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 | F | A | A | A | A | A | F | F | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 30 | 22 | 21 | 23 | 20 | 0 | 123 | 21 |
N.S. |
1 | 0.00 | 1.25 | 0.92 | 0.88 | 0.96 | 0.83 | 0.00 | 5.12 | 0.88 |
time (sec) |
N/A | 0.000 | 0.692 | 0.575 | 0.246 | 0.109 | 0.237 | 0.000 | 0.218 | 3.413 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 18 | 16 | 13 | 26 | 15 | 20 | 25 | 15 |
N.S. |
1 | 1.00 | 1.00 | 0.89 | 0.72 | 1.44 | 0.83 | 1.11 | 1.39 | 0.83 |
time (sec) |
N/A | 0.329 | 0.030 | 0.268 | 0.058 | 0.092 | 0.041 | 0.131 | 0.206 | 3.374 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | A | A | A | A | A | B | B |
verified | N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 0 | 25 | 19 | 25 | 22 | 36 | 23 | 36 |
N.S. |
1 | 0.00 | 0.00 | 1.04 | 0.79 | 1.04 | 0.92 | 1.50 | 0.96 | 1.50 |
time (sec) |
N/A | 0.000 | 0.000 | 0.745 | 0.229 | 0.079 | 0.299 | 0.120 | 0.227 | 4.670 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | B | B | B | B | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 73 | 68 | 59 | 67 | 71 | 65 | 66 | 77 | 71 |
N.S. |
1 | 3.48 | 3.24 | 2.81 | 3.19 | 3.38 | 3.10 | 3.14 | 3.67 | 3.38 |
time (sec) |
N/A | 0.370 | 0.026 | 0.169 | 0.033 | 0.079 | 0.184 | 0.121 | 0.209 | 3.341 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 0 | 18 | 19 | 18 | 18 | 20 | 29 | 16 | 14 |
N.S. |
1 | 0.00 | 0.90 | 0.95 | 0.90 | 0.90 | 1.00 | 1.45 | 0.80 | 0.70 |
time (sec) |
N/A | 0.000 | 0.023 | 0.119 | 0.072 | 0.081 | 0.568 | 0.126 | 0.205 | 3.391 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 26 | 25 | 21 | 25 | 25 | 22 | 25 | 21 | 23 |
N.S. |
1 | 1.24 | 1.19 | 1.00 | 1.19 | 1.19 | 1.05 | 1.19 | 1.00 | 1.10 |
time (sec) |
N/A | 0.157 | 0.001 | 0.082 | 0.048 | 0.067 | 0.021 | 0.116 | 0.208 | 3.318 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 39 | 17 | 23 | 165 | 24 | 22 | 24 | 41 | 22 |
N.S. |
1 | 1.44 | 0.63 | 0.85 | 6.11 | 0.89 | 0.81 | 0.89 | 1.52 | 0.81 |
time (sec) |
N/A | 0.231 | 0.050 | 0.285 | 0.086 | 0.101 | 0.071 | 0.129 | 0.213 | 0.080 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | F | A | A | A | B | F | B |
verified | N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 40 | 0 | 38 | 46 | 46 | 106 | 0 | 44 |
N.S. |
1 | 0.00 | 1.38 | 0.00 | 1.31 | 1.59 | 1.59 | 3.66 | 0.00 | 1.52 |
time (sec) |
N/A | 0.000 | 0.155 | 0.000 | 0.232 | 0.085 | 0.587 | 2.742 | 0.549 | 4.356 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | A | A | B | B | B | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 22 | 41 | 30 | 29 | 42 | 40 | 48 | 0 |
N.S. |
1 | 0.00 | 1.00 | 1.86 | 1.36 | 1.32 | 1.91 | 1.82 | 2.18 | 0.00 |
time (sec) |
N/A | 0.000 | 0.228 | 1.156 | 0.204 | 0.082 | 0.139 | 0.191 | 0.205 | 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 | 23 | 28 | 24 | 25 | 43 | 38 | 22 | 32 | 33 | 24 |
N.S. |
1 | 1.22 | 1.04 | 1.09 | 1.87 | 1.65 | 0.96 | 1.39 | 1.43 | 1.04 |
time (sec) |
N/A | 0.564 | 0.086 | 2.596 | 0.133 | 0.078 | 0.087 | 0.151 | 0.210 | 3.501 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 73 | 29 | 31 | 30 | 30 | 26 | 30 | 29 | 33 |
N.S. |
1 | 2.61 | 1.04 | 1.11 | 1.07 | 1.07 | 0.93 | 1.07 | 1.04 | 1.18 |
time (sec) |
N/A | 0.351 | 0.092 | 0.249 | 0.149 | 0.081 | 0.096 | 0.143 | 0.315 | 3.418 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 16 | 17 | 16 | 16 | 15 | 17 | 16 | 22 | 19 |
N.S. |
1 | 0.84 | 0.89 | 0.84 | 0.84 | 0.79 | 0.89 | 0.84 | 1.16 | 1.00 |
time (sec) |
N/A | 0.296 | 0.059 | 0.109 | 0.103 | 0.075 | 0.063 | 0.119 | 2.567 | 3.257 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | F | F | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 32 | 34 | 33 | 33 | 32 | 0 | 839 | 36 |
