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 | B | B | F | B | B | F | F | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 88 | 140 | 0 | 72 | 117 | 0 | 243 | 0 |
N.S. |
1 | 0.00 | 3.38 | 5.38 | 0.00 | 2.77 | 4.50 | 0.00 | 9.35 | 0.00 |
time (sec) |
N/A | 0.000 | 0.073 | 81.650 | 0.000 | 0.100 | 3.516 | 0.000 | 200.018 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | F | A | A | F | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 62 | 25 | 29 | 0 | 28 | 22 | 0 | 29 | 24 |
N.S. |
1 | 2.14 | 0.86 | 1.00 | 0.00 | 0.97 | 0.76 | 0.00 | 1.00 | 0.83 |
time (sec) |
N/A | 0.226 | 0.240 | 3.530 | 0.000 | 0.092 | 0.793 | 0.000 | 0.377 | 2.976 |
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 | 26 | 0 | 25 | 32 | 33 | 32 | 29 | 0 | 101 | 23 |
N.S. |
1 | 0.00 | 0.96 | 1.23 | 1.27 | 1.23 | 1.12 | 0.00 | 3.88 | 0.88 |
time (sec) |
N/A | 0.000 | 0.105 | 12.023 | 0.097 | 0.085 | 34.941 | 0.000 | 200.014 | 3.100 |
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 | 28 | 0 | 24 | 36 | 44 | 36 | 22 | 36 | 38 | 0 |
N.S. |
1 | 0.00 | 0.86 | 1.29 | 1.57 | 1.29 | 0.79 | 1.29 | 1.36 | 0.00 |
time (sec) |
N/A | 0.000 | 0.247 | 0.353 | 0.163 | 0.090 | 0.110 | 0.212 | 0.193 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | A | A | F(-1) | F(-1) | F | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 29 | 58 | 47 | 38 | 0 | 0 | 0 | 53 |
N.S. |
1 | 0.00 | 1.00 | 2.00 | 1.62 | 1.31 | 0.00 | 0.00 | 0.00 | 1.83 |
time (sec) |
N/A | 0.000 | 0.171 | 12.809 | 0.049 | 0.112 | 0.000 | 0.000 | 0.256 | 5.729 |
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 | 20 | 19 | 16 | 18 | 17 | 26 | 18 | 18 |
N.S. |
1 | 0.00 | 0.83 | 0.79 | 0.67 | 0.75 | 0.71 | 1.08 | 0.75 | 0.75 |
time (sec) |
N/A | 0.000 | 0.117 | 0.987 | 0.156 | 0.081 | 0.056 | 0.110 | 0.175 | 3.078 |
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 | 33 | 47 | 33 | 29 | 26 | 37 | 37 |
N.S. |
1 | 1.21 | 0.89 | 1.18 | 1.68 | 1.18 | 1.04 | 0.93 | 1.32 | 1.32 |
time (sec) |
N/A | 0.489 | 0.037 | 0.641 | 0.072 | 0.088 | 0.107 | 0.115 | 0.174 | 3.021 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | B | A | A | B | B | F | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 153 | 96 | 38 | 37 | 75 | 73 | 581 | 0 |
N.S. |
1 | 0.00 | 4.78 | 3.00 | 1.19 | 1.16 | 2.34 | 2.28 | 18.16 | 0.00 |
time (sec) |
N/A | 0.000 | 0.153 | 2.483 | 0.220 | 0.095 | 13.107 | 0.159 | 0.198 | 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 | 37 | 36 | 579 | 30 | 31 | 32 | 37 | 30 |
N.S. |
1 | 0.00 | 1.23 | 1.20 | 19.30 | 1.00 | 1.03 | 1.07 | 1.23 | 1.00 |
time (sec) |
N/A | 0.000 | 0.410 | 0.227 | 0.115 | 0.092 | 0.639 | 0.111 | 0.183 | 0.541 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F | A | A | B | B | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 0 | 33 | 44 | 0 | 29 | 29 | 58 | 31 | 0 |
N.S. |
1 | 0.00 | 0.97 | 1.29 | 0.00 | 0.85 | 0.85 | 1.71 | 0.91 | 0.00 |
time (sec) |
