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 | 30 | 53 | 50 | 37 | 34 | 34 | 34 | 42 | 41 | 36 |
N.S. |
1 | 1.77 | 1.67 | 1.23 | 1.13 | 1.13 | 1.13 | 1.40 | 1.37 | 1.20 |
time (sec) |
N/A | 0.258 | 0.098 | 0.324 | 0.030 | 0.083 | 0.083 | 0.119 | 0.193 | 0.065 |
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 | 30 | 28 | 30 | 23 | 0 | 29 | 26 | 31 | 26 | 22 |
N.S. |
1 | 0.93 | 1.00 | 0.77 | 0.00 | 0.97 | 0.87 | 1.03 | 0.87 | 0.73 |
time (sec) |
N/A | 0.346 | 0.040 | 0.492 | 0.000 | 0.090 | 0.119 | 0.116 | 0.183 | 0.087 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | A | F(-1) | A | F | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 21 | 23 | 68 | 26 | 0 | 34 | 106 | 49 |
N.S. |
1 | 0.00 | 0.88 | 0.96 | 2.83 | 1.08 | 0.00 | 1.42 | 4.42 | 2.04 |
time (sec) |
N/A | 0.000 | 0.109 | 17.433 | 0.250 | 0.085 | 0.000 | 0.300 | 200.026 | 2.850 |
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 | 17 | 18 | 18 | 25 | 25 | 26 | 26 | 33 | 20 |
N.S. |
1 | 0.65 | 0.69 | 0.69 | 0.96 | 0.96 | 1.00 | 1.00 | 1.27 | 0.77 |
time (sec) |
N/A | 0.176 | 0.003 | 0.093 | 0.031 | 0.078 | 0.047 | 0.108 | 0.164 | 0.040 |
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 | 28 | 0 | 47 | 48 | 46 | 46 | 44 | 72 | 952 | 0 |
N.S. |
1 | 0.00 | 1.68 | 1.71 | 1.64 | 1.64 | 1.57 | 2.57 | 34.00 | 0.00 |
time (sec) |
N/A | 0.000 | 3.446 | 0.737 | 0.070 | 0.105 | 0.138 | 0.142 | 0.192 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F(-2) | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 40 | 25 | 21 | 28 | 33 | 31 | 0 | 33 | 86 |
N.S. |
1 | 1.38 | 0.86 | 0.72 | 0.97 | 1.14 | 1.07 | 0.00 | 1.14 | 2.97 |
time (sec) |
N/A | 0.301 | 0.020 | 0.755 | 0.025 | 0.080 | 0.413 | 0.000 | 0.179 | 0.176 |
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 | 28 | 23 | 26 | 27 | 26 | 0 | 27 |
N.S. |
1 | 0.93 | 0.93 | 0.93 | 0.77 | 0.87 | 0.90 | 0.87 | 0.00 | 0.90 |
time (sec) |
N/A | 0.602 | 1.012 | 2.725 | 0.284 | 0.080 | 0.325 | 0.114 | 0.250 | 3.337 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | A | B | B | B | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 87 | 64 | 25 | 64 | 62 | 68 | 64 | 73 | 51 |
N.S. |
1 | 3.78 | 2.78 | 1.09 | 2.78 | 2.70 | 2.96 | 2.78 | 3.17 | 2.22 |
time (sec) |
N/A | 0.205 | 0.010 | 0.167 | 0.030 | 0.094 | 0.028 | 0.113 | 0.179 | 0.069 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | F(-2) | A | F(-2) | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 95 | 27 | 52 | 0 | 51 | 0 | 51 | 47 | 43 |
N.S. |
1 | 3.06 | 0.87 | 1.68 | 0.00 | 1.65 | 0.00 | 1.65 | 1.52 | 1.39 |
time (sec) |
N/A | 0.624 | 0.088 | 0.391 | 0.000 | 0.082 | 0.000 | 0.122 | 0.165 | 2.929 |
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 | 18 | 0 | 18 | 20 | 15 | 51 | 15 | 0 | 22 | 16 |
N.S. |
1 | 0.00 | 1.00 | 1.11 | 0.83 | 2.83 | 0.83 | 0.00 | 1.22 | 0.89 |
time (sec) |
N/A | 0.000 | 0.489 | 0.276 | 0.221 | 0.078 | 0.153 | 0.000 | 5.087 | 2.813 |
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 | 21 | 0 | 21 | 19 | 22 | 35 | 19 | 0 | 21 | 20 |
N.S. |
1 | 0.00 | 1.00 | 0.90 | 1.05 | 1.67 | 0.90 | 0.00 | 1.00 | 0.95 |
time (sec) |
N/A | 0.000 | 0.555 | 3.085 | 0.156 | 0.090 | 0.164 | 0.000 | 0.174 | 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 | 31 | 13 | 11 | 10 | 9 | 12 | 7 | 9 | 12 | 9 |
N.S. |
1 | 0.42 | 0.35 | 0.32 | 0.29 | 0.39 | 0.23 | 0.29 | 0.39 | 0.29 |
time (sec) |
N/A | 0.146 | 0.001 | 0.039 | 0.025 | 0.065 | 0.027 | 0.110 | 0.166 | 0.014 |
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 | 24 | 28 | 25 | 24 | 24 | 24 | 24 | 23 | 23 |
N.S. |
