Detailed conclusion table per each integral is given by the table below. The elapsed time is in seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2) if the failure was due to an exception being raised, which could indicate a bug in the system. If the failure was due to integral not being evaluated within the time limit, then it is given as F.
In this table, the column N.S.
means normalized size and is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To make the table
fit the page, the name Mathematica
was abbreviated to MMA
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 15 | 15 | 15 | 14 | 14 | 17 | 14 | 14 | 14 |
N.S. |
1 | 0.88 | 0.88 | 0.88 | 0.82 | 0.82 | 1.00 | 0.82 | 0.82 | 0.82 |
time (sec) |
N/A | 0.151 | 0.002 | 0.230 | 0.028 | 0.057 | 0.060 | 0.111 | 0.178 | 2.159 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | A | A | F | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 83 | 30 | 27 | 49 | 43 | 31 | 0 | 261 | 29 |
N.S. |
1 | 2.86 | 1.03 | 0.93 | 1.69 | 1.48 | 1.07 | 0.00 | 9.00 | 1.00 |
time (sec) |
N/A | 0.535 | 1.067 | 157.930 | 0.180 | 0.069 | 0.202 | 0.000 | 0.229 | 2.526 |
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 | 22 | 177 | 32 | 107 | 134 | 103 | 121 | 132 | 114 | 106 |
N.S. |
1 | 8.05 | 1.45 | 4.86 | 6.09 | 4.68 | 5.50 | 6.00 | 5.18 | 4.82 |
time (sec) |
N/A | 0.426 | 0.044 | 0.030 | 0.111 | 0.069 | 0.270 | 0.113 | 0.187 | 2.272 |
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 | 16 | 16 | 29 | 21 | 15 | 16 | 21 | 13 |
N.S. |
1 | 0.00 | 0.70 | 0.70 | 1.26 | 0.91 | 0.65 | 0.70 | 0.91 | 0.57 |
time (sec) |
N/A | 0.000 | 0.115 | 0.115 | 0.035 | 0.066 | 31.066 | 0.129 | 0.195 | 3.262 |
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 | 28 | 129 | 32 | 62 | 67 | 64 | 58 | 220 | 78 | 77 |
N.S. |
1 | 4.61 | 1.14 | 2.21 | 2.39 | 2.29 | 2.07 | 7.86 | 2.79 | 2.75 |
time (sec) |
N/A | 1.024 | 0.240 | 0.349 | 0.192 | 0.073 | 0.267 | 0.200 | 0.219 | 2.619 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F | A | A | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 0 | 17 | 16 | 0 | 20 | 17 | 79 | 22 | 31 |
N.S. |
1 | 0.00 | 1.00 | 0.94 | 0.00 | 1.18 | 1.00 | 4.65 | 1.29 | 1.82 |
time (sec) |
N/A | 0.000 | 0.214 | 0.213 | 0.000 | 0.063 | 0.182 | 0.123 | 0.207 | 2.610 |
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 | 24 | 25 | 23 | 28 | 22 | 27 | 22 | 22 | 58 | 25 |
N.S. |
1 | 1.04 | 0.96 | 1.17 | 0.92 | 1.12 | 0.92 | 0.92 | 2.42 | 1.04 |
time (sec) |
N/A | 0.564 | 0.107 | 0.210 | 0.147 | 0.062 | 0.140 | 0.115 | 70.869 | 2.235 |
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 | 27 | 0 | 35 | 69 | 46 | 45 | 54 | 209 | 50 | 0 |
N.S. |
1 | 0.00 | 1.30 | 2.56 | 1.70 | 1.67 | 2.00 | 7.74 | 1.85 | 0.00 |
time (sec) |
N/A | 0.000 | 0.092 | 0.033 | 0.128 | 0.071 | 0.160 | 0.230 | 0.222 | 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 | 21 | 23 | 21 | 27 | 25 | 34 | 32 | 34 | 29 | 20 |
N.S. |
1 | 1.10 | 1.00 | 1.29 | 1.19 | 1.62 | 1.52 | 1.62 | 1.38 | 0.95 |
time (sec) |
N/A | 0.365 | 0.040 | 0.769 | 0.166 | 0.067 | 0.118 | 0.114 | 0.242 | 2.389 |
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 | 20 | 19 | 20 | 16 | 17 | 17 | 17 | 0 | 37 | 17 |
N.S. |
1 | 0.95 | 1.00 | 0.80 | 0.85 | 0.85 | 0.85 | 0.00 | 1.85 | 0.85 |
time (sec) |
N/A | 0.187 | 0.008 | 0.382 | 0.028 | 0.067 | 0.232 | 0.000 | 0.218 | 2.209 |
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 | 28 | 29 | 29 | 22 | 22 | 21 | 19 | 87 | 28 | 24 |
N.S. |
1 | 1.04 | 1.04 | 0.79 | 0.79 | 0.75 | 0.68 | 3.11 | 1.00 | 0.86 |
time (sec) |