N/A | 0.000 | 0.265 | 0.987 | 0.000 | 0.115 | 0.128 | 0.125 | 0.181 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | A | B | B | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 34 | 66 | 41 | 64 | 102 | 64 | 179 | 62 |
N.S. |
1 | 0.00 | 1.36 | 2.64 | 1.64 | 2.56 | 4.08 | 2.56 | 7.16 | 2.48 |
time (sec) |
N/A | 0.000 | 0.074 | 10.813 | 0.072 | 0.112 | 0.660 | 0.848 | 0.198 | 3.129 |
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 | 16 | 14 | 16 | 15 | 24 | 14 | 16 | 30 | 15 |
N.S. |
1 | 0.67 | 0.58 | 0.67 | 0.62 | 1.00 | 0.58 | 0.67 | 1.25 | 0.62 |
time (sec) |
N/A | 0.239 | 0.009 | 0.083 | 0.030 | 0.082 | 0.087 | 0.105 | 0.188 | 0.036 |
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 | 28 | 0 | 39 | 368 | 1994 | 279 | 333 | 2318 | 98 | 367 |
N.S. |
1 | 0.00 | 1.39 | 13.14 | 71.21 | 9.96 | 11.89 | 82.79 | 3.50 | 13.11 |
time (sec) |
N/A | 0.000 | 0.466 | 0.020 | 0.198 | 0.089 | 0.600 | 0.730 | 0.181 | 4.776 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 53 | 56 | 29 | 45 | 43 | 51 | 45 | 27 | 29 |
N.S. |
1 | 1.89 | 2.00 | 1.04 | 1.61 | 1.54 | 1.82 | 1.61 | 0.96 | 1.04 |
time (sec) |
N/A | 0.358 | 0.015 | 0.309 | 0.027 | 0.090 | 0.105 | 0.104 | 0.179 | 0.071 |
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 | 24 | 25 | 46 | 24 | 19 | 0 | 25 | 24 |
N.S. |
1 | 0.00 | 1.00 | 1.04 | 1.92 | 1.00 | 0.79 | 0.00 | 1.04 | 1.00 |
time (sec) |
N/A | 0.000 | 0.181 | 19.301 | 0.036 | 0.078 | 0.102 | 0.000 | 0.174 | 3.396 |
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 | 20 | 20 | 15 | 14 | 14 | 14 | 14 | 14 | 14 |
N.S. |
1 | 1.18 | 1.18 | 0.88 | 0.82 | 0.82 | 0.82 | 0.82 | 0.82 | 0.82 |
time (sec) |
N/A | 0.809 | 0.043 | 0.303 | 0.056 | 0.121 | 0.069 | 0.114 | 0.175 | 3.058 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | F | A | B | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 73 | 26 | 21 | 0 | 20 | 51 | 20 | 61 | 21 |
N.S. |
1 | 3.17 | 1.13 | 0.91 | 0.00 | 0.87 | 2.22 | 0.87 | 2.65 | 0.91 |
time (sec) |
N/A | 0.601 | 0.016 | 0.286 | 0.000 | 0.088 | 0.716 | 0.120 | 0.182 | 3.029 |
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 | 36 | 0 | 61 | 69 | 83 | 83 | 75 | 85 | 87 | 76 |
N.S. |
1 | 0.00 | 1.69 | 1.92 | 2.31 | 2.31 | 2.08 | 2.36 | 2.42 | 2.11 |
time (sec) |
N/A | 0.000 | 9.391 | 1.253 | 0.175 | 0.089 | 0.285 | 0.159 | 0.174 | 3.239 |
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 | 29 | 30 | 36 | 29 | 19 | 38 | 37 | 30 |
N.S. |
1 | 0.00 | 1.04 | 1.07 | 1.29 | 1.04 | 0.68 | 1.36 | 1.32 | 1.07 |
time (sec) |
N/A | 0.000 | 2.371 | 0.220 | 0.087 | 0.094 | 0.088 | 0.120 | 0.175 | 0.091 |
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 | 21 | 0 | 30 | 26 | 67 | 67 | 32 | 128 | 126 | 0 |
N.S. |
1 | 0.00 | 1.43 | 1.24 | 3.19 | 3.19 | 1.52 | 6.10 | 6.00 | 0.00 |
time (sec) |
N/A | 0.000 | 0.029 | 27.218 | 0.166 | 0.097 | 0.089 | 0.168 | 0.183 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | B | A | A | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 123 | 46 | 35 | 67 | 39 | 29 | 52 | 62 | 48 |
