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 | B | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 0 | 29 | 32 | 41 | 37 | 44 | 49 | 35 | 26 |
N.S. |
1 | 0.00 | 0.85 | 0.94 | 1.21 | 1.09 | 1.29 | 1.44 | 1.03 | 0.76 |
time (sec) |
N/A | 0.000 | 0.053 | 0.026 | 0.092 | 0.097 | 0.145 | 0.154 | 0.160 | 3.238 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | B | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 56 | 25 | 51 | 21 | 32 | 19 | 23 | 43 | 23 |
N.S. |
1 | 2.24 | 1.00 | 2.04 | 0.84 | 1.28 | 0.76 | 0.92 | 1.72 | 0.92 |
time (sec) |
N/A | 1.023 | 2.056 | 0.868 | 0.072 | 0.103 | 1.112 | 0.139 | 0.157 | 3.212 |
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 | 22 | 19 | 19 | 18 | 18 | 31 | 18 | 41 | 18 |
N.S. |
1 | 0.81 | 0.70 | 0.70 | 0.67 | 0.67 | 1.15 | 0.67 | 1.52 | 0.67 |
time (sec) |
N/A | 0.176 | 0.022 | 0.095 | 0.031 | 0.084 | 0.063 | 0.105 | 0.153 | 3.151 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | F | B | B | A | F(-1) | A | B | B |
verified | N/A | Yes | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 88 | 0 | 52 | 58 | 45 | 0 | 47 | 54 | 48 |
N.S. |
1 | 3.14 | 0.00 | 1.86 | 2.07 | 1.61 | 0.00 | 1.68 | 1.93 | 1.71 |
time (sec) |
N/A | 0.490 | 0.000 | 5.267 | 0.213 | 0.095 | 0.000 | 1.350 | 0.156 | 3.792 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | F | B | B | B | B | F | B | B |
verified | N/A | Yes | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 112 | 0 | 48 | 56 | 49 | 51 | 0 | 68 | 58 |
N.S. |
1 | 4.67 | 0.00 | 2.00 | 2.33 | 2.04 | 2.12 | 0.00 | 2.83 | 2.42 |
time (sec) |
N/A | 0.713 | 0.000 | 0.548 | 0.317 | 0.108 | 0.216 | 0.000 | 9.873 | 3.240 |
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 | 25 | 35 | 33 | 27 | 287 | 38 | 29 | 38 | 35 | 38 |
N.S. |
1 | 1.40 | 1.32 | 1.08 | 11.48 | 1.52 | 1.16 | 1.52 | 1.40 | 1.52 |
time (sec) |
N/A | 1.166 | 0.030 | 0.467 | 0.175 | 0.086 | 0.057 | 0.137 | 0.152 | 3.136 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | B | A | F | F | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 32 | 24 | 28 | 91 | 26 | 0 | 537 | 31 |
N.S. |
1 | 0.00 | 1.10 | 0.83 | 0.97 | 3.14 | 0.90 | 0.00 | 18.52 | 1.07 |
time (sec) |
N/A | 0.000 | 5.069 | 0.296 | 0.239 | 0.097 | 0.627 | 0.000 | 0.639 | 3.249 |
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 | 21 | 0 | 23 | 24 | 23 | 23 | 0 | 23 | 23 | 23 |
N.S. |
1 | 0.00 | 1.10 | 1.14 | 1.10 | 1.10 | 0.00 | 1.10 | 1.10 | 1.10 |
time (sec) |
N/A | 0.000 | 0.041 | 0.546 | 0.075 | 0.085 | 0.000 | 0.132 | 0.147 | 3.177 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | B | A | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 87 | 45 | 41 | 38 | 53 | 44 | 45 | 57 | 43 |
N.S. |
1 | 3.62 | 1.88 | 1.71 | 1.58 | 2.21 | 1.83 | 1.88 | 2.38 | 1.79 |
time (sec) |
N/A | 0.481 | 0.192 | 0.207 | 0.098 | 0.098 | 0.185 | 0.121 | 0.146 | 0.308 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 11 | 7 | 9 | 8 | 7 | 9 | 7 | 7 | 7 | 8 |
N.S. |
1 | 0.64 | 0.82 | 0.73 | 0.64 | 0.82 | 0.64 | 0.64 | 0.64 | 0.73 |
time (sec) |
N/A | 0.134 | 0.000 | 0.021 | 0.027 | 0.063 | 0.015 | 0.111 | 0.142 | 0.001 |
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 | 25 | 0 | 27 | 26 | 34 | 25 | 37 | 25 | 27 | 66 |
N.S. |
1 | 0.00 | 1.08 | 1.04 | 1.36 | 1.00 | 1.48 | 1.00 | 1.08 | 2.64 |
time (sec) |
N/A | 0.000 | 0.611 | 0.914 | 0.206 | 0.083 | 0.110 | 0.136 | 0.151 | 3.354 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | B | F(-1) | F | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 98 | 29 | 38 | 44 | 133 | 0 | 0 | 189 | 41 |
N.S. |
1 | 3.38 | 1.00 | 1.31 | 1.52 | 4.59 | 0.00 | 0.00 | 6.52 | 1.41 |
time (sec) |