N/A | 0.762 | 5.084 | 0.143 | 0.074 | 0.069 | 0.113 | 0.180 | 0.248 | 0.179 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | C | A | A | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 36 | 14 | 16 | 23 | 15 | 12 | 99 | 13 | 11 |
N.S. |
1 | 2.57 | 1.00 | 1.14 | 1.64 | 1.07 | 0.86 | 7.07 | 0.93 | 0.79 |
time (sec) |
N/A | 0.198 | 0.006 | 0.094 | 0.059 | 0.064 | 0.062 | 0.123 | 0.212 | 2.185 |
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 | 14 | 13 | 13 | 12 | 13 | 17 | 15 |
N.S. |
1 | 0.78 | 0.78 | 0.78 | 0.72 | 0.72 | 0.67 | 0.72 | 0.94 | 0.83 |
time (sec) |
N/A | 0.169 | 0.017 | 0.056 | 0.025 | 0.066 | 0.047 | 0.113 | 0.253 | 2.138 |
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 | 7 | 7 | 6 | 5 | 5 | 5 | 5 | 5 | 5 |
N.S. |
1 | 0.30 | 0.30 | 0.26 | 0.22 | 0.22 | 0.22 | 0.22 | 0.22 | 0.22 |
time (sec) |
N/A | 0.123 | 0.000 | 0.012 | 0.030 | 0.054 | 0.027 | 0.110 | 0.222 | 0.015 |
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 | 13 | 13 | 14 | 13 | 13 | 12 | 14 | 13 | 13 |
N.S. |
1 | 0.81 | 0.81 | 0.88 | 0.81 | 0.81 | 0.75 | 0.88 | 0.81 | 0.81 |
time (sec) |
N/A | 0.153 | 0.001 | 0.023 | 0.030 | 0.055 | 0.030 | 0.108 | 0.199 | 0.026 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 21 | 21 | 18 | 17 | 17 | 17 | 19 | 17 | 17 |
N.S. |
1 | 0.72 | 0.72 | 0.62 | 0.59 | 0.59 | 0.59 | 0.66 | 0.59 | 0.59 |
time (sec) |
N/A | 0.347 | 0.006 | 0.036 | 0.030 | 0.062 | 0.068 | 0.116 | 0.209 | 2.092 |
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 | 30 | 0 | 45 | 36 | 49 | 50 | 39 | 46 | 104 | 161 |
N.S. |
1 | 0.00 | 1.50 | 1.20 | 1.63 | 1.67 | 1.30 | 1.53 | 3.47 | 5.37 |
time (sec) |
N/A | 0.000 | 0.171 | 6.566 | 0.210 | 0.073 | 0.203 | 0.244 | 200.021 | 2.441 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | B | A | F | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 26 | 19 | 20 | 50 | 17 | 0 | 30 | 21 |
N.S. |
1 | 0.00 | 1.13 | 0.83 | 0.87 | 2.17 | 0.74 | 0.00 | 1.30 | 0.91 |
time (sec) |
N/A | 0.000 | 0.358 | 0.238 | 0.205 | 0.066 | 0.121 | 0.000 | 0.199 | 2.212 |
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 | 27 | 24 | 27 | 23 | 24 | 32 | 63 | 26 |
N.S. |
1 | 0.00 | 1.17 | 1.04 | 1.17 | 1.00 | 1.04 | 1.39 | 2.74 | 1.13 |
time (sec) |
N/A | 0.000 | 0.081 | 0.050 | 0.077 | 0.066 | 0.105 | 0.127 | 0.203 | 2.140 |
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 | 29 | 36 | 25 | 22 | 258 | 43 | 22 | 28 | 57 | 28 |
N.S. |
1 | 1.24 | 0.86 | 0.76 | 8.90 | 1.48 | 0.76 | 0.97 | 1.97 | 0.97 |
time (sec) |
N/A | 0.474 | 0.131 | 0.297 | 0.225 | 0.070 | 0.092 | 0.116 | 0.200 | 0.211 |
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 | 28 | 26 | 23 | 25 | 29 | 29 | 20 | 28 | 23 |
N.S. |
1 | 1.00 | 0.93 | 0.82 | 0.89 | 1.04 | 1.04 | 0.71 | 1.00 | 0.82 |
time (sec) |
N/A | 0.221 | 0.008 | 0.039 | 0.029 | 0.055 | 0.103 | 0.111 | 0.197 | 2.051 |
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 | 26 | 0 | 25 | 30 | 26 | 26 | 22 | 29 | 50 | 0 |
N.S. |
1 | 0.00 | 0.96 | 1.15 | 1.00 | 1.00 | 0.85 | 1.12 | 1.92 | 0.00 |
time (sec) |
N/A | 0.000 | 0.213 | 0.362 | 0.074 | 0.061 | 0.149 | 0.137 | 0.205 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | B | B | F | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 42 | 44 | 38 | 38 | 110 | 55 | 0 | 0 |
N.S. |
1 | 0.00 | 1.56 | 1.63 | 1.41 | 1.41 | 4.07 | 2.04 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 0.115 | 0.039 | 0.180 | 0.066 | 0.474 | 0.220 | 0.282 | 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 | 32 | 43 | 33 | 31 | 0 | 46 | 20 | 58 | 51 | 29 |
N.S. |
1 | 1.34 | 1.03 | 0.97 | 0.00 | 1.44 | 0.62 | 1.81 | 1.59 | 0.91 |
time (sec) |
N/A | 1.025 | 0.072 | 1.183 | 0.000 | 0.069 | 0.188 | 0.117 | 0.737 | 2.355 |