N.S. |
1 | 4.92 | 1.84 | 1.40 | 2.68 | 1.56 | 1.16 | 2.08 | 2.48 | 1.92 |
time (sec) |
N/A | 1.200 | 0.077 | 4.069 | 0.163 | 0.108 | 0.248 | 0.119 | 0.184 | 3.154 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 38 | 212 | 35 | 33 | 32 | 31 | 36 | 33 | 9651 |
N.S. |
1 | 1.46 | 8.15 | 1.35 | 1.27 | 1.23 | 1.19 | 1.38 | 1.27 | 371.19 |
time (sec) |
N/A | 0.526 | 0.125 | 0.265 | 0.036 | 0.086 | 5.835 | 0.131 | 0.182 | 17.178 |
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 | 36 | 34 | 35 | 31 | 59 | 35 | 27 | 36 | 41 | 30 |
N.S. |
1 | 0.94 | 0.97 | 0.86 | 1.64 | 0.97 | 0.75 | 1.00 | 1.14 | 0.83 |
time (sec) |
N/A | 0.402 | 0.019 | 0.363 | 0.057 | 0.088 | 0.066 | 0.113 | 0.180 | 0.052 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 26 | 23 | 23 | 18 | 22 | 22 | 18 | 17 |
N.S. |
1 | 0.00 | 1.04 | 0.92 | 0.92 | 0.72 | 0.88 | 0.88 | 0.72 | 0.68 |
time (sec) |
N/A | 0.000 | 0.118 | 0.346 | 0.149 | 0.087 | 0.120 | 0.135 | 0.181 | 3.254 |
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 | 35 | 25 | 20 | 18 | 12 | 18 | 39 | 38 |
N.S. |
1 | 0.00 | 1.46 | 1.04 | 0.83 | 0.75 | 0.50 | 0.75 | 1.62 | 1.58 |
time (sec) |
N/A | 0.000 | 1.509 | 0.231 | 0.089 | 0.089 | 0.102 | 0.162 | 0.198 | 3.226 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | C | A | C | A | A | A | B | B |
verified | N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 15 | 15 | 12 | 15 | 11 | 10 | 11 | 12 | 11 |
N.S. |
1 | 0.56 | 0.56 | 0.44 | 0.56 | 0.41 | 0.37 | 0.41 | 0.44 | 0.41 |
time (sec) |
N/A | 0.385 | 0.007 | 0.116 | 0.054 | 0.092 | 0.041 | 0.113 | 0.177 | 3.041 |
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 | 18 | 20 | 20 | 19 | 18 | 20 | 15 | 18 | 30 | 18 |
N.S. |
1 | 1.11 | 1.11 | 1.06 | 1.00 | 1.11 | 0.83 | 1.00 | 1.67 | 1.00 |
time (sec) |
N/A | 0.437 | 0.016 | 0.062 | 0.033 | 0.096 | 0.059 | 0.116 | 0.171 | 0.064 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | F | A | A | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 36 | 14 | 14 | 0 | 13 | 10 | 37 | 16 | 13 |
N.S. |
1 | 2.57 | 1.00 | 1.00 | 0.00 | 0.93 | 0.71 | 2.64 | 1.14 | 0.93 |
time (sec) |
N/A | 0.487 | 0.045 | 0.254 | 0.000 | 0.089 | 0.067 | 0.113 | 0.176 | 3.167 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | A | B | B | B | B | F | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 59 | 51 | 56 | 55 | 49 | 54 | 740 | 0 |
N.S. |
1 | 0.00 | 2.27 | 1.96 | 2.15 | 2.12 | 1.88 | 2.08 | 28.46 | 0.00 |
time (sec) |
N/A | 0.000 | 10.079 | 3.105 | 0.109 | 0.110 | 0.744 | 1.334 | 0.204 | 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 | 28 | 21 | 24 | 23 | 23 | 20 | 25 | 21 | 20 |
N.S. |
1 | 1.33 | 1.00 | 1.14 | 1.10 | 1.10 | 0.95 | 1.19 | 1.00 | 0.95 |
time (sec) |
N/A | 3.396 | 0.204 | 0.292 | 0.070 | 0.093 | 0.840 | 0.128 | 0.174 | 3.217 |
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 | 21 | 0 | 18 | 17 | 16 | 16 | 15 | 16 | 18 | 16 |
N.S. |
1 | 0.00 | 0.86 | 0.81 | 0.76 | 0.76 | 0.71 | 0.76 | 0.86 | 0.76 |
