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 | B | B | B | B | F | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 47 | 107 | 117 | 64 | 56 | 0 | 106 | 61 |
N.S. |
1 | 0.00 | 1.81 | 4.12 | 4.50 | 2.46 | 2.15 | 0.00 | 4.08 | 2.35 |
time (sec) |
N/A | 0.000 | 0.052 | 29.369 | 0.123 | 0.095 | 0.175 | 0.000 | 0.202 | 3.079 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | B | F | B | B | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 67 | 97 | 0 | 77 | 70 | 104 | 105 | 83 |
N.S. |
1 | 0.00 | 2.31 | 3.34 | 0.00 | 2.66 | 2.41 | 3.59 | 3.62 | 2.86 |
time (sec) |
N/A | 0.000 | 0.057 | 0.025 | 0.000 | 0.090 | 0.166 | 0.131 | 0.192 | 2.983 |
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 | 25 | 37 | 25 | 36 | 36 | 22 | 41 | 25 |
N.S. |
1 | 0.00 | 1.00 | 1.48 | 1.00 | 1.44 | 1.44 | 0.88 | 1.64 | 1.00 |
time (sec) |
N/A | 0.000 | 0.043 | 1.017 | 0.320 | 0.077 | 0.190 | 0.369 | 0.237 | 2.855 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | A | F(-2) | A | A | A | B | B |
verified |
N/A | Yes | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 34 | 0 | 31 | 0 | 25 | 34 | 30 | 32 | 28 |
N.S. |
1 | 1.06 | 0.00 | 0.97 | 0.00 | 0.78 | 1.06 | 0.94 | 1.00 | 0.88 |
time (sec) |
N/A | 0.688 | 0.000 | 0.384 | 0.000 | 0.087 | 0.209 | 0.123 | 0.217 | 3.517 |
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 | 24 | 29 | 24 | 26 | 62 | 20 | 31 | 25 | 23 | 22 |
N.S. |
1 | 1.21 | 1.00 | 1.08 | 2.58 | 0.83 | 1.29 | 1.04 | 0.96 | 0.92 |
time (sec) |
N/A | 0.211 | 0.037 | 0.132 | 0.028 | 0.082 | 0.089 | 0.112 | 0.198 | 2.870 |
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 | 14 | 12 | 12 | 12 | 24 | 11 | 12 | 11 | 12 | 11 |
N.S. |
1 | 0.86 | 0.86 | 0.86 | 1.71 | 0.79 | 0.86 | 0.79 | 0.86 | 0.79 |
time (sec) |
N/A | 0.164 | 0.003 | 0.062 | 0.038 | 0.091 | 0.061 | 0.110 | 0.201 | 2.832 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 21 | 19 | 42 | 225 | 34 | 44 | 41 | 38 | 41 |
N.S. |
1 | 1.24 | 1.12 | 2.47 | 13.24 | 2.00 | 2.59 | 2.41 | 2.24 | 2.41 |
time (sec) |
N/A | 0.363 | 0.011 | 1.283 | 0.037 | 0.082 | 0.111 | 0.119 | 0.208 | 0.143 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 34 | 54 | 54 | 450 | 53 | 53 | 99 | 59 | 56 |
N.S. |
1 | 1.26 | 2.00 | 2.00 | 16.67 | 1.96 | 1.96 | 3.67 | 2.19 | 2.07 |
time (sec) |
N/A | 2.181 | 0.069 | 0.974 | 0.399 | 0.090 | 0.408 | 0.343 | 0.212 | 3.055 |
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 | 11 | 10 | 12 | 8 | 10 | 12 | 10 |
N.S. |
1 | 0.81 | 0.81 | 0.69 | 0.62 | 0.75 | 0.50 | 0.62 | 0.75 | 0.62 |
time (sec) |
N/A | 0.157 | 0.002 | 0.044 | 0.025 | 0.076 | 0.048 | 0.116 | 0.201 | 2.717 |
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 | 35 | 20 | 19 | 0 | 18 | 15 | 33 | 20 | 19 |
N.S. |
1 | 1.75 | 1.00 | 0.95 | 0.00 | 0.90 | 0.75 | 1.65 | 1.00 | 0.95 |
time (sec) |
N/A | 0.202 | 0.258 | 0.108 | 0.000 | 0.076 | 4.428 | 0.126 | 0.232 | 0.061 |
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 | 35 | 0 | 40 | 44 | 69 | 81 | 95 | 842 | 108 | 0 |
N.S. |
1 | 0.00 | 1.14 | 1.26 | 1.97 | 2.31 | 2.71 | 24.06 | 3.09 | 0.00 |
time (sec) |
N/A | 0.000 | 0.143 | 0.069 | 0.150 | 0.104 | 0.247 | 0.757 | 0.212 | 0.000 |
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 | 49 | 24 | 19 | 32 | 17 | 26 | 17 | 14 | 13 |
N.S. |
1 | 2.72 | 1.33 | 1.06 | 1.78 | 0.94 | 1.44 | 0.94 | 0.78 | 0.72 |
time (sec) |
N/A | 0.206 | 0.007 | 0.126 | 0.028 | 0.077 | 0.067 | 0.113 | 0.200 | 2.929 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | B | B | F | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 56 | 36 | 65 | 137 | 49 | 0 | 102 | 0 |
