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 | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 8 | 8 | 8 | 7 | 6 | 14 | 0 | 6 | 18 | 6 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 0.75 | 1.75 | 0.00 | 0.75 | 2.25 | 0.75 |
time (sec) |
N/A | 0.185 | 0.002 | 0.253 | 0.029 | 0.066 | 0.000 | 0.128 | 0.168 | 16.841 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 17 | 17 | 14 | 103 | 14 | 0 | 59 | 48 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.82 | 6.06 | 0.82 | 0.00 | 3.47 | 2.82 | 0.76 |
time (sec) |
N/A | 0.241 | 0.027 | 0.404 | 0.044 | 0.066 | 0.000 | 0.151 | 0.169 | 16.834 |
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 | 17 | 17 | 37 | 14 | 13 | 26 | 0 | 13 | 38 | 23 |
N.S. |
1 | 1.00 | 2.18 | 0.82 | 0.76 | 1.53 | 0.00 | 0.76 | 2.24 | 1.35 |
time (sec) |
N/A | 0.203 | 0.021 | 0.561 | 0.039 | 0.063 | 0.000 | 0.126 | 0.167 | 15.761 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 25 | 20 | 187 | 20 | 0 | 101 | 82 | 19 |
N.S. |
1 | 1.00 | 1.00 | 0.80 | 7.48 | 0.80 | 0.00 | 4.04 | 3.28 | 0.76 |
time (sec) |
N/A | 0.245 | 0.020 | 0.855 | 0.041 | 0.068 | 0.000 | 0.162 | 0.174 | 15.636 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | B | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 57 | 20 | 19 | 40 | 0 | 19 | 56 | 33 |
N.S. |
1 | 1.00 | 2.28 | 0.80 | 0.76 | 1.60 | 0.00 | 0.76 | 2.24 | 1.32 |
time (sec) |
N/A | 0.207 | 0.022 | 1.325 | 0.036 | 0.079 | 0.000 | 0.109 | 0.166 | 15.453 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 33 | 33 | 26 | 271 | 26 | 0 | 143 | 116 | 25 |
N.S. |
1 | 1.00 | 1.00 | 0.79 | 8.21 | 0.79 | 0.00 | 4.33 | 3.52 | 0.76 |
time (sec) |
N/A | 0.253 | 0.021 | 2.040 | 0.050 | 0.079 | 0.000 | 0.120 | 0.165 | 15.863 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 73 | 97 | 37 | 36 | 578 | 44 | 0 | 0 | 71 | 0 |
N.S. |
1 | 1.33 | 0.51 | 0.49 | 7.92 | 0.60 | 0.00 | 0.00 | 0.97 | 0.00 |
time (sec) |
N/A | 0.588 | 0.102 | 1.691 | 0.243 | 0.090 | 0.000 | 0.000 | 0.181 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 50 | 76 | 29 | 29 | 427 | 35 | 0 | 0 | 48 | 0 |
N.S. |
1 | 1.52 | 0.58 | 0.58 | 8.54 | 0.70 | 0.00 | 0.00 | 0.96 | 0.00 |
time (sec) |
N/A | 0.466 | 0.052 | 1.431 | 0.216 | 0.080 | 0.000 | 0.000 | 0.228 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 55 | 21 | 17 | 314 | 23 | 0 | 0 | 29 | 0 |
N.S. |
1 | 1.77 | 0.68 | 0.55 | 10.13 | 0.74 | 0.00 | 0.00 | 0.94 | 0.00 |
time (sec) |
N/A | 0.369 | 0.020 | 0.770 | 0.191 | 0.076 | 0.000 | 0.000 | 0.166 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 13 | 13 | 13 | 12 | 188 | 19 | 0 | 0 | 10 | 15 |
N.S. |
1 | 1.00 | 1.00 | 0.92 | 14.46 | 1.46 | 0.00 | 0.00 | 0.77 | 1.15 |
time (sec) |
N/A | 0.290 | 0.010 | 0.691 | 0.180 | 0.075 | 0.000 | 0.000 | 0.153 | 15.870 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | B | F | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 60 | 36 | 44 | 0 | 0 | 126 | 0 | 0 | 20 | 0 |
N.S. |
1 | 0.60 | 0.73 | 0.00 | 0.00 | 2.10 | 0.00 | 0.00 | 0.33 | 0.00 |
time (sec) |
N/A | 0.395 | 0.173 | 0.000 | 0.000 | 0.104 | 0.000 | 0.000 | 0.152 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | F | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 80 | 78 | 60 | 95 | 0 | 155 | 0 | 0 | 28 | 0 |
N.S. |
1 | 0.98 | 0.75 | 1.19 | 0.00 | 1.94 | 0.00 | 0.00 | 0.35 | 0.00 |
time (sec) |
N/A | 0.489 | 0.171 | 10.904 | 0.000 | 0.108 | 0.000 | 0.000 | 0.153 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | F | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 99 | 99 | 69 | 113 | 0 | 167 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.00 | 0.70 | 1.14 | 0.00 | 1.69 | 0.00 | 0.00 | 0.40 | 0.00 |