time (sec) |
N/A | 0.000 | 0.100 | 0.137 | 0.074 | 0.093 | 0.119 | 0.114 | 0.167 | 3.003 |
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 | 16 | 46 | 16 | 24 | 41 | 21 | 24 | 21 | 14 | 12 |
N.S. |
1 | 2.88 | 1.00 | 1.50 | 2.56 | 1.31 | 1.50 | 1.31 | 0.88 | 0.75 |
time (sec) |
N/A | 0.373 | 0.113 | 0.089 | 0.035 | 0.085 | 0.062 | 0.109 | 0.176 | 0.033 |
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 | 14 | 14 | 15 | 14 | 11 | 15 | 14 | 14 | 14 |
N.S. |
1 | 0.93 | 0.93 | 1.00 | 0.93 | 0.73 | 1.00 | 0.93 | 0.93 | 0.93 |
time (sec) |
N/A | 0.500 | 0.016 | 0.049 | 0.050 | 0.084 | 0.113 | 0.112 | 0.168 | 3.067 |
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 | 109 | 114 | 323 | 136 | 136 | 246 | 291 | 218 |
N.S. |
1 | 0.00 | 3.41 | 3.56 | 10.09 | 4.25 | 4.25 | 7.69 | 9.09 | 6.81 |
time (sec) |
N/A | 0.000 | 0.810 | 13.141 | 0.182 | 0.098 | 0.353 | 0.160 | 0.223 | 3.194 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | F(-2) | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 30 | 34 | 33 | 33 | 0 | 41 | 38 | 41 |
N.S. |
1 | 0.00 | 1.36 | 1.55 | 1.50 | 1.50 | 0.00 | 1.86 | 1.73 | 1.86 |
time (sec) |
N/A | 0.000 | 0.267 | 6.835 | 0.078 | 0.118 | 0.000 | 0.131 | 0.186 | 3.217 |
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 | 46 | 38 | 32 | 45 | 32 | 44 | 39 | 32 | 24 |
N.S. |
1 | 1.59 | 1.31 | 1.10 | 1.55 | 1.10 | 1.52 | 1.34 | 1.10 | 0.83 |
time (sec) |
N/A | 0.308 | 0.165 | 0.259 | 0.055 | 0.089 | 0.078 | 0.121 | 0.176 | 3.049 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 14 | 15 | 25 | 16 | 14 | 16 | 16 | 14 |
N.S. |
1 | 1.00 | 1.00 | 1.07 | 1.79 | 1.14 | 1.00 | 1.14 | 1.14 | 1.00 |
time (sec) |
N/A | 1.720 | 0.085 | 0.437 | 0.076 | 0.097 | 0.069 | 0.145 | 0.181 | 3.075 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | B | B | B | B | F | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 51 | 50 | 60 | 60 | 53 | 64 | 615 | 61 |
N.S. |
1 | 0.00 | 1.89 | 1.85 | 2.22 | 2.22 | 1.96 | 2.37 | 22.78 | 2.26 |
time (sec) |
N/A | 0.000 | 10.045 | 0.549 | 0.083 | 0.108 | 0.186 | 0.810 | 0.193 | 0.274 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | A | A | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 16 | 15 | 15 | 0 | 18 | 15 | 33 | 17 | 0 |
N.S. |
1 | 0.89 | 0.83 | 0.83 | 0.00 | 1.00 | 0.83 | 1.83 | 0.94 | 0.00 |
time (sec) |
N/A | 0.504 | 0.007 | 0.504 | 0.000 | 0.084 | 12.339 | 0.136 | 0.186 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | A | A | F | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 69 | 33 | 26 | 25 | 25 | 26 | 0 | 26 | 25 |
N.S. |
1 | 3.00 | 1.43 | 1.13 | 1.09 | 1.09 | 1.13 | 0.00 | 1.13 | 1.09 |
time (sec) |
N/A | 0.378 | 4.037 | 0.364 | 0.128 | 0.098 | 0.108 | 0.000 | 0.184 | 3.156 |
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 | 26 | 26 | 24 | 34 | 22 | 27 | 26 | 23 | 16 |
N.S. |
1 | 1.44 | 1.44 | 1.33 | 1.89 | 1.22 | 1.50 | 1.44 | 1.28 | 0.89 |
time (sec) |