N.S. |
1 | 0.00 | 1.81 | 1.16 | 2.10 | 4.42 | 1.58 | 0.00 | 3.29 | 0.00 |
time (sec) |
N/A | 0.000 | 0.172 | 3.574 | 0.292 | 0.093 | 0.183 | 0.000 | 0.617 | 0.000 |
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 | 23 | 21 | 51 | 32 | 22 | 36 | 34 | 28 |
N.S. |
1 | 1.19 | 1.10 | 1.00 | 2.43 | 1.52 | 1.05 | 1.71 | 1.62 | 1.33 |
time (sec) |
N/A | 0.695 | 0.065 | 2.094 | 0.074 | 0.085 | 0.088 | 0.135 | 0.189 | 2.718 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | C | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 24 | 34 | 59 | 33 | 20 | 22 | 43 | 22 |
N.S. |
1 | 0.00 | 0.83 | 1.17 | 2.03 | 1.14 | 0.69 | 0.76 | 1.48 | 0.76 |
time (sec) |
N/A | 0.000 | 0.318 | 1.379 | 0.156 | 0.082 | 0.083 | 0.135 | 0.196 | 2.970 |
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 | 23 | 18 | 19 | 18 | 24 | 24 | 18 | 13 | 12 |
N.S. |
1 | 1.53 | 1.20 | 1.27 | 1.20 | 1.60 | 1.60 | 1.20 | 0.87 | 0.80 |
time (sec) |
N/A | 0.178 | 0.011 | 0.292 | 0.080 | 0.095 | 0.081 | 0.112 | 0.204 | 2.920 |
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 | 51 | 14 | 15 | 13 | 16 | 14 | 16 | 19 | 14 |
N.S. |
1 | 3.19 | 0.88 | 0.94 | 0.81 | 1.00 | 0.88 | 1.00 | 1.19 | 0.88 |
time (sec) |
N/A | 0.235 | 0.011 | 0.132 | 0.090 | 0.090 | 0.065 | 0.117 | 0.955 | 2.974 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | F | A | F(-2) | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 121 | 25 | 23 | 0 | 22 | 0 | 0 | 27 | 22 |
N.S. |
1 | 5.04 | 1.04 | 0.96 | 0.00 | 0.92 | 0.00 | 0.00 | 1.12 | 0.92 |
time (sec) |
N/A | 0.629 | 0.143 | 2.705 | 0.000 | 0.094 | 0.000 | 0.000 | 0.209 | 3.221 |
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 | 19 | 0 | 16 | 19 | 14 | 51 | 15 | 0 | 46 | 17 |
N.S. |
1 | 0.00 | 0.84 | 1.00 | 0.74 | 2.68 | 0.79 | 0.00 | 2.42 | 0.89 |
time (sec) |
N/A | 0.000 | 0.108 | 0.238 | 1.564 | 0.105 | 0.105 | 0.000 | 71.292 | 3.020 |
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 | 33 | 44 | 35 | 39 | 31 | 34 | 41 | 80 |
N.S. |
1 | 0.00 | 1.22 | 1.63 | 1.30 | 1.44 | 1.15 | 1.26 | 1.52 | 2.96 |
time (sec) |
N/A | 0.000 | 0.055 | 0.203 | 0.147 | 0.083 | 0.064 | 0.195 | 0.190 | 3.031 |
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 | 26 | 37 | 21 | 20 | 0 | 22 | 17 | 22 | 31 | 22 |
N.S. |
1 | 1.42 | 0.81 | 0.77 | 0.00 | 0.85 | 0.65 | 0.85 | 1.19 | 0.85 |
time (sec) |
N/A | 0.246 | 0.293 | 0.188 | 0.000 | 0.080 | 0.071 | 0.113 | 0.196 | 0.050 |
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 | 23 | 58 | 23 | 20 | 19 | 19 | 19 | 0 | 23 | 22 |
N.S. |
1 | 2.52 | 1.00 | 0.87 | 0.83 | 0.83 | 0.83 | 0.00 | 1.00 | 0.96 |
time (sec) |
N/A | 0.345 | 0.049 | 0.246 | 0.120 | 0.078 | 0.096 | 0.000 | 0.193 | 2.905 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | F(-1) | B | B | A | F(-1) | B | B |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 29 | 0 | 67 | 73 | 42 | 0 | 55 | 51 |
N.S. |
1 | 0.00 | 1.00 | 0.00 | 2.31 | 2.52 | 1.45 | 0.00 | 1.90 | 1.76 |
time (sec) |
N/A | 0.000 | 0.077 | 0.000 | 1.232 | 0.092 | 0.334 | 0.000 | 0.250 | 3.007 |
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 | 61 | 13 | 14 | 13 | 13 | 10 | 13 | 13 | 13 |
N.S. |
1 | 3.81 | 0.81 | 0.88 | 0.81 | 0.81 | 0.62 | 0.81 | 0.81 | 0.81 |
time (sec) |
N/A | 0.871 | 0.143 | 0.260 | 0.070 | 0.070 | 0.053 | 0.111 | 0.201 | 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 | 16 | 23 | 23 | 19 | 19 | 19 | 17 | 19 | 15 | 18 |
N.S. |