N.S. |
1 | 0.00 | 1.07 | 1.13 | 1.10 | 1.10 | 1.07 | 0.00 | 27.97 | 1.20 |
time (sec) |
N/A | 0.000 | 0.212 | 0.353 | 0.123 | 0.086 | 0.150 | 0.000 | 1.240 | 3.560 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 0 | 19 | 39 | 38 | 34 | 19 | 38 | 39 | 18 |
N.S. |
1 | 0.00 | 0.95 | 1.95 | 1.90 | 1.70 | 0.95 | 1.90 | 1.95 | 0.90 |
time (sec) |
N/A | 0.000 | 0.192 | 2.135 | 0.185 | 0.088 | 0.134 | 0.132 | 0.188 | 3.761 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F(-1) | B | A | A | B | B | B |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 27 | 27 | 0 | 61 | 24 | 22 | 68 | 104 | 22 |
N.S. |
1 | 0.96 | 0.96 | 0.00 | 2.18 | 0.86 | 0.79 | 2.43 | 3.71 | 0.79 |
time (sec) |
N/A | 0.397 | 0.106 | 180.000 | 0.182 | 0.074 | 0.078 | 0.145 | 0.183 | 4.171 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | F(-2) | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 25 | 25 | 36 | 36 | 0 | 24 | 27 | 24 |
N.S. |
1 | 0.00 | 0.86 | 0.86 | 1.24 | 1.24 | 0.00 | 0.83 | 0.93 | 0.83 |
time (sec) |
N/A | 0.000 | 2.970 | 0.223 | 0.089 | 0.085 | 0.000 | 0.169 | 0.178 | 3.484 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | B | B | A | B | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 141 | 76 | 61 | 108 | 56 | 61 | 118 | 55 | 31 |
N.S. |
1 | 4.86 | 2.62 | 2.10 | 3.72 | 1.93 | 2.10 | 4.07 | 1.90 | 1.07 |
time (sec) |
N/A | 0.282 | 0.069 | 0.436 | 0.031 | 0.089 | 0.116 | 0.112 | 0.195 | 3.447 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | A | B | B | B | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 70 | 42 | 61 | 63 | 51 | 33 | 44 | 59 |
N.S. |
1 | 0.00 | 2.69 | 1.62 | 2.35 | 2.42 | 1.96 | 1.27 | 1.69 | 2.27 |
time (sec) |
N/A | 0.000 | 0.224 | 0.314 | 0.143 | 0.093 | 0.340 | 0.127 | 0.199 | 4.051 |
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 | 19 | 28 | 21 | 20 | 25 | 19 | 20 | 19 | 21 | 19 |
N.S. |
1 | 1.47 | 1.11 | 1.05 | 1.32 | 1.00 | 1.05 | 1.00 | 1.11 | 1.00 |
time (sec) |
N/A | 0.195 | 0.013 | 0.156 | 0.035 | 0.078 | 0.060 | 0.120 | 0.196 | 0.053 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | B | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 25 | 42 | 34 | 73 | 37 | 38 | 93 | 99 |
N.S. |
1 | 0.00 | 1.09 | 1.83 | 1.48 | 3.17 | 1.61 | 1.65 | 4.04 | 4.30 |
time (sec) |
N/A | 0.000 | 0.120 | 0.928 | 0.085 | 0.105 | 0.109 | 0.218 | 0.199 | 3.601 |
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 | 27 | 25 | 23 | 27 | 22 | 17 | 22 | 52 | 25 |
N.S. |
1 | 1.08 | 1.00 | 0.92 | 1.08 | 0.88 | 0.68 | 0.88 | 2.08 | 1.00 |
time (sec) |
N/A | 0.864 | 0.051 | 12.566 | 0.264 | 0.088 | 0.493 | 0.292 | 0.210 | 4.281 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | B | B | B | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 107 | 34 | 31 | 108 | 72 | 136 | 256 | 82 | 1729 |
N.S. |
1 | 3.24 | 1.03 | 0.94 | 3.27 | 2.18 | 4.12 | 7.76 | 2.48 | 52.39 |
time (sec) |
N/A | 2.938 | 5.123 | 263.205 | 0.206 | 0.086 | 0.361 | 1.756 | 0.185 | 4.692 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 40 | 16 | 16 | 15 | 26 | 17 | 15 | 19 | 17 |
N.S. |
1 | 2.50 | 1.00 | 1.00 | 0.94 | 1.62 | 1.06 | 0.94 | 1.19 | 1.06 |
time (sec) |
N/A | 0.351 | 0.020 | 0.151 | 0.106 | 0.087 | 0.097 | 0.118 | 0.185 | 0.077 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 5 | 7 | 6 | 7 | 7 | 5 | 7 | 5 | 5 |
N.S. |
1 | 0.24 | 0.33 | 0.29 | 0.33 | 0.33 | 0.24 | 0.33 | 0.24 | 0.24 |
time (sec) |
N/A | 0.123 | 0.000 | 0.019 | 0.030 | 0.061 | 0.017 | 0.121 | 0.196 | 0.026 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | B | A | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 0 | 64 | 36 | 76 | 86 | 48 | 861 | 100 | 34 |