N/A | 0.204 | 0.005 | 0.138 | 0.033 | 0.095 | 0.077 | 0.109 | 0.178 | 2.977 |
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 | 19 | 0 | 19 | 22 | 20 | 20 | 27 | 21 | 24 | 31 |
N.S. |
1 | 0.00 | 1.00 | 1.16 | 1.05 | 1.05 | 1.42 | 1.11 | 1.26 | 1.63 |
time (sec) |
N/A | 0.000 | 1.087 | 0.102 | 0.071 | 0.086 | 0.117 | 0.113 | 0.174 | 0.090 |
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 | 37 | 213 | 323 | 53 | 269 | 51 | 46 | 56 | 207 | 53 |
N.S. |
1 | 5.76 | 8.73 | 1.43 | 7.27 | 1.38 | 1.24 | 1.51 | 5.59 | 1.43 |
time (sec) |
N/A | 1.178 | 0.215 | 2.190 | 0.199 | 0.085 | 0.144 | 0.290 | 0.173 | 2.134 |
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 | 24 | 0 | 52 | 47 | 53 | 43 | 51 | 46 | 714 | 0 |
N.S. |
1 | 0.00 | 2.17 | 1.96 | 2.21 | 1.79 | 2.12 | 1.92 | 29.75 | 0.00 |
time (sec) |
N/A | 0.000 | 0.050 | 0.594 | 0.144 | 0.091 | 0.167 | 0.117 | 0.180 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 548 | 22 | 20 | 19 | 19 | 15 | 19 | 19 | 18 |
N.S. |
1 | 22.83 | 0.92 | 0.83 | 0.79 | 0.79 | 0.62 | 0.79 | 0.79 | 0.75 |
time (sec) |
N/A | 1.472 | 0.107 | 0.116 | 0.068 | 0.084 | 0.051 | 0.111 | 0.175 | 3.067 |
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 | 22 | 31 | 22 | 21 | 26 | 25 | 24 | 26 | 32 | 19 |
N.S. |
1 | 1.41 | 1.00 | 0.95 | 1.18 | 1.14 | 1.09 | 1.18 | 1.45 | 0.86 |
time (sec) |
N/A | 0.208 | 0.009 | 0.178 | 0.026 | 0.082 | 0.067 | 0.120 | 0.171 | 2.936 |
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 | 17 | 18 | 17 | 19 | 17 | 16 | 19 | 19 |
N.S. |
1 | 1.21 | 1.21 | 1.29 | 1.21 | 1.36 | 1.21 | 1.14 | 1.36 | 1.36 |
time (sec) |
N/A | 0.223 | 0.008 | 0.213 | 0.031 | 0.087 | 0.054 | 0.111 | 0.178 | 2.963 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | F | B | B | B | B | B | B | B |
verified | N/A | Yes | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 56 | 0 | 52 | 57 | 52 | 54 | 57 | 66 | 65 |
N.S. |
1 | 3.29 | 0.00 | 3.06 | 3.35 | 3.06 | 3.18 | 3.35 | 3.88 | 3.82 |
time (sec) |
N/A | 1.419 | 0.000 | 0.356 | 0.279 | 0.093 | 0.097 | 0.117 | 2.859 | 3.050 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | B | B | B | B | B | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 53 | 84 | 57 | 61 | 63 | 85 | 85 | 0 |
N.S. |
1 | 0.00 | 1.96 | 3.11 | 2.11 | 2.26 | 2.33 | 3.15 | 3.15 | 0.00 |
time (sec) |
N/A | 0.000 | 0.058 | 1.386 | 0.185 | 0.088 | 0.428 | 0.468 | 0.201 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | A | A | B | F(-1) | A | F | B |
verified | N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 0 | 58 | 55 | 77 | 0 | 57 | 313 | 57 |
N.S. |
1 | 0.00 | 0.00 | 1.81 | 1.72 | 2.41 | 0.00 | 1.78 | 9.78 | 1.78 |
time (sec) |
N/A | 0.000 | 0.000 | 0.065 | 0.294 | 0.108 | 0.000 | 0.125 | 200.018 | 21.583 |
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 | 22 | 30 | 32 | 29 | 30 | 28 | 29 | 30 | 32 | 30 |
N.S. |
1 | 1.36 | 1.45 | 1.32 | 1.36 | 1.27 | 1.32 | 1.36 | 1.45 | 1.36 |
time (sec) |