time (sec) |
N/A | 0.594 | 0.427 | 11.663 | 0.000 | 0.115 | 0.000 | 0.000 | 0.157 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 118 | 120 | 74 | 121 | 0 | 169 | 0 | 0 | 48 | 0 |
N.S. |
1 | 1.02 | 0.63 | 1.03 | 0.00 | 1.43 | 0.00 | 0.00 | 0.41 | 0.00 |
time (sec) |
N/A | 0.732 | 0.221 | 23.754 | 0.000 | 0.115 | 0.000 | 0.000 | 0.153 | 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 | 44 | 58 | 38 | 40 | 26 | 37 | 44 | 35 | 67 | 80 |
N.S. |
1 | 1.32 | 0.86 | 0.91 | 0.59 | 0.84 | 1.00 | 0.80 | 1.52 | 1.82 |
time (sec) |
N/A | 0.232 | 0.033 | 0.914 | 0.032 | 0.072 | 3.994 | 0.108 | 0.158 | 14.985 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 39 | 38 | 30 | 37 | 49 | 42 | 39 | 72 | 68 |
N.S. |
1 | 1.15 | 1.12 | 0.88 | 1.09 | 1.44 | 1.24 | 1.15 | 2.12 | 2.00 |
time (sec) |
N/A | 0.267 | 0.009 | 0.686 | 0.033 | 0.076 | 1.540 | 0.111 | 0.156 | 15.837 |
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 | 29 | 16 | 13 | 12 | 22 | 14 | 18 | 23 | 49 |
N.S. |
1 | 1.32 | 0.73 | 0.59 | 0.55 | 1.00 | 0.64 | 0.82 | 1.05 | 2.23 |
time (sec) |
N/A | 0.200 | 0.021 | 0.347 | 0.033 | 0.070 | 0.582 | 0.110 | 0.152 | 15.668 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 8 | 8 | 8 | 12 | 11 | 21 | 19 | 29 | 21 | 14 |
N.S. |
1 | 1.00 | 1.00 | 1.50 | 1.38 | 2.62 | 2.38 | 3.62 | 2.62 | 1.75 |
time (sec) |
N/A | 0.143 | 0.005 | 0.134 | 0.030 | 0.074 | 0.048 | 0.106 | 0.197 | 15.012 |
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 | 4 | 4 | 4 | 7 | 21 | 6 | 0 | 6 | 6 | 6 |
N.S. |
1 | 1.00 | 1.00 | 1.75 | 5.25 | 1.50 | 0.00 | 1.50 | 1.50 | 1.50 |
time (sec) |
N/A | 0.214 | 0.005 | 0.146 | 0.038 | 0.060 | 0.000 | 0.118 | 0.155 | 15.379 |
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 | 8 | 8 | 8 | 7 | 6 | 18 | 0 | 6 | 14 | 6 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 0.75 | 2.25 | 0.00 | 0.75 | 1.75 | 0.75 |
time (sec) |
N/A | 0.177 | 0.002 | 0.176 | 0.035 | 0.061 | 0.000 | 0.113 | 0.157 | 15.194 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 17 | 17 | 14 | 73 | 28 | 0 | 14 | 14 | 14 |
N.S. |
1 | 1.00 | 1.00 | 0.82 | 4.29 | 1.65 | 0.00 | 0.82 | 0.82 | 0.82 |
time (sec) |
N/A | 0.251 | 0.011 | 0.214 | 0.034 | 0.066 | 0.000 | 0.113 | 0.157 | 14.824 |
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 | 17 | 17 | 37 | 14 | 14 | 39 | 0 | 14 | 28 | 16 |
N.S. |
1 | 1.00 | 2.18 | 0.82 | 0.82 | 2.29 | 0.00 | 0.82 | 1.65 | 0.94 |
time (sec) |
N/A | 0.196 | 0.027 | 0.232 | 0.030 | 0.066 | 0.000 | 0.117 | 0.162 | 15.144 |
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 | 25 | 25 | 25 | 20 | 121 | 46 | 0 | 20 | 20 | 20 |
N.S. |
1 | 1.00 | 1.00 | 0.80 | 4.84 | 1.84 | 0.00 | 0.80 | 0.80 | 0.80 |
time (sec) |
N/A | 0.256 | 0.009 | 0.290 | 0.037 | 0.080 | 0.000 | 0.102 | 0.156 | 15.089 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | B | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 57 | 20 | 20 | 57 | 0 | 20 | 40 | 46 |
N.S. |
1 | 1.00 | 2.28 | 0.80 | 0.80 | 2.28 | 0.00 | 0.80 | 1.60 | 1.84 |
time (sec) |
N/A | 0.203 | 0.028 | 0.289 | 0.037 | 0.067 | 0.000 | 0.121 | 0.161 | 15.569 |
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 | 33 | 33 | 33 | 26 | 169 | 64 | 0 | 26 | 26 | 109 |
N.S. |
1 | 1.00 | 1.00 | 0.79 | 5.12 | 1.94 | 0.00 | 0.79 | 0.79 | 3.30 |
time (sec) |
N/A | 0.260 | 0.011 | 0.364 | 0.041 | 0.071 | 0.000 | 0.111 | 0.175 | 15.195 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 73 | 97 | 37 | 171 | 82 | 44 | 0 | 0 | 71 | 0 |
N.S. |