1 | 1.44 | 1.44 | 1.19 | 1.19 | 1.19 | 1.06 | 1.19 | 0.94 | 1.12 |
time (sec) |
N/A | 0.182 | 0.003 | 0.192 | 0.034 | 0.073 | 0.097 | 0.114 | 0.204 | 0.061 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | B | C | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 168 | 19 | 92 | 167 | 91 | 88 | 156 | 92 | 90 |
N.S. |
1 | 10.50 | 1.19 | 5.75 | 10.44 | 5.69 | 5.50 | 9.75 | 5.75 | 5.62 |
time (sec) |
N/A | 8.176 | 0.578 | 1.153 | 0.137 | 0.091 | 0.155 | 0.116 | 0.200 | 2.846 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | A | B | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 12 | 41 | 47 | 16 | 97 | 15 | 14 | 15 | 15 | 12 |
N.S. |
1 | 3.42 | 3.92 | 1.33 | 8.08 | 1.25 | 1.17 | 1.25 | 1.25 | 1.00 |
time (sec) |
N/A | 0.595 | 0.037 | 0.309 | 0.031 | 0.082 | 0.069 | 0.110 | 0.192 | 0.129 |
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 | 18 | 35 | 31 | 28 | 24 | 26 | 31 | 25 | 24 | 28 |
N.S. |
1 | 1.94 | 1.72 | 1.56 | 1.33 | 1.44 | 1.72 | 1.39 | 1.33 | 1.56 |
time (sec) |
N/A | 0.213 | 0.006 | 0.198 | 0.034 | 0.085 | 0.073 | 0.110 | 0.191 | 2.800 |
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 | 22 | 0 | 22 | 38 | 62 | 35 | 34 | 137 | 29 | 401 |
N.S. |
1 | 0.00 | 1.00 | 1.73 | 2.82 | 1.59 | 1.55 | 6.23 | 1.32 | 18.23 |
time (sec) |
N/A | 0.000 | 0.118 | 1.061 | 0.293 | 0.077 | 0.354 | 0.532 | 0.210 | 2.937 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 14 | 14 | 13 | 12 | 12 | 0 | 12 | 16 | 0 |
N.S. |
1 | 0.88 | 0.88 | 0.81 | 0.75 | 0.75 | 0.00 | 0.75 | 1.00 | 0.00 |
time (sec) |
N/A | 0.250 | 0.020 | 7.557 | 0.089 | 0.087 | 0.000 | 0.140 | 0.207 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F | A | A | F | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 28 | 29 | 0 | 27 | 22 | 0 | 30 | 22 |
N.S. |
1 | 0.00 | 0.97 | 1.00 | 0.00 | 0.93 | 0.76 | 0.00 | 1.03 | 0.76 |
time (sec) |
N/A | 0.000 | 2.380 | 1.203 | 0.000 | 0.088 | 0.094 | 0.000 | 0.645 | 2.859 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | B | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 51 | 37 | 40 | 46 | 34 | 56 | 109 | 0 |
N.S. |
1 | 0.00 | 1.70 | 1.23 | 1.33 | 1.53 | 1.13 | 1.87 | 3.63 | 0.00 |
time (sec) |
N/A | 0.000 | 0.059 | 0.532 | 0.115 | 0.085 | 0.108 | 0.170 | 200.022 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | A | A | A | B | B | B | F(-1) |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 0 | 0 | 63 | 43 | 60 | 61 | 114 | 72 | 0 |
N.S. |
1 | 0.00 | 0.00 | 1.85 | 1.26 | 1.76 | 1.79 | 3.35 | 2.12 | 0.00 |
time (sec) |
N/A | 0.000 | 0.000 | 32.276 | 0.273 | 0.094 | 0.832 | 16.046 | 0.238 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F(-2) | A | F(-2) | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 0 | 30 | 41 | 0 | 38 | 0 | 53 | 44 | 56 |
N.S. |
1 | 0.00 | 0.88 | 1.21 | 0.00 | 1.12 | 0.00 | 1.56 | 1.29 | 1.65 |
time (sec) |
N/A | 0.000 | 0.066 | 41.321 | 0.000 | 0.084 | 0.000 | 0.296 | 0.169 | 3.301 |
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 | 9 | 9 | 9 | 8 | 8 | 8 | 8 | 12 | 10 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.89 | 0.89 | 0.89 | 0.89 | 1.33 | 1.11 |
time (sec) |
N/A | 0.292 | 0.029 | 0.047 | 0.086 | 0.084 | 0.076 | 0.110 | 0.172 | 2.897 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 18 | 18 | 18 | 72 | 25 | 0 | 17 | 18 | 17 |
N.S. |
1 | 0.90 | 0.90 | 0.90 | 3.60 | 1.25 | 0.00 | 0.85 | 0.90 | 0.85 |
time (sec) |
N/A | 0.567 | 0.150 | 36.804 | 0.047 | 0.071 | 0.000 | 0.114 | 0.173 | 2.887 |
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 | 26 | 25 | 26 | 26 | 42 | 26 | 28 | 24 |