1 | 1.20 | 1.40 | 1.25 | 1.20 | 1.20 | 1.20 | 1.20 | 1.15 | 1.15 |
time (sec) |
N/A | 0.142 | 0.004 | 0.111 | 0.029 | 0.072 | 0.020 | 0.111 | 0.165 | 0.150 |
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 | 3 | 3 | 3 | 4 | 3 | 3 | 3 | 4 | 3 | 3 |
N.S. |
1 | 1.00 | 1.00 | 1.33 | 1.00 | 1.00 | 1.00 | 1.33 | 1.00 | 1.00 |
time (sec) |
N/A | 0.146 | 0.001 | 0.043 | 0.027 | 0.087 | 0.043 | 0.119 | 0.179 | 2.777 |
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 | 21 | 0 | 21 | 19 | 32 | 26 | 27 | 0 | 425 | 34 |
N.S. |
1 | 0.00 | 1.00 | 0.90 | 1.52 | 1.24 | 1.29 | 0.00 | 20.24 | 1.62 |
time (sec) |
N/A | 0.000 | 5.055 | 0.533 | 0.126 | 0.083 | 1.168 | 0.000 | 0.364 | 2.637 |
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 | 24 | 26 | 28 | 28 | 22 | 28 | 27 | 130 |
N.S. |
1 | 0.00 | 0.92 | 1.00 | 1.08 | 1.08 | 0.85 | 1.08 | 1.04 | 5.00 |
time (sec) |
N/A | 0.000 | 0.488 | 1.906 | 0.076 | 0.082 | 0.105 | 0.155 | 0.178 | 0.226 |
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 | 28 | 46 | 38 | 25 | 39 | 47 | 36 | 24 | 43 | 23 |
N.S. |
1 | 1.64 | 1.36 | 0.89 | 1.39 | 1.68 | 1.29 | 0.86 | 1.54 | 0.82 |
time (sec) |
N/A | 0.269 | 0.009 | 0.066 | 0.024 | 0.072 | 0.051 | 0.114 | 0.162 | 2.631 |
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 | 21 | 18 | 20 | 16 | 51 | 16 | 15 | 16 | 18 | 15 |
N.S. |
1 | 0.86 | 0.95 | 0.76 | 2.43 | 0.76 | 0.71 | 0.76 | 0.86 | 0.71 |
time (sec) |
N/A | 0.353 | 0.033 | 0.376 | 0.106 | 0.092 | 0.079 | 0.112 | 0.171 | 0.090 |
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 | 16 | 13 | 12 | 11 | 15 | 10 | 11 | 15 | 11 |
N.S. |
1 | 0.76 | 0.62 | 0.57 | 0.52 | 0.71 | 0.48 | 0.52 | 0.71 | 0.52 |
time (sec) |
N/A | 0.151 | 0.001 | 0.079 | 0.025 | 0.073 | 0.043 | 0.107 | 0.166 | 2.488 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | A | B | B | B | B | B | B |
verified | N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 0 | 0 | 55 | 277 | 93 | 100 | 128 | 173 | 96 |
N.S. |
1 | 0.00 | 0.00 | 1.57 | 7.91 | 2.66 | 2.86 | 3.66 | 4.94 | 2.74 |
time (sec) |
N/A | 0.000 | 0.000 | 4.315 | 0.176 | 0.096 | 0.182 | 0.140 | 0.203 | 2.583 |
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 | 25 | 17 | 16 | 18 | 18 | 24 | 27 | 19 | 23 |
N.S. |
1 | 1.47 | 1.00 | 0.94 | 1.06 | 1.06 | 1.41 | 1.59 | 1.12 | 1.35 |
time (sec) |
N/A | 0.178 | 0.335 | 0.175 | 0.091 | 0.079 | 6.403 | 0.114 | 0.177 | 2.527 |
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 | 31 | 23 | 19 | 18 | 18 | 20 | 18 | 39 | 18 |
N.S. |
1 | 1.48 | 1.10 | 0.90 | 0.86 | 0.86 | 0.95 | 0.86 | 1.86 | 0.86 |
time (sec) |
N/A | 0.205 | 0.118 | 0.142 | 0.026 | 0.092 | 0.058 | 0.116 | 0.191 | 0.056 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | B | F | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 0 | 32 | 30 | 31 | 29 | 54 | 0 | 85 | 29 |
N.S. |
1 | 0.00 | 0.97 | 0.91 | 0.94 | 0.88 | 1.64 | 0.00 | 2.58 | 0.88 |
time (sec) |
N/A | 0.000 | 0.119 | 83.875 | 0.084 | 0.101 | 1.578 | 0.000 | 0.198 | 3.197 |
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 | 25 | 0 | 31 | 29 | 42 | 33 | 27 | 41 | 42 | 0 |
N.S. |
1 | 0.00 | 1.24 | 1.16 | 1.68 | 1.32 | 1.08 | 1.64 | 1.68 | 0.00 |
time (sec) |
N/A | 0.000 | 0.436 | 0.795 | 0.143 | 0.088 | 0.159 | 0.142 | 0.169 | 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 | 27 | 0 | 27 | 25 | 53 | 43 | 29 | 46 | 40 | 30 |
N.S. |
1 | 0.00 | 1.00 | 0.93 | 1.96 | 1.59 | 1.07 | 1.70 | 1.48 | 1.11 |
time (sec) |
N/A | 0.000 | 0.063 | 42.068 | 0.144 | 0.086 | 0.120 | 0.153 | 0.448 | 2.575 |
