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 | F(-2) | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 78 | 80 | 67 | 39 | 0 | 39 | 51 | 53 | 13 | 49 |
N.S. |
1 | 1.03 | 0.86 | 0.50 | 0.00 | 0.50 | 0.65 | 0.68 | 0.17 | 0.63 |
time (sec) |
N/A | 0.250 | 0.054 | 19.886 | 0.000 | 0.077 | 0.101 | 0.126 | 0.186 | 0.856 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 31 | 51 | 31 | 0 | 26 | 37 | 71 | 13 | 59 |
N.S. |
1 | 1.07 | 1.76 | 1.07 | 0.00 | 0.90 | 1.28 | 2.45 | 0.45 | 2.03 |
time (sec) |
N/A | 0.390 | 0.036 | 5.505 | 0.000 | 0.074 | 0.096 | 0.126 | 0.214 | 1.020 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 50 | 52 | 39 | 19 | 0 | 25 | 31 | 41 | 13 | 35 |
N.S. |
1 | 1.04 | 0.78 | 0.38 | 0.00 | 0.50 | 0.62 | 0.82 | 0.26 | 0.70 |
time (sec) |
N/A | 0.239 | 0.061 | 3.025 | 0.000 | 0.071 | 0.093 | 0.125 | 0.157 | 0.791 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 23 | 33 | 18 | 0 | 14 | 17 | 33 | 11 | 39 |
N.S. |
1 | 1.21 | 1.74 | 0.95 | 0.00 | 0.74 | 0.89 | 1.74 | 0.58 | 2.05 |
time (sec) |
N/A | 0.342 | 0.014 | 1.474 | 0.000 | 0.074 | 0.073 | 0.132 | 0.154 | 0.847 |
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 | 16 | 18 | 31 | 21 | 28 | 25 | 0 | 20 | 11 | 20 |
N.S. |
1 | 1.12 | 1.94 | 1.31 | 1.75 | 1.56 | 0.00 | 1.25 | 0.69 | 1.25 |
time (sec) |
N/A | 0.330 | 0.025 | 1.427 | 0.043 | 0.087 | 0.000 | 0.129 | 0.156 | 0.870 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 19 | 15 | 20 | 17 | 25 | 0 | 18 | 13 | 19 |
N.S. |
1 | 1.06 | 0.83 | 1.11 | 0.94 | 1.39 | 0.00 | 1.00 | 0.72 | 1.06 |
time (sec) |
N/A | 0.214 | 0.026 | 2.800 | 0.031 | 0.072 | 0.000 | 0.127 | 0.158 | 0.794 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | F | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 26 | 75 | 42 | 59 | 73 | 0 | 46 | 13 | 41 |
N.S. |
1 | 1.08 | 3.12 | 1.75 | 2.46 | 3.04 | 0.00 | 1.92 | 0.54 | 1.71 |
time (sec) |
N/A | 0.386 | 0.028 | 5.879 | 0.037 | 0.080 | 0.000 | 0.133 | 0.185 | 0.867 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 29 | 15 | 12 | 36 | 0 | 12 | 13 | 13 |
N.S. |
1 | 1.00 | 1.53 | 0.79 | 0.63 | 1.89 | 0.00 | 0.63 | 0.68 | 0.68 |
time (sec) |
N/A | 0.223 | 0.028 | 7.690 | 0.041 | 0.069 | 0.000 | 0.121 | 0.164 | 0.790 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | B | B | F | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 40 | 40 | 139 | 58 | 83 | 123 | 0 | 62 | 13 | 57 |
N.S. |
1 | 1.00 | 3.48 | 1.45 | 2.08 | 3.08 | 0.00 | 1.55 | 0.32 | 1.42 |
time (sec) |
N/A | 0.412 | 0.028 | 164.334 | 0.047 | 0.085 | 0.000 | 0.129 | 0.159 | 0.848 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 37 | 37 | 41 | 28 | 24 | 54 | 0 | 24 | 13 | 27 |
N.S. |
1 | 1.00 | 1.11 | 0.76 | 0.65 | 1.46 | 0.00 | 0.65 | 0.35 | 0.73 |
time (sec) |
N/A | 0.232 | 0.029 | 0.342 | 0.035 | 0.078 | 0.000 | 0.121 | 0.155 | 0.749 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 101 | 101 | 103 | 80 | 91 | 97 | 0 | 10412 | 113 | 121 |
N.S. |
1 | 1.00 | 1.02 | 0.79 | 0.90 | 0.96 | 0.00 | 103.09 | 1.12 | 1.20 |
time (sec) |
N/A | 0.300 | 0.062 | 5.517 | 0.030 | 0.095 | 0.000 | 1.536 | 0.156 | 0.930 |
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 | 79 | 95 | 82 | 73 | 87 | 74 | 0 | 81 | 116 | 155 |