N/A | 1.221 | 0.248 | 164.250 | 0.121 | 0.110 | 0.000 | 0.000 | 200.015 | 3.566 |
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 | 16 | 16 | 16 | 17 | 19 | 16 | 34 | 19 | 16 | 16 |
N.S. |
1 | 1.00 | 1.00 | 1.06 | 1.19 | 1.00 | 2.12 | 1.19 | 1.00 | 1.00 |
time (sec) |
N/A | 1.061 | 0.171 | 0.398 | 0.063 | 0.090 | 0.334 | 0.137 | 0.169 | 3.707 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | A | A | A | A | F | B | B |
verified | N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 37 | 0 | 0 | 22 | 31 | 24 | 22 | 0 | 26 | 31 |
N.S. |
1 | 0.00 | 0.00 | 0.59 | 0.84 | 0.65 | 0.59 | 0.00 | 0.70 | 0.84 |
time (sec) |
N/A | 0.000 | 0.000 | 0.339 | 0.152 | 0.097 | 0.115 | 0.000 | 0.153 | 3.170 |
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 | 11 | 9 | 8 | 9 | 9 | 7 | 9 | 7 | 7 |
N.S. |
1 | 0.69 | 0.56 | 0.50 | 0.56 | 0.56 | 0.44 | 0.56 | 0.44 | 0.44 |
time (sec) |
N/A | 0.131 | 0.000 | 0.017 | 0.039 | 0.071 | 0.018 | 0.110 | 0.154 | 0.017 |
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 | 27 | 0 | 16 | 23 | 22 | 22 | 20 | 22 | 22 | 41 |
N.S. |
1 | 0.00 | 0.59 | 0.85 | 0.81 | 0.81 | 0.74 | 0.81 | 0.81 | 1.52 |
time (sec) |
N/A | 0.000 | 0.126 | 0.600 | 0.072 | 0.109 | 0.077 | 0.285 | 0.156 | 3.300 |
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 | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 16 | 19 | 14 | 12 | 14 | 12 | 17 | 12 |
N.S. |
1 | 1.00 | 1.00 | 1.19 | 0.88 | 0.75 | 0.88 | 0.75 | 1.06 | 0.75 |
time (sec) |
N/A | 0.222 | 0.018 | 0.061 | 0.064 | 0.096 | 0.068 | 0.112 | 0.153 | 0.052 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | B | B | B | B | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 306 | 18 | 48 | 45 | 45 | 42 | 51 | 48 | 17 |
N.S. |
1 | 14.57 | 0.86 | 2.29 | 2.14 | 2.14 | 2.00 | 2.43 | 2.29 | 0.81 |
time (sec) |
N/A | 1.289 | 0.097 | 0.858 | 0.149 | 0.104 | 0.124 | 0.118 | 0.151 | 3.119 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 15 | 15 | 14 | 13 | 13 | 12 | 13 | 16 | 13 |
N.S. |
1 | 0.79 | 0.79 | 0.74 | 0.68 | 0.68 | 0.63 | 0.68 | 0.84 | 0.68 |
time (sec) |
N/A | 0.152 | 0.006 | 0.059 | 0.032 | 0.099 | 0.070 | 0.115 | 0.157 | 3.101 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | C | F(-1) | C | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 17 | 74 | 30 | 27 | 49 | 0 | 51 | 69 | 16 |
N.S. |
1 | 1.00 | 4.35 | 1.76 | 1.59 | 2.88 | 0.00 | 3.00 | 4.06 | 0.94 |
time (sec) |
N/A | 0.343 | 0.046 | 0.263 | 0.065 | 0.100 | 0.000 | 0.135 | 0.163 | 3.749 |
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 | 32 | 25 | 28 | 26 | 71 | 28 | 22 | 25 | 28 | 54 |
N.S. |
1 | 0.78 | 0.88 | 0.81 | 2.22 | 0.88 | 0.69 | 0.78 | 0.88 | 1.69 |
time (sec) |
N/A | 0.492 | 0.036 | 0.157 | 0.130 | 0.094 | 0.092 | 0.140 | 0.150 | 0.154 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | A | F | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 14 | 21 | 16 | 0 | 21 | 17 | 0 | 15 | 18 |
N.S. |
1 | 0.67 | 1.00 | 0.76 | 0.00 | 1.00 | 0.81 | 0.00 | 0.71 | 0.86 |
time (sec) |
N/A | 0.278 | 0.092 | 0.125 | 0.000 | 0.107 | 0.109 | 0.000 | 0.152 | 3.443 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 19 | 18 | 20 | 21 | 22 | 23 | 29 | 17 |
N.S. |
1 | 1.00 | 0.90 | 0.86 | 0.95 | 1.00 | 1.05 | 1.10 | 1.38 | 0.81 |
time (sec) |
N/A | 0.396 | 0.013 | 0.296 | 0.128 | 0.080 | 0.192 | 0.114 | 0.153 | 3.487 |
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 | 14 | 13 | 13 | 12 | 15 | 12 | 15 | 12 | 13 |
N.S. |
1 | 1.17 | 1.08 | 1.08 | 1.00 | 1.25 | 1.00 | 1.25 | 1.00 | 1.08 |
time (sec) |
N/A | 0.186 | 0.000 | 0.046 | 0.027 | 0.090 | 0.022 | 0.104 | 0.156 | 3.046 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | B | A | B | B | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 29 | 30 | 62 | 62 | 29 | 6706 | 72 | 0 |