1 | 1.33 | 0.51 | 2.34 | 1.12 | 0.60 | 0.00 | 0.00 | 0.97 | 0.00 |
time (sec) |
N/A | 0.556 | 0.193 | 12.548 | 0.134 | 0.082 | 0.000 | 0.000 | 0.228 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 50 | 76 | 29 | 162 | 82 | 38 | 0 | 0 | 48 | 0 |
N.S. |
1 | 1.52 | 0.58 | 3.24 | 1.64 | 0.76 | 0.00 | 0.00 | 0.96 | 0.00 |
time (sec) |
N/A | 0.439 | 0.048 | 11.750 | 0.128 | 0.077 | 0.000 | 0.000 | 0.201 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 55 | 23 | 147 | 57 | 26 | 0 | 0 | 29 | 0 |
N.S. |
1 | 1.77 | 0.74 | 4.74 | 1.84 | 0.84 | 0.00 | 0.00 | 0.94 | 0.00 |
time (sec) |
N/A | 0.357 | 0.020 | 1.461 | 0.123 | 0.076 | 0.000 | 0.000 | 0.205 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | B | A | F | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 13 | 13 | 13 | 50 | 57 | 22 | 0 | 46 | 10 | 20 |
N.S. |
1 | 1.00 | 1.00 | 3.85 | 4.38 | 1.69 | 0.00 | 3.54 | 0.77 | 1.54 |
time (sec) |
N/A | 0.273 | 0.012 | 1.019 | 0.127 | 0.084 | 0.000 | 0.162 | 0.164 | 15.017 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 52 | 42 | 43 | 89 | 0 | 72 | 0 | 35 | 22 | 0 |
N.S. |
1 | 0.81 | 0.83 | 1.71 | 0.00 | 1.38 | 0.00 | 0.67 | 0.42 | 0.00 |
time (sec) |
N/A | 0.367 | 0.143 | 0.516 | 0.000 | 0.094 | 0.000 | 0.184 | 0.171 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 72 | 84 | 56 | 166 | 0 | 119 | 0 | 95 | 28 | 0 |
N.S. |
1 | 1.17 | 0.78 | 2.31 | 0.00 | 1.65 | 0.00 | 1.32 | 0.39 | 0.00 |
time (sec) |
N/A | 0.453 | 0.174 | 0.545 | 0.000 | 0.094 | 0.000 | 0.181 | 0.173 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 91 | 105 | 73 | 130 | 0 | 147 | 0 | 151 | 42 | 0 |
N.S. |
1 | 1.15 | 0.80 | 1.43 | 0.00 | 1.62 | 0.00 | 1.66 | 0.46 | 0.00 |
time (sec) |
N/A | 0.530 | 0.506 | 0.594 | 0.000 | 0.099 | 0.000 | 0.197 | 0.176 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F(-1) | B | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 110 | 126 | 74 | 133 | 0 | 171 | 0 | 210 | 48 | 0 |
N.S. |
1 | 1.15 | 0.67 | 1.21 | 0.00 | 1.55 | 0.00 | 1.91 | 0.44 | 0.00 |
time (sec) |
N/A | 0.622 | 0.302 | 0.608 | 0.000 | 0.101 | 0.000 | 0.329 | 0.168 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | C | C | F | B | F | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 125 | 505 | 64 | 0 | 254 | 0 | 122 | 21 | 316 |
N.S. |
1 | 2.16 | 8.71 | 1.10 | 0.00 | 4.38 | 0.00 | 2.10 | 0.36 | 5.45 |
time (sec) |
N/A | 0.442 | 2.944 | 0.569 | 0.000 | 0.090 | 0.000 | 0.123 | 0.172 | 15.221 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | C | C | F | B | F | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 56 | 125 | 665 | 64 | 0 | 254 | 0 | 122 | 23 | 399 |
N.S. |
1 | 2.23 | 11.88 | 1.14 | 0.00 | 4.54 | 0.00 | 2.18 | 0.41 | 7.12 |
time (sec) |
N/A | 0.386 | 2.600 | 0.582 | 0.000 | 0.088 | 0.000 | 0.122 | 0.173 | 15.118 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 145 | 172 | 303 | 164 | 204 | 166 | 308 | 178 | 508 | 272 |
N.S. |
1 | 1.19 | 2.09 | 1.13 | 1.41 | 1.14 | 2.12 | 1.23 | 3.50 | 1.88 |
time (sec) |
N/A | 0.461 | 0.880 | 154.505 | 0.036 | 0.093 | 2.232 | 0.127 | 0.191 | 15.359 |
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 | 100 | 107 | 96 | 74 | 72 | 80 | 97 | 131 | 172 | 115 |
N.S. |
1 | 1.07 | 0.96 | 0.74 | 0.72 | 0.80 | 0.97 | 1.31 | 1.72 | 1.15 |
time (sec) |
N/A | 0.558 | 0.222 | 29.221 | 0.109 | 0.076 | 1.238 | 0.136 | 0.167 | 15.473 |
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 | 77 | 95 | 123 | 74 | 95 | 85 | 122 | 86 | 199 | 126 |
N.S. |
1 | 1.23 | 1.60 | 0.96 | 1.23 | 1.10 | 1.58 | 1.12 | 2.58 | 1.64 |
time (sec) |
N/A | 0.366 | 0.440 | 5.873 | 0.032 | 0.088 | 1.315 | 0.139 | 0.207 | 15.617 |