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 | 13 | 5 | 5 | 5 | 4 | 4 | 3 | 4 | 5 | 4 |
N.S. |
1 | 0.38 | 0.38 | 0.38 | 0.31 | 0.31 | 0.23 | 0.31 | 0.38 | 0.31 |
time (sec) |
N/A | 0.133 | 0.001 | 0.044 | 0.030 | 0.075 | 0.030 | 0.112 | 0.174 | 0.016 |
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 | 29 | 0 | 33 | 30 | 78 | 81 | 51 | 100 | 87 | 129 |
N.S. |
1 | 0.00 | 1.14 | 1.03 | 2.69 | 2.79 | 1.76 | 3.45 | 3.00 | 4.45 |
time (sec) |
N/A | 0.000 | 0.117 | 176.277 | 0.146 | 0.089 | 0.179 | 0.193 | 0.180 | 2.974 |
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 | 31 | 352 | 84 | 86 | 638 | 78 | 151 | 106 | 164 | 43 |
N.S. |
1 | 11.35 | 2.71 | 2.77 | 20.58 | 2.52 | 4.87 | 3.42 | 5.29 | 1.39 |
time (sec) |
N/A | 1.544 | 0.078 | 11.270 | 0.173 | 0.094 | 0.280 | 0.124 | 0.174 | 2.736 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | B | B | B | B | B | F | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 0 | 114 | 83 | 125 | 141 | 155 | 992 | 0 | 0 |
N.S. |
1 | 0.00 | 3.35 | 2.44 | 3.68 | 4.15 | 4.56 | 29.18 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 10.343 | 14.966 | 0.346 | 0.121 | 3.585 | 7.377 | 10.723 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | A | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 27 | 62 | 44 | 44 | 24 | 27 | 42 | 171 |
N.S. |
1 | 0.00 | 0.93 | 2.14 | 1.52 | 1.52 | 0.83 | 0.93 | 1.45 | 5.90 |
time (sec) |
N/A | 0.000 | 0.103 | 159.332 | 0.072 | 0.092 | 0.103 | 0.179 | 0.186 | 2.853 |
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 | 19 | 0 | 20 | 26 | 26 | 22 | 17 | 28 | 29 | 0 |
N.S. |
1 | 0.00 | 1.05 | 1.37 | 1.37 | 1.16 | 0.89 | 1.47 | 1.53 | 0.00 |
time (sec) |
N/A | 0.000 | 4.517 | 0.242 | 0.067 | 0.082 | 0.094 | 0.130 | 0.171 | 0.000 |
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 | 30 | 0 | 29 | 27 | 61 | 31 | 27 | 31 | 57 | 51 |
N.S. |
1 | 0.00 | 0.97 | 0.90 | 2.03 | 1.03 | 0.90 | 1.03 | 1.90 | 1.70 |
time (sec) |
N/A | 0.000 | 0.062 | 10.733 | 0.217 | 0.079 | 0.186 | 22.075 | 0.170 | 2.856 |
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 | 31 | 36 | 36 | 31 | 63 | 44 | 31 | 30 | 46 | 38 |
N.S. |
1 | 1.16 | 1.16 | 1.00 | 2.03 | 1.42 | 1.00 | 0.97 | 1.48 | 1.23 |
time (sec) |
N/A | 0.529 | 0.045 | 0.595 | 0.148 | 0.085 | 0.097 | 0.115 | 0.167 | 2.786 |
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 | 25 | 0 | 22 | 28 | 76 | 32 | 24 | 44 | 50 | 37 |
N.S. |
1 | 0.00 | 0.88 | 1.12 | 3.04 | 1.28 | 0.96 | 1.76 | 2.00 | 1.48 |
time (sec) |
N/A | 0.000 | 0.676 | 1.034 | 0.152 | 0.096 | 0.112 | 0.256 | 0.169 | 2.800 |
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 | 22 | 0 | 24 | 26 | 25 | 25 | 20 | 30 | 30 | 0 |
N.S. |
1 | 0.00 | 1.09 | 1.18 | 1.14 | 1.14 | 0.91 | 1.36 | 1.36 | 0.00 |
time (sec) |
N/A | 0.000 | 0.225 | 0.217 | 0.069 | 0.084 | 0.083 | 0.116 | 0.167 | 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 | 27 | 8 | 10 | 9 | 8 | 8 | 7 | 9 | 8 | 8 |
N.S. |
1 | 0.30 | 0.37 | 0.33 | 0.30 | 0.30 | 0.26 | 0.33 | 0.30 | 0.30 |
time (sec) |
N/A | 0.142 | 0.001 | 0.040 | 0.023 | 0.078 | 0.028 | 0.111 | 0.169 | 0.013 |
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 | 26 | 19 | 24 | 16 | 23 | 20 | 16 | 23 | 19 |
N.S. |
1 | 1.08 | 0.79 | 1.00 | 0.67 | 0.96 | 0.83 | 0.67 | 0.96 | 0.79 |
time (sec) |
N/A | 0.363 | 0.036 | 0.143 | 0.107 | 0.077 | 0.082 | 0.112 | 0.191 | 2.639 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | B | F | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 0 | 22 | 22 | 19 | 32 | 17 | 37 | 64 | 17 |
N.S. |
1 | 0.00 | 1.05 | 1.05 | 0.90 | 1.52 | 0.81 | 1.76 | 3.05 | 0.81 |