N.S. |
1 | 0.00 | 1.00 | 0.96 | 1.00 | 1.00 | 1.62 | 1.00 | 1.08 | 0.92 |
time (sec) |
N/A | 0.000 | 0.080 | 26.324 | 0.070 | 0.082 | 0.692 | 0.137 | 0.171 | 0.221 |
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 | 30 | 0 | 23 | 34 | 101 | 37 | 32 | 56 | 38 | 69 |
N.S. |
1 | 0.00 | 0.77 | 1.13 | 3.37 | 1.23 | 1.07 | 1.87 | 1.27 | 2.30 |
time (sec) |
N/A | 0.000 | 5.070 | 3.434 | 0.235 | 0.089 | 0.161 | 0.203 | 0.169 | 3.090 |
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 | 36 | 0 | 30 | 29 | 36 | 94 | 27 | 0 | 0 | 31 |
N.S. |
1 | 0.00 | 0.83 | 0.81 | 1.00 | 2.61 | 0.75 | 0.00 | 0.00 | 0.86 |
time (sec) |
N/A | 0.000 | 0.116 | 18.793 | 0.484 | 0.084 | 0.369 | 0.000 | 0.539 | 0.212 |
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 | 17 | 26 | 25 | 13 | 15 | 28 | 17 | 12 | 32 | 15 |
N.S. |
1 | 1.53 | 1.47 | 0.76 | 0.88 | 1.65 | 1.00 | 0.71 | 1.88 | 0.88 |
time (sec) |
N/A | 0.257 | 0.113 | 0.116 | 0.032 | 0.085 | 0.042 | 0.110 | 0.167 | 3.002 |
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 | 31 | 26 | 26 | 94 | 31 | 24 | 30 | 28 | 25 |
N.S. |
1 | 1.07 | 0.90 | 0.90 | 3.24 | 1.07 | 0.83 | 1.03 | 0.97 | 0.86 |
time (sec) |
N/A | 0.243 | 0.028 | 0.247 | 0.065 | 0.089 | 0.110 | 0.123 | 0.173 | 2.943 |
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 | 17 | 17 | 12 | 14 | 15 | 10 | 15 | 16 | 11 |
N.S. |
1 | 0.81 | 0.81 | 0.57 | 0.67 | 0.71 | 0.48 | 0.71 | 0.76 | 0.52 |
time (sec) |
N/A | 0.193 | 0.040 | 0.102 | 0.057 | 0.090 | 0.043 | 0.115 | 0.167 | 2.996 |
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 | 5 | 5 | 5 | 5 | 4 | 4 | 3 | 4 | 5 | 4 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.80 | 0.80 | 0.60 | 0.80 | 1.00 | 0.80 |
time (sec) |
N/A | 0.129 | 0.000 | 0.043 | 0.033 | 0.080 | 0.018 | 0.113 | 0.165 | 0.011 |
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 | 26 | 0 | 34 | 46 | 46 | 34 | 41 | 36 | 56 | 50 |
N.S. |
1 | 0.00 | 1.31 | 1.77 | 1.77 | 1.31 | 1.58 | 1.38 | 2.15 | 1.92 |
time (sec) |
N/A | 0.000 | 0.133 | 0.044 | 0.134 | 0.091 | 0.235 | 0.205 | 1.787 | 2.859 |
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 | 28 | 26 | 25 | 20 | 24 | 19 | 17 | 21 | 23 | 18 |
N.S. |
1 | 0.93 | 0.89 | 0.71 | 0.86 | 0.68 | 0.61 | 0.75 | 0.82 | 0.64 |
time (sec) |
N/A | 0.250 | 0.081 | 0.138 | 0.058 | 0.079 | 0.066 | 0.110 | 0.168 | 0.036 |
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 | 20 | 18 | 18 | 18 | 17 | 18 | 15 | 44 | 19 | 24 |
N.S. |
1 | 0.90 | 0.90 | 0.90 | 0.85 | 0.90 | 0.75 | 2.20 | 0.95 | 1.20 |
time (sec) |
N/A | 0.604 | 0.078 | 0.286 | 0.032 | 0.078 | 0.075 | 0.151 | 0.170 | 0.061 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | B | B | B | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 40 | 0 | 56 | 158 | 104 | 105 | 61 | 151 | 108 | 460 |
N.S. |
1 | 0.00 | 1.40 | 3.95 | 2.60 | 2.62 | 1.52 | 3.78 | 2.70 | 11.50 |
time (sec) |
N/A | 0.000 | 0.170 | 34.542 | 0.272 | 0.104 | 0.680 | 9.726 | 0.213 | 4.152 |
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 | 20 | 15 | 13 | 12 | 12 | 12 | 12 | 13 | 12 |
N.S. |
1 | 1.00 | 0.75 | 0.65 | 0.60 | 0.60 | 0.60 | 0.60 | 0.65 | 0.60 |
time (sec) |
N/A | 0.181 | 0.010 | 0.091 | 0.031 | 0.078 | 0.044 | 0.112 | 0.171 | 3.064 |
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 | 20 | 21 | 16 | 13 | 15 | 17 | 15 | 14 | 15 |
N.S. |
1 | 0.87 | 0.91 | 0.70 | 0.57 | 0.65 | 0.74 | 0.65 | 0.61 | 0.65 |
time (sec) |