N.S. |
1 | 0.00 | 1.00 | 1.03 | 2.14 | 2.14 | 1.00 | 231.24 | 2.48 | 0.00 |
time (sec) |
N/A | 0.000 | 0.150 | 0.047 | 0.106 | 0.106 | 0.950 | 0.855 | 0.162 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | A | A | F | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 100 | 26 | 28 | 28 | 28 | 29 | 0 | 33 | 30 |
N.S. |
1 | 3.57 | 0.93 | 1.00 | 1.00 | 1.00 | 1.04 | 0.00 | 1.18 | 1.07 |
time (sec) |
N/A | 0.453 | 0.097 | 1.931 | 0.101 | 0.099 | 0.174 | 0.000 | 0.152 | 0.182 |
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 | 27 | 0 | 26 | 29 | 22 | 25 | 24 | 24 | 37 | 29 |
N.S. |
1 | 0.00 | 0.96 | 1.07 | 0.81 | 0.93 | 0.89 | 0.89 | 1.37 | 1.07 |
time (sec) |
N/A | 0.000 | 0.071 | 0.489 | 0.174 | 0.099 | 0.128 | 0.198 | 0.157 | 3.382 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | A | A | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 24 | 24 | 323 | 36 | 32 | 77 | 38 | 78 |
N.S. |
1 | 0.00 | 1.04 | 1.04 | 14.04 | 1.57 | 1.39 | 3.35 | 1.65 | 3.39 |
time (sec) |
N/A | 0.000 | 0.324 | 3.105 | 2.289 | 0.112 | 0.129 | 0.221 | 0.152 | 3.304 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | B | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 40 | 26 | 24 | 33 | 28 | 22 | 22 | 33 | 19 |
N.S. |
1 | 2.22 | 1.44 | 1.33 | 1.83 | 1.56 | 1.22 | 1.22 | 1.83 | 1.06 |
time (sec) |
N/A | 0.286 | 0.042 | 0.136 | 0.027 | 0.084 | 0.068 | 0.112 | 0.149 | 0.046 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | B | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 25 | 26 | 30 | 28 | 36 | 30 | 26 | 25 |
N.S. |
1 | 0.00 | 1.04 | 1.08 | 1.25 | 1.17 | 1.50 | 1.25 | 1.08 | 1.04 |
time (sec) |
N/A | 0.000 | 0.009 | 0.064 | 0.027 | 0.091 | 0.176 | 0.109 | 0.152 | 0.052 |
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 | 13 | 13 | 14 | 10 | 13 | 14 | 10 | 12 | 10 |
N.S. |
1 | 0.68 | 0.68 | 0.74 | 0.53 | 0.68 | 0.74 | 0.53 | 0.63 | 0.53 |
time (sec) |
N/A | 0.196 | 0.004 | 0.046 | 0.025 | 0.077 | 0.060 | 0.110 | 0.149 | 3.124 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 9 | 13 | 9 | 13 | 13 | 12 | 10 | 12 | 13 | 8 |
N.S. |
1 | 1.44 | 1.00 | 1.44 | 1.44 | 1.33 | 1.11 | 1.33 | 1.44 | 0.89 |
time (sec) |
N/A | 0.267 | 0.064 | 0.152 | 0.073 | 0.102 | 0.130 | 0.113 | 0.148 | 3.328 |
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 | 19 | 54 | 54 | 43 | 45 | 42 | 76 | 45 | 43 | 60 |
N.S. |
1 | 2.84 | 2.84 | 2.26 | 2.37 | 2.21 | 4.00 | 2.37 | 2.26 | 3.16 |
time (sec) |
N/A | 0.252 | 0.005 | 0.072 | 0.029 | 0.076 | 0.089 | 0.113 | 0.149 | 0.039 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | B | A | B | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 40 | 15 | 16 | 39 | 15 | 114 | 41 | 15 | 18 |
N.S. |
1 | 2.86 | 1.07 | 1.14 | 2.79 | 1.07 | 8.14 | 2.93 | 1.07 | 1.29 |
time (sec) |
N/A | 0.202 | 0.007 | 0.108 | 0.029 | 0.085 | 0.177 | 0.114 | 0.145 | 0.168 |
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 | 30 | 0 | 34 | 43 | 41 | 37 | 32 | 42 | 42 | 0 |
N.S. |
1 | 0.00 | 1.13 | 1.43 | 1.37 | 1.23 | 1.07 | 1.40 | 1.40 | 0.00 |
time (sec) |
N/A | 0.000 | 0.291 | 0.348 | 0.145 | 0.081 | 0.187 | 0.144 | 0.151 | 0.000 |
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 | 19 | 42 | 25 | 18 | 35 | 17 | 15 | 21 | 15 | 21 |
N.S. |
1 | 2.21 | 1.32 | 0.95 | 1.84 | 0.89 | 0.79 | 1.11 | 0.79 | 1.11 |
time (sec) |
N/A | 0.429 | 0.074 | 0.079 | 0.061 | 0.087 | 0.048 | 0.114 | 0.150 | 3.019 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | B | A | A | A | B | F | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 128 | 73 | 53 | 53 | 53 | 49 | 0 | 68 | 61 |
N.S. |