time (sec) |
N/A | 0.000 | 0.128 | 0.357 | 0.147 | 0.077 | 0.131 | 0.113 | 0.174 | 2.756 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | A | A | A | A | F | B | F(-1) |
verified | N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 0 | 36 | 29 | 27 | 26 | 0 | 33 | 0 |
N.S. |
1 | 0.00 | 0.00 | 1.44 | 1.16 | 1.08 | 1.04 | 0.00 | 1.32 | 0.00 |
time (sec) |
N/A | 0.000 | 0.000 | 20.645 | 0.110 | 0.096 | 0.574 | 0.000 | 0.170 | 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 | 18 | 26 | 16 | 17 | 25 | 27 | 15 | 25 | 22 | 18 |
N.S. |
1 | 1.44 | 0.89 | 0.94 | 1.39 | 1.50 | 0.83 | 1.39 | 1.22 | 1.00 |
time (sec) |
N/A | 0.163 | 0.005 | 0.068 | 0.032 | 0.101 | 0.058 | 0.124 | 0.164 | 2.671 |
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 | 20 | 21 | 45 | 40 | 44 | 48 | 40 | 46 | 21 |
N.S. |
1 | 0.77 | 0.81 | 1.73 | 1.54 | 1.69 | 1.85 | 1.54 | 1.77 | 0.81 |
time (sec) |
N/A | 0.544 | 0.044 | 8.027 | 0.072 | 0.105 | 0.212 | 0.138 | 0.177 | 2.943 |
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 | 14 | 37 | 37 | 38 | 37 | 33 | 37 | 36 | 37 | 24 |
N.S. |
1 | 2.64 | 2.64 | 2.71 | 2.64 | 2.36 | 2.64 | 2.57 | 2.64 | 1.71 |
time (sec) |
N/A | 0.224 | 0.005 | 0.432 | 0.030 | 0.089 | 0.086 | 0.109 | 0.173 | 2.619 |
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 | 33 | 0 | 26 | 34 | 30 | 32 | 37 | 58 | 92 | 44 |
N.S. |
1 | 0.00 | 0.79 | 1.03 | 0.91 | 0.97 | 1.12 | 1.76 | 2.79 | 1.33 |
time (sec) |
N/A | 0.000 | 0.083 | 11.311 | 0.145 | 0.092 | 0.245 | 0.177 | 0.197 | 2.712 |
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 | 15 | 25 | 15 | 24 | 66 | 23 | 22 | 23 | 25 | 16 |
N.S. |
1 | 1.67 | 1.00 | 1.60 | 4.40 | 1.53 | 1.47 | 1.53 | 1.67 | 1.07 |
time (sec) |
N/A | 0.226 | 0.018 | 0.290 | 0.052 | 0.088 | 0.082 | 0.121 | 0.174 | 2.850 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 34 | 23 | 41 | 22 | 20 | 22 | 43 | 26 |
N.S. |
1 | 0.00 | 1.17 | 0.79 | 1.41 | 0.76 | 0.69 | 0.76 | 1.48 | 0.90 |
time (sec) |
N/A | 0.000 | 1.661 | 0.196 | 0.076 | 0.076 | 0.152 | 0.138 | 2.917 | 3.063 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F | A | F(-2) | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 0 | 21 | 21 | 0 | 20 | 0 | 37 | 21 | 20 |
N.S. |
1 | 0.00 | 1.00 | 1.00 | 0.00 | 0.95 | 0.00 | 1.76 | 1.00 | 0.95 |
time (sec) |
N/A | 0.000 | 3.741 | 0.961 | 0.000 | 0.085 | 0.000 | 0.157 | 0.169 | 2.772 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | B | A | F(-1) | F | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 25 | 62 | 56 | 45 | 0 | 0 | 60 | 29 |
N.S. |
1 | 0.00 | 0.96 | 2.38 | 2.15 | 1.73 | 0.00 | 0.00 | 2.31 | 1.12 |
time (sec) |
N/A | 0.000 | 5.052 | 0.936 | 0.127 | 0.090 | 0.000 | 0.000 | 0.179 | 2.975 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | B | A | A | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 57 | 28 | 38 | 64 | 46 | 26 | 70 | 47 | 25 |
N.S. |
1 | 2.28 | 1.12 | 1.52 | 2.56 | 1.84 | 1.04 | 2.80 | 1.88 | 1.00 |
time (sec) |
N/A | 0.593 | 0.166 | 1.477 | 0.150 | 0.082 | 0.155 | 0.267 | 0.164 | 2.808 |
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 | 13 | 12 | 12 | 12 | 12 | 10 | 12 | 16 | 12 |
N.S. |
1 | 0.72 | 0.67 | 0.67 | 0.67 | 0.67 | 0.56 | 0.67 | 0.89 | 0.67 |
time (sec) |
N/A | 0.155 | 0.037 | 0.046 | 0.038 | 0.092 | 0.039 | 0.111 | 0.171 | 0.046 |
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 | 34 | 0 | 69 | 330 | 400 | 400 | 532 | 670 | 713 | 1647 |
N.S. |
1 | 0.00 | 2.03 | 9.71 | 11.76 | 11.76 | 15.65 | 19.71 | 20.97 | 48.44 |
time (sec) |