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 | 25 | 26 | 26 | 29 | 22 | 40 | 38 | 40 |
N.S. |
1 | 1.00 | 0.93 | 0.96 | 0.96 | 1.07 | 0.81 | 1.48 | 1.41 | 1.48 |
time (sec) |
N/A | 0.273 | 0.037 | 0.903 | 0.114 | 0.071 | 0.354 | 0.122 | 0.167 | 14.979 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 12 | 16 | 14 | 25 | 24 | 34 | 30 | 37 |
N.S. |
1 | 1.00 | 1.00 | 1.33 | 1.17 | 2.08 | 2.00 | 2.83 | 2.50 | 3.08 |
time (sec) |
N/A | 0.148 | 0.006 | 0.193 | 0.030 | 0.080 | 0.052 | 0.105 | 0.160 | 15.367 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 11 | 11 | 11 | 12 | 50 | 11 | 32 | 12 | 27 | 55 |
N.S. |
1 | 1.00 | 1.00 | 1.09 | 4.55 | 1.00 | 2.91 | 1.09 | 2.45 | 5.00 |
time (sec) |
N/A | 0.226 | 0.007 | 0.318 | 0.115 | 0.081 | 0.147 | 0.131 | 0.164 | 16.756 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | F(-2) | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 66 | 77 | 344 | 92 | 0 | 308 | 0 | 94 | 148 | 604 |
N.S. |
1 | 1.17 | 5.21 | 1.39 | 0.00 | 4.67 | 0.00 | 1.42 | 2.24 | 9.15 |
time (sec) |
N/A | 0.415 | 1.641 | 1.544 | 0.000 | 0.097 | 0.000 | 0.138 | 0.166 | 15.668 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 51 | 46 | 40 | 50 | 201 | 83 | 503 | 43 | 156 | 106 |
N.S. |
1 | 0.90 | 0.78 | 0.98 | 3.94 | 1.63 | 9.86 | 0.84 | 3.06 | 2.08 |
time (sec) |
N/A | 0.294 | 0.127 | 7.447 | 0.120 | 0.084 | 1.141 | 0.108 | 0.170 | 16.194 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | F(-2) | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 156 | 182 | 2661 | 358 | 0 | 931 | 0 | 369 | 820 | 2782 |
N.S. |
1 | 1.17 | 17.06 | 2.29 | 0.00 | 5.97 | 0.00 | 2.37 | 5.26 | 17.83 |
time (sec) |
N/A | 0.848 | 6.878 | 39.683 | 0.000 | 0.133 | 0.000 | 0.130 | 0.174 | 20.127 |
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 | 101 | 89 | 86 | 102 | 483 | 217 | 1719 | 91 | 348 | 541 |
N.S. |
1 | 0.88 | 0.85 | 1.01 | 4.78 | 2.15 | 17.02 | 0.90 | 3.45 | 5.36 |
time (sec) |
N/A | 0.345 | 0.271 | 176.095 | 0.136 | 0.097 | 5.914 | 0.119 | 0.165 | 16.901 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | B | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 30 | 52 | 51 | 141 | 38 | 68 | 62 | 190 | 59 |
N.S. |
1 | 1.00 | 1.73 | 1.70 | 4.70 | 1.27 | 2.27 | 2.07 | 6.33 | 1.97 |
time (sec) |
N/A | 0.263 | 0.037 | 8.667 | 0.033 | 0.080 | 1.893 | 0.117 | 0.164 | 15.050 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | C | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 30 | 64 | 32 | 28 | 61 | 44 | 20 | 93 | 20 |
N.S. |
1 | 1.00 | 2.13 | 1.07 | 0.93 | 2.03 | 1.47 | 0.67 | 3.10 | 0.67 |
time (sec) |
N/A | 0.360 | 0.119 | 2.727 | 0.106 | 0.072 | 1.160 | 0.121 | 0.167 | 15.472 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | B | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 21 | 35 | 52 | 21 | 44 | 48 | 101 | 43 |
N.S. |
1 | 1.00 | 1.17 | 1.94 | 2.89 | 1.17 | 2.44 | 2.67 | 5.61 | 2.39 |
time (sec) |
N/A | 0.249 | 0.020 | 0.839 | 0.028 | 0.074 | 1.205 | 0.122 | 0.215 | 15.739 |
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 | 14 | 15 | 14 | 28 | 10 | 14 | 23 | 14 |
N.S. |
1 | 1.00 | 0.88 | 0.94 | 0.88 | 1.75 | 0.62 | 0.88 | 1.44 | 0.88 |
time (sec) |
N/A | 0.281 | 0.012 | 0.336 | 0.101 | 0.068 | 0.322 | 0.113 | 0.161 | 15.168 |
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 | 13 | 9 | 9 | 13 | 10 | 9 | 20 | 31 | 26 | 19 |
N.S. |
1 | 0.69 | 0.69 | 1.00 | 0.77 | 0.69 | 1.54 | 2.38 | 2.00 | 1.46 |
time (sec) |