1 | 4.57 | 2.61 | 1.89 | 1.89 | 1.89 | 1.75 | 0.00 | 2.43 | 2.18 |
time (sec) |
N/A | 0.881 | 0.081 | 1.580 | 0.096 | 0.107 | 0.127 | 0.000 | 0.149 | 0.095 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | F | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 24 | 21 | 20 | 37 | 19 | 0 | 24 | 20 |
N.S. |
1 | 0.00 | 0.86 | 0.75 | 0.71 | 1.32 | 0.68 | 0.00 | 0.86 | 0.71 |
time (sec) |
N/A | 0.000 | 2.286 | 0.382 | 0.075 | 0.115 | 0.171 | 0.000 | 0.155 | 3.206 |
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 | 29 | 24 | 25 | 38 | 28 | 22 | 24 | 29 | 20 |
N.S. |
1 | 0.88 | 0.73 | 0.76 | 1.15 | 0.85 | 0.67 | 0.73 | 0.88 | 0.61 |
time (sec) |
N/A | 0.311 | 0.090 | 0.121 | 0.031 | 0.097 | 0.075 | 0.116 | 0.147 | 0.043 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F | A | A | F(-1) | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 0 | 29 | 27 | 0 | 27 | 19 | 0 | 29 | 27 |
N.S. |
1 | 0.00 | 0.88 | 0.82 | 0.00 | 0.82 | 0.58 | 0.00 | 0.88 | 0.82 |
time (sec) |
N/A | 0.000 | 0.508 | 16.567 | 0.000 | 0.100 | 0.589 | 0.000 | 0.217 | 3.774 |
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 | 22 | 35 | 31 | 30 | 40 | 40 | 41 | 40 | 43 | 29 |
N.S. |
1 | 1.59 | 1.41 | 1.36 | 1.82 | 1.82 | 1.86 | 1.82 | 1.95 | 1.32 |
time (sec) |
N/A | 0.794 | 0.327 | 1.970 | 0.079 | 0.095 | 0.096 | 3.487 | 0.163 | 3.233 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 20 | 13 | 14 | 14 | 17 | 14 | 12 | 14 |
N.S. |
1 | 1.00 | 1.33 | 0.87 | 0.93 | 0.93 | 1.13 | 0.93 | 0.80 | 0.93 |
time (sec) |
N/A | 0.136 | 0.001 | 0.027 | 0.025 | 0.071 | 0.019 | 0.109 | 0.159 | 0.028 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 32 | 33 | 28 | 27 | 28 | 29 | 27 | 24 | 16 |
N.S. |
1 | 1.78 | 1.83 | 1.56 | 1.50 | 1.56 | 1.61 | 1.50 | 1.33 | 0.89 |
time (sec) |
N/A | 0.382 | 0.038 | 0.113 | 0.069 | 0.092 | 0.139 | 0.123 | 0.165 | 3.317 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | F | A | A | F | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 102 | 23 | 30 | 0 | 30 | 22 | 0 | 27 | 38 |
N.S. |
1 | 4.43 | 1.00 | 1.30 | 0.00 | 1.30 | 0.96 | 0.00 | 1.17 | 1.65 |
time (sec) |
N/A | 2.490 | 1.397 | 4.373 | 0.000 | 0.121 | 0.313 | 0.000 | 0.163 | 3.394 |
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 | 15 | 20 | 20 | 13 | 12 | 12 | 15 | 12 | 53 | 20 |
N.S. |
1 | 1.33 | 1.33 | 0.87 | 0.80 | 0.80 | 1.00 | 0.80 | 3.53 | 1.33 |
time (sec) |
N/A | 0.206 | 0.072 | 0.203 | 0.028 | 0.098 | 1.482 | 0.130 | 0.172 | 2.932 |
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 | 26 | 0 | 32 | 31 | 23 | 23 | 31 | 32 | 32 | 30 |
N.S. |
1 | 0.00 | 1.23 | 1.19 | 0.88 | 0.88 | 1.19 | 1.23 | 1.23 | 1.15 |
time (sec) |
N/A | 0.000 | 0.105 | 0.070 | 0.061 | 0.088 | 0.128 | 0.119 | 0.163 | 2.952 |
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 | 34 | 0 | 37 | 35 | 68 | 68 | 39 | 83 | 90 | 27 |
N.S. |
1 | 0.00 | 1.09 | 1.03 | 2.00 | 2.00 | 1.15 | 2.44 | 2.65 | 0.79 |
time (sec) |
N/A | 0.000 | 12.539 | 0.446 | 0.073 | 0.088 | 0.106 | 0.131 | 0.170 | 2.997 |
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 | 18 | 18 | 19 | 18 | 26 | 14 | 19 | 27 | 18 |
N.S. |
1 | 0.67 | 0.67 | 0.70 | 0.67 | 0.96 | 0.52 | 0.70 | 1.00 | 0.67 |
time (sec) |
N/A | 0.262 | 0.011 | 0.038 | 0.025 | 0.073 | 0.046 | 0.113 | 0.162 | 0.029 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | B | A | B | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 113 | 32 | 40 | 104 | 30 | 76 | 30 | 59 | 64 |
N.S. |
1 | 3.42 | 0.97 | 1.21 | 3.15 | 0.91 | 2.30 | 0.91 | 1.79 | 1.94 |
time (sec) |
N/A | 3.166 | 0.625 | 0.838 | 0.150 | 0.085 | 0.237 | 0.117 | 0.150 | 3.099 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F(-1) | A | A | A | A | A | F | B |