N/A | 0.000 | 0.612 | 0.431 | 0.157 | 0.108 | 0.900 | 0.717 | 0.210 | 3.907 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | C | A | B | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 68 | 28 | 26 | 88 | 33 | 56 | 51 | 35 | 27 |
N.S. |
1 | 2.27 | 0.93 | 0.87 | 2.93 | 1.10 | 1.87 | 1.70 | 1.17 | 0.90 |
time (sec) |
N/A | 0.516 | 0.585 | 0.148 | 0.088 | 0.085 | 0.086 | 0.115 | 0.175 | 0.086 |
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 | 8 | 8 | 9 | 8 | 8 | 7 | 9 | 8 | 8 |
N.S. |
1 | 0.73 | 0.73 | 0.82 | 0.73 | 0.73 | 0.64 | 0.82 | 0.73 | 0.73 |
time (sec) |
N/A | 0.140 | 0.001 | 0.036 | 0.023 | 0.085 | 0.042 | 0.109 | 0.167 | 0.010 |
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 | 30 | 46 | 54 | 41 | 39 | 39 | 46 | 41 | 64 | 41 |
N.S. |
1 | 1.53 | 1.80 | 1.37 | 1.30 | 1.30 | 1.53 | 1.37 | 2.13 | 1.37 |
time (sec) |
N/A | 0.285 | 0.199 | 0.735 | 0.032 | 0.092 | 0.078 | 0.112 | 0.170 | 2.911 |
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 | 24 | 59 | 23 | 22 | 49 | 20 | 26 | 20 | 22 | 20 |
N.S. |
1 | 2.46 | 0.96 | 0.92 | 2.04 | 0.83 | 1.08 | 0.83 | 0.92 | 0.83 |
time (sec) |
N/A | 1.000 | 1.675 | 0.313 | 0.082 | 0.086 | 0.072 | 0.123 | 0.169 | 2.960 |
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 | 25 | 15 | 13 | 16 | 18 | 12 | 21 | 23 | 12 |
N.S. |
1 | 1.47 | 0.88 | 0.76 | 0.94 | 1.06 | 0.71 | 1.24 | 1.35 | 0.71 |
time (sec) |
N/A | 0.180 | 0.007 | 0.103 | 0.032 | 0.078 | 0.049 | 0.114 | 0.173 | 0.043 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | A | A | A | A | A | B | B |
verified | N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 0 | 33 | 34 | 32 | 27 | 36 | 35 | 32 |
N.S. |
1 | 0.00 | 0.00 | 1.43 | 1.48 | 1.39 | 1.17 | 1.57 | 1.52 | 1.39 |
time (sec) |
N/A | 0.000 | 0.000 | 7.694 | 0.203 | 0.082 | 0.691 | 0.240 | 0.169 | 3.818 |
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 | 19 | 19 | 19 | 18 | 18 | 15 | 18 | 30 | 18 |
N.S. |
1 | 0.95 | 0.95 | 0.95 | 0.90 | 0.90 | 0.75 | 0.90 | 1.50 | 0.90 |
time (sec) |
N/A | 0.535 | 0.056 | 0.201 | 0.123 | 0.085 | 0.122 | 0.132 | 0.162 | 2.925 |
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 | 17 | 70 | 28 | 18 | 42 | 19 | 26 | 19 | 19 | 19 |
N.S. |
1 | 4.12 | 1.65 | 1.06 | 2.47 | 1.12 | 1.53 | 1.12 | 1.12 | 1.12 |
time (sec) |
N/A | 0.211 | 0.041 | 0.302 | 0.111 | 0.075 | 0.070 | 0.116 | 0.168 | 0.052 |
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 | 32 | 0 | 38 | 36 | 40 | 34 | 29 | 0 | 50 | 44 |
N.S. |
1 | 0.00 | 1.19 | 1.12 | 1.25 | 1.06 | 0.91 | 0.00 | 1.56 | 1.38 |
time (sec) |
N/A | 0.000 | 0.081 | 1.378 | 0.185 | 0.102 | 0.220 | 0.000 | 0.165 | 2.739 |
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 | 27 | 24 | 36 | 23 | 24 | 23 | 27 | 24 |
N.S. |
1 | 0.00 | 1.00 | 0.89 | 1.33 | 0.85 | 0.89 | 0.85 | 1.00 | 0.89 |
time (sec) |
N/A | 0.000 | 2.279 | 0.161 | 0.076 | 0.096 | 0.109 | 0.123 | 0.167 | 0.092 |
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 | 11 | 11 | 11 | 10 | 10 | 8 | 10 | 11 | 10 |
N.S. |
1 | 0.92 | 0.92 | 0.92 | 0.83 | 0.83 | 0.67 | 0.83 | 0.92 | 0.83 |
time (sec) |
N/A | 0.164 | 0.003 | 0.096 | 0.028 | 0.091 | 0.047 | 0.116 | 0.172 | 2.737 |
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 | 33 | 41 | 31 | 31 | 31 | 29 | 29 | 59 | 34 | 27 |
N.S. |
1 | 1.24 | 0.94 | 0.94 | 0.94 | 0.88 | 0.88 | 1.79 | 1.03 | 0.82 |
time (sec) |
N/A | 1.011 | 0.076 | 0.615 | 0.076 | 0.096 | 0.169 | 0.179 | 0.179 | 0.591 |
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 | 28 | 46 | 46 | 40 | 39 | 43 | 42 | 46 | 700 | 57 |
N.S. |
1 | 1.64 | 1.64 | 1.43 | 1.39 | 1.54 | 1.50 | 1.64 | 25.00 | 2.04 |