N.S. |
1 | 0.00 | 1.78 | 1.00 | 2.11 | 2.39 | 1.33 | 23.92 | 2.78 | 0.94 |
time (sec) |
N/A | 0.000 | 0.065 | 1.329 | 0.168 | 0.092 | 0.101 | 0.227 | 0.189 | 3.726 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | A | F(-1) | A | A | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 69 | 37 | 0 | 34 | 32 | 72 | 42 | 64 |
N.S. |
1 | 0.00 | 2.76 | 1.48 | 0.00 | 1.36 | 1.28 | 2.88 | 1.68 | 2.56 |
time (sec) |
N/A | 0.000 | 0.113 | 2.992 | 0.000 | 0.083 | 0.318 | 0.148 | 0.219 | 3.842 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | B | B | B | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 41 | 54 | 25 | 58 | 65 | 83 | 58 | 27 | 196 |
N.S. |
1 | 1.78 | 2.35 | 1.09 | 2.52 | 2.83 | 3.61 | 2.52 | 1.17 | 8.52 |
time (sec) |
N/A | 0.259 | 0.027 | 0.281 | 0.043 | 0.082 | 0.370 | 0.122 | 0.191 | 4.159 |
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 | 15 | 26 | 19 | 15 | 22 | 14 | 17 | 22 | 13 | 13 |
N.S. |
1 | 1.73 | 1.27 | 1.00 | 1.47 | 0.93 | 1.13 | 1.47 | 0.87 | 0.87 |
time (sec) |
N/A | 0.150 | 0.001 | 0.036 | 0.056 | 0.079 | 0.019 | 0.114 | 0.186 | 0.264 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 28 | 24 | 24 | 24 | 26 | 28 | 26 | 23 |
N.S. |
1 | 0.00 | 1.22 | 1.04 | 1.04 | 1.04 | 1.13 | 1.22 | 1.13 | 1.00 |
time (sec) |
N/A | 0.000 | 0.239 | 0.228 | 0.170 | 0.086 | 0.128 | 0.123 | 0.194 | 3.642 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | B | A | A | F | B | B |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 23 | 0 | 54 | 39 | 34 | 0 | 50 | 39 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 2.35 | 1.70 | 1.48 | 0.00 | 2.17 | 1.70 |
time (sec) |
N/A | 13.624 | 0.068 | 0.000 | 0.155 | 0.092 | 4.071 | 0.000 | 0.235 | 8.843 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 12 | 12 | 13 | 10 | 15 | 8 | 10 | 15 | 11 |
N.S. |
1 | 0.52 | 0.52 | 0.57 | 0.43 | 0.65 | 0.35 | 0.43 | 0.65 | 0.48 |
time (sec) |
N/A | 0.189 | 0.004 | 0.052 | 0.029 | 0.082 | 0.062 | 0.124 | 0.188 | 3.493 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 25 | 25 | 24 | 25 | 27 | 24 | 25 | 0 |
N.S. |
1 | 0.00 | 0.89 | 0.89 | 0.86 | 0.89 | 0.96 | 0.86 | 0.89 | 0.00 |
time (sec) |
N/A | 0.000 | 0.214 | 0.403 | 0.086 | 0.080 | 0.147 | 0.177 | 0.183 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 23 | 22 | 22 | 22 | 22 | 22 | 24 | 33 |
N.S. |
1 | 0.00 | 0.82 | 0.79 | 0.79 | 0.79 | 0.79 | 0.79 | 0.86 | 1.18 |
time (sec) |
N/A | 0.000 | 0.076 | 0.684 | 0.074 | 0.075 | 0.060 | 0.121 | 0.185 | 3.571 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | A | C | A | A | A | B | B |
verified | N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 0 | 39 | 40 | 23 | 41 | 41 | 42 | 41 |
N.S. |
1 | 0.00 | 0.00 | 1.50 | 1.54 | 0.88 | 1.58 | 1.58 | 1.62 | 1.58 |
time (sec) |
N/A | 0.000 | 0.000 | 0.309 | 0.157 | 0.093 | 0.229 | 0.158 | 0.179 | 3.880 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | B | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 0 | 18 | 18 | 31 | 35 | 34 | 17 | 19 | 29 |
N.S. |
1 | 0.00 | 0.95 | 0.95 | 1.63 | 1.84 | 1.79 | 0.89 | 1.00 | 1.53 |
time (sec) |
N/A | 0.000 | 0.392 | 0.204 | 0.085 | 0.083 | 0.397 | 0.133 | 0.190 | 3.716 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | B | F(-1) | B | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 0 | 44 | 38 | 47 | 40 | 58 | 0 | 54 | 0 |
N.S. |
1 | 0.00 | 1.26 | 1.09 | 1.34 | 1.14 | 1.66 | 0.00 | 1.54 | 0.00 |
time (sec) |
N/A | 0.000 | 0.075 | 0.670 | 0.126 | 0.080 | 0.174 | 0.000 | 0.230 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | C | A | A | A | A | F | B |