verified | N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 0 | 25 | 37 | 36 | 26 | 42 | 93 | 34 |
N.S. |
1 | 0.00 | 0.00 | 0.93 | 1.37 | 1.33 | 0.96 | 1.56 | 3.44 | 1.26 |
time (sec) |
N/A | 0.000 | 0.000 | 0.426 | 0.075 | 0.092 | 0.157 | 0.120 | 48.841 | 2.935 |
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 | 34 | 40 | 39 | 44 | 41 | 41 | 46 | 41 | 82 | 39 |
N.S. |
1 | 1.18 | 1.15 | 1.29 | 1.21 | 1.21 | 1.35 | 1.21 | 2.41 | 1.15 |
time (sec) |
N/A | 0.228 | 0.012 | 0.240 | 0.031 | 0.100 | 0.199 | 0.109 | 0.152 | 0.151 |
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 | 26 | 31 | 30 | 28 | 34 | 1672 | 26 | 266 |
N.S. |
1 | 0.00 | 0.90 | 1.07 | 1.03 | 0.97 | 1.17 | 57.66 | 0.90 | 9.17 |
time (sec) |
N/A | 0.000 | 0.125 | 49.974 | 0.101 | 0.094 | 4.736 | 1.191 | 0.157 | 3.328 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | B | F(-2) | B | B | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 155 | 22 | 58 | 0 | 56 | 49 | 54 | 61 | 43 |
N.S. |
1 | 7.05 | 1.00 | 2.64 | 0.00 | 2.55 | 2.23 | 2.45 | 2.77 | 1.95 |
time (sec) |
N/A | 2.761 | 0.183 | 2.012 | 0.000 | 0.108 | 1.618 | 0.399 | 0.152 | 3.075 |
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 | 25 | 0 | 20 | 27 | 11 | 11 | 22 | 27 | 34 | 29 |
N.S. |
1 | 0.00 | 0.80 | 1.08 | 0.44 | 0.44 | 0.88 | 1.08 | 1.36 | 1.16 |
time (sec) |
N/A | 0.000 | 0.171 | 0.536 | 0.114 | 0.088 | 0.116 | 0.157 | 0.150 | 3.136 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | A | A | A | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 34 | 43 | 30 | 32 | 32 | 29 | 34 | 153 | 88 |
N.S. |
1 | 2.00 | 2.53 | 1.76 | 1.88 | 1.88 | 1.71 | 2.00 | 9.00 | 5.18 |
time (sec) |
N/A | 0.369 | 0.017 | 0.108 | 0.031 | 0.081 | 0.595 | 0.117 | 0.149 | 0.150 |
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 | 18 | 27 | 15 | 20 | 29 | 19 | 14 | 23 | 18 | 17 |
N.S. |
1 | 1.50 | 0.83 | 1.11 | 1.61 | 1.06 | 0.78 | 1.28 | 1.00 | 0.94 |
time (sec) |
N/A | 0.239 | 0.035 | 0.129 | 0.053 | 0.081 | 0.116 | 0.109 | 0.145 | 2.943 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | F(-2) | A | F(-1) | B | F | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 36 | 60 | 0 | 50 | 0 | 85 | 245 | 35 |
N.S. |
1 | 0.00 | 1.20 | 2.00 | 0.00 | 1.67 | 0.00 | 2.83 | 8.17 | 1.17 |
time (sec) |
N/A | 0.000 | 0.106 | 42.193 | 0.000 | 0.096 | 0.000 | 0.419 | 200.017 | 3.137 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 14 | 14 | 15 | 14 | 13 | 14 | 14 | 14 | 19 |
N.S. |
1 | 0.78 | 0.78 | 0.83 | 0.78 | 0.72 | 0.78 | 0.78 | 0.78 | 1.06 |
time (sec) |
N/A | 0.182 | 0.004 | 0.087 | 0.025 | 0.092 | 0.048 | 0.113 | 0.166 | 2.922 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 26 | 26 | 25 | 30 | 36 | 22 | 36 | 36 | 24 |
N.S. |
1 | 0.87 | 0.87 | 0.83 | 1.00 | 1.20 | 0.73 | 1.20 | 1.20 | 0.80 |
time (sec) |
N/A | 1.010 | 0.636 | 1.608 | 0.063 | 0.107 | 0.166 | 0.116 | 0.160 | 3.004 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F | B | A | F | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 0 | 43 | 38 | 0 | 57 | 36 | 0 | 41 | 37 |
N.S. |
1 | 0.00 | 1.30 | 1.15 | 0.00 | 1.73 | 1.09 | 0.00 | 1.24 | 1.12 |
time (sec) |
N/A | 0.000 | 2.911 | 0.225 | 0.000 | 0.092 | 0.183 | 0.000 | 0.164 | 3.019 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 27 | 26 | 18 | 15 | 20 | 54 | 20 | 17 | 20 |
N.S. |
1 | 1.04 | 1.00 | 0.69 | 0.58 | 0.77 | 2.08 | 0.77 | 0.65 | 0.77 |
time (sec) |
N/A | 0.154 | 0.006 | 0.129 | 0.109 | 0.091 | 1.085 | 0.114 | 0.163 | 2.897 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | A | A | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 24 | 30 | 224 | 38 | 19 | 58 | 60 | 111 |
N.S. |