N/A | 0.145 | 0.002 | 0.148 | 0.042 | 0.070 | 0.050 | 0.111 | 0.185 | 15.754 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | B | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 5 | 5 | 16 | 6 | 31 | 5 | 17 | 22 | 16 | 21 |
N.S. |
1 | 1.00 | 3.20 | 1.20 | 6.20 | 1.00 | 3.40 | 4.40 | 3.20 | 4.20 |
time (sec) |
N/A | 0.211 | 0.014 | 0.195 | 0.028 | 0.073 | 0.067 | 0.111 | 0.173 | 15.252 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 27 | 17 | 28 | 25 | 0 | 14 | 26 | 14 |
N.S. |
1 | 1.00 | 1.93 | 1.21 | 2.00 | 1.79 | 0.00 | 1.00 | 1.86 | 1.00 |
time (sec) |
N/A | 0.228 | 0.023 | 0.349 | 0.109 | 0.072 | 0.000 | 0.114 | 0.173 | 15.251 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | B | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 34 | 17 | 64 | 20 | 301 | 45 | 107 | 41 |
N.S. |
1 | 1.00 | 2.12 | 1.06 | 4.00 | 1.25 | 18.81 | 2.81 | 6.69 | 2.56 |
time (sec) |
N/A | 0.248 | 0.020 | 2.248 | 0.104 | 0.072 | 0.407 | 0.129 | 0.192 | 15.170 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | B | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 62 | 29 | 64 | 63 | 0 | 20 | 69 | 19 |
N.S. |
1 | 1.00 | 2.38 | 1.12 | 2.46 | 2.42 | 0.00 | 0.77 | 2.65 | 0.73 |
time (sec) |
N/A | 0.298 | 0.058 | 2.643 | 0.113 | 0.076 | 0.000 | 0.116 | 0.168 | 14.750 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 39 | 23 | 92 | 35 | 1059 | 64 | 233 | 61 |
N.S. |
1 | 1.00 | 1.77 | 1.05 | 4.18 | 1.59 | 48.14 | 2.91 | 10.59 | 2.77 |
time (sec) |
N/A | 0.250 | 0.040 | 7.293 | 0.114 | 0.075 | 1.159 | 0.132 | 0.183 | 15.382 |
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 | 145 | 173 | 143 | 167 | 188 | 292 | 308 | 169 | 218 | 174 |
N.S. |
1 | 1.19 | 0.99 | 1.15 | 1.30 | 2.01 | 2.12 | 1.17 | 1.50 | 1.20 |
time (sec) |
N/A | 0.468 | 0.594 | 30.077 | 0.033 | 0.090 | 54.137 | 0.107 | 0.181 | 15.332 |
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 | 101 | 107 | 95 | 72 | 80 | 95 | 97 | 215 | 105 | 127 |
N.S. |
1 | 1.06 | 0.94 | 0.71 | 0.79 | 0.94 | 0.96 | 2.13 | 1.04 | 1.26 |
time (sec) |
N/A | 0.566 | 0.286 | 10.509 | 0.108 | 0.079 | 16.294 | 0.129 | 0.208 | 15.266 |
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 | 79 | 98 | 79 | 80 | 87 | 128 | 124 | 86 | 112 | 82 |
N.S. |
1 | 1.24 | 1.00 | 1.01 | 1.10 | 1.62 | 1.57 | 1.09 | 1.42 | 1.04 |
time (sec) |
N/A | 0.366 | 0.258 | 2.877 | 0.026 | 0.086 | 5.650 | 0.133 | 0.172 | 16.381 |
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 | 24 | 29 | 29 | 28 | 31 | 52 | 34 | 30 |
N.S. |
1 | 1.00 | 0.83 | 1.00 | 1.00 | 0.97 | 1.07 | 1.79 | 1.17 | 1.03 |
time (sec) |
N/A | 0.270 | 0.157 | 0.337 | 0.104 | 0.075 | 1.116 | 0.114 | 0.171 | 16.508 |
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 | 12 | 12 | 12 | 16 | 15 | 27 | 24 | 15 | 27 | 27 |
N.S. |
1 | 1.00 | 1.00 | 1.33 | 1.25 | 2.25 | 2.00 | 1.25 | 2.25 | 2.25 |
time (sec) |
N/A | 0.144 | 0.005 | 0.159 | 0.026 | 0.082 | 0.062 | 0.130 | 0.188 | 15.139 |
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 | 12 | 12 | 12 | 13 | 45 | 12 | 0 | 13 | 41 | 36 |
N.S. |
1 | 1.00 | 1.00 | 1.08 | 3.75 | 1.00 | 0.00 | 1.08 | 3.42 | 3.00 |
time (sec) |
N/A | 0.232 | 0.026 | 0.279 | 0.106 | 0.077 | 0.000 | 0.108 | 0.176 | 16.485 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 67 | 72 | 71 | 86 | 0 | 307 | 0 | 107 | 161 | 440 |
N.S. |
1 | 1.07 | 1.06 | 1.28 | 0.00 | 4.58 | 0.00 | 1.60 | 2.40 | 6.57 |
time (sec) |
N/A | 0.417 | 0.242 | 1.269 | 0.000 | 0.098 | 0.000 | 0.127 | 0.175 | 16.555 |
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 | 50 | 47 | 77 | 49 | 177 | 70 | 0 | 45 | 492 | 311 |
N.S. |
1 | 0.94 | 1.54 | 0.98 | 3.54 | 1.40 | 0.00 | 0.90 | 9.84 | 6.22 |