N/A | 0.164 | 0.003 | 0.104 | 0.031 | 0.079 | 0.120 | 0.117 | 0.165 | 0.043 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 43 | 35 | 33 | 48 | 34 | 24 | 109 | 45 | 40 |
N.S. |
1 | 1.54 | 1.25 | 1.18 | 1.71 | 1.21 | 0.86 | 3.89 | 1.61 | 1.43 |
time (sec) |
N/A | 0.360 | 0.069 | 0.296 | 0.064 | 0.079 | 0.069 | 0.128 | 0.168 | 2.804 |
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 | 19 | 19 | 18 | 17 | 17 | 14 | 19 | 17 | 17 |
N.S. |
1 | 1.00 | 1.00 | 0.95 | 0.89 | 0.89 | 0.74 | 1.00 | 0.89 | 0.89 |
time (sec) |
N/A | 0.238 | 0.006 | 0.113 | 0.029 | 0.089 | 0.045 | 0.108 | 0.172 | 2.765 |
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 | 22 | 0 | 20 | 19 | 27 | 23 | 20 | 53 | 23 | 23 |
N.S. |
1 | 0.00 | 0.91 | 0.86 | 1.23 | 1.05 | 0.91 | 2.41 | 1.05 | 1.05 |
time (sec) |
N/A | 0.000 | 0.111 | 0.245 | 0.163 | 0.078 | 0.096 | 0.131 | 0.172 | 2.889 |
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 | 39 | 24 | 25 | 32 | 27 | 15 | 27 | 27 | 18 |
N.S. |
1 | 1.44 | 0.89 | 0.93 | 1.19 | 1.00 | 0.56 | 1.00 | 1.00 | 0.67 |
time (sec) |
N/A | 0.228 | 0.017 | 0.162 | 0.031 | 0.089 | 0.095 | 0.111 | 0.177 | 0.063 |
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 | 19 | 37 | 37 | 26 | 22 | 37 | 25 | 23 |
N.S. |
1 | 0.00 | 0.83 | 1.61 | 1.61 | 1.13 | 0.96 | 1.61 | 1.09 | 1.00 |
time (sec) |
N/A | 0.000 | 0.175 | 1.582 | 0.074 | 0.091 | 0.173 | 0.144 | 0.175 | 3.069 |
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 | 5 | 5 | 6 | 5 | 5 | 3 | 5 | 5 | 5 |
N.S. |
1 | 0.31 | 0.31 | 0.38 | 0.31 | 0.31 | 0.19 | 0.31 | 0.31 | 0.31 |
time (sec) |
N/A | 0.129 | 0.000 | 0.018 | 0.026 | 0.058 | 0.016 | 0.112 | 0.169 | 0.014 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | C | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 0 | 46 | 1449 | 51 | 49 | 41 | 53 | 49 | 48 |
N.S. |
1 | 0.00 | 1.31 | 41.40 | 1.46 | 1.40 | 1.17 | 1.51 | 1.40 | 1.37 |
time (sec) |
N/A | 0.000 | 0.783 | 0.119 | 0.322 | 0.109 | 0.796 | 1.205 | 0.650 | 3.412 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | F(-2) | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 26 | 26 | 25 | 25 | 20 | 0 | 26 | 25 |
N.S. |
1 | 0.00 | 0.93 | 0.93 | 0.89 | 0.89 | 0.71 | 0.00 | 0.93 | 0.89 |
time (sec) |
N/A | 0.000 | 0.185 | 3.480 | 0.147 | 0.085 | 0.142 | 0.000 | 0.176 | 3.078 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | B | B | B | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 57 | 103 | 195 | 88 | 386 | 189 | 112 | 107 |
N.S. |
1 | 0.00 | 1.97 | 3.55 | 6.72 | 3.03 | 13.31 | 6.52 | 3.86 | 3.69 |
time (sec) |
N/A | 0.000 | 0.104 | 2.538 | 0.163 | 0.081 | 0.448 | 0.130 | 0.169 | 3.104 |
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 | 23 | 21 | 21 | 31 | 37 | 15 | 39 | 38 | 22 |
N.S. |
1 | 0.77 | 0.70 | 0.70 | 1.03 | 1.23 | 0.50 | 1.30 | 1.27 | 0.73 |
time (sec) |
N/A | 0.818 | 0.221 | 0.569 | 0.069 | 0.097 | 0.080 | 0.120 | 0.169 | 2.792 |
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 | 32 | 0 | 36 | 55 | 33 | 55 | 49 | 159 | 81 | 147 |
N.S. |
1 | 0.00 | 1.12 | 1.72 | 1.03 | 1.72 | 1.53 | 4.97 | 2.53 | 4.59 |
time (sec) |
N/A | 0.000 | 0.090 | 4.559 | 89.733 | 0.085 | 1.295 | 0.151 | 0.170 | 3.485 |
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 | 20 | 20 | 20 | 19 | 22 | 17 | 22 | 24 | 24 |
N.S. |
1 | 0.87 | 0.87 | 0.87 | 0.83 | 0.96 | 0.74 | 0.96 | 1.04 | 1.04 |
time (sec) |
N/A | 0.196 | 0.293 | 0.234 | 0.032 | 0.084 | 0.058 | 0.111 | 0.163 | 0.042 |
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 | 26 | 25 | 48 | 24 | 19 | 24 | 38 | 24 |
N.S. |