N.S. |
1 | 1.20 | 1.04 | 0.92 | 1.10 | 0.94 | 0.00 | 1.03 | 1.47 | 1.96 |
time (sec) |
N/A | 0.353 | 0.087 | 2.877 | 0.109 | 0.095 | 0.000 | 0.149 | 0.158 | 0.825 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 69 | 69 | 71 | 60 | 70 | 74 | 0 | 4486 | 85 | 87 |
N.S. |
1 | 1.00 | 1.03 | 0.87 | 1.01 | 1.07 | 0.00 | 65.01 | 1.23 | 1.26 |
time (sec) |
N/A | 0.266 | 0.051 | 1.939 | 0.051 | 0.091 | 0.000 | 0.761 | 0.184 | 0.853 |
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 | 46 | 59 | 56 | 52 | 52 | 47 | 0 | 58 | 86 | 50 |
N.S. |
1 | 1.28 | 1.22 | 1.13 | 1.13 | 1.02 | 0.00 | 1.26 | 1.87 | 1.09 |
time (sec) |
N/A | 0.271 | 0.064 | 0.909 | 0.133 | 0.106 | 0.000 | 0.142 | 0.204 | 0.812 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 37 | 37 | 48 | 40 | 46 | 49 | 0 | 1020 | 53 | 53 |
N.S. |
1 | 1.00 | 1.30 | 1.08 | 1.24 | 1.32 | 0.00 | 27.57 | 1.43 | 1.43 |
time (sec) |
N/A | 0.230 | 0.029 | 0.730 | 0.035 | 0.095 | 0.000 | 0.233 | 0.224 | 0.892 |
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 | 26 | 26 | 26 | 40 | 46 | 58 | 0 | 49 | 46 | 86 |
N.S. |
1 | 1.00 | 1.00 | 1.54 | 1.77 | 2.23 | 0.00 | 1.88 | 1.77 | 3.31 |
time (sec) |
N/A | 0.218 | 0.012 | 0.807 | 0.039 | 0.098 | 0.000 | 0.157 | 0.210 | 0.866 |
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 | 25 | 23 | 38 | 26 | 25 | 62 | 0 | 26 | 82 | 25 |
N.S. |
1 | 0.92 | 1.52 | 1.04 | 1.00 | 2.48 | 0.00 | 1.04 | 3.28 | 1.00 |
time (sec) |
N/A | 0.255 | 0.057 | 0.737 | 0.040 | 0.085 | 0.000 | 0.149 | 0.181 | 0.783 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 60 | 60 | 107 | 68 | 83 | 142 | 0 | 118 | 98 | 149 |
N.S. |
1 | 1.00 | 1.78 | 1.13 | 1.38 | 2.37 | 0.00 | 1.97 | 1.63 | 2.48 |
time (sec) |
N/A | 0.272 | 0.054 | 2.127 | 0.031 | 0.114 | 0.000 | 0.181 | 0.152 | 0.884 |
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 | 57 | 49 | 78 | 46 | 50 | 122 | 0 | 51 | 127 | 49 |
N.S. |
1 | 0.86 | 1.37 | 0.81 | 0.88 | 2.14 | 0.00 | 0.89 | 2.23 | 0.86 |
time (sec) |
N/A | 0.278 | 0.050 | 3.215 | 0.034 | 0.113 | 0.000 | 0.161 | 0.154 | 0.822 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 98 | 98 | 151 | 90 | 123 | 213 | 0 | 177 | 127 | 211 |
N.S. |
1 | 1.00 | 1.54 | 0.92 | 1.26 | 2.17 | 0.00 | 1.81 | 1.30 | 2.15 |
time (sec) |
N/A | 0.331 | 0.053 | 5.382 | 0.039 | 0.110 | 0.000 | 0.196 | 0.180 | 0.931 |
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 | 87 | 73 | 116 | 66 | 72 | 174 | 0 | 73 | 155 | 70 |
N.S. |
1 | 0.84 | 1.33 | 0.76 | 0.83 | 2.00 | 0.00 | 0.84 | 1.78 | 0.80 |
time (sec) |
N/A | 0.296 | 0.056 | 9.488 | 0.034 | 0.096 | 0.000 | 0.181 | 0.171 | 0.974 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 122 | 171 | 250 | 140 | 128 | 137 | 0 | 124 | 241 | 127 |
N.S. |
1 | 1.40 | 2.05 | 1.15 | 1.05 | 1.12 | 0.00 | 1.02 | 1.98 | 1.04 |
time (sec) |
N/A | 0.463 | 1.943 | 3.464 | 0.115 | 0.101 | 0.000 | 0.198 | 0.207 | 0.853 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 122 | 122 | 152 | 113 | 104 | 126 | 0 | 32694 | 174 | 174 |
N.S. |
1 | 1.00 | 1.25 | 0.93 | 0.85 | 1.03 | 0.00 | 267.98 | 1.43 | 1.43 |
time (sec) |
N/A | 0.353 | 1.039 | 2.870 | 0.039 | 0.122 | 0.000 | 14.654 | 0.203 | 3.897 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 76 | 101 | 162 | 109 | 82 | 101 | 0 | 89 | 195 | 75 |