verified | N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 24 | 2484 | 35 | 34 | 27 | 46 | 151 | 35 |
N.S. |
1 | 0.00 | 1.00 | 103.50 | 1.46 | 1.42 | 1.12 | 1.92 | 6.29 | 1.46 |
time (sec) |
N/A | 0.000 | 0.070 | 154.815 | 0.179 | 0.088 | 0.635 | 0.289 | 200.032 | 4.261 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 32 | 26 | 24 | 26 | 31 | 28 | 31 | 27 |
N.S. |
1 | 0.00 | 1.00 | 0.81 | 0.75 | 0.81 | 0.97 | 0.88 | 0.97 | 0.84 |
time (sec) |
N/A | 0.000 | 0.985 | 0.085 | 0.097 | 0.090 | 0.116 | 0.132 | 0.372 | 0.100 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | F(-1) | A | A | A | F(-1) | B | B |
verified | N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 38 | 0 | 33 | 36 | 34 | 0 | 38 | 36 |
N.S. |
1 | 0.00 | 1.19 | 0.00 | 1.03 | 1.12 | 1.06 | 0.00 | 1.19 | 1.12 |
time (sec) |
N/A | 0.000 | 0.181 | 0.000 | 0.088 | 0.107 | 0.197 | 0.000 | 0.374 | 3.889 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F | A | A | F | B | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 26 | 23 | 0 | 25 | 20 | 0 | 54 | 0 |
N.S. |
1 | 0.00 | 0.96 | 0.85 | 0.00 | 0.93 | 0.74 | 0.00 | 2.00 | 0.00 |
time (sec) |
N/A | 0.000 | 0.102 | 0.297 | 0.000 | 0.086 | 0.094 | 0.000 | 0.199 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 36 | 18 | 15 | 0 | 14 | 15 | 14 | 19 | 14 |
N.S. |
1 | 1.80 | 0.90 | 0.75 | 0.00 | 0.70 | 0.75 | 0.70 | 0.95 | 0.70 |
time (sec) |
N/A | 0.199 | 0.015 | 0.088 | 0.000 | 0.083 | 0.080 | 0.115 | 0.156 | 0.070 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | C | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 124 | 42 | 30 | 135 | 36 | 29 | 47 | 50 | 37 |
N.S. |
1 | 4.96 | 1.68 | 1.20 | 5.40 | 1.44 | 1.16 | 1.88 | 2.00 | 1.48 |
time (sec) |
N/A | 0.436 | 0.071 | 0.410 | 0.150 | 0.089 | 0.082 | 0.130 | 0.166 | 3.550 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | B | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 36 | 26 | 21 | 89 | 29 | 52 | 28 | 22 |
N.S. |
1 | 0.00 | 1.29 | 0.93 | 0.75 | 3.18 | 1.04 | 1.86 | 1.00 | 0.79 |
time (sec) |
N/A | 0.000 | 0.075 | 119.625 | 0.155 | 0.092 | 2.945 | 0.159 | 0.253 | 0.260 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | F | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 30 | 28 | 27 | 27 | 26 | 27 | 436 | 27 |
N.S. |
1 | 0.00 | 1.30 | 1.22 | 1.17 | 1.17 | 1.13 | 1.17 | 18.96 | 1.17 |
time (sec) |
N/A | 0.000 | 4.015 | 0.121 | 0.159 | 0.096 | 0.113 | 0.128 | 0.295 | 3.541 |
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 | 20 | 18 | 18 | 20 | 20 | 20 | 35 | 22 | 17 |
N.S. |
1 | 0.91 | 0.82 | 0.82 | 0.91 | 0.91 | 0.91 | 1.59 | 1.00 | 0.77 |
time (sec) |
N/A | 0.300 | 0.022 | 0.077 | 0.030 | 0.088 | 0.068 | 0.120 | 0.169 | 3.515 |
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 | 7 | 7 | 8 | 7 | 7 | 7 | 7 | 7 | 7 |
N.S. |
1 | 0.58 | 0.58 | 0.67 | 0.58 | 0.58 | 0.58 | 0.58 | 0.58 | 0.58 |
time (sec) |
N/A | 0.130 | 0.000 | 0.009 | 0.031 | 0.058 | 0.015 | 0.126 | 0.163 | 0.002 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 313 | 16 | 16 | 15 | 15 | 12 | 15 | 16 | 15 |
N.S. |
1 | 13.61 | 0.70 | 0.70 | 0.65 | 0.65 | 0.52 | 0.65 | 0.70 | 0.65 |
time (sec) |
N/A | 0.847 | 0.205 | 0.063 | 0.068 | 0.074 | 0.057 | 0.124 | 0.156 | 0.155 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | A | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 36 | 32 | 37 | 67 | 64 | 31 | 223 | 173 | 37 |
N.S. |
1 | 1.57 | 1.39 | 1.61 | 2.91 | 2.78 | 1.35 | 9.70 | 7.52 | 1.61 |
time (sec) |
N/A | 1.859 | 0.077 | 23.891 | 0.204 | 0.104 | 0.182 | 0.415 | 0.192 | 58.378 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | A | F(-1) | F | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 71 | 28 | 21 | 20 | 20 | 0 | 0 | 30 | 22 |