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 | 34 | 0 | 29 | 28 | 41 | 41 | 19 | 33 | 45 | 88 |
N.S. |
1 | 0.00 | 0.85 | 0.82 | 1.21 | 1.21 | 0.56 | 0.97 | 1.32 | 2.59 |
time (sec) |
N/A | 0.000 | 0.377 | 2.345 | 0.160 | 0.066 | 0.079 | 0.150 | 0.192 | 0.523 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | B | B | B | B | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 101 | 93 | 92 | 95 | 104 | 113 | 125 | 95 |
N.S. |
1 | 0.00 | 3.16 | 2.91 | 2.88 | 2.97 | 3.25 | 3.53 | 3.91 | 2.97 |
time (sec) |
N/A | 0.000 | 0.085 | 52.085 | 0.300 | 0.074 | 7.200 | 1.494 | 0.201 | 3.599 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | B | B | B | B | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 39 | 26 | 66 | 86 | 68 | 123800 | 101 | 0 |
N.S. |
1 | 0.00 | 1.50 | 1.00 | 2.54 | 3.31 | 2.62 | 4761.54 | 3.88 | 0.00 |
time (sec) |
N/A | 0.000 | 2.973 | 0.688 | 0.297 | 0.070 | 0.165 | 73.071 | 0.240 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | C | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 49 | 42 | 51 | 44 | 45 | 42 | 52 | 51 | 38 |
N.S. |
1 | 1.96 | 1.68 | 2.04 | 1.76 | 1.80 | 1.68 | 2.08 | 2.04 | 1.52 |
time (sec) |
N/A | 0.299 | 0.059 | 0.581 | 0.082 | 0.066 | 0.124 | 0.117 | 0.214 | 2.267 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | B | F(-2) | B | F(-1) | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 2153 | 101 | 60 | 0 | 76 | 0 | 105 | 164 | 49 |
N.S. |
1 | 59.81 | 2.81 | 1.67 | 0.00 | 2.11 | 0.00 | 2.92 | 4.56 | 1.36 |
time (sec) |
N/A | 7.922 | 0.161 | 2.921 | 0.000 | 0.072 | 0.000 | 0.150 | 0.212 | 2.947 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | F | A | A | A | A | F | F | B |
verified | N/A | Yes | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 255 | 0 | 26 | 31 | 26 | 24 | 0 | 220 | 25 |
N.S. |
1 | 8.23 | 0.00 | 0.84 | 1.00 | 0.84 | 0.77 | 0.00 | 7.10 | 0.81 |
time (sec) |
N/A | 0.819 | 0.000 | 0.057 | 0.210 | 0.073 | 1.240 | 0.000 | 200.028 | 3.287 |
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 | 16 | 12 | 12 | 0 | 22 | 8 | 24 | 28 | 11 |
N.S. |
1 | 0.80 | 0.60 | 0.60 | 0.00 | 1.10 | 0.40 | 1.20 | 1.40 | 0.55 |
time (sec) |
N/A | 0.382 | 0.087 | 0.206 | 0.000 | 0.068 | 0.071 | 0.110 | 0.218 | 0.086 |
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 | 18 | 0 | 21 | 20 | 20 | 19 | 26 | 21 | 21 | 21 |
N.S. |
1 | 0.00 | 1.17 | 1.11 | 1.11 | 1.06 | 1.44 | 1.17 | 1.17 | 1.17 |
time (sec) |
N/A | 0.000 | 2.529 | 0.147 | 0.163 | 0.070 | 0.101 | 0.113 | 0.205 | 2.650 |
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 | 19 | 0 | 19 | 18 | 33 | 17 | 14 | 23 | 17 | 17 |
N.S. |
1 | 0.00 | 1.00 | 0.95 | 1.74 | 0.89 | 0.74 | 1.21 | 0.89 | 0.89 |
time (sec) |
N/A | 0.000 | 0.053 | 0.309 | 0.154 | 0.060 | 0.083 | 0.118 | 0.211 | 2.191 |
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 | 23 | 35 | 37 | 28 | 28 | 52 | 26 | 22 | 53 | 29 |
N.S. |
1 | 1.52 | 1.61 | 1.22 | 1.22 | 2.26 | 1.13 | 0.96 | 2.30 | 1.26 |
time (sec) |
N/A | 0.299 | 0.032 | 0.085 | 0.041 | 0.059 | 0.090 | 0.114 | 0.201 | 2.146 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | A | A | A | A | B | B | F(-1) |
verified | N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 0 | 44 | 46 | 46 | 48 | 69 | 67 | 0 |
N.S. |
1 | 0.00 | 0.00 | 1.57 | 1.64 | 1.64 | 1.71 | 2.46 | 2.39 | 0.00 |
time (sec) |
N/A | 0.000 | 0.000 | 0.858 | 0.185 | 0.070 | 0.205 | 0.195 | 0.195 | 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 | 24 | 27 | 17 | 15 | 14 | 14 | 17 | 14 | 20 | 15 |
N.S. |
1 | 1.12 | 0.71 | 0.62 | 0.58 | 0.58 | 0.71 | 0.58 | 0.83 | 0.62 |
time (sec) |