1 | 0.00 | 0.96 | 1.20 | 8.96 | 1.52 | 0.76 | 2.32 | 2.40 | 4.44 |
time (sec) |
N/A | 0.000 | 0.070 | 1.346 | 0.187 | 0.100 | 0.076 | 0.144 | 0.167 | 3.121 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | A | B | A | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 63 | 25 | 42 | 45 | 39 | 53 | 47 | 42 | 0 |
N.S. |
1 | 2.42 | 0.96 | 1.62 | 1.73 | 1.50 | 2.04 | 1.81 | 1.62 | 0.00 |
time (sec) |
N/A | 1.210 | 0.207 | 0.502 | 0.197 | 0.094 | 0.189 | 0.144 | 0.169 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 28 | 28 | 23 | 22 | 37 | 22 | 24 | 193 | 26 |
N.S. |
1 | 0.93 | 0.93 | 0.77 | 0.73 | 1.23 | 0.73 | 0.80 | 6.43 | 0.87 |
time (sec) |
N/A | 0.571 | 0.640 | 0.101 | 0.027 | 0.090 | 0.168 | 0.124 | 0.259 | 0.073 |
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 | 19 | 40 | 17 | 16 | 15 | 15 | 15 | 15 | 21 | 16 |
N.S. |
1 | 2.11 | 0.89 | 0.84 | 0.79 | 0.79 | 0.79 | 0.79 | 1.11 | 0.84 |
time (sec) |
N/A | 0.250 | 0.032 | 0.084 | 0.098 | 0.094 | 0.087 | 0.114 | 0.171 | 0.035 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 34 | 20 | 17 | 30 | 22 | 20 | 30 | 31 | 32 |
N.S. |
1 | 1.62 | 0.95 | 0.81 | 1.43 | 1.05 | 0.95 | 1.43 | 1.48 | 1.52 |
time (sec) |
N/A | 0.300 | 0.191 | 0.211 | 0.210 | 0.095 | 0.071 | 0.113 | 0.169 | 0.065 |
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 | 25 | 45 | 28 | 38 | 51 | 28 | 36 | 37 | 41 | 24 |
N.S. |
1 | 1.80 | 1.12 | 1.52 | 2.04 | 1.12 | 1.44 | 1.48 | 1.64 | 0.96 |
time (sec) |
N/A | 0.371 | 0.034 | 0.835 | 0.037 | 0.095 | 0.137 | 0.117 | 0.172 | 3.013 |
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 | 19 | 44 | 16 | 20 | 31 | 19 | 17 | 19 | 16 | 13 |
N.S. |
1 | 2.32 | 0.84 | 1.05 | 1.63 | 1.00 | 0.89 | 1.00 | 0.84 | 0.68 |
time (sec) |
N/A | 0.259 | 0.065 | 0.106 | 0.034 | 0.084 | 0.096 | 0.115 | 0.174 | 2.903 |
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 | 18 | 0 | 26 | 24 | 33 | 33 | 0 | 23 | 26 | 23 |
N.S. |
1 | 0.00 | 1.44 | 1.33 | 1.83 | 1.83 | 0.00 | 1.28 | 1.44 | 1.28 |
time (sec) |
N/A | 0.000 | 5.347 | 0.078 | 0.076 | 0.111 | 0.000 | 0.130 | 0.170 | 2.929 |
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 | 22 | 0 | 21 | 21 | 19 | 23 | 17 | 23 | 23 | 28 |
N.S. |
1 | 0.00 | 0.95 | 0.95 | 0.86 | 1.05 | 0.77 | 1.05 | 1.05 | 1.27 |
time (sec) |
N/A | 0.000 | 0.109 | 0.190 | 0.106 | 0.093 | 0.089 | 0.123 | 0.200 | 2.948 |
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 | 29 | 27 | 29 | 30 | 22 | 48 | 42 | 37 |
N.S. |
1 | 0.00 | 0.97 | 0.90 | 0.97 | 1.00 | 0.73 | 1.60 | 1.40 | 1.23 |
time (sec) |
N/A | 0.000 | 5.039 | 1.154 | 0.125 | 0.101 | 0.103 | 0.120 | 0.198 | 2.967 |
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 | 9 | 9 | 10 | 9 | 9 | 7 | 9 | 9 | 9 |
N.S. |
1 | 0.36 | 0.36 | 0.40 | 0.36 | 0.36 | 0.28 | 0.36 | 0.36 | 0.36 |
time (sec) |
N/A | 0.136 | 0.000 | 0.021 | 0.030 | 0.078 | 0.024 | 0.112 | 0.195 | 0.016 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | B | B | B | F(-2) | A | B | F(-1) |
verified | N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 0 | 61 | 89 | 74 | 0 | 60 | 67 | 0 |
N.S. |
1 | 0.00 | 0.00 | 1.91 | 2.78 | 2.31 | 0.00 | 1.88 | 2.09 | 0.00 |
time (sec) |
N/A | 0.000 | 0.000 | 0.934 | 0.217 | 0.109 | 0.000 | 0.523 | 0.234 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | B | A | B | A | B | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 141 | 48 | 34 | 87 | 38 | 36 | 33 | 47 | 47 |
N.S. |
1 | 6.71 | 2.29 | 1.62 | 4.14 | 1.81 | 1.71 | 1.57 | 2.24 | 2.24 |
time (sec) |
N/A | 1.425 | 0.149 | 1.688 | 0.074 | 0.081 | 0.120 | 0.114 | 0.192 | 0.127 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | F | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 0 | 16 | 15 | 14 | 14 | 14 | 0 | 16 | 14 |