N.S. |
1 | 1.33 | 2.13 | 1.43 | 1.08 | 1.33 | 0.00 | 1.17 | 2.57 | 0.99 |
time (sec) |
N/A | 0.301 | 1.690 | 1.793 | 0.122 | 0.111 | 0.000 | 0.179 | 0.213 | 0.818 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 68 | 68 | 111 | 83 | 67 | 90 | 0 | 2405 | 129 | 93 |
N.S. |
1 | 1.00 | 1.63 | 1.22 | 0.99 | 1.32 | 0.00 | 35.37 | 1.90 | 1.37 |
time (sec) |
N/A | 0.281 | 0.523 | 1.588 | 0.038 | 0.121 | 0.000 | 0.731 | 0.218 | 1.193 |
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 | 43 | 43 | 43 | 56 | 60 | 102 | 0 | 74 | 91 | 125 |
N.S. |
1 | 1.00 | 1.00 | 1.30 | 1.40 | 2.37 | 0.00 | 1.72 | 2.12 | 2.91 |
time (sec) |
N/A | 0.257 | 0.025 | 0.856 | 0.036 | 0.116 | 0.000 | 0.208 | 0.210 | 0.912 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 42 | 40 | 91 | 38 | 39 | 96 | 0 | 40 | 132 | 44 |
N.S. |
1 | 0.95 | 2.17 | 0.90 | 0.93 | 2.29 | 0.00 | 0.95 | 3.14 | 1.05 |
time (sec) |
N/A | 0.239 | 0.945 | 2.709 | 0.036 | 0.092 | 0.000 | 0.163 | 0.188 | 0.810 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 95 | 95 | 250 | 101 | 122 | 230 | 0 | 172 | 225 | 292 |
N.S. |
1 | 1.00 | 2.63 | 1.06 | 1.28 | 2.42 | 0.00 | 1.81 | 2.37 | 3.07 |
time (sec) |
N/A | 0.325 | 1.622 | 3.325 | 0.038 | 0.116 | 0.000 | 0.237 | 0.216 | 0.923 |
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 | 79 | 73 | 127 | 80 | 69 | 174 | 0 | 70 | 201 | 72 |
N.S. |
1 | 0.92 | 1.61 | 1.01 | 0.87 | 2.20 | 0.00 | 0.89 | 2.54 | 0.91 |
time (sec) |
N/A | 0.270 | 1.737 | 5.984 | 0.034 | 0.095 | 0.000 | 0.186 | 0.198 | 0.812 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 165 | 165 | 994 | 145 | 187 | 333 | 0 | 269 | 269 | 378 |
N.S. |
1 | 1.00 | 6.02 | 0.88 | 1.13 | 2.02 | 0.00 | 1.63 | 1.63 | 2.29 |
time (sec) |
N/A | 0.396 | 6.684 | 9.386 | 0.042 | 0.122 | 0.000 | 0.255 | 0.153 | 0.929 |
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 | 122 | 112 | 114 | 119 | 104 | 240 | 0 | 105 | 245 | 107 |
N.S. |
1 | 0.92 | 0.93 | 0.98 | 0.85 | 1.97 | 0.00 | 0.86 | 2.01 | 0.88 |
time (sec) |
N/A | 0.308 | 1.746 | 17.295 | 0.041 | 0.099 | 0.000 | 0.204 | 0.160 | 1.105 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 205 | 205 | 289 | 184 | 173 | 188 | 0 | 66584 | 406 | 291 |
N.S. |
1 | 1.00 | 1.41 | 0.90 | 0.84 | 0.92 | 0.00 | 324.80 | 1.98 | 1.42 |
time (sec) |
N/A | 0.460 | 5.564 | 4.288 | 0.042 | 0.104 | 0.000 | 117.946 | 0.166 | 3.686 |
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 | 103 | 125 | 203 | 163 | 113 | 149 | 0 | 128 | 496 | 151 |
N.S. |
1 | 1.21 | 1.97 | 1.58 | 1.10 | 1.45 | 0.00 | 1.24 | 4.82 | 1.47 |
time (sec) |
N/A | 0.320 | 2.976 | 2.722 | 0.135 | 0.097 | 0.000 | 0.221 | 0.166 | 0.836 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 133 | 133 | 241 | 144 | 128 | 144 | 0 | 12476 | 340 | 193 |
N.S. |
1 | 1.00 | 1.81 | 1.08 | 0.96 | 1.08 | 0.00 | 93.80 | 2.56 | 1.45 |
time (sec) |
N/A | 0.358 | 3.627 | 2.254 | 0.060 | 0.106 | 0.000 | 7.554 | 0.207 | 3.125 |
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 | 86 | 86 | 86 | 107 | 111 | 148 | 0 | 144 | 269 | 278 |
N.S. |
1 | 1.00 | 1.00 | 1.24 | 1.29 | 1.72 | 0.00 | 1.67 | 3.13 | 3.23 |
time (sec) |