time (sec) |
N/A | 0.303 | 0.121 | 5.973 | 0.116 | 0.092 | 0.000 | 0.107 | 0.174 | 17.041 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 159 | 179 | 150 | 197 | 0 | 878 | 0 | 282 | 860 | 3068 |
N.S. |
1 | 1.13 | 0.94 | 1.24 | 0.00 | 5.52 | 0.00 | 1.77 | 5.41 | 19.30 |
time (sec) |
N/A | 0.850 | 0.382 | 28.224 | 0.000 | 0.134 | 0.000 | 0.127 | 0.217 | 21.786 |
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 | 100 | 87 | 138 | 107 | 497 | 166 | 0 | 93 | 1653 | 538 |
N.S. |
1 | 0.87 | 1.38 | 1.07 | 4.97 | 1.66 | 0.00 | 0.93 | 16.53 | 5.38 |
time (sec) |
N/A | 0.333 | 0.310 | 84.645 | 0.151 | 0.103 | 0.000 | 0.128 | 0.179 | 17.126 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | B | A | B | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 32 | 45 | 125 | 37 | 68 | 22 | 55 | 34 |
N.S. |
1 | 1.00 | 1.14 | 1.61 | 4.46 | 1.32 | 2.43 | 0.79 | 1.96 | 1.21 |
time (sec) |
N/A | 0.268 | 0.055 | 0.713 | 0.033 | 0.071 | 74.882 | 0.111 | 0.171 | 15.564 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | B | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 30 | 30 | 31 | 56 | 36 | 44 | 20 | 38 | 16 |
N.S. |
1 | 1.00 | 1.00 | 1.03 | 1.87 | 1.20 | 1.47 | 0.67 | 1.27 | 0.53 |
time (sec) |
N/A | 0.377 | 0.051 | 0.553 | 0.109 | 0.077 | 22.101 | 0.110 | 0.164 | 15.107 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | B | A | B | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 20 | 32 | 46 | 22 | 46 | 18 | 41 | 25 |
N.S. |
1 | 1.00 | 1.00 | 1.60 | 2.30 | 1.10 | 2.30 | 0.90 | 2.05 | 1.25 |
time (sec) |
N/A | 0.257 | 0.035 | 0.339 | 0.026 | 0.073 | 6.776 | 0.125 | 0.169 | 15.094 |
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 | 16 | 16 | 12 | 15 | 16 | 16 | 17 | 12 | 20 | 10 |
N.S. |
1 | 1.00 | 0.75 | 0.94 | 1.00 | 1.00 | 1.06 | 0.75 | 1.25 | 0.62 |
time (sec) |
N/A | 0.295 | 0.023 | 0.268 | 0.105 | 0.069 | 1.203 | 0.115 | 0.169 | 15.393 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 9 | 9 | 9 | 13 | 12 | 7 | 20 | 11 | 10 | 19 |
N.S. |
1 | 1.00 | 1.00 | 1.44 | 1.33 | 0.78 | 2.22 | 1.22 | 1.11 | 2.11 |
time (sec) |
N/A | 0.143 | 0.005 | 0.121 | 0.024 | 0.070 | 0.059 | 0.122 | 0.173 | 15.300 |
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 | 7 | 7 | 9 | 8 | 14 | 9 | 0 | 7 | 9 | 9 |
N.S. |
1 | 1.00 | 1.29 | 1.14 | 2.00 | 1.29 | 0.00 | 1.00 | 1.29 | 1.29 |
time (sec) |
N/A | 0.214 | 0.013 | 0.172 | 0.106 | 0.072 | 0.000 | 0.111 | 0.217 | 15.776 |
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 | 14 | 14 | 12 | 15 | 23 | 18 | 0 | 10 | 10 | 10 |
N.S. |
1 | 1.00 | 0.86 | 1.07 | 1.64 | 1.29 | 0.00 | 0.71 | 0.71 | 0.71 |
time (sec) |
N/A | 0.236 | 0.014 | 0.288 | 0.103 | 0.068 | 0.000 | 0.131 | 0.196 | 15.287 |
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 | 14 | 14 | 18 | 15 | 28 | 21 | 0 | 14 | 18 | 18 |
N.S. |
1 | 1.00 | 1.29 | 1.07 | 2.00 | 1.50 | 0.00 | 1.00 | 1.29 | 1.29 |
time (sec) |
N/A | 0.270 | 0.015 | 0.625 | 0.111 | 0.080 | 0.000 | 0.111 | 0.167 | 15.196 |
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 | 26 | 26 | 30 | 23 | 35 | 40 | 0 | 16 | 16 | 16 |
N.S. |
1 | 1.00 | 1.15 | 0.88 | 1.35 | 1.54 | 0.00 | 0.62 | 0.62 | 0.62 |
time (sec) |
N/A | 0.308 | 0.015 | 1.552 | 0.117 | 0.073 | 0.000 | 0.127 | 0.167 | 15.163 |
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 | 24 | 24 | 32 | 25 | 39 | 38 | 0 | 22 | 26 | 26 |
N.S. |
1 | 1.00 | 1.33 | 1.04 | 1.62 | 1.58 | 0.00 | 0.92 | 1.08 | 1.08 |
time (sec) |
N/A | 0.255 | 0.015 | 3.947 | 0.117 | 0.078 | 0.000 | 0.125 | 0.168 | 14.982 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 74 | 74 | 68 | 117 | 153 | 144 | 638 | 131 | 66 | 695 |