time (sec) |
N/A | 0.621 | 0.036 | 1.616 | 0.059 | 0.098 | 0.174 | 0.142 | 0.187 | 2.796 |
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 | 23 | 25 | 26 | 26 | 25 | 20 | 26 | 25 | 25 |
N.S. |
1 | 0.92 | 1.00 | 1.04 | 1.04 | 1.00 | 0.80 | 1.04 | 1.00 | 1.00 |
time (sec) |
N/A | 0.813 | 0.272 | 3.187 | 0.092 | 0.104 | 0.130 | 0.142 | 0.177 | 3.120 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | C | A | A | A | B | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 32 | 29 | 35 | 30 | 27 | 30 | 32 | 0 |
N.S. |
1 | 0.00 | 1.07 | 0.97 | 1.17 | 1.00 | 0.90 | 1.00 | 1.07 | 0.00 |
time (sec) |
N/A | 0.000 | 0.059 | 4.020 | 0.224 | 0.103 | 0.164 | 1.103 | 0.184 | 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 | 29 | 12 | 12 | 14 | 11 | 11 | 10 | 11 | 15 | 11 |
N.S. |
1 | 0.41 | 0.41 | 0.48 | 0.38 | 0.38 | 0.34 | 0.38 | 0.52 | 0.38 |
time (sec) |
N/A | 0.150 | 0.014 | 0.105 | 0.027 | 0.073 | 0.038 | 0.111 | 0.176 | 0.028 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | B | B | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 29 | 25 | 28 | 26 | 22 | 92 | 25 | 0 |
N.S. |
1 | 0.00 | 1.00 | 0.86 | 0.97 | 0.90 | 0.76 | 3.17 | 0.86 | 0.00 |
time (sec) |
N/A | 0.000 | 5.850 | 0.924 | 0.150 | 0.090 | 0.073 | 0.143 | 0.168 | 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 | 19 | 17 | 20 | 13 | 12 | 12 | 12 | 12 | 13 | 12 |
N.S. |
1 | 0.89 | 1.05 | 0.68 | 0.63 | 0.63 | 0.63 | 0.63 | 0.68 | 0.63 |
time (sec) |
N/A | 0.136 | 0.002 | 0.063 | 0.029 | 0.077 | 0.034 | 0.110 | 0.170 | 0.022 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | A | F | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 26 | 25 | 67 | 31 | 22 | 24 | 0 | 25 | 25 |
N.S. |
1 | 1.04 | 1.00 | 2.68 | 1.24 | 0.88 | 0.96 | 0.00 | 1.00 | 1.00 |
time (sec) |
N/A | 2.585 | 0.072 | 25.093 | 0.170 | 0.096 | 7.142 | 0.000 | 0.219 | 2.876 |
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 | 7 | 7 | 6 | 5 | 5 | 7 | 5 | 5 | 5 |
N.S. |
1 | 0.47 | 0.47 | 0.40 | 0.33 | 0.33 | 0.47 | 0.33 | 0.33 | 0.33 |
time (sec) |
N/A | 0.121 | 0.000 | 0.029 | 0.025 | 0.069 | 0.016 | 0.115 | 0.175 | 0.001 |
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 | 22 | 41 | 19 | 29 | 0 | 29 | 32 | 29 | 31 | 102 |
N.S. |
1 | 1.86 | 0.86 | 1.32 | 0.00 | 1.32 | 1.45 | 1.32 | 1.41 | 4.64 |
time (sec) |
N/A | 0.293 | 0.047 | 2.138 | 0.000 | 0.099 | 0.118 | 0.127 | 0.176 | 2.745 |
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 | 32 | 37 | 32 | 34 | 40 | 31 | 31 | 39 | 31 |
N.S. |
1 | 1.19 | 1.37 | 1.19 | 1.26 | 1.48 | 1.15 | 1.15 | 1.44 | 1.15 |
time (sec) |
N/A | 0.711 | 0.074 | 0.618 | 0.073 | 0.099 | 0.147 | 0.116 | 0.170 | 2.755 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 51 | 43 | 37 | 39 | 42 | 34 | 0 | 84 | 34 |
N.S. |
1 | 1.55 | 1.30 | 1.12 | 1.18 | 1.27 | 1.03 | 0.00 | 2.55 | 1.03 |
time (sec) |
N/A | 0.831 | 0.603 | 1.008 | 0.242 | 0.092 | 0.206 | 0.000 | 200.030 | 2.751 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | F | A | A | F | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 76 | 42 | 27 | 0 | 30 | 27 | 0 | 47 | 0 |
N.S. |
1 | 2.81 | 1.56 | 1.00 | 0.00 | 1.11 | 1.00 | 0.00 | 1.74 | 0.00 |
time (sec) |
N/A | 3.507 | 0.120 | 13.468 | 0.000 | 0.116 | 0.195 | 0.000 | 0.182 | 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 | 23 | 26 | 22 | 26 | 30 | 27 | 24 | 27 | 26 | 27 |
N.S. |
1 | 1.13 | 0.96 | 1.13 | 1.30 | 1.17 | 1.04 | 1.17 | 1.13 | 1.17 |
time (sec) |