N/A | 1.009 | 0.108 | 0.094 | 0.090 | 0.066 | 0.148 | 0.123 | 0.199 | 2.307 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | A | A | B | B | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 28 | 51 | 689 | 48 | 46 | 6083 | 51 | 0 |
N.S. |
1 | 0.00 | 0.97 | 1.76 | 23.76 | 1.66 | 1.59 | 209.76 | 1.76 | 0.00 |
time (sec) |
N/A | 0.000 | 0.075 | 51.862 | 2.951 | 0.066 | 0.621 | 0.404 | 0.233 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | C | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 47 | 53 | 25 | 26 | 19 | 29 | 24 | 26 | 14 |
N.S. |
1 | 2.14 | 2.41 | 1.14 | 1.18 | 0.86 | 1.32 | 1.09 | 1.18 | 0.64 |
time (sec) |
N/A | 0.494 | 0.048 | 0.069 | 0.064 | 0.063 | 0.117 | 0.110 | 0.211 | 0.152 |
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 | 25 | 26 | 24 | 26 | 24 | 32 | 25 | 25 |
N.S. |
1 | 0.00 | 0.96 | 1.00 | 0.92 | 1.00 | 0.92 | 1.23 | 0.96 | 0.96 |
time (sec) |
N/A | 0.000 | 0.252 | 1.139 | 0.154 | 0.065 | 0.070 | 0.126 | 0.194 | 2.356 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | B | C | B | B | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 113 | 82 | 81 | 148 | 88 | 88 | 104 | 115 | 86 |
N.S. |
1 | 3.65 | 2.65 | 2.61 | 4.77 | 2.84 | 2.84 | 3.35 | 3.71 | 2.77 |
time (sec) |
N/A | 0.818 | 3.637 | 2.711 | 0.097 | 0.068 | 0.138 | 0.111 | 0.198 | 2.215 |
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 | 10 | 11 | 9 | 12 | 12 | 7 | 12 | 7 | 8 |
N.S. |
1 | 0.71 | 0.79 | 0.64 | 0.86 | 0.86 | 0.50 | 0.86 | 0.50 | 0.57 |
time (sec) |
N/A | 0.133 | 0.000 | 0.023 | 0.033 | 0.059 | 0.016 | 0.114 | 0.193 | 2.126 |
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 | 30 | 28 | 29 | 30 | 24 | 30 | 48 | 27 |
N.S. |
1 | 0.00 | 1.07 | 1.00 | 1.04 | 1.07 | 0.86 | 1.07 | 1.71 | 0.96 |
time (sec) |
N/A | 0.000 | 0.019 | 0.329 | 0.040 | 0.068 | 0.759 | 0.143 | 0.193 | 0.190 |
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 | 4 | 4 | 4 | 5 | 4 | 4 | 3 | 5 | 4 | 4 |
N.S. |
1 | 1.00 | 1.00 | 1.25 | 1.00 | 1.00 | 0.75 | 1.25 | 1.00 | 1.00 |
time (sec) |
N/A | 0.125 | 0.000 | 0.020 | 0.025 | 0.058 | 0.018 | 0.115 | 0.195 | 0.010 |
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 | 64 | 41 | 29 | 37 | 47 | 32 | 37 | 63 | 28 |
N.S. |
1 | 1.94 | 1.24 | 0.88 | 1.12 | 1.42 | 0.97 | 1.12 | 1.91 | 0.85 |
time (sec) |
N/A | 0.563 | 0.042 | 0.185 | 0.035 | 0.067 | 0.264 | 0.114 | 0.198 | 2.277 |
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 | 16 | 16 | 15 | 14 | 14 | 19 | 14 | 14 | 14 |
N.S. |
1 | 0.94 | 0.94 | 0.88 | 0.82 | 0.82 | 1.12 | 0.82 | 0.82 | 0.82 |
time (sec) |
N/A | 0.149 | 0.004 | 0.092 | 0.031 | 0.063 | 0.069 | 0.106 | 0.222 | 2.294 |
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 | 30 | 30 | 30 | 31 | 32 | 46 | 32 | 0 | 37 | 32 |
N.S. |
1 | 1.00 | 1.00 | 1.03 | 1.07 | 1.53 | 1.07 | 0.00 | 1.23 | 1.07 |
time (sec) |
N/A | 1.390 | 0.194 | 1.299 | 0.117 | 0.068 | 0.533 | 0.000 | 0.297 | 2.881 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | B | B | B | B | F | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 83 | 78 | 71 | 71 | 90 | 78 | 0 | 100 | 85 |
N.S. |
1 | 2.44 | 2.29 | 2.09 | 2.09 | 2.65 | 2.29 | 0.00 | 2.94 | 2.50 |
time (sec) |
N/A | 0.286 | 0.094 | 0.250 | 0.050 | 0.069 | 0.198 | 0.000 | 0.194 | 2.408 |
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 | 33 | 0 | 30 | 59 | 0 | 46 | 34 | 0 | 38 | 0 |
N.S. |
1 | 0.00 | 0.91 | 1.79 | 0.00 | 1.39 | 1.03 | 0.00 | 1.15 | 0.00 |
time (sec) |
N/A | 0.000 | 0.089 | 3.000 | 0.000 | 0.070 | 0.208 | 0.000 | 0.381 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | A | A | F | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 0 | 26 | 36 | 40 | 30 | 31 | 0 | 62 | 297 |