1 | 1.24 | 0.90 | 0.86 | 1.66 | 0.83 | 0.66 | 0.83 | 1.31 | 0.83 |
time (sec) |
N/A | 0.269 | 0.398 | 0.212 | 0.064 | 0.078 | 0.123 | 0.115 | 0.159 | 0.084 |
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 | 32 | 19 | 17 | 19 | 19 | 17 | 19 | 33 | 19 |
N.S. |
1 | 1.45 | 0.86 | 0.77 | 0.86 | 0.86 | 0.77 | 0.86 | 1.50 | 0.86 |
time (sec) |
N/A | 0.221 | 1.047 | 0.118 | 0.037 | 0.102 | 0.051 | 0.110 | 0.174 | 3.194 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 50 | 29 | 114 | 54 | 36 | 46 | 43 | 45 | 32 |
N.S. |
1 | 1.79 | 1.04 | 4.07 | 1.93 | 1.29 | 1.64 | 1.54 | 1.61 | 1.14 |
time (sec) |
N/A | 0.347 | 0.065 | 0.053 | 0.073 | 0.094 | 0.218 | 0.137 | 0.171 | 2.932 |
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 | 13 | 13 | 12 | 11 | 11 | 12 | 11 | 25 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.92 | 0.85 | 0.85 | 0.92 | 0.85 | 1.92 | 1.00 |
time (sec) |
N/A | 0.186 | 0.005 | 0.149 | 0.032 | 0.066 | 0.105 | 0.111 | 0.167 | 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 | 26 | 0 | 31 | 26 | 31 | 30 | 29 | 31 | 33 | 26 |
N.S. |
1 | 0.00 | 1.19 | 1.00 | 1.19 | 1.15 | 1.12 | 1.19 | 1.27 | 1.00 |
time (sec) |
N/A | 0.000 | 3.267 | 0.913 | 0.151 | 0.092 | 0.216 | 0.128 | 0.197 | 4.402 |
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 | 58 | 56 | 40 | 73 | 51 | 42 | 56 | 47 | 50 |
N.S. |
1 | 2.00 | 1.93 | 1.38 | 2.52 | 1.76 | 1.45 | 1.93 | 1.62 | 1.72 |
time (sec) |
N/A | 0.893 | 0.198 | 0.932 | 0.077 | 0.082 | 0.055 | 0.121 | 0.176 | 2.964 |
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 | 17 | 11 | 9 | 8 | 8 | 8 | 8 | 17 | 8 |
N.S. |
1 | 1.21 | 0.79 | 0.64 | 0.57 | 0.57 | 0.57 | 0.57 | 1.21 | 0.57 |
time (sec) |
N/A | 0.142 | 0.009 | 0.042 | 0.025 | 0.078 | 0.035 | 0.113 | 0.170 | 2.869 |
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 | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 17 | 17 | 15 | 14 | 34 | 15 | 34 | 28 | 14 |
N.S. |
1 | 0.85 | 0.85 | 0.75 | 0.70 | 1.70 | 0.75 | 1.70 | 1.40 | 0.70 |
time (sec) |
N/A | 0.417 | 0.020 | 0.681 | 0.032 | 0.106 | 0.135 | 0.133 | 0.172 | 2.889 |
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 | 15 | 15 | 16 | 13 | 19 | 14 | 15 | 15 | 21 |
N.S. |
1 | 0.75 | 0.75 | 0.80 | 0.65 | 0.95 | 0.70 | 0.75 | 0.75 | 1.05 |
time (sec) |
N/A | 0.279 | 0.062 | 0.186 | 0.055 | 0.097 | 0.064 | 0.129 | 0.173 | 3.110 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | B | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 23 | 29 | 49 | 71 | 29 | 18 | 21 | 277 |
N.S. |
1 | 0.00 | 1.00 | 1.26 | 2.13 | 3.09 | 1.26 | 0.78 | 0.91 | 12.04 |
time (sec) |
N/A | 0.000 | 0.179 | 18.452 | 0.271 | 0.108 | 0.393 | 0.448 | 0.171 | 2.976 |
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 | 38 | 23 | 29 | 28 | 28 | 31 | 30 | 33 | 15 |
N.S. |
1 | 1.58 | 0.96 | 1.21 | 1.17 | 1.17 | 1.29 | 1.25 | 1.38 | 0.62 |
time (sec) |
N/A | 0.250 | 0.018 | 0.917 | 0.057 | 0.090 | 0.125 | 0.112 | 0.171 | 2.960 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | B | F | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 80 | 64 | 88 | 0 | 69 | 75 | 126 | 86 | 78 |
N.S. |
1 | 3.20 | 2.56 | 3.52 | 0.00 | 2.76 | 3.00 | 5.04 | 3.44 | 3.12 |
time (sec) |
N/A | 0.490 | 0.097 | 0.058 | 0.000 | 0.091 | 0.340 | 0.136 | 0.195 | 2.940 |
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 | 30 | 0 | 41 | 38 | 66 | 71 | 37 | 5359 | 92 | 0 |
N.S. |
1 | 0.00 | 1.37 | 1.27 | 2.20 | 2.37 | 1.23 | 178.63 | 3.07 | 0.00 |
time (sec) |