N.S. |
1 | 1.00 | 0.92 | 1.58 | 2.07 | 1.95 | 8.62 | 1.77 | 0.89 | 9.39 |
time (sec) |
N/A | 0.310 | 0.235 | 0.396 | 0.108 | 0.091 | 11.963 | 0.149 | 0.165 | 20.036 |
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 | 75 | 75 | 82 | 108 | 146 | 200 | 0 | 130 | 174 | 105 |
N.S. |
1 | 1.00 | 1.09 | 1.44 | 1.95 | 2.67 | 0.00 | 1.73 | 2.32 | 1.40 |
time (sec) |
N/A | 0.327 | 0.299 | 0.407 | 0.115 | 0.085 | 0.000 | 0.134 | 0.183 | 15.461 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | B | B | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 116 | 128 | 132 | 177 | 338 | 279 | 0 | 199 | 1327 | 227 |
N.S. |
1 | 1.10 | 1.14 | 1.53 | 2.91 | 2.41 | 0.00 | 1.72 | 11.44 | 1.96 |
time (sec) |
N/A | 0.483 | 0.385 | 0.579 | 0.128 | 0.090 | 0.000 | 0.161 | 0.185 | 15.650 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 73 | 73 | 67 | 117 | 153 | 143 | 670 | 131 | 65 | 692 |
N.S. |
1 | 1.00 | 0.92 | 1.60 | 2.10 | 1.96 | 9.18 | 1.79 | 0.89 | 9.48 |
time (sec) |
N/A | 0.305 | 0.145 | 0.368 | 0.119 | 0.087 | 11.578 | 0.146 | 0.174 | 19.294 |
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 | 76 | 76 | 82 | 109 | 156 | 201 | 0 | 132 | 179 | 126 |
N.S. |
1 | 1.00 | 1.08 | 1.43 | 2.05 | 2.64 | 0.00 | 1.74 | 2.36 | 1.66 |
time (sec) |
N/A | 0.321 | 0.216 | 0.376 | 0.117 | 0.087 | 0.000 | 0.138 | 0.175 | 15.272 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | B | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 116 | 128 | 118 | 204 | 366 | 279 | 0 | 245 | 1313 | 251 |
N.S. |
1 | 1.10 | 1.02 | 1.76 | 3.16 | 2.41 | 0.00 | 2.11 | 11.32 | 2.16 |
time (sec) |
N/A | 0.466 | 0.284 | 0.531 | 0.144 | 0.093 | 0.000 | 0.167 | 0.185 | 15.550 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 246 | 248 | 238 | 331 | 354 | 221 | 857 | 287 | 744 | 522 |
N.S. |
1 | 1.01 | 0.97 | 1.35 | 1.44 | 0.90 | 3.48 | 1.17 | 3.02 | 2.12 |
time (sec) |
N/A | 0.637 | 2.099 | 17.731 | 0.037 | 0.084 | 0.595 | 0.196 | 0.199 | 20.343 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 178 | 177 | 163 | 250 | 207 | 145 | 415 | 199 | 336 | 261 |
N.S. |
1 | 0.99 | 0.92 | 1.40 | 1.16 | 0.81 | 2.33 | 1.12 | 1.89 | 1.47 |
time (sec) |
N/A | 0.433 | 1.527 | 0.800 | 0.036 | 0.080 | 0.340 | 0.141 | 0.190 | 20.038 |
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 | 116 | 106 | 111 | 106 | 113 | 81 | 192 | 92 | 155 | 100 |
N.S. |
1 | 0.91 | 0.96 | 0.91 | 0.97 | 0.70 | 1.66 | 0.79 | 1.34 | 0.86 |
time (sec) |
N/A | 0.280 | 1.220 | 1.117 | 0.034 | 0.077 | 0.153 | 0.119 | 0.231 | 15.776 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 37 | 37 | 36 | 36 | 35 | 34 | 42 | 35 | 33 | 48 |
N.S. |
1 | 1.00 | 0.97 | 0.97 | 0.95 | 0.92 | 1.14 | 0.95 | 0.89 | 1.30 |
time (sec) |
N/A | 0.160 | 0.057 | 0.326 | 0.023 | 0.071 | 0.069 | 0.112 | 0.201 | 15.155 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 49 | 49 | 49 | 50 | 40 | 75 | 0 | 0 | 46 | 38 |
N.S. |
1 | 1.00 | 1.00 | 1.02 | 0.82 | 1.53 | 0.00 | 0.00 | 0.94 | 0.78 |
time (sec) |
N/A | 0.228 | 0.207 | 0.426 | 0.033 | 0.075 | 0.000 | 0.000 | 1.226 | 15.955 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F(-2) | A | F(-1) | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 129 | 129 | 98 | 129 | 0 | 192 | 0 | 0 | 1090 | 274 |
N.S. |
1 | 1.00 | 0.76 | 1.00 | 0.00 | 1.49 | 0.00 | 0.00 | 8.45 | 2.12 |
time (sec) |
N/A | 0.406 | 0.272 | 0.708 | 0.000 | 0.088 | 0.000 | 0.000 | 0.201 | 16.246 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | C | F(-2) | B | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 191 | 211 | 420 | 246 | 0 | 490 | 0 | 0 | 30 | 592 |