N.S. |
1 | 2.54 | 1.00 | 0.75 | 0.71 | 0.71 | 0.00 | 0.00 | 1.07 | 0.79 |
time (sec) |
N/A | 0.432 | 0.889 | 7.738 | 0.489 | 0.099 | 0.000 | 0.000 | 0.195 | 3.510 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 7 | 7 | 8 | 7 | 9 | 3 | 7 | 9 | 7 |
N.S. |
1 | 0.39 | 0.39 | 0.44 | 0.39 | 0.50 | 0.17 | 0.39 | 0.50 | 0.39 |
time (sec) |
N/A | 0.142 | 0.001 | 0.017 | 0.027 | 0.070 | 0.031 | 0.126 | 0.162 | 0.019 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | F(-1) | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 15 | 15 | 11 | 45 | 11 | 0 | 11 | 11 | 10 |
N.S. |
1 | 1.07 | 1.07 | 0.79 | 3.21 | 0.79 | 0.00 | 0.79 | 0.79 | 0.71 |
time (sec) |
N/A | 0.183 | 1.114 | 0.034 | 0.065 | 0.088 | 0.000 | 0.120 | 0.184 | 3.469 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 21 | 24 | 32 | 32 | 19 | 32 | 33 | 23 |
N.S. |
1 | 0.00 | 0.75 | 0.86 | 1.14 | 1.14 | 0.68 | 1.14 | 1.18 | 0.82 |
time (sec) |
N/A | 0.000 | 0.280 | 0.147 | 0.150 | 0.099 | 0.050 | 0.133 | 0.178 | 3.476 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 18 | 17 | 23 | 26 | 20 | 17 | 22 | 20 | 16 |
N.S. |
1 | 1.06 | 1.00 | 1.35 | 1.53 | 1.18 | 1.00 | 1.29 | 1.18 | 0.94 |
time (sec) |
N/A | 0.453 | 0.032 | 0.243 | 0.094 | 0.081 | 2.127 | 0.124 | 0.171 | 3.555 |
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 | 48 | 26 | 25 | 33 | 33 | 34 | 33 | 41 | 22 |
N.S. |
1 | 1.78 | 0.96 | 0.93 | 1.22 | 1.22 | 1.26 | 1.22 | 1.52 | 0.81 |
time (sec) |
N/A | 0.205 | 0.003 | 0.073 | 0.031 | 0.078 | 0.024 | 0.120 | 0.173 | 3.465 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | A | B | B | A | B | B | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 0 | 54 | 30 | 57 | 57 | 29 | 53 | 53 | 0 |
N.S. |
1 | 0.00 | 2.84 | 1.58 | 3.00 | 3.00 | 1.53 | 2.79 | 2.79 | 0.00 |
time (sec) |
N/A | 0.000 | 0.477 | 0.310 | 0.079 | 0.102 | 0.278 | 0.124 | 0.167 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | A | B | A | A | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 94 | 51 | 32 | 69 | 31 | 31 | 68 | 30 | 58 |
N.S. |
1 | 3.76 | 2.04 | 1.28 | 2.76 | 1.24 | 1.24 | 2.72 | 1.20 | 2.32 |
time (sec) |
N/A | 0.785 | 0.666 | 0.585 | 0.245 | 0.088 | 0.167 | 0.156 | 0.167 | 3.714 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 24 | 23 | 37 | 35 | 19 | 28 | 40 | 40 |
N.S. |
1 | 0.00 | 0.83 | 0.79 | 1.28 | 1.21 | 0.66 | 0.97 | 1.38 | 1.38 |
time (sec) |
N/A | 0.000 | 0.191 | 4.421 | 0.203 | 0.110 | 0.113 | 0.202 | 0.172 | 3.915 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 28 | 36 | 26 | 27 | 27 | 27 | 27 | 25 | 24 |
N.S. |
1 | 1.33 | 1.71 | 1.24 | 1.29 | 1.29 | 1.29 | 1.29 | 1.19 | 1.14 |
time (sec) |
N/A | 0.161 | 0.002 | 0.041 | 0.034 | 0.075 | 0.023 | 0.124 | 0.167 | 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 | 22 | 19 | 26 | 23 | 19 | 24 | 27 | 24 | 27 | 23 |
N.S. |
1 | 0.86 | 1.18 | 1.05 | 0.86 | 1.09 | 1.23 | 1.09 | 1.23 | 1.05 |
time (sec) |
N/A | 0.488 | 0.124 | 0.203 | 0.065 | 0.083 | 0.105 | 0.129 | 0.178 | 3.769 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 13 | 13 | 14 | 13 | 13 | 10 | 13 | 13 | 13 |
N.S. |
1 | 0.65 | 0.65 | 0.70 | 0.65 | 0.65 | 0.50 | 0.65 | 0.65 | 0.65 |
time (sec) |
N/A | 0.338 | 0.010 | 0.120 | 0.071 | 0.079 | 0.052 | 0.120 | 0.170 | 3.833 |
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 | 6 | 6 | 6 | 7 | 6 | 6 | 7 | 6 | 6 | 6 |
N.S. |
1 | 1.00 | 1.00 | 1.17 | 1.00 | 1.00 | 1.17 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.147 | 0.002 | 0.034 | 0.031 | 0.086 | 0.040 | 0.121 | 0.169 | 3.771 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 35 | 30 | 37 | 41 | 37 | 29 | 32 | 29 |