N/A | 0.303 | 0.057 | 0.882 | 0.036 | 0.119 | 0.000 | 0.267 | 0.197 | 1.328 |
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 | 64 | 59 | 126 | 55 | 56 | 127 | 0 | 57 | 235 | 62 |
N.S. |
1 | 0.92 | 1.97 | 0.86 | 0.88 | 1.98 | 0.00 | 0.89 | 3.67 | 0.97 |
time (sec) |
N/A | 0.251 | 1.641 | 3.612 | 0.032 | 0.111 | 0.000 | 0.202 | 0.231 | 0.811 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 141 | 141 | 897 | 140 | 171 | 299 | 0 | 304 | 466 | 581 |
N.S. |
1 | 1.00 | 6.36 | 0.99 | 1.21 | 2.12 | 0.00 | 2.16 | 3.30 | 4.12 |
time (sec) |
N/A | 0.369 | 6.831 | 5.871 | 0.048 | 0.158 | 0.000 | 0.279 | 0.204 | 1.095 |
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 | 113 | 104 | 212 | 106 | 98 | 237 | 0 | 99 | 452 | 103 |
N.S. |
1 | 0.92 | 1.88 | 0.94 | 0.87 | 2.10 | 0.00 | 0.88 | 4.00 | 0.91 |
time (sec) |
N/A | 0.300 | 2.607 | 10.041 | 0.050 | 0.100 | 0.000 | 0.209 | 0.219 | 0.790 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 229 | 229 | 1229 | 198 | 250 | 427 | 0 | 373 | 533 | 698 |
N.S. |
1 | 1.00 | 5.37 | 0.86 | 1.09 | 1.86 | 0.00 | 1.63 | 2.33 | 3.05 |
time (sec) |
N/A | 0.465 | 7.010 | 16.484 | 0.047 | 0.178 | 0.000 | 0.308 | 0.207 | 1.112 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 167 | 154 | 515 | 165 | 142 | 343 | 0 | 143 | 545 | 146 |
N.S. |
1 | 0.92 | 3.08 | 0.99 | 0.85 | 2.05 | 0.00 | 0.86 | 3.26 | 0.87 |
time (sec) |
N/A | 0.341 | 2.148 | 28.849 | 0.032 | 0.106 | 0.000 | 0.222 | 0.207 | 0.932 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | A | F | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 275 | 275 | 1017 | 267 | 218 | 224 | 0 | 0 | 591 | 319 |
N.S. |
1 | 1.00 | 3.70 | 0.97 | 0.79 | 0.81 | 0.00 | 0.00 | 2.15 | 1.16 |
time (sec) |
N/A | 0.550 | 7.174 | 8.026 | 0.043 | 0.102 | 0.000 | 0.000 | 0.223 | 4.529 |
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 | 139 | 157 | 263 | 250 | 154 | 186 | 0 | 178 | 780 | 161 |
N.S. |
1 | 1.13 | 1.89 | 1.80 | 1.11 | 1.34 | 0.00 | 1.28 | 5.61 | 1.16 |
time (sec) |
N/A | 0.346 | 6.192 | 5.326 | 0.127 | 0.126 | 0.000 | 0.274 | 0.155 | 0.904 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 180 | 180 | 383 | 217 | 166 | 176 | 0 | 19074 | 354 | 268 |
N.S. |
1 | 1.00 | 2.13 | 1.21 | 0.92 | 0.98 | 0.00 | 105.97 | 1.97 | 1.49 |
time (sec) |
N/A | 0.411 | 4.046 | 4.220 | 0.040 | 0.107 | 0.000 | 8.112 | 0.154 | 4.448 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 118 | 118 | 352 | 170 | 139 | 175 | 0 | 193 | 426 | 496 |
N.S. |
1 | 1.00 | 2.98 | 1.44 | 1.18 | 1.48 | 0.00 | 1.64 | 3.61 | 4.20 |
time (sec) |
N/A | 0.342 | 4.690 | 1.683 | 0.060 | 0.126 | 0.000 | 0.341 | 0.155 | 1.357 |
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 | 83 | 75 | 162 | 79 | 72 | 159 | 0 | 73 | 312 | 81 |
N.S. |
1 | 0.90 | 1.95 | 0.95 | 0.87 | 1.92 | 0.00 | 0.88 | 3.76 | 0.98 |
time (sec) |
N/A | 0.257 | 2.235 | 5.641 | 0.037 | 0.097 | 0.000 | 0.227 | 0.178 | 0.775 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 161 | 161 | 1128 | 157 | 188 | 346 | 0 | 300 | 666 | 670 |
N.S. |
1 | 1.00 | 7.01 | 0.98 | 1.17 | 2.15 | 0.00 | 1.86 | 4.14 | 4.16 |
time (sec) |
N/A | 0.400 | 7.289 | 9.934 | 0.043 | 0.159 | 0.000 | 0.382 | 0.208 | 1.203 |