N.S. |
1 | 1.10 | 2.20 | 1.29 | 0.00 | 2.57 | 0.00 | 0.00 | 0.16 | 3.10 |
time (sec) |
N/A | 0.589 | 1.758 | 1.378 | 0.000 | 0.124 | 0.000 | 0.000 | 200.025 | 21.313 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | C | F(-2) | B | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 259 | 293 | 533 | 511 | 0 | 739 | 0 | 0 | 30 | 1004 |
N.S. |
1 | 1.13 | 2.06 | 1.97 | 0.00 | 2.85 | 0.00 | 0.00 | 0.12 | 3.88 |
time (sec) |
N/A | 0.789 | 1.858 | 2.175 | 0.000 | 0.282 | 0.000 | 0.000 | 200.020 | 25.669 |
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 | 157 | 170 | 135 | 177 | 191 | 134 | 291 | 151 | 239 | 239 |
N.S. |
1 | 1.08 | 0.86 | 1.13 | 1.22 | 0.85 | 1.85 | 0.96 | 1.52 | 1.52 |
time (sec) |
N/A | 0.478 | 1.401 | 0.381 | 0.035 | 0.079 | 0.191 | 0.129 | 0.181 | 15.532 |
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 | 81 | 86 | 92 | 77 | 99 | 71 | 170 | 78 | 135 | 96 |
N.S. |
1 | 1.06 | 1.14 | 0.95 | 1.22 | 0.88 | 2.10 | 0.96 | 1.67 | 1.19 |
time (sec) |
N/A | 0.267 | 0.470 | 1.150 | 0.028 | 0.074 | 0.107 | 0.131 | 0.170 | 15.966 |
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 | 53 | 30 | 29 | 27 | 39 | 29 | 27 | 29 |
N.S. |
1 | 1.00 | 1.83 | 1.03 | 1.00 | 0.93 | 1.34 | 1.00 | 0.93 | 1.00 |
time (sec) |
N/A | 0.159 | 0.048 | 0.304 | 0.031 | 0.072 | 0.071 | 0.134 | 0.162 | 15.975 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 57 | 23 | 29 | 60 | 63 | 23 | 22 | 22 |
N.S. |
1 | 1.00 | 2.28 | 0.92 | 1.16 | 2.40 | 2.52 | 0.92 | 0.88 | 0.88 |
time (sec) |
N/A | 0.200 | 0.109 | 0.393 | 0.024 | 0.079 | 0.709 | 0.124 | 0.176 | 17.101 |
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 | 75 | 75 | 115 | 68 | 90 | 154 | 0 | 83 | 119 | 79 |
N.S. |
1 | 1.00 | 1.53 | 0.91 | 1.20 | 2.05 | 0.00 | 1.11 | 1.59 | 1.05 |
time (sec) |
N/A | 0.332 | 0.462 | 0.583 | 0.040 | 0.085 | 0.000 | 0.112 | 0.171 | 16.911 |
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 | 134 | 139 | 186 | 131 | 190 | 433 | 0 | 164 | 290 | 162 |
N.S. |
1 | 1.04 | 1.39 | 0.98 | 1.42 | 3.23 | 0.00 | 1.22 | 2.16 | 1.21 |
time (sec) |
N/A | 0.506 | 2.010 | 0.824 | 0.056 | 0.092 | 0.000 | 0.137 | 0.180 | 17.258 |
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 | 207 | 218 | 397 | 215 | 307 | 791 | 0 | 291 | 474 | 260 |
N.S. |
1 | 1.05 | 1.92 | 1.04 | 1.48 | 3.82 | 0.00 | 1.41 | 2.29 | 1.26 |
time (sec) |
N/A | 0.847 | 4.147 | 1.191 | 0.063 | 0.104 | 0.000 | 0.137 | 0.213 | 16.584 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 50 | 21 | 28 | 31 | 36 | 21 | 20 | 20 |
N.S. |
1 | 1.00 | 2.17 | 0.91 | 1.22 | 1.35 | 1.57 | 0.91 | 0.87 | 0.87 |
time (sec) |
N/A | 0.189 | 0.074 | 0.355 | 0.025 | 0.077 | 0.347 | 0.146 | 0.163 | 15.715 |
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 | 75 | 75 | 93 | 48 | 80 | 100 | 168 | 65 | 81 | 59 |
N.S. |
1 | 1.00 | 1.24 | 0.64 | 1.07 | 1.33 | 2.24 | 0.87 | 1.08 | 0.79 |
time (sec) |
N/A | 0.313 | 0.180 | 0.489 | 0.033 | 0.078 | 0.928 | 0.129 | 0.165 | 15.214 |
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 | 123 | 134 | 135 | 78 | 146 | 143 | 423 | 102 | 135 | 90 |
N.S. |
1 | 1.09 | 1.10 | 0.63 | 1.19 | 1.16 | 3.44 | 0.83 | 1.10 | 0.73 |
time (sec) |
N/A | 0.511 | 0.460 | 0.622 | 0.040 | 0.093 | 3.023 | 0.129 | 0.177 | 15.430 |
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 | 168 | 188 | 247 | 106 | 208 | 237 | 792 | 132 | 197 | 161 |
N.S. |
1 | 1.12 | 1.47 | 0.63 | 1.24 | 1.41 | 4.71 | 0.79 | 1.17 | 0.96 |
time (sec) |
N/A | 0.744 | 1.120 | 0.667 | 0.050 | 0.084 | 11.202 | 0.165 | 0.172 | 15.419 |