N.S. |
1 | 0.00 | 1.17 | 1.00 | 1.23 | 1.37 | 1.23 | 0.97 | 1.07 | 0.97 |
time (sec) |
N/A | 0.000 | 4.591 | 0.287 | 0.094 | 0.089 | 0.386 | 0.170 | 0.178 | 3.885 |
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 | 34 | 34 | 28 | 33 | 37 | 26 | 31 | 47 | 27 |
N.S. |
1 | 1.17 | 1.17 | 0.97 | 1.14 | 1.28 | 0.90 | 1.07 | 1.62 | 0.93 |
time (sec) |
N/A | 1.291 | 5.044 | 1.166 | 0.084 | 0.092 | 0.139 | 0.129 | 0.169 | 3.546 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 19 | 19 | 18 | 17 | 17 | 19 | 18 | 19 | 17 |
N.S. |
1 | 0.83 | 0.83 | 0.78 | 0.74 | 0.74 | 0.83 | 0.78 | 0.83 | 0.74 |
time (sec) |
N/A | 0.142 | 0.005 | 0.141 | 0.034 | 0.084 | 0.046 | 0.117 | 0.176 | 0.164 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 13 | 11 | 10 | 9 | 9 | 10 | 9 | 11 | 11 |
N.S. |
1 | 0.93 | 0.79 | 0.71 | 0.64 | 0.64 | 0.71 | 0.64 | 0.79 | 0.79 |
time (sec) |
N/A | 0.146 | 0.001 | 0.033 | 0.033 | 0.080 | 0.034 | 0.119 | 0.205 | 3.476 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | B | B |
verified | N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 19 | 17 | 13 | 12 | 23 | 12 | 0 | 16 | 12 |
N.S. |
1 | 0.90 | 0.81 | 0.62 | 0.57 | 1.10 | 0.57 | 0.00 | 0.76 | 0.57 |
time (sec) |
N/A | 0.219 | 0.014 | 0.067 | 0.107 | 0.092 | 0.083 | 0.000 | 0.166 | 3.539 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 11 | 15 | 7 | 9 | 9 | 10 | 9 | 8 | 6 |
N.S. |
1 | 0.55 | 0.75 | 0.35 | 0.45 | 0.45 | 0.50 | 0.45 | 0.40 | 0.30 |
time (sec) |
N/A | 0.128 | 0.000 | 0.011 | 0.033 | 0.060 | 0.019 | 0.119 | 0.170 | 0.030 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 14 | 14 | 14 | 0 | 13 | 14 | 20 | 14 | 13 |
N.S. |
1 | 0.82 | 0.82 | 0.82 | 0.00 | 0.76 | 0.82 | 1.18 | 0.82 | 0.76 |
time (sec) |
N/A | 0.461 | 0.045 | 1.074 | 0.000 | 0.092 | 0.124 | 0.132 | 0.179 | 3.744 |
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 | 11 | 11 | 10 | 9 | 9 | 8 | 9 | 9 | 9 |
N.S. |
1 | 0.85 | 0.85 | 0.77 | 0.69 | 0.69 | 0.62 | 0.69 | 0.69 | 0.69 |
time (sec) |
N/A | 0.244 | 0.014 | 0.026 | 0.044 | 0.080 | 0.044 | 0.121 | 0.217 | 3.419 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 17 | 13 | 11 | 10 | 10 | 10 | 10 | 11 | 10 |
N.S. |
1 | 1.06 | 0.81 | 0.69 | 0.62 | 0.62 | 0.62 | 0.62 | 0.69 | 0.62 |
time (sec) |
N/A | 0.172 | 0.003 | 0.066 | 0.043 | 0.078 | 0.045 | 0.117 | 0.188 | 0.037 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 27 | 25 | 23 | 24 | 34 | 50 | 27 | 24 |
N.S. |
1 | 0.00 | 0.93 | 0.86 | 0.79 | 0.83 | 1.17 | 1.72 | 0.93 | 0.83 |
time (sec) |
N/A | 0.000 | 0.407 | 149.628 | 0.118 | 0.095 | 0.281 | 49.112 | 0.211 | 5.580 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | A | A | A | A | A | B | B |
verified | N/A | Yes | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 37 | 26 | 0 | 26 | 38 | 34 | 29 | 27 | 25 | 35 |
N.S. |
1 | 0.70 | 0.00 | 0.70 | 1.03 | 0.92 | 0.78 | 0.73 | 0.68 | 0.95 |
time (sec) |
N/A | 0.518 | 0.000 | 0.476 | 0.177 | 0.098 | 0.184 | 0.143 | 0.178 | 6.030 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 0 | 46 | 45 | 42 | 48 | 24 | 48 | 72 | 27 |
N.S. |
1 | 0.00 | 1.28 | 1.25 | 1.17 | 1.33 | 0.67 | 1.33 | 2.00 | 0.75 |
time (sec) |
N/A | 0.000 | 0.084 | 55.944 | 0.343 | 0.109 | 0.975 | 78.780 | 0.238 | 3.677 |
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 | 16 | 16 | 14 | 13 | 13 | 14 | 13 | 19 | 14 |
N.S. |
1 | 0.48 | 0.48 | 0.42 | 0.39 | 0.39 | 0.42 | 0.39 | 0.58 | 0.42 |
time (sec) |
N/A | 0.200 | 0.012 | 0.031 | 0.028 | 0.078 | 0.044 | 0.123 | 0.176 | 0.072 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 21 | 21 | 0 | 20 | 15 | 30 | 21 | 20 |
N.S. |