N/A | 0.000 | 0.110 | 0.040 | 0.206 | 0.095 | 0.215 | 1.169 | 0.188 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 37 | 31 | 35 | 32 | 29 | 27 | 0 | 70 | 0 |
N.S. |
1 | 1.16 | 0.97 | 1.09 | 1.00 | 0.91 | 0.84 | 0.00 | 2.19 | 0.00 |
time (sec) |
N/A | 1.582 | 0.218 | 59.136 | 0.625 | 0.081 | 0.860 | 0.000 | 0.208 | 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 | 25 | 25 | 18 | 17 | 17 | 19 | 17 | 18 | 17 |
N.S. |
1 | 1.09 | 1.09 | 0.78 | 0.74 | 0.74 | 0.83 | 0.74 | 0.78 | 0.74 |
time (sec) |
N/A | 0.156 | 0.001 | 0.033 | 0.024 | 0.086 | 0.019 | 0.106 | 0.171 | 0.018 |
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 | 7 | 7 | 8 | 7 | 7 | 7 | 8 | 7 | 7 |
N.S. |
1 | 0.37 | 0.37 | 0.42 | 0.37 | 0.37 | 0.37 | 0.42 | 0.37 | 0.37 |
time (sec) |
N/A | 0.155 | 0.002 | 0.044 | 0.030 | 0.067 | 0.037 | 0.112 | 0.173 | 0.012 |
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 | 24 | 28 | 14 | 14 | 22 | 13 | 8 | 27 | 13 | 13 |
N.S. |
1 | 1.17 | 0.58 | 0.58 | 0.92 | 0.54 | 0.33 | 1.12 | 0.54 | 0.54 |
time (sec) |
N/A | 0.200 | 0.006 | 0.143 | 0.070 | 0.072 | 0.046 | 0.111 | 0.176 | 2.934 |
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 | 19 | 19 | 23 | 18 | 27 | 21 | 28 | 23 |
N.S. |
1 | 0.80 | 0.76 | 0.76 | 0.92 | 0.72 | 1.08 | 0.84 | 1.12 | 0.92 |
time (sec) |
N/A | 0.171 | 0.011 | 0.411 | 0.033 | 0.083 | 0.178 | 0.110 | 0.193 | 0.104 |
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 | 28 | 24 | 26 | 21 | 22 | 0 | 28 | 21 |
N.S. |
1 | 0.00 | 0.97 | 0.83 | 0.90 | 0.72 | 0.76 | 0.00 | 0.97 | 0.72 |
time (sec) |
N/A | 0.000 | 0.860 | 3.211 | 0.206 | 0.090 | 24.009 | 0.000 | 0.175 | 2.959 |
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 | 25 | 25 | 20 | 26 | 24 | 19 | 24 | 27 | 25 |
N.S. |
1 | 1.39 | 1.39 | 1.11 | 1.44 | 1.33 | 1.06 | 1.33 | 1.50 | 1.39 |
time (sec) |
N/A | 0.188 | 0.092 | 0.175 | 0.027 | 0.076 | 0.058 | 0.112 | 0.175 | 0.053 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 40 | 15 | 19 | 0 | 23 | 61 | 23 | 25 | 14 |
N.S. |
1 | 1.82 | 0.68 | 0.86 | 0.00 | 1.05 | 2.77 | 1.05 | 1.14 | 0.64 |
time (sec) |
N/A | 0.525 | 0.727 | 0.162 | 0.000 | 0.086 | 0.105 | 0.113 | 0.184 | 0.073 |
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 | 27 | 25 | 41 | 28 | 43 | 37 | 43 | 43 | 43 |
N.S. |
1 | 1.04 | 0.96 | 1.58 | 1.08 | 1.65 | 1.42 | 1.65 | 1.65 | 1.65 |
time (sec) |
N/A | 0.551 | 0.026 | 0.737 | 0.148 | 0.080 | 0.169 | 0.231 | 0.186 | 3.511 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | F(-1) | F(-2) | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 51 | 51 | 51 | 51 | 0 | 0 | 225 | 46 |
N.S. |
1 | 0.00 | 1.65 | 1.65 | 1.65 | 1.65 | 0.00 | 0.00 | 7.26 | 1.48 |
time (sec) |
N/A | 0.000 | 0.118 | 198.982 | 0.130 | 0.096 | 0.000 | 0.000 | 200.023 | 3.644 |
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 | 23 | 24 | 21 | 23 | 0 | 23 | 23 | 21 |
N.S. |
1 | 0.00 | 0.79 | 0.83 | 0.72 | 0.79 | 0.00 | 0.79 | 0.79 | 0.72 |
time (sec) |
N/A | 0.000 | 0.214 | 2.165 | 0.088 | 0.088 | 0.000 | 0.150 | 0.199 | 3.006 |
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 | 7 | 10 | 10 | 11 | 10 | 7 | 10 | 10 | 7 | 7 |
N.S. |
1 | 1.43 | 1.43 | 1.57 | 1.43 | 1.00 | 1.43 | 1.43 | 1.00 | 1.00 |
time (sec) |
N/A | 0.163 | 0.002 | 0.069 | 0.026 | 0.084 | 0.047 | 0.114 | 0.195 | 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 | 29 | 28 | 27 | 26 | 26 | 24 | 24 | 43 | 27 | 46 |
N.S. |
1 | 0.97 | 0.93 | 0.90 | 0.90 | 0.83 | 0.83 | 1.48 | 0.93 | 1.59 |
time (sec) |
N/A | 0.292 | 0.011 | 0.255 | 0.035 | 0.080 | 0.596 | 0.108 | 0.188 | 3.063 |