N.S. |
1 | 0.00 | 1.30 | 1.80 | 2.00 | 1.50 | 1.55 | 0.00 | 3.10 | 14.85 |
time (sec) |
N/A | 0.000 | 0.284 | 0.267 | 0.150 | 0.066 | 0.129 | 0.000 | 0.203 | 0.356 |
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 | 17 | 17 | 10 | 9 | 9 | 7 | 11 | 9 | 8 |
N.S. |
1 | 0.68 | 0.68 | 0.40 | 0.36 | 0.36 | 0.28 | 0.44 | 0.36 | 0.32 |
time (sec) |
N/A | 0.157 | 0.003 | 0.070 | 0.029 | 0.059 | 0.050 | 0.116 | 0.225 | 2.245 |
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 | 29 | 0 | 27 | 35 | 37 | 33 | 39 | 34 | 37 | 0 |
N.S. |
1 | 0.00 | 0.93 | 1.21 | 1.28 | 1.14 | 1.34 | 1.17 | 1.28 | 0.00 |
time (sec) |
N/A | 0.000 | 5.025 | 0.823 | 0.157 | 0.069 | 0.093 | 0.124 | 0.220 | 0.000 |
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 | 21 | 35 | 26 | 21 | 30 | 37 | 27 | 55 | 41 | 33 |
N.S. |
1 | 1.67 | 1.24 | 1.00 | 1.43 | 1.76 | 1.29 | 2.62 | 1.95 | 1.57 |
time (sec) |
N/A | 1.177 | 0.510 | 2.011 | 0.235 | 0.071 | 0.208 | 0.196 | 0.421 | 2.525 |
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 | 21 | 19 | 31 | 18 | 41 | 38 | 39 | 37 | 41 | 101 |
N.S. |
1 | 0.90 | 1.48 | 0.86 | 1.95 | 1.81 | 1.86 | 1.76 | 1.95 | 4.81 |
time (sec) |
N/A | 0.304 | 0.019 | 0.075 | 0.030 | 0.062 | 0.414 | 0.116 | 0.205 | 2.335 |
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 | 16 | 4 | 4 | 5 | 4 | 4 | 5 | 5 | 4 | 4 |
N.S. |
1 | 0.25 | 0.25 | 0.31 | 0.25 | 0.25 | 0.31 | 0.31 | 0.25 | 0.25 |
time (sec) |
N/A | 0.124 | 0.000 | 0.014 | 0.026 | 0.055 | 0.017 | 0.113 | 0.214 | 0.008 |
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 | 21 | 21 | 21 | 20 | 20 | 17 | 20 | 23 | 22 |
N.S. |
1 | 0.91 | 0.91 | 0.91 | 0.87 | 0.87 | 0.74 | 0.87 | 1.00 | 0.96 |
time (sec) |
N/A | 0.186 | 0.024 | 0.112 | 0.046 | 0.068 | 0.053 | 0.109 | 0.210 | 0.070 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 26 | 26 | 59 | 38 | 17 | 34 | 45 | 45 |
N.S. |
1 | 0.00 | 1.13 | 1.13 | 2.57 | 1.65 | 0.74 | 1.48 | 1.96 | 1.96 |
time (sec) |
N/A | 0.000 | 0.094 | 0.585 | 0.155 | 0.066 | 0.066 | 0.115 | 0.204 | 2.424 |
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 | 23 | 33 | 22 | 25 | 33 | 22 | 26 | 27 | 24 | 27 |
N.S. |
1 | 1.43 | 0.96 | 1.09 | 1.43 | 0.96 | 1.13 | 1.17 | 1.04 | 1.17 |
time (sec) |
N/A | 0.249 | 0.053 | 0.131 | 0.060 | 0.065 | 0.075 | 0.112 | 0.207 | 2.300 |
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 | 18 | 18 | 21 | 0 | 19 | 19 | 15 | 21 | 16 |
N.S. |
1 | 0.90 | 0.90 | 1.05 | 0.00 | 0.95 | 0.95 | 0.75 | 1.05 | 0.80 |
time (sec) |
N/A | 0.665 | 0.124 | 0.440 | 0.000 | 0.065 | 0.212 | 0.113 | 0.215 | 2.347 |
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 | 22 | 22 | 23 | 19 | 23 | 18 | 19 | 18 | 19 | 20 |
N.S. |
1 | 1.00 | 1.05 | 0.86 | 1.05 | 0.82 | 0.86 | 0.82 | 0.86 | 0.91 |
time (sec) |
N/A | 0.210 | 0.021 | 0.168 | 0.059 | 0.067 | 0.064 | 0.110 | 0.198 | 2.240 |
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 | 22 | 0 | 30 | 29 | 56 | 56 | 31 | 56 | 65 | 0 |
N.S. |
1 | 0.00 | 1.36 | 1.32 | 2.55 | 2.55 | 1.41 | 2.55 | 2.95 | 0.00 |
time (sec) |
N/A | 0.000 | 3.686 | 0.978 | 0.103 | 0.074 | 0.126 | 0.189 | 0.209 | 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 | 24 | 0 | 27 | 20 | 29 | 28 | 26 | 20 | 20 | 19 |
N.S. |
1 | 0.00 | 1.12 | 0.83 | 1.21 | 1.17 | 1.08 | 0.83 | 0.83 | 0.79 |
time (sec) |
N/A | 0.000 | 0.141 | 0.180 | 0.072 | 0.078 | 0.176 | 0.119 | 0.205 | 2.352 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | B | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 56 | 52 | 25 | 26 | 45 | 22 | 23 | 75 | 20 |
N.S. |
1 | 2.07 | 1.93 | 0.93 | 0.96 | 1.67 | 0.81 | 0.85 | 2.78 | 0.74 |