1 | 0.00 | 0.68 | 0.68 | 0.00 | 0.65 | 0.48 | 0.97 | 0.68 | 0.65 |
time (sec) |
N/A | 0.000 | 0.485 | 0.669 | 0.000 | 0.079 | 0.208 | 0.143 | 0.192 | 4.150 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 18 | 28 | 18 | 0 | 39 | 19 | 34 | 50 | 17 |
N.S. |
1 | 0.75 | 1.17 | 0.75 | 0.00 | 1.62 | 0.79 | 1.42 | 2.08 | 0.71 |
time (sec) |
N/A | 0.377 | 0.265 | 0.132 | 0.000 | 0.075 | 0.059 | 0.121 | 0.179 | 0.125 |
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 | 22 | 21 | 21 | 20 | 21 | 21 | 17 |
N.S. |
1 | 1.18 | 1.00 | 1.00 | 0.95 | 0.95 | 0.91 | 0.95 | 0.95 | 0.77 |
time (sec) |
N/A | 0.217 | 0.048 | 0.110 | 0.044 | 0.069 | 0.042 | 0.122 | 0.220 | 0.040 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | B | A | C | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 31 | 22 | 18 | 270 | 45 | 32 | 179 | 47 | 24 |
N.S. |
1 | 1.24 | 0.88 | 0.72 | 10.80 | 1.80 | 1.28 | 7.16 | 1.88 | 0.96 |
time (sec) |
N/A | 0.757 | 1.065 | 0.344 | 0.167 | 0.087 | 0.086 | 0.172 | 0.185 | 0.244 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 17 | 23 | 17 | 40 | 22 | 17 | 22 | 19 | 16 |
N.S. |
1 | 0.65 | 0.88 | 0.65 | 1.54 | 0.85 | 0.65 | 0.85 | 0.73 | 0.62 |
time (sec) |
N/A | 0.292 | 0.052 | 0.115 | 0.070 | 0.083 | 0.044 | 0.123 | 0.184 | 3.502 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | A | A | F | F | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 42 | 44 | 66 | 44 | 37 | 0 | 1178 | 42 |
N.S. |
1 | 0.00 | 1.62 | 1.69 | 2.54 | 1.69 | 1.42 | 0.00 | 45.31 | 1.62 |
time (sec) |
N/A | 0.000 | 0.119 | 28.933 | 1.105 | 0.094 | 2.811 | 0.000 | 1.124 | 4.335 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 29 | 28 | 29 | 40 | 33 | 37 | 33 | 32 | 38 |
N.S. |
1 | 1.26 | 1.22 | 1.26 | 1.74 | 1.43 | 1.61 | 1.43 | 1.39 | 1.65 |
time (sec) |
N/A | 0.199 | 0.006 | 0.100 | 0.036 | 0.083 | 0.061 | 0.127 | 0.193 | 3.529 |
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 | 28 | 37 | 25 | 21 | 32 | 32 | 36 | 32 | 29 | 30 |
N.S. |
1 | 1.32 | 0.89 | 0.75 | 1.14 | 1.14 | 1.29 | 1.14 | 1.04 | 1.07 |
time (sec) |
N/A | 0.177 | 0.004 | 0.040 | 0.034 | 0.078 | 0.024 | 0.124 | 0.201 | 3.524 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | B | F | B | B | B | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 170 | 24 | 154 | 0 | 77 | 148 | 285 | 107 | 0 |
N.S. |
1 | 7.08 | 1.00 | 6.42 | 0.00 | 3.21 | 6.17 | 11.88 | 4.46 | 0.00 |
time (sec) |
N/A | 1.696 | 0.109 | 0.057 | 0.000 | 0.089 | 0.289 | 0.136 | 0.187 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | A | B | A | A | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 117 | 71 | 32 | 115 | 19 | 29 | 42 | 113 | 31 |
N.S. |
1 | 5.85 | 3.55 | 1.60 | 5.75 | 0.95 | 1.45 | 2.10 | 5.65 | 1.55 |
time (sec) |
N/A | 0.415 | 0.059 | 0.323 | 0.185 | 0.080 | 0.156 | 0.136 | 0.197 | 3.672 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 22 | 22 | 20 | 19 | 19 | 17 | 0 | 23 | 20 |
N.S. |
1 | 0.92 | 0.92 | 0.83 | 0.79 | 0.79 | 0.71 | 0.00 | 0.96 | 0.83 |
time (sec) |
N/A | 0.237 | 0.030 | 0.076 | 0.031 | 0.092 | 0.124 | 0.000 | 0.208 | 3.504 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | B | B | B | F | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 0 | 66 | 60 | 58 | 63 | 65 | 0 | 59 | 56 |
N.S. |
1 | 0.00 | 1.94 | 1.76 | 1.71 | 1.85 | 1.91 | 0.00 | 1.74 | 1.65 |
time (sec) |
N/A | 0.000 | 0.115 | 12.224 | 0.384 | 0.092 | 0.243 | 0.000 | 0.198 | 4.077 |
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 | 28 | 29 | 26 | 26 | 34 | 32 | 30 | 26 | 4850 |
N.S. |
1 | 1.12 | 1.16 | 1.04 | 1.04 | 1.36 | 1.28 | 1.20 | 1.04 | 194.00 |
time (sec) |