N.S. |
1 | 0.00 | 0.94 | 0.88 | 0.82 | 0.82 | 0.82 | 0.00 | 0.94 | 0.82 |
time (sec) |
N/A | 0.000 | 0.347 | 0.072 | 0.122 | 0.088 | 0.094 | 0.000 | 0.484 | 2.920 |
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 | 25 | 0 | 26 | 23 | 30 | 22 | 20 | 30 | 24 | 22 |
N.S. |
1 | 0.00 | 1.04 | 0.92 | 1.20 | 0.88 | 0.80 | 1.20 | 0.96 | 0.88 |
time (sec) |
N/A | 0.000 | 0.032 | 0.773 | 0.152 | 0.092 | 0.143 | 0.133 | 0.195 | 3.005 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 57 | 132 | 28 | 34 | 35 | 31 | 34 | 34 | 26 |
N.S. |
1 | 1.78 | 4.12 | 0.88 | 1.06 | 1.09 | 0.97 | 1.06 | 1.06 | 0.81 |
time (sec) |
N/A | 0.468 | 0.067 | 0.191 | 0.025 | 0.083 | 1.069 | 0.127 | 0.207 | 0.121 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 47 | 46 | 44 | 47 | 44 | 42 | 44 | 47 | 40 |
N.S. |
1 | 1.52 | 1.48 | 1.42 | 1.52 | 1.42 | 1.35 | 1.42 | 1.52 | 1.29 |
time (sec) |
N/A | 21.552 | 0.149 | 56.620 | 0.125 | 0.108 | 4.874 | 0.802 | 0.213 | 3.967 |
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 | 31 | 0 | 34 | 28 | 0 | 35 | 27 | 0 | 28 | 0 |
N.S. |
1 | 0.00 | 1.10 | 0.90 | 0.00 | 1.13 | 0.87 | 0.00 | 0.90 | 0.00 |
time (sec) |
N/A | 0.000 | 1.291 | 0.459 | 0.000 | 0.100 | 0.173 | 0.000 | 0.186 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 12 | 16 | 25 | 17 | 15 | 17 | 14 | 15 | 16 | 12 |
N.S. |
1 | 1.33 | 2.08 | 1.42 | 1.25 | 1.42 | 1.17 | 1.25 | 1.33 | 1.00 |
time (sec) |
N/A | 0.175 | 0.029 | 0.099 | 0.032 | 0.106 | 0.056 | 0.110 | 0.180 | 2.940 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | B | F(-2) | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 26 | 26 | 74 | 75 | 73 | 75 | 0 | 145 | 38 |
N.S. |
1 | 0.93 | 0.93 | 2.64 | 2.68 | 2.61 | 2.68 | 0.00 | 5.18 | 1.36 |
time (sec) |
N/A | 0.764 | 0.046 | 61.461 | 0.115 | 0.119 | 0.136 | 0.000 | 0.184 | 3.162 |
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 | 13 | 13 | 14 | 9 | 12 | 10 | 9 | 11 | 10 |
N.S. |
1 | 1.08 | 1.08 | 1.17 | 0.75 | 1.00 | 0.83 | 0.75 | 0.92 | 0.83 |
time (sec) |
N/A | 0.139 | 0.000 | 0.042 | 0.025 | 0.073 | 0.016 | 0.110 | 0.176 | 0.001 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 18 | 20 | 14 | 13 | 13 | 15 | 13 | 15 | 14 |
N.S. |
1 | 1.06 | 1.18 | 0.82 | 0.76 | 0.76 | 0.88 | 0.76 | 0.88 | 0.82 |
time (sec) |
N/A | 0.154 | 0.002 | 0.096 | 0.034 | 0.077 | 0.021 | 0.108 | 0.176 | 0.018 |
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 | 36 | 35 | 38 | 35 | 41 | 38 | 79 | 43 |
N.S. |
1 | 0.00 | 1.29 | 1.25 | 1.36 | 1.25 | 1.46 | 1.36 | 2.82 | 1.54 |
time (sec) |
N/A | 0.000 | 5.072 | 0.425 | 0.176 | 0.092 | 0.245 | 0.130 | 200.019 | 3.066 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | B | A | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 26 | 28 | 35 | 67 | 36 | 88 | 82 | 36 |
N.S. |
1 | 0.00 | 0.87 | 0.93 | 1.17 | 2.23 | 1.20 | 2.93 | 2.73 | 1.20 |
time (sec) |
N/A | 0.000 | 0.047 | 2.777 | 0.114 | 0.101 | 1.019 | 0.260 | 0.157 | 3.163 |
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 | 23 | 33 | 21 | 22 | 0 | 20 | 22 | 22 | 24 | 21 |
N.S. |
1 | 1.43 | 0.91 | 0.96 | 0.00 | 0.87 | 0.96 | 0.96 | 1.04 | 0.91 |
time (sec) |
N/A | 0.249 | 0.032 | 0.465 | 0.000 | 0.100 | 0.089 | 0.112 | 0.151 | 2.915 |
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 | 11 | 19 | 19 | 10 | 9 | 9 | 7 | 11 | 9 | 8 |
N.S. |
1 | 1.73 | 1.73 | 0.91 | 0.82 | 0.82 | 0.64 | 1.00 | 0.82 | 0.73 |
time (sec) |
N/A | 0.160 | 0.002 | 0.096 | 0.031 | 0.072 | 0.045 | 0.108 | 0.152 | 2.908 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | A | B | B | F | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 0 | 53 | 63 | 52 | 130 | 58 | 0 | 80 | 54 |
N.S. |