N/A | 0.366 | 0.036 | 6.713 | 0.185 | 0.088 | 0.192 | 0.162 | 0.171 | 3.025 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | A | B | F(-1) | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 32 | 53 | 44 | 52 | 0 | 44 | 55 | 24 |
N.S. |
1 | 0.00 | 1.23 | 2.04 | 1.69 | 2.00 | 0.00 | 1.69 | 2.12 | 0.92 |
time (sec) |
N/A | 0.000 | 0.159 | 0.474 | 0.073 | 0.102 | 0.000 | 0.144 | 0.168 | 2.688 |
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 | 22 | 94 | 22 | 24 | 80 | 30 | 19 | 31 | 34 | 26 |
N.S. |
1 | 4.27 | 1.00 | 1.09 | 3.64 | 1.36 | 0.86 | 1.41 | 1.55 | 1.18 |
time (sec) |
N/A | 0.656 | 0.103 | 0.246 | 0.135 | 0.091 | 0.077 | 0.112 | 0.169 | 0.067 |
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 | 36 | 30 | 26 | 32 | 38 | 32 | 30 | 37 | 32 |
N.S. |
1 | 1.16 | 0.97 | 0.84 | 1.03 | 1.23 | 1.03 | 0.97 | 1.19 | 1.03 |
time (sec) |
N/A | 0.257 | 0.012 | 0.135 | 0.042 | 0.081 | 0.355 | 0.113 | 0.166 | 2.581 |
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 | 34 | 51 | 39 | 60 | 90 | 46 | 29 | 51 | 61 | 34 |
N.S. |
1 | 1.50 | 1.15 | 1.76 | 2.65 | 1.35 | 0.85 | 1.50 | 1.79 | 1.00 |
time (sec) |
N/A | 4.261 | 0.082 | 4.935 | 0.092 | 0.108 | 0.207 | 0.132 | 0.161 | 2.700 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | C | B | A | A | B | B | B |
verified | N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 22 | 835 | 48 | 23 | 26 | 114 | 23 | 467 |
N.S. |
1 | 0.00 | 0.96 | 36.30 | 2.09 | 1.00 | 1.13 | 4.96 | 1.00 | 20.30 |
time (sec) |
N/A | 0.000 | 0.044 | 4.296 | 0.096 | 0.094 | 0.094 | 0.161 | 0.165 | 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 | 20 | 21 | 21 | 18 | 17 | 15 | 15 | 17 | 18 | 15 |
N.S. |
1 | 1.05 | 1.05 | 0.90 | 0.85 | 0.75 | 0.75 | 0.85 | 0.90 | 0.75 |
time (sec) |
N/A | 0.164 | 0.008 | 0.127 | 0.027 | 0.118 | 0.271 | 0.112 | 0.167 | 2.550 |
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 | 21 | 28 | 18 | 16 | 17 | 17 | 16 | 28 | 16 |
N.S. |
1 | 0.95 | 1.27 | 0.82 | 0.73 | 0.77 | 0.77 | 0.73 | 1.27 | 0.73 |
time (sec) |
N/A | 0.639 | 0.105 | 0.227 | 0.074 | 0.094 | 0.110 | 0.120 | 0.179 | 2.729 |
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 | 17 | 0 | 17 | 13 | 12 | 41 | 15 | 0 | 15 | 12 |
N.S. |
1 | 0.00 | 1.00 | 0.76 | 0.71 | 2.41 | 0.88 | 0.00 | 0.88 | 0.71 |
time (sec) |
N/A | 0.000 | 0.082 | 0.638 | 0.209 | 0.085 | 0.135 | 0.000 | 0.178 | 2.763 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | B | B | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 276 | 58 | 50 | 148 | 65 | 27 | 35 | 89 | 35 |
N.S. |
1 | 8.36 | 1.76 | 1.52 | 4.48 | 1.97 | 0.82 | 1.06 | 2.70 | 1.06 |
time (sec) |
N/A | 3.902 | 0.073 | 7.130 | 0.115 | 0.094 | 0.226 | 0.132 | 0.170 | 2.897 |
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 | 11 | 11 | 11 | 10 | 10 | 5 | 10 | 16 | 10 |
N.S. |
1 | 0.92 | 0.92 | 0.92 | 0.83 | 0.83 | 0.42 | 0.83 | 1.33 | 0.83 |
time (sec) |
N/A | 0.141 | 0.012 | 0.064 | 0.023 | 0.097 | 0.037 | 0.109 | 0.167 | 2.712 |
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 | 24 | 0 | 19 | 20 | 17 | 17 | 17 | 17 | 43 | 11 |
N.S. |
1 | 0.00 | 0.79 | 0.83 | 0.71 | 0.71 | 0.71 | 0.71 | 1.79 | 0.46 |
time (sec) |
N/A | 0.000 | 0.016 | 0.558 | 0.120 | 0.073 | 0.040 | 0.124 | 0.169 | 2.630 |
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 | 17 | 19 | 19 | 15 | 19 | 15 | 22 | 17 |
N.S. |
1 | 0.00 | 0.89 | 1.00 | 1.00 | 0.79 | 1.00 | 0.79 | 1.16 | 0.89 |
time (sec) |
N/A | 0.000 | 0.047 | 0.146 | 0.094 | 0.081 | 0.065 | 0.118 | 0.167 | 2.796 |
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 | 27 | 32 | 28 | 26 | 37 | 25 | 24 | 64 | 26 | 25 |
N.S. |
1 | 1.19 | 1.04 | 0.96 | 1.37 | 0.93 | 0.89 | 2.37 | 0.96 | 0.93 |