N/A | 0.208 | 0.005 | 0.062 | 0.030 | 0.070 | 0.089 | 0.114 | 0.170 | 2.871 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 27 | 28 | 29 | 28 | 27 | 24 | 28 | 27 | 27 |
N.S. |
1 | 1.08 | 1.12 | 1.16 | 1.12 | 1.08 | 0.96 | 1.12 | 1.08 | 1.08 |
time (sec) |
N/A | 0.288 | 0.010 | 0.108 | 0.031 | 0.079 | 0.176 | 0.114 | 0.169 | 0.045 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | B | A | A | B | B |
verified | N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 19 | 21 | 48 | 20 | 96 | 34 | 34 | 25 | 22 |
N.S. |
1 | 0.90 | 1.00 | 2.29 | 0.95 | 4.57 | 1.62 | 1.62 | 1.19 | 1.05 |
time (sec) |
N/A | 1.559 | 0.236 | 72.948 | 0.041 | 0.114 | 0.648 | 0.142 | 0.165 | 3.441 |
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 | 11 | 9 | 9 | 9 | 9 | 7 | 9 | 7 | 8 |
N.S. |
1 | 0.61 | 0.50 | 0.50 | 0.50 | 0.50 | 0.39 | 0.50 | 0.39 | 0.44 |
time (sec) |
N/A | 0.217 | 0.000 | 0.023 | 0.022 | 0.066 | 0.016 | 0.113 | 0.157 | 0.016 |
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 | 26 | 0 | 25 | 24 | 28 | 25 | 20 | 0 | 27 | 28 |
N.S. |
1 | 0.00 | 0.96 | 0.92 | 1.08 | 0.96 | 0.77 | 0.00 | 1.04 | 1.08 |
time (sec) |
N/A | 0.000 | 0.135 | 1.755 | 0.204 | 0.104 | 0.481 | 0.000 | 0.164 | 3.846 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | B | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 40 | 32 | 52 | 106 | 65 | 131 | 46 | 98 | 75 |
N.S. |
1 | 1.43 | 1.14 | 1.86 | 3.79 | 2.32 | 4.68 | 1.64 | 3.50 | 2.68 |
time (sec) |
N/A | 0.261 | 0.010 | 0.568 | 0.027 | 0.083 | 0.658 | 0.126 | 0.168 | 3.035 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 23 | 23 | 19 | 21 | 21 | 20 | 21 | 17 | 19 |
N.S. |
1 | 0.96 | 0.96 | 0.79 | 0.88 | 0.88 | 0.83 | 0.88 | 0.71 | 0.79 |
time (sec) |
N/A | 0.143 | 0.001 | 0.067 | 0.023 | 0.074 | 0.021 | 0.110 | 0.166 | 2.967 |
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 | 23 | 23 | 19 | 26 | 20 | 23 |
N.S. |
1 | 0.00 | 1.00 | 0.96 | 1.00 | 1.00 | 0.83 | 1.13 | 0.87 | 1.00 |
time (sec) |
N/A | 0.000 | 0.193 | 1.306 | 0.149 | 0.094 | 0.854 | 0.290 | 0.167 | 3.331 |
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 | 33 | 30 | 33 | 38 | 20 | 40 | 44 | 26 |
N.S. |
1 | 0.00 | 1.10 | 1.00 | 1.10 | 1.27 | 0.67 | 1.33 | 1.47 | 0.87 |
time (sec) |
N/A | 0.000 | 0.398 | 0.428 | 0.097 | 0.093 | 0.078 | 0.137 | 0.218 | 2.944 |
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 | 7 | 7 | 7 | 6 | 6 | 5 | 6 | 13 | 6 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.86 | 0.86 | 0.71 | 0.86 | 1.86 | 0.86 |
time (sec) |
N/A | 0.141 | 0.002 | 0.135 | 0.027 | 0.079 | 0.040 | 0.109 | 0.178 | 2.874 |
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 | 47 | 34 | 49 | 49 | 31 | 49 | 49 | 0 |
N.S. |
1 | 0.00 | 1.62 | 1.17 | 1.69 | 1.69 | 1.07 | 1.69 | 1.69 | 0.00 |
time (sec) |
N/A | 0.000 | 0.038 | 0.514 | 0.076 | 0.089 | 0.251 | 0.119 | 0.166 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 24 | 34 | 36 | 36 | 31 | 44 | 44 | 28 |
N.S. |
1 | 0.00 | 0.86 | 1.21 | 1.29 | 1.29 | 1.11 | 1.57 | 1.57 | 1.00 |