N/A | 0.268 | 0.021 | 0.137 | 0.028 | 0.076 | 0.709 | 0.133 | 0.193 | 6.298 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 36 | 30 | 17 | 16 | 16 | 14 | 17 | 16 | 16 |
N.S. |
1 | 1.29 | 1.07 | 0.61 | 0.57 | 0.57 | 0.50 | 0.61 | 0.57 | 0.57 |
time (sec) |
N/A | 0.215 | 0.023 | 0.106 | 0.025 | 0.066 | 0.046 | 0.125 | 0.177 | 0.071 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | B | B | A | F(-2) | B | B | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 79 | 74 | 159 | 41 | 0 | 85 | 85 | 0 |
N.S. |
1 | 0.00 | 3.04 | 2.85 | 6.12 | 1.58 | 0.00 | 3.27 | 3.27 | 0.00 |
time (sec) |
N/A | 0.000 | 44.288 | 20.176 | 0.181 | 0.086 | 0.000 | 0.988 | 0.224 | 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 | 8 | 8 | 8 | 8 | 7 | 7 | 5 | 7 | 8 | 7 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.88 | 0.88 | 0.62 | 0.88 | 1.00 | 0.88 |
time (sec) |
N/A | 0.136 | 0.000 | 0.017 | 0.038 | 0.071 | 0.041 | 0.111 | 0.174 | 0.020 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | A | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 40 | 36 | 28 | 68 | 63 | 20 | 87 | 83 | 27 |
N.S. |
1 | 1.38 | 1.24 | 0.97 | 2.34 | 2.17 | 0.69 | 3.00 | 2.86 | 0.93 |
time (sec) |
N/A | 1.760 | 2.592 | 1.002 | 0.140 | 0.099 | 0.144 | 0.174 | 0.184 | 0.366 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 31 | 30 | 25 | 31 | 32 | 24 | 32 | 59 | 28 |
N.S. |
1 | 1.03 | 1.00 | 0.83 | 1.03 | 1.07 | 0.80 | 1.07 | 1.97 | 0.93 |
time (sec) |
N/A | 0.288 | 0.061 | 0.199 | 0.063 | 0.090 | 0.091 | 0.128 | 0.173 | 3.702 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 36 | 28 | 26 | 31 | 30 | 34 | 32 | 26 | 26 |
N.S. |
1 | 1.71 | 1.33 | 1.24 | 1.48 | 1.43 | 1.62 | 1.52 | 1.24 | 1.24 |
time (sec) |
N/A | 0.273 | 0.008 | 0.051 | 0.045 | 0.076 | 0.207 | 0.126 | 0.190 | 0.088 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 20 | 20 | 18 | 373 | 19 | 20 | 36 | 20 | 19 |
N.S. |
1 | 0.91 | 0.91 | 0.82 | 16.95 | 0.86 | 0.91 | 1.64 | 0.91 | 0.86 |
time (sec) |
N/A | 0.221 | 0.199 | 0.107 | 0.119 | 0.089 | 0.087 | 0.122 | 0.181 | 3.660 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | F | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 32 | 39 | 51 | 51 | 39 | 33 | 179 | 47 |
N.S. |
1 | 0.00 | 1.14 | 1.39 | 1.82 | 1.82 | 1.39 | 1.18 | 6.39 | 1.68 |
time (sec) |
N/A | 0.000 | 0.132 | 0.030 | 0.119 | 0.099 | 0.372 | 0.190 | 200.014 | 5.126 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 33 | 40 | 39 | 40 | 37 | 33 | 48 | 36 |
N.S. |
1 | 0.00 | 1.18 | 1.43 | 1.39 | 1.43 | 1.32 | 1.18 | 1.71 | 1.29 |
time (sec) |
N/A | 0.000 | 0.112 | 1.765 | 0.188 | 0.082 | 0.483 | 0.233 | 0.175 | 3.697 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 21 | 21 | 16 | 16 | 16 | 19 | 16 | 18 | 15 |
N.S. |
1 | 1.50 | 1.50 | 1.14 | 1.14 | 1.14 | 1.36 | 1.14 | 1.29 | 1.07 |
time (sec) |
N/A | 0.155 | 0.003 | 0.070 | 0.029 | 0.088 | 0.055 | 0.120 | 0.168 | 0.043 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 23 | 64 | 71 | 62 | 54 | 66 | 97 | 69 | 66 |
N.S. |
1 | 0.85 | 2.37 | 2.63 | 2.30 | 2.00 | 2.44 | 3.59 | 2.56 | 2.44 |
time (sec) |
N/A | 0.877 | 0.040 | 0.738 | 0.167 | 0.091 | 0.219 | 0.235 | 0.173 | 3.869 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 21 | 21 | 19 | 0 | 18 | 17 | 21 | 19 | 18 |
N.S. |
1 | 0.84 | 0.84 | 0.76 | 0.00 | 0.72 | 0.68 | 0.84 | 0.76 | 0.72 |
time (sec) |
N/A | 0.427 | 0.012 | 6.047 | 0.000 | 0.080 | 0.112 | 0.116 | 0.169 | 3.678 |
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 | 34 | 29 | 29 | 28 | 32 | 29 | 32 | 33 | 32 |
N.S. |
1 | 1.26 | 1.07 | 1.07 | 1.04 | 1.19 | 1.07 | 1.19 | 1.22 | 1.19 |
time (sec) |
N/A | 0.231 | 0.400 | 0.256 | 0.035 | 0.076 | 0.065 | 0.131 | 0.163 | 0.136 |