time (sec) |
N/A | 0.396 | 0.030 | 0.300 | 0.036 | 0.067 | 0.398 | 0.114 | 0.213 | 2.237 |
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 | 19 | 17 | 17 | 17 | 21 | 17 | 16 | 22 | 16 |
N.S. |
1 | 0.79 | 0.71 | 0.71 | 0.71 | 0.88 | 0.71 | 0.67 | 0.92 | 0.67 |
time (sec) |
N/A | 0.184 | 0.005 | 0.047 | 0.026 | 0.060 | 0.045 | 0.114 | 0.216 | 2.090 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | F(-1) | A | B | F(-1) | A | B | B |
verified | N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 0 | 37 | 0 | 37 | 67 | 0 | 38 | 48 | 44 |
N.S. |
1 | 0.00 | 1.03 | 0.00 | 1.03 | 1.86 | 0.00 | 1.06 | 1.33 | 1.22 |
time (sec) |
N/A | 0.000 | 5.109 | 0.000 | 0.177 | 0.079 | 0.000 | 0.132 | 2.863 | 2.831 |
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 | 21 | 25 | 21 | 15 | 26 | 15 | 20 | 15 | 19 | 17 |
N.S. |
1 | 1.19 | 1.00 | 0.71 | 1.24 | 0.71 | 0.95 | 0.71 | 0.90 | 0.81 |
time (sec) |
N/A | 0.224 | 0.082 | 0.224 | 0.076 | 0.064 | 0.066 | 0.121 | 0.231 | 0.056 |
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 | 26 | 20 | 23 | 24 | 36 | 19 | 22 | 33 | 24 |
N.S. |
1 | 1.13 | 0.87 | 1.00 | 1.04 | 1.57 | 0.83 | 0.96 | 1.43 | 1.04 |
time (sec) |
N/A | 0.274 | 0.015 | 0.155 | 0.025 | 0.058 | 0.087 | 0.115 | 0.205 | 0.071 |
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 | 25 | 0 | 25 | 25 | 38 | 36 | 20 | 0 | 171 | 21 |
N.S. |
1 | 0.00 | 1.00 | 1.00 | 1.52 | 1.44 | 0.80 | 0.00 | 6.84 | 0.84 |
time (sec) |
N/A | 0.000 | 0.236 | 0.857 | 0.162 | 0.073 | 0.300 | 0.000 | 0.228 | 2.279 |
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 | 3 | 3 | 4 | 3 | 3 | 2 | 3 | 3 | 3 |
N.S. |
1 | 0.50 | 0.50 | 0.67 | 0.50 | 0.50 | 0.33 | 0.50 | 0.50 | 0.50 |
time (sec) |
N/A | 0.122 | 0.000 | 0.026 | 0.024 | 0.051 | 0.016 | 0.112 | 0.213 | 0.017 |
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 | 12 | 11 | 11 | 12 | 12 | 11 | 11 |
N.S. |
1 | 0.85 | 0.85 | 0.92 | 0.85 | 0.85 | 0.92 | 0.92 | 0.85 | 0.85 |
time (sec) |
N/A | 0.152 | 0.004 | 0.043 | 0.031 | 0.059 | 0.038 | 0.115 | 0.213 | 0.048 |
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 | 13 | 0 | 13 | 12 | 11 | 12 | 10 | 11 | 12 | 12 |
N.S. |
1 | 0.00 | 1.00 | 0.92 | 0.85 | 0.92 | 0.77 | 0.85 | 0.92 | 0.92 |
time (sec) |
N/A | 0.000 | 0.078 | 0.155 | 0.076 | 0.062 | 0.073 | 0.111 | 0.224 | 2.319 |
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 | 29 | 0 | 27 | 26 | 27 | 34 | 26 | 0 | 49 | 28 |
N.S. |
1 | 0.00 | 0.93 | 0.90 | 0.93 | 1.17 | 0.90 | 0.00 | 1.69 | 0.97 |
time (sec) |
N/A | 0.000 | 4.329 | 0.265 | 0.160 | 0.074 | 0.166 | 0.000 | 0.218 | 2.247 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 24 | 22 | 19 | 36 | 20 | 17 | 37 | 18 | 16 |
N.S. |
1 | 0.92 | 0.85 | 0.73 | 1.38 | 0.77 | 0.65 | 1.42 | 0.69 | 0.62 |
time (sec) |
N/A | 0.163 | 0.004 | 0.086 | 0.043 | 0.056 | 0.059 | 0.108 | 0.201 | 2.118 |
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 | 24 | 25 | 24 | 33 | 29 | 24 | 24 | 33 |
N.S. |
1 | 1.26 | 1.04 | 1.09 | 1.04 | 1.43 | 1.26 | 1.04 | 1.04 | 1.43 |
time (sec) |
N/A | 0.317 | 0.009 | 0.115 | 0.026 | 0.056 | 0.081 | 0.114 | 0.205 | 0.068 |
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 | 25 | 77 | 17 | 17 | 36 | 16 | 17 | 16 | 16 | 16 |
N.S. |
1 | 3.08 | 0.68 | 0.68 | 1.44 | 0.64 | 0.68 | 0.64 | 0.64 | 0.64 |
time (sec) |
N/A | 0.262 | 0.016 | 0.253 | 0.034 | 0.077 | 0.103 | 0.119 | 0.208 | 2.279 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | A | F(-1) | F | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 60 | 28 | 23 | 23 | 30 | 0 | 0 | 28 | 0 |
N.S. |
1 | 2.14 | 1.00 | 0.82 | 0.82 | 1.07 | 0.00 | 0.00 | 1.00 | 0.00 |