time (sec) |
N/A | 0.477 | 0.036 | 55.173 | 0.191 | 0.094 | 0.799 | 2.872 | 0.182 | 4.181 |
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 | 25 | 25 | 22 | 25 | 25 | 22 | 27 | 25 | 23 |
N.S. |
1 | 0.86 | 0.86 | 0.76 | 0.86 | 0.86 | 0.76 | 0.93 | 0.86 | 0.79 |
time (sec) |
N/A | 0.221 | 0.007 | 0.053 | 0.025 | 0.067 | 0.055 | 0.112 | 0.191 | 2.675 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | B | A | A | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 233 | 39 | 29 | 242 | 30 | 26 | 200 | 84 | 21 |
N.S. |
1 | 10.13 | 1.70 | 1.26 | 10.52 | 1.30 | 1.13 | 8.70 | 3.65 | 0.91 |
time (sec) |
N/A | 1.037 | 3.561 | 1.783 | 0.190 | 0.086 | 0.169 | 2.919 | 0.180 | 2.992 |
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 | 30 | 105 | 69 | 83 | 70 | 70 | 73 | 70 | 85 | 86 |
N.S. |
1 | 3.50 | 2.30 | 2.77 | 2.33 | 2.33 | 2.43 | 2.33 | 2.83 | 2.87 |
time (sec) |
N/A | 0.441 | 0.163 | 1.107 | 0.116 | 0.102 | 0.091 | 0.117 | 0.187 | 2.814 |
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 | 11 | 11 | 9 | 8 | 8 | 8 | 8 | 13 | 9 |
N.S. |
1 | 1.00 | 1.00 | 0.82 | 0.73 | 0.73 | 0.73 | 0.73 | 1.18 | 0.82 |
time (sec) |
N/A | 0.145 | 0.010 | 0.069 | 0.026 | 0.076 | 0.030 | 0.124 | 0.161 | 0.020 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | F | B | A | F | F | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 25 | 43 | 0 | 51 | 34 | 0 | 80 | 19 |
N.S. |
1 | 0.00 | 1.00 | 1.72 | 0.00 | 2.04 | 1.36 | 0.00 | 3.20 | 0.76 |
time (sec) |
N/A | 0.000 | 0.032 | 0.152 | 0.000 | 0.088 | 0.272 | 0.000 | 58.096 | 2.746 |
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 | 16 | 0 | 17 | 18 | 22 | 21 | 20 | 29 | 22 | 17 |
N.S. |
1 | 0.00 | 1.06 | 1.12 | 1.38 | 1.31 | 1.25 | 1.81 | 1.38 | 1.06 |
time (sec) |
N/A | 0.000 | 0.051 | 0.203 | 0.035 | 0.091 | 0.138 | 0.128 | 0.205 | 2.693 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | A | F(-2) | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 23 | 18 | 23 | 137 | 69 | 22 | 0 | 23 | 25 |
N.S. |
1 | 1.15 | 0.90 | 1.15 | 6.85 | 3.45 | 1.10 | 0.00 | 1.15 | 1.25 |
time (sec) |
N/A | 5.307 | 2.945 | 1.293 | 0.479 | 0.083 | 0.736 | 0.000 | 0.206 | 0.661 |
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 | 24 | 0 | 36 | 37 | 36 | 36 | 31 | 36 | 36 | 0 |
N.S. |
1 | 0.00 | 1.50 | 1.54 | 1.50 | 1.50 | 1.29 | 1.50 | 1.50 | 0.00 |
time (sec) |
N/A | 0.000 | 0.051 | 2.189 | 0.118 | 0.089 | 0.276 | 0.158 | 0.187 | 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 | 42 | 21 | 24 | 24 | 24 | 22 | 24 | 41 | 18 |
N.S. |
1 | 2.00 | 1.00 | 1.14 | 1.14 | 1.14 | 1.05 | 1.14 | 1.95 | 0.86 |
time (sec) |
N/A | 0.194 | 0.028 | 0.131 | 0.043 | 0.084 | 0.077 | 0.112 | 0.211 | 2.442 |
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 | 22 | 21 | 21 | 19 | 20 | 19 | 20 | 22 | 21 |
N.S. |
1 | 0.79 | 0.75 | 0.75 | 0.68 | 0.71 | 0.68 | 0.71 | 0.79 | 0.75 |
time (sec) |
N/A | 0.278 | 0.082 | 0.363 | 0.058 | 0.091 | 0.065 | 0.116 | 0.167 | 2.352 |
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 | 25 | 27 | 31 | 27 | 22 | 31 | 26 | 27 |
N.S. |
1 | 0.00 | 0.83 | 0.90 | 1.03 | 0.90 | 0.73 | 1.03 | 0.87 | 0.90 |
time (sec) |
N/A | 0.000 | 0.182 | 2.231 | 0.167 | 0.080 | 0.183 | 0.174 | 0.176 | 3.289 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | A | A | B | B | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 141 | 49 | 39 | 40 | 54 | 39 | 46 | 67 | 40 |
N.S. |
1 | 6.13 | 2.13 | 1.70 | 1.74 | 2.35 | 1.70 | 2.00 | 2.91 | 1.74 |
time (sec) |
N/A | 0.490 | 0.020 | 0.198 | 0.036 | 0.076 | 0.946 | 0.121 | 0.170 | 0.103 |