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 | 137 | 125 | 188 | 133 | 120 | 267 | 0 | 126 | 593 | 132 |
N.S. |
1 | 0.91 | 1.37 | 0.97 | 0.88 | 1.95 | 0.00 | 0.92 | 4.33 | 0.96 |
time (sec) |
N/A | 0.318 | 3.820 | 17.823 | 0.040 | 0.125 | 0.000 | 0.255 | 0.216 | 0.808 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | B | F | A | B | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 274 | 274 | 1491 | 241 | 304 | 547 | 0 | 479 | 806 | 857 |
N.S. |
1 | 1.00 | 5.44 | 0.88 | 1.11 | 2.00 | 0.00 | 1.75 | 2.94 | 3.13 |
time (sec) |
N/A | 0.529 | 7.199 | 26.997 | 0.044 | 0.219 | 0.000 | 0.395 | 0.159 | 1.243 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 194 | 178 | 233 | 218 | 171 | 386 | 0 | 177 | 708 | 181 |
N.S. |
1 | 0.92 | 1.20 | 1.12 | 0.88 | 1.99 | 0.00 | 0.91 | 3.65 | 0.93 |
time (sec) |
N/A | 0.389 | 4.101 | 40.719 | 0.039 | 0.108 | 0.000 | 0.272 | 0.175 | 0.959 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 402 | 402 | 660 | 327 | 387 | 697 | 0 | 647 | 888 | 990 |
N.S. |
1 | 1.00 | 1.64 | 0.81 | 0.96 | 1.73 | 0.00 | 1.61 | 2.21 | 2.46 |
time (sec) |
N/A | 0.635 | 7.810 | 80.345 | 0.046 | 0.242 | 0.000 | 0.426 | 0.186 | 1.235 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 274 | 251 | 289 | 358 | 658 | 370 | 0 | 464 | 456 | 683 |
N.S. |
1 | 0.92 | 1.05 | 1.31 | 2.40 | 1.35 | 0.00 | 1.69 | 1.66 | 2.49 |
time (sec) |
N/A | 1.283 | 3.367 | 16.872 | 0.139 | 0.119 | 0.000 | 0.230 | 0.174 | 4.071 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 168 | 166 | 139 | 202 | 364 | 261 | 0 | 241 | 258 | 324 |
N.S. |
1 | 0.99 | 0.83 | 1.20 | 2.17 | 1.55 | 0.00 | 1.43 | 1.54 | 1.93 |
time (sec) |
N/A | 0.874 | 0.921 | 3.984 | 0.143 | 0.107 | 0.000 | 0.219 | 0.212 | 3.818 |
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 | 90 | 90 | 79 | 101 | 141 | 185 | 0 | 118 | 116 | 110 |
N.S. |
1 | 1.00 | 0.88 | 1.12 | 1.57 | 2.06 | 0.00 | 1.31 | 1.29 | 1.22 |
time (sec) |
N/A | 0.511 | 0.357 | 1.304 | 0.113 | 0.110 | 0.000 | 0.213 | 0.218 | 0.968 |
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 | 66 | 66 | 75 | 63 | 107 | 183 | 0 | 94 | 86 | 174 |
N.S. |
1 | 1.00 | 1.14 | 0.95 | 1.62 | 2.77 | 0.00 | 1.42 | 1.30 | 2.64 |
time (sec) |
N/A | 0.388 | 0.259 | 1.075 | 0.119 | 0.116 | 0.000 | 0.206 | 0.224 | 1.065 |
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 | 122 | 122 | 179 | 140 | 215 | 270 | 0 | 209 | 132 | 764 |
N.S. |
1 | 1.00 | 1.47 | 1.15 | 1.76 | 2.21 | 0.00 | 1.71 | 1.08 | 6.26 |
time (sec) |
N/A | 0.559 | 1.124 | 1.883 | 0.136 | 0.134 | 0.000 | 0.215 | 0.223 | 1.675 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 158 | 241 | 249 | 208 | 280 | 216 | 0 | 287 | 336 | 313 |
N.S. |
1 | 1.53 | 1.58 | 1.32 | 1.77 | 1.37 | 0.00 | 1.82 | 2.13 | 1.98 |
time (sec) |
N/A | 0.610 | 3.185 | 8.120 | 0.118 | 0.106 | 0.000 | 0.170 | 0.232 | 1.375 |
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 | 94 | 146 | 170 | 122 | 144 | 122 | 0 | 172 | 176 | 147 |
N.S. |
1 | 1.55 | 1.81 | 1.30 | 1.53 | 1.30 | 0.00 | 1.83 | 1.87 | 1.56 |
time (sec) |
N/A | 0.379 | 0.717 | 1.963 | 0.117 | 0.108 | 0.000 | 0.150 | 0.212 | 1.030 |
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 | 50 | 49 | 47 | 48 | 47 | 95 | 0 | 54 | 82 | 39 |