time (sec) |
N/A | 0.320 | 0.058 | 2.324 | 0.242 | 0.078 | 0.000 | 0.000 | 0.205 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | F | F | A | A | F | F | B |
verified | N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 0 | 20 | 0 | 0 | 18 | 24 | 0 | 68 | 19 |
N.S. |
1 | 0.00 | 0.95 | 0.00 | 0.00 | 0.86 | 1.14 | 0.00 | 3.24 | 0.90 |
time (sec) |
N/A | 0.000 | 0.533 | 0.000 | 0.000 | 0.091 | 1.345 | 0.000 | 200.015 | 2.920 |
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 | 27 | 0 | 33 | 28 | 30 | 27 | 48 | 30 | 24 | 27 |
N.S. |
1 | 0.00 | 1.22 | 1.04 | 1.11 | 1.00 | 1.78 | 1.11 | 0.89 | 1.00 |
time (sec) |
N/A | 0.000 | 0.033 | 1.497 | 0.145 | 0.075 | 0.388 | 0.167 | 0.178 | 2.686 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | B | B | B | B | B | B | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 302 | 110 | 99 | 95 | 131 | 109 | 116 | 0 |
N.S. |
1 | 0.00 | 9.74 | 3.55 | 3.19 | 3.06 | 4.23 | 3.52 | 3.74 | 0.00 |
time (sec) |
N/A | 0.000 | 0.434 | 0.096 | 0.166 | 0.074 | 0.753 | 0.170 | 0.191 | 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 | 23 | 0 | 22 | 21 | 32 | 20 | 15 | 25 | 20 | 20 |
N.S. |
1 | 0.00 | 0.96 | 0.91 | 1.39 | 0.87 | 0.65 | 1.09 | 0.87 | 0.87 |
time (sec) |
N/A | 0.000 | 0.218 | 3.190 | 0.146 | 0.058 | 0.080 | 0.139 | 0.211 | 2.317 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 44 | 20 | 52 | 33 | 33 | 20 | 39 | 40 | 34 |
N.S. |
1 | 1.83 | 0.83 | 2.17 | 1.38 | 1.38 | 0.83 | 1.62 | 1.67 | 1.42 |
time (sec) |
N/A | 0.533 | 0.066 | 0.014 | 0.150 | 0.067 | 0.132 | 0.139 | 0.211 | 2.294 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | A | B | B | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 199 | 34 | 47 | 47 | 40 | 49 | 50 | 149 | 0 |
N.S. |
1 | 8.65 | 1.48 | 2.04 | 2.04 | 1.74 | 2.13 | 2.17 | 6.48 | 0.00 |
time (sec) |
N/A | 0.751 | 0.038 | 1.102 | 0.037 | 0.066 | 2.773 | 0.124 | 0.227 | 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 | 7 | 7 | 8 | 7 | 7 | 5 | 7 | 7 | 7 |
N.S. |
1 | 0.88 | 0.88 | 1.00 | 0.88 | 0.88 | 0.62 | 0.88 | 0.88 | 0.88 |
time (sec) |
N/A | 0.240 | 0.001 | 0.055 | 0.032 | 0.066 | 0.043 | 0.113 | 0.234 | 1.907 |
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 | 33 | 30 | 31 | 27 | 30 | 29 | 30 | 35 | 34 |
N.S. |
1 | 1.10 | 1.00 | 1.03 | 0.90 | 1.00 | 0.97 | 1.00 | 1.17 | 1.13 |
time (sec) |
N/A | 3.141 | 0.149 | 18.898 | 0.187 | 0.073 | 2.003 | 0.139 | 0.202 | 0.244 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | A | B | B | B | B | B | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 88 | 54 | 90 | 66 | 92 | 120 | 102 | 0 |
N.S. |
1 | 0.00 | 3.03 | 1.86 | 3.10 | 2.28 | 3.17 | 4.14 | 3.52 | 0.00 |
time (sec) |
N/A | 0.000 | 0.085 | 2.756 | 0.092 | 0.078 | 4.665 | 0.213 | 0.241 | 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 | 33 | 0 | 31 | 35 | 43 | 34 | 27 | 48 | 36 | 34 |
N.S. |
1 | 0.00 | 0.94 | 1.06 | 1.30 | 1.03 | 0.82 | 1.45 | 1.09 | 1.03 |
time (sec) |
N/A | 0.000 | 0.046 | 5.668 | 0.103 | 0.080 | 0.117 | 0.280 | 0.203 | 3.367 |
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 | 14 | 17 | 17 | 17 | 17 | 14 | 13 |
N.S. |
1 | 1.00 | 0.88 | 0.88 | 1.06 | 1.06 | 1.06 | 1.06 | 0.88 | 0.81 |
time (sec) |
N/A | 0.135 | 0.001 | 0.049 | 0.026 | 0.059 | 0.030 | 0.113 | 0.225 | 0.052 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | F | B | B | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 21 | 173 | 0 | 107 | 122 | 107 | 172 | 120 |
N.S. |
1 | 0.00 | 0.95 | 7.86 | 0.00 | 4.86 | 5.55 | 4.86 | 7.82 | 5.45 |
time (sec) |
N/A | 0.000 | 5.035 | 1.977 | 0.000 | 0.072 | 0.348 | 0.282 | 0.233 | 2.168 |