1 | 0.00 | 1.61 | 1.91 | 1.58 | 3.94 | 1.76 | 0.00 | 2.42 | 1.64 |
time (sec) |
N/A | 0.000 | 0.098 | 1.546 | 0.328 | 0.089 | 0.241 | 0.000 | 0.187 | 3.134 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 20 | 20 | 19 | 17 | 18 | 15 | 33 | 19 | 17 |
N.S. |
1 | 0.83 | 0.83 | 0.79 | 0.71 | 0.75 | 0.62 | 1.38 | 0.79 | 0.71 |
time (sec) |
N/A | 0.213 | 0.008 | 0.215 | 0.027 | 0.071 | 0.139 | 0.111 | 0.155 | 2.890 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | F | A | A | A | A | B | F(-1) |
verified | N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 31 | 0 | 30 | 38 | 34 | 46 | 31 | 0 |
N.S. |
1 | 0.00 | 1.00 | 0.00 | 0.97 | 1.23 | 1.10 | 1.48 | 1.00 | 0.00 |
time (sec) |
N/A | 0.000 | 0.078 | 0.000 | 0.191 | 0.095 | 0.176 | 0.128 | 0.164 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | A | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 48 | 48 | 36 | 0 | 60 | 39 | 63 | 62 | 37 |
N.S. |
1 | 1.60 | 1.60 | 1.20 | 0.00 | 2.00 | 1.30 | 2.10 | 2.07 | 1.23 |
time (sec) |
N/A | 0.780 | 1.923 | 1.049 | 0.000 | 0.084 | 0.092 | 0.111 | 0.159 | 2.933 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | A | F(-2) | A | F | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 42 | 37 | 102 | 36 | 0 | 36 | 0 | 0 |
N.S. |
1 | 0.00 | 1.50 | 1.32 | 3.64 | 1.29 | 0.00 | 1.29 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 0.070 | 13.778 | 0.179 | 0.105 | 0.000 | 0.818 | 0.403 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | A | B | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 42 | 22 | 47 | 21 | 41 | 21 | 22 | 43 |
N.S. |
1 | 0.00 | 1.75 | 0.92 | 1.96 | 0.88 | 1.71 | 0.88 | 0.92 | 1.79 |
time (sec) |
N/A | 0.000 | 0.050 | 6.826 | 0.076 | 0.085 | 0.277 | 0.138 | 0.163 | 3.263 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | B | B | B | B | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 75 | 28 | 63 | 57 | 57 | 85 | 57 | 68 | 80 |
N.S. |
1 | 2.88 | 1.08 | 2.42 | 2.19 | 2.19 | 3.27 | 2.19 | 2.62 | 3.08 |
time (sec) |
N/A | 0.206 | 0.018 | 0.174 | 0.034 | 0.069 | 0.030 | 0.107 | 0.151 | 2.961 |
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 | 13 | 13 | 13 | 11 | 37 | 10 | 12 | 17 | 14 | 10 |
N.S. |
1 | 1.00 | 1.00 | 0.85 | 2.85 | 0.77 | 0.92 | 1.31 | 1.08 | 0.77 |
time (sec) |
N/A | 0.267 | 0.051 | 0.102 | 0.026 | 0.071 | 0.053 | 0.114 | 0.151 | 0.024 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 10 | 10 | 7 | 8 | 8 | 8 | 9 | 8 | 6 |
N.S. |
1 | 0.50 | 0.50 | 0.35 | 0.40 | 0.40 | 0.40 | 0.45 | 0.40 | 0.30 |
time (sec) |
N/A | 0.129 | 0.001 | 0.089 | 0.031 | 0.094 | 0.031 | 0.109 | 0.148 | 0.030 |
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 | 28 | 25 | 25 | 23 | 45 | 89 | 39 | 0 | 25 | 24 |
N.S. |
1 | 0.89 | 0.89 | 0.82 | 1.61 | 3.18 | 1.39 | 0.00 | 0.89 | 0.86 |
time (sec) |
N/A | 0.288 | 0.010 | 0.428 | 0.182 | 0.086 | 106.379 | 0.000 | 0.159 | 0.575 |
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 | 9 | 8 | 8 | 14 | 8 | 8 | 8 |
N.S. |
1 | 1.00 | 1.00 | 1.12 | 1.00 | 1.00 | 1.75 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.132 | 0.001 | 0.049 | 0.035 | 0.063 | 0.025 | 0.110 | 0.151 | 0.018 |
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 | 24 | 114 | 79 | 98 | 179 | 92 | 83 | 111 | 108 | 88 |
N.S. |
1 | 4.75 | 3.29 | 4.08 | 7.46 | 3.83 | 3.46 | 4.62 | 4.50 | 3.67 |
time (sec) |
N/A | 1.140 | 0.041 | 3.270 | 0.096 | 0.083 | 0.513 | 0.117 | 0.151 | 3.114 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 14 | 15 | 10 | 10 | 12 | 10 | 13 | 10 |
N.S. |
1 | 1.00 | 1.00 | 1.07 | 0.71 | 0.71 | 0.86 | 0.71 | 0.93 | 0.71 |
time (sec) |
N/A | 0.151 | 0.002 | 0.055 | 0.024 | 0.072 | 0.047 | 0.112 | 0.151 | 2.929 |