N.S. |
1 | 0.98 | 0.94 | 0.96 | 0.94 | 1.90 | 0.00 | 1.08 | 1.64 | 0.78 |
time (sec) |
N/A | 0.266 | 0.513 | 1.119 | 0.032 | 0.100 | 0.000 | 0.156 | 0.193 | 0.845 |
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 | 108 | 103 | 95 | 96 | 97 | 208 | 0 | 112 | 227 | 102 |
N.S. |
1 | 0.95 | 0.88 | 0.89 | 0.90 | 1.93 | 0.00 | 1.04 | 2.10 | 0.94 |
time (sec) |
N/A | 0.316 | 2.457 | 2.243 | 0.034 | 0.104 | 0.000 | 0.160 | 0.172 | 0.926 |
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 | 169 | 160 | 150 | 165 | 168 | 385 | 0 | 183 | 408 | 167 |
N.S. |
1 | 0.95 | 0.89 | 0.98 | 0.99 | 2.28 | 0.00 | 1.08 | 2.41 | 0.99 |
time (sec) |
N/A | 0.376 | 5.099 | 6.944 | 0.070 | 0.106 | 0.000 | 0.160 | 0.172 | 1.401 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | B | B | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 297 | 405 | 664 | 383 | 799 | 619 | 0 | 575 | 1222 | 757 |
N.S. |
1 | 1.36 | 2.24 | 1.29 | 2.69 | 2.08 | 0.00 | 1.94 | 4.11 | 2.55 |
time (sec) |
N/A | 1.513 | 6.575 | 62.463 | 0.135 | 0.153 | 0.000 | 0.203 | 1.190 | 2.715 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 217 | 304 | 392 | 269 | 507 | 444 | 0 | 413 | 886 | 481 |
N.S. |
1 | 1.40 | 1.81 | 1.24 | 2.34 | 2.05 | 0.00 | 1.90 | 4.08 | 2.22 |
time (sec) |
N/A | 0.985 | 3.730 | 16.891 | 0.127 | 0.135 | 0.000 | 0.195 | 0.291 | 2.039 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 148 | 207 | 246 | 171 | 293 | 292 | 0 | 281 | 620 | 255 |
N.S. |
1 | 1.40 | 1.66 | 1.16 | 1.98 | 1.97 | 0.00 | 1.90 | 4.19 | 1.72 |
time (sec) |
N/A | 0.605 | 3.164 | 4.238 | 0.122 | 0.107 | 0.000 | 0.197 | 0.207 | 1.171 |
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 | 72 | 67 | 109 | 67 | 74 | 293 | 0 | 79 | 235 | 79 |
N.S. |
1 | 0.93 | 1.51 | 0.93 | 1.03 | 4.07 | 0.00 | 1.10 | 3.26 | 1.10 |
time (sec) |
N/A | 0.279 | 0.722 | 1.543 | 0.042 | 0.099 | 0.000 | 0.177 | 0.224 | 0.945 |
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 | 140 | 131 | 244 | 127 | 144 | 442 | 0 | 154 | 488 | 150 |
N.S. |
1 | 0.94 | 1.74 | 0.91 | 1.03 | 3.16 | 0.00 | 1.10 | 3.49 | 1.07 |
time (sec) |
N/A | 0.356 | 3.476 | 2.630 | 0.039 | 0.111 | 0.000 | 0.188 | 0.163 | 1.041 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 219 | 206 | 589 | 205 | 225 | 787 | 0 | 235 | 772 | 237 |
N.S. |
1 | 0.94 | 2.69 | 0.94 | 1.03 | 3.59 | 0.00 | 1.07 | 3.53 | 1.08 |
time (sec) |
N/A | 0.445 | 7.025 | 4.701 | 0.038 | 0.129 | 0.000 | 0.194 | 0.171 | 2.170 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F(-2) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 382 | 498 | 746 | 466 | 1088 | 932 | 0 | 733 | 2081 | 1068 |
N.S. |
1 | 1.30 | 1.95 | 1.22 | 2.85 | 2.44 | 0.00 | 1.92 | 5.45 | 2.80 |
time (sec) |
N/A | 2.219 | 6.429 | 120.932 | 0.159 | 0.191 | 0.000 | 0.263 | 5.697 | 2.989 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F(-2) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 285 | 378 | 521 | 331 | 744 | 705 | 0 | 613 | 1663 | 717 |
N.S. |
1 | 1.33 | 1.83 | 1.16 | 2.61 | 2.47 | 0.00 | 2.15 | 5.84 | 2.52 |
time (sec) |
N/A | 1.403 | 6.303 | 36.311 | 0.131 | 0.159 | 0.000 | 0.250 | 0.394 | 2.569 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F(-2) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 206 | 270 | 316 | 236 | 463 | 526 | 0 | 372 | 1517 | 433 |