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 | 34 | 25 | 23 | 23 | 23 | 20 | 23 | 30 | 20 |
N.S. |
1 | 1.21 | 0.89 | 0.82 | 0.82 | 0.82 | 0.71 | 0.82 | 1.07 | 0.71 |
time (sec) |
N/A | 0.173 | 0.040 | 0.146 | 0.039 | 0.059 | 0.059 | 0.117 | 0.201 | 1.947 |
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 | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 0 | 20 | 17 | 16 | 14 | 17 | 16 | 14 | 14 |
N.S. |
1 | 0.00 | 1.25 | 1.06 | 1.00 | 0.88 | 1.06 | 1.00 | 0.88 | 0.88 |
time (sec) |
N/A | 0.000 | 0.103 | 0.200 | 0.100 | 0.066 | 0.096 | 0.118 | 0.229 | 2.017 |
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 | 35 | 35 | 28 | 27 | 27 | 29 | 29 | 27 | 30 |
N.S. |
1 | 1.13 | 1.13 | 0.90 | 0.87 | 0.87 | 0.94 | 0.94 | 0.87 | 0.97 |
time (sec) |
N/A | 0.236 | 0.006 | 0.125 | 0.037 | 0.058 | 0.047 | 0.112 | 0.230 | 0.046 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | C | C | A | A | A | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 204 | 220 | 247 | 31 | 26 | 24 | 60 | 27 | 28 |
N.S. |
1 | 7.56 | 8.15 | 9.15 | 1.15 | 0.96 | 0.89 | 2.22 | 1.00 | 1.04 |
time (sec) |
N/A | 2.052 | 0.112 | 4.860 | 0.377 | 0.066 | 0.170 | 0.147 | 0.208 | 2.228 |
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 | 20 | 18 | 22 | 48 | 21 | 19 | 23 | 64 | 21 |
N.S. |
1 | 1.11 | 1.00 | 1.22 | 2.67 | 1.17 | 1.06 | 1.28 | 3.56 | 1.17 |
time (sec) |
N/A | 0.318 | 0.062 | 0.507 | 0.158 | 0.070 | 0.208 | 0.155 | 0.217 | 2.263 |
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 | 26 | 27 | 35 | 35 | 31 | 56 | 36 | 27 |
N.S. |
1 | 0.00 | 0.93 | 0.96 | 1.25 | 1.25 | 1.11 | 2.00 | 1.29 | 0.96 |
time (sec) |
N/A | 0.000 | 0.268 | 2.402 | 0.064 | 0.064 | 0.084 | 0.164 | 0.243 | 2.070 |
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 | 20 | 16 | 20 | 19 | 21 | 20 | 19 | 22 | 18 |
N.S. |
1 | 0.80 | 0.64 | 0.80 | 0.76 | 0.84 | 0.80 | 0.76 | 0.88 | 0.72 |
time (sec) |
N/A | 0.404 | 0.546 | 2.229 | 0.063 | 0.069 | 0.111 | 0.131 | 0.224 | 0.227 |
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 | 21 | 16 | 24 | 23 | 19 | 16 | 18 | 15 |
N.S. |
1 | 0.00 | 0.81 | 0.62 | 0.92 | 0.88 | 0.73 | 0.62 | 0.69 | 0.58 |
time (sec) |
N/A | 0.000 | 0.145 | 0.108 | 0.068 | 0.069 | 0.106 | 0.115 | 0.225 | 0.076 |
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 | 21 | 18 | 22 | 24 | 28 | 24 | 28 | 23 | 23 |
N.S. |
1 | 0.91 | 0.78 | 0.96 | 1.04 | 1.22 | 1.04 | 1.22 | 1.00 | 1.00 |
time (sec) |
N/A | 0.153 | 0.007 | 0.161 | 0.043 | 0.064 | 0.036 | 0.110 | 0.193 | 0.068 |
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 | 19 | 0 | 28 | 22 | 19 | 21 | 15 | 21 | 26 | 18 |
N.S. |
1 | 0.00 | 1.47 | 1.16 | 1.00 | 1.11 | 0.79 | 1.11 | 1.37 | 0.95 |
time (sec) |
N/A | 0.000 | 0.505 | 0.563 | 0.071 | 0.066 | 0.069 | 0.120 | 0.202 | 2.221 |
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 | 23 | 22 | 35 | 35 | 34 | 35 | 41 | 35 |
N.S. |
1 | 0.00 | 1.00 | 0.96 | 1.52 | 1.52 | 1.48 | 1.52 | 1.78 | 1.52 |
time (sec) |
N/A | 0.000 | 0.197 | 0.515 | 0.110 | 0.066 | 0.094 | 0.131 | 0.209 | 2.119 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | C | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 64 | 26 | 19 | 42 | 23 | 17 | 18 | 23 | 15 |
N.S. |
1 | 3.76 | 1.53 | 1.12 | 2.47 | 1.35 | 1.00 | 1.06 | 1.35 | 0.88 |
time (sec) |
N/A | 0.621 | 0.057 | 0.320 | 0.075 | 0.065 | 0.041 | 0.119 | 0.196 | 1.995 |
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 | 24 | 19 | 18 | 17 | 17 | 17 | 17 | 31 | 18 |
N.S. |
1 | 1.50 | 1.19 | 1.12 | 1.06 | 1.06 | 1.06 | 1.06 | 1.94 | 1.12 |
time (sec) |
N/A | 0.175 | 0.003 | 0.265 | 0.027 | 0.063 | 0.093 | 0.120 | 0.188 | 0.104 |