165 | 171 | 171 | 189 | 188 | 189 | 164 |
N.S. |
1 | 1.00 | 1.00 | 0.99 | 1.02 | 1.02 | 1.13 | 1.13 | 1.13 | 0.98 |
time (sec) |
N/A | 0.369 | 0.021 | 0.203 | 0.026 | 0.059 | 0.029 | 0.122 | 0.151 | 0.137 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 263 | 263 | 263 | 264 | 273 | 273 | 313 | 307 | 309 | 263 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 1.04 | 1.04 | 1.19 | 1.17 | 1.17 | 1.00 |
time (sec) |
N/A | 0.524 | 0.038 | 0.181 | 0.033 | 0.058 | 0.037 | 0.119 | 0.156 | 0.149 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 159 | 159 | 267 | 0 | 0 | 0 | 0 | 0 | 836 | 0 |
N.S. |
1 | 1.00 | 1.68 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 5.26 | 0.00 |
time (sec) |
N/A | 0.257 | 0.418 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.162 | 0.000 |
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 | 65 | 71 | 66 | 63 | 0 | 203 | 246 | 60 | 117 | 155 |
N.S. |
1 | 1.09 | 1.02 | 0.97 | 0.00 | 3.12 | 3.78 | 0.92 | 1.80 | 2.38 |
time (sec) |
N/A | 0.207 | 0.034 | 0.267 | 0.000 | 0.072 | 0.359 | 0.123 | 0.152 | 0.157 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 89 | 95 | 88 | 103 | 0 | 447 | 323 | 92 | 384 | 159 |
N.S. |
1 | 1.07 | 0.99 | 1.16 | 0.00 | 5.02 | 3.63 | 1.03 | 4.31 | 1.79 |
time (sec) |
N/A | 0.214 | 0.048 | 0.259 | 0.000 | 0.072 | 0.482 | 0.125 | 0.148 | 0.172 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 130 | 143 | 127 | 155 | 0 | 1104 | 622 | 194 | 952 | 360 |
N.S. |
1 | 1.10 | 0.98 | 1.19 | 0.00 | 8.49 | 4.78 | 1.49 | 7.32 | 2.77 |
time (sec) |
N/A | 0.253 | 0.079 | 0.275 | 0.000 | 0.085 | 0.885 | 0.120 | 0.161 | 0.291 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 173 | 191 | 168 | 206 | 0 | 1950 | 1027 | 363 | 1706 | 640 |
N.S. |
1 | 1.10 | 0.97 | 1.19 | 0.00 | 11.27 | 5.94 | 2.10 | 9.86 | 3.70 |
time (sec) |
N/A | 0.288 | 0.119 | 0.267 | 0.000 | 0.111 | 1.442 | 0.122 | 0.155 | 0.399 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 169 | 169 | 264 | 0 | 0 | 0 | 0 | 0 | 41 | 0 |
N.S. |
1 | 1.00 | 1.56 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.24 | 0.00 |
time (sec) |
N/A | 0.253 | 0.513 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.157 | 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 | 49 | 51 | 44 | 31 | 41 | 52 | 46 | 46 | 49 | 36 |
N.S. |
1 | 1.04 | 0.90 | 0.63 | 0.84 | 1.06 | 0.94 | 0.94 | 1.00 | 0.73 |
time (sec) |
N/A | 0.194 | 0.016 | 0.132 | 0.106 | 0.060 | 0.039 | 0.118 | 0.154 | 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 | 61 | 93 | 70 | 56 | 67 | 97 | 76 | 61 | 188 | 53 |
N.S. |
1 | 1.52 | 1.15 | 0.92 | 1.10 | 1.59 | 1.25 | 1.00 | 3.08 | 0.87 |
time (sec) |
N/A | 0.228 | 0.031 | 0.128 | 0.105 | 0.062 | 0.066 | 0.122 | 0.144 | 0.123 |