N.S. |
1 | 1.31 | 1.53 | 1.15 | 2.25 | 2.55 | 0.00 | 1.81 | 7.36 | 2.10 |
time (sec) |
N/A | 0.784 | 2.607 | 9.989 | 0.146 | 0.132 | 0.000 | 0.238 | 0.206 | 1.809 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 95 | 86 | 241 | 85 | 108 | 565 | 0 | 99 | 452 | 99 |
N.S. |
1 | 0.91 | 2.54 | 0.89 | 1.14 | 5.95 | 0.00 | 1.04 | 4.76 | 1.04 |
time (sec) |
N/A | 0.294 | 2.337 | 2.273 | 0.039 | 0.114 | 0.000 | 0.213 | 0.175 | 0.893 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 178 | 165 | 456 | 158 | 192 | 811 | 0 | 185 | 798 | 200 |
N.S. |
1 | 0.93 | 2.56 | 0.89 | 1.08 | 4.56 | 0.00 | 1.04 | 4.48 | 1.12 |
time (sec) |
N/A | 0.385 | 3.668 | 3.975 | 0.039 | 0.138 | 0.000 | 0.221 | 0.192 | 1.438 |
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 | 265 | 248 | 494 | 246 | 281 | 1018 | 0 | 274 | 1176 | 297 |
N.S. |
1 | 0.94 | 1.86 | 0.93 | 1.06 | 3.84 | 0.00 | 1.03 | 4.44 | 1.12 |
time (sec) |
N/A | 0.500 | 4.292 | 7.074 | 0.046 | 0.146 | 0.000 | 0.242 | 0.201 | 2.608 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F(-2) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 366 | 464 | 590 | 425 | 997 | 1053 | 0 | 670 | 3021 | 962 |
N.S. |
1 | 1.27 | 1.61 | 1.16 | 2.72 | 2.88 | 0.00 | 1.83 | 8.25 | 2.63 |
time (sec) |
N/A | 2.032 | 3.579 | 89.269 | 0.150 | 0.283 | 0.000 | 0.302 | 6.486 | 2.865 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F(-2) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 264 | 329 | 395 | 288 | 662 | 802 | 0 | 486 | 2289 | 597 |
N.S. |
1 | 1.25 | 1.50 | 1.09 | 2.51 | 3.04 | 0.00 | 1.84 | 8.67 | 2.26 |
time (sec) |
N/A | 1.016 | 2.400 | 29.537 | 0.129 | 0.162 | 0.000 | 0.280 | 0.242 | 2.277 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 116 | 103 | 259 | 103 | 140 | 874 | 0 | 115 | 710 | 131 |
N.S. |
1 | 0.89 | 2.23 | 0.89 | 1.21 | 7.53 | 0.00 | 0.99 | 6.12 | 1.13 |
time (sec) |
N/A | 0.317 | 2.081 | 3.734 | 0.047 | 0.155 | 0.000 | 0.242 | 0.214 | 1.023 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 205 | 188 | 528 | 184 | 228 | 1235 | 0 | 227 | 1158 | 232 |
N.S. |
1 | 0.92 | 2.58 | 0.90 | 1.11 | 6.02 | 0.00 | 1.11 | 5.65 | 1.13 |
time (sec) |
N/A | 0.419 | 1.824 | 7.048 | 0.041 | 0.174 | 0.000 | 0.270 | 0.244 | 2.294 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 300 | 279 | 673 | 280 | 325 | 1536 | 0 | 303 | 1650 | 337 |
N.S. |
1 | 0.93 | 2.24 | 0.93 | 1.08 | 5.12 | 0.00 | 1.01 | 5.50 | 1.12 |
time (sec) |
N/A | 0.554 | 1.989 | 12.543 | 0.045 | 0.209 | 0.000 | 0.273 | 0.273 | 2.887 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | B | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 41 | 26 | 50 | 55 | 0 | 44 | 34 | 38 |
N.S. |
1 | 1.00 | 1.58 | 1.00 | 1.92 | 2.12 | 0.00 | 1.69 | 1.31 | 1.46 |
time (sec) |
N/A | 0.306 | 0.066 | 0.483 | 0.118 | 0.090 | 0.000 | 0.159 | 0.159 | 0.949 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 229 | 229 | 205 | 0 | 0 | 0 | 0 | 0 | 86 | 0 |
N.S. |
1 | 1.00 | 0.90 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.38 | 0.00 |
time (sec) |
N/A | 0.733 | 1.726 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.171 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 179 | 179 | 166 | 0 | 0 | 0 | 0 | 0 | 59 | 0 |