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 | 17 | 0 | 15 | 14 | 13 | 11 | 14 | 13 | 25 | 16 |
N.S. |
1 | 0.00 | 0.88 | 0.82 | 0.76 | 0.65 | 0.82 | 0.76 | 1.47 | 0.94 |
time (sec) |
N/A | 0.000 | 0.040 | 0.057 | 0.092 | 0.076 | 0.089 | 0.115 | 0.203 | 0.043 |
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 | 13 | 13 | 14 | 13 | 13 | 14 | 13 | 13 | 13 |
N.S. |
1 | 0.62 | 0.62 | 0.67 | 0.62 | 0.62 | 0.67 | 0.62 | 0.62 | 0.62 |
time (sec) |
N/A | 0.195 | 0.023 | 0.072 | 0.054 | 0.086 | 0.071 | 0.110 | 0.214 | 2.892 |
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 | 31 | 0 | 29 | 32 | 28 | 31 | 31 | 41 | 34 | 129 |
N.S. |
1 | 0.00 | 0.94 | 1.03 | 0.90 | 1.00 | 1.00 | 1.32 | 1.10 | 4.16 |
time (sec) |
N/A | 0.000 | 0.056 | 1.427 | 0.101 | 0.095 | 0.151 | 0.189 | 0.202 | 3.156 |
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 | 18 | 17 | 17 | 16 | 17 | 16 | 16 | 16 |
N.S. |
1 | 0.00 | 0.75 | 0.71 | 0.71 | 0.67 | 0.71 | 0.67 | 0.67 | 0.67 |
time (sec) |
N/A | 0.000 | 0.078 | 0.247 | 0.143 | 0.089 | 0.082 | 0.117 | 0.196 | 3.185 |
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 | 24 | 39 | 35 | 29 | 34 | 34 | 32 | 34 | 28 | 31 |
N.S. |
1 | 1.62 | 1.46 | 1.21 | 1.42 | 1.42 | 1.33 | 1.42 | 1.17 | 1.29 |
time (sec) |
N/A | 0.185 | 0.007 | 0.079 | 0.029 | 0.076 | 0.027 | 0.106 | 0.191 | 2.946 |
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 | 31 | 29 | 25 | 42 | 30 | 29 | 56 | 28 | 24 |
N.S. |
1 | 1.11 | 1.04 | 0.89 | 1.50 | 1.07 | 1.04 | 2.00 | 1.00 | 0.86 |
time (sec) |
N/A | 0.645 | 0.032 | 0.286 | 0.156 | 0.089 | 0.361 | 0.124 | 0.203 | 2.778 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 65 | 28 | 54 | 42 | 42 | 46 | 46 | 47 | 28 |
N.S. |
1 | 2.10 | 0.90 | 1.74 | 1.35 | 1.35 | 1.48 | 1.48 | 1.52 | 0.90 |
time (sec) |
N/A | 1.737 | 0.037 | 0.164 | 0.072 | 0.088 | 0.137 | 0.139 | 0.207 | 2.621 |
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 | 19 | 18 | 34 | 31 | 33 | 32 | 33 | 33 | 33 |
N.S. |
1 | 0.90 | 0.86 | 1.62 | 1.48 | 1.57 | 1.52 | 1.57 | 1.57 | 1.57 |
time (sec) |
N/A | 1.055 | 0.104 | 0.444 | 0.150 | 0.085 | 0.177 | 0.128 | 0.188 | 3.137 |
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 | 24 | 0 | 23 | 25 | 38 | 22 | 19 | 0 | 25 | 22 |
N.S. |
1 | 0.00 | 0.96 | 1.04 | 1.58 | 0.92 | 0.79 | 0.00 | 1.04 | 0.92 |
time (sec) |
N/A | 0.000 | 0.964 | 31.487 | 0.239 | 0.087 | 0.271 | 0.000 | 0.211 | 3.440 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | B | B | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 11 | 0 | 11 | 12 | 25 | 41 | 37 | 122 | 28 | 126 |
N.S. |
1 | 0.00 | 1.00 | 1.09 | 2.27 | 3.73 | 3.36 | 11.09 | 2.55 | 11.45 |
time (sec) |
N/A | 0.000 | 0.077 | 0.287 | 0.046 | 0.091 | 0.096 | 0.116 | 0.205 | 2.792 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 26 | 24 | 49 | 47 | 72 | 20 | 932 | 73 | 26 |
N.S. |
1 | 1.08 | 1.00 | 2.04 | 1.96 | 3.00 | 0.83 | 38.83 | 3.04 | 1.08 |
time (sec) |
N/A | 2.651 | 0.090 | 236.970 | 0.144 | 0.092 | 0.508 | 0.300 | 0.189 | 3.018 |
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 | 24 | 20 | 23 | 19 | 23 | 44 | 21 |
N.S. |
1 | 0.00 | 1.00 | 1.26 | 1.05 | 1.21 | 1.00 | 1.21 | 2.32 | 1.11 |
time (sec) |
N/A | 0.000 | 0.030 | 0.671 | 0.092 | 0.082 | 0.073 | 0.114 | 0.790 | 2.842 |
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 | 29 | 26 | 25 | 25 | 22 | 786 | 40 | 286 |
N.S. |
1 | 0.00 | 1.00 | 0.90 | 0.86 | 0.86 | 0.76 | 27.10 | 1.38 | 9.86 |
time (sec) |
N/A | 0.000 | 0.215 | 1.597 | 0.110 | 0.080 | 1.440 | 13.036 | 0.286 | 2.923 |