N.S. |
1 | 1.00 | 0.93 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.33 | 0.00 |
time (sec) |
N/A | 0.500 | 0.797 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.171 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 109 | 109 | 109 | 0 | 0 | 0 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 0.362 | 0.208 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.167 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 765 | 580 | 0 | 0 | 0 | 0 | 0 | 0 | 23 | 0 |
N.S. |
1 | 0.76 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.03 | 0.00 |
time (sec) |
N/A | 2.419 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.214 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 23 | 21 | 23 | 23 | 20 | 23 | 23 | 23 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 1.10 | 1.10 | 0.95 | 1.10 | 1.10 | 1.10 |
time (sec) |
N/A | 2.769 | 4.133 | 2.125 | 1.317 | 0.134 | 66.264 | 0.514 | 0.204 | 3.719 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 435 | 476 | 910 | 0 | 0 | 0 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.09 | 2.09 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 0.909 | 6.502 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.163 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 276 | 281 | 270 | 0 | 0 | 0 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.02 | 0.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 0.484 | 0.798 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.158 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 49 | 48 | 48 | 0 | 0 | 0 | 0 | 0 | 23 | 0 |
N.S. |
1 | 0.98 | 0.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.47 | 0.00 |
time (sec) |
N/A | 0.234 | 4.257 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.158 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 141 | 147 | 78 | 0 | 0 | 0 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.04 | 0.55 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.16 | 0.00 |
time (sec) |
N/A | 0.302 | 6.395 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.174 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 23 | 21 | 23 | 32 | 0 | 23 | 23 | 23 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 1.10 | 1.52 | 0.00 | 1.10 | 1.10 | 1.10 |
time (sec) |
N/A | 2.332 | 3.141 | 5.200 | 2.387 | 0.091 | 0.000 | 0.952 | 0.214 | 3.632 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 21 | 19 | 21 | 21 | 19 | 21 | 21 | 21 |
N.S. |
1 | 1.00 | 1.11 | 1.00 | 1.11 | 1.11 | 1.00 | 1.11 | 1.11 | 1.11 |
time (sec) |
N/A | 1.295 | 1.739 | 1.244 | 1.709 | 0.084 | 7.200 | 0.788 | 0.196 | 1.455 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 21 | 19 | 21 | 21 | 19 | 21 | 21 | 23 |
N.S. |
1 | 1.00 | 1.11 | 1.00 | 1.11 | 1.11 | 1.00 | 1.11 | 1.11 | 1.21 |
time (sec) |
N/A | 0.825 | 2.794 | 2.165 | 1.457 | 0.080 | 5.148 | 0.619 | 0.162 | 1.010 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 23 | 21 | 23 | 23 | 20 | 23 | 23 | 23 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 1.10 | 1.10 | 0.95 | 1.10 | 1.10 | 1.10 |
time (sec) |
N/A | 2.110 | 16.379 | 2.170 | 3.154 | 0.098 | 61.961 | 0.907 | 0.158 | 2.878 |