time (sec) |
N/A | 0.000 | 0.167 | 0.302 | 0.155 | 0.089 | 0.073 | 0.122 | 0.173 | 0.112 |
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 | 23 | 12 | 16 | 17 | 13 | 17 | 13 | 19 | 17 |
N.S. |
1 | 1.05 | 0.55 | 0.73 | 0.77 | 0.59 | 0.77 | 0.59 | 0.86 | 0.77 |
time (sec) |
N/A | 0.198 | 0.043 | 0.065 | 0.025 | 0.074 | 0.047 | 0.111 | 0.164 | 2.859 |
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 | 12 | 16 | 8 | 7 | 9 | 12 | 7 | 8 | 8 |
N.S. |
1 | 0.80 | 1.07 | 0.53 | 0.47 | 0.60 | 0.80 | 0.47 | 0.53 | 0.53 |
time (sec) |
N/A | 0.139 | 0.000 | 0.033 | 0.033 | 0.071 | 0.015 | 0.108 | 0.157 | 0.001 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 0 | 30 | 38 | 35 | 33 | 34 | 36 | 33 | 21 |
N.S. |
1 | 0.00 | 1.43 | 1.81 | 1.67 | 1.57 | 1.62 | 1.71 | 1.57 | 1.00 |
time (sec) |
N/A | 0.000 | 0.164 | 2.815 | 0.074 | 0.089 | 0.169 | 0.123 | 0.164 | 3.162 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | A | A | B | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 40 | 49 | 38 | 44 | 41 | 131 | 29 | 97 |
N.S. |
1 | 0.00 | 1.67 | 2.04 | 1.58 | 1.83 | 1.71 | 5.46 | 1.21 | 4.04 |
time (sec) |
N/A | 0.000 | 0.111 | 8.925 | 0.276 | 0.086 | 0.295 | 0.215 | 0.168 | 3.085 |
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 | 18 | 0 | 28 | 35 | 305 | 46 | 41 | 126 | 34 | 130 |
N.S. |
1 | 0.00 | 1.56 | 1.94 | 16.94 | 2.56 | 2.28 | 7.00 | 1.89 | 7.22 |
time (sec) |
N/A | 0.000 | 0.060 | 1.949 | 0.289 | 0.092 | 0.100 | 0.273 | 0.162 | 2.972 |
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 | 27 | 18 | 25 | 24 | 20 | 18 | 19 | 18 |
N.S. |
1 | 0.00 | 1.69 | 1.12 | 1.56 | 1.50 | 1.25 | 1.12 | 1.19 | 1.12 |
time (sec) |
N/A | 0.000 | 0.315 | 0.065 | 0.086 | 0.090 | 0.126 | 0.113 | 0.165 | 0.069 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | B | F | B | B | B | B | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 104 | 230 | 0 | 172 | 231 | 717 | 336 | 0 |
N.S. |
1 | 0.00 | 3.85 | 8.52 | 0.00 | 6.37 | 8.56 | 26.56 | 12.44 | 0.00 |
time (sec) |
N/A | 0.000 | 0.137 | 0.066 | 0.000 | 0.098 | 0.373 | 0.154 | 0.163 | 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 | 31 | 0 | 28 | 31 | 83 | 34 | 32 | 0 | 56 | 87 |
N.S. |
1 | 0.00 | 0.90 | 1.00 | 2.68 | 1.10 | 1.03 | 0.00 | 1.81 | 2.81 |
time (sec) |
N/A | 0.000 | 0.124 | 1.960 | 0.232 | 0.092 | 0.254 | 0.000 | 0.165 | 3.237 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | B | F | B | B | B | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 65 | 65 | 56 | 0 | 61 | 70 | 61 | 68 | 0 |
N.S. |
1 | 2.60 | 2.60 | 2.24 | 0.00 | 2.44 | 2.80 | 2.44 | 2.72 | 0.00 |
time (sec) |
N/A | 0.837 | 0.056 | 0.068 | 0.000 | 0.097 | 0.179 | 0.156 | 0.161 | 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 | 22 | 53 | 22 | 28 | 57 | 27 | 32 | 27 | 36 | 24 |
N.S. |
1 | 2.41 | 1.00 | 1.27 | 2.59 | 1.23 | 1.45 | 1.23 | 1.64 | 1.09 |
time (sec) |
N/A | 1.864 | 4.325 | 0.349 | 0.103 | 0.092 | 0.072 | 0.122 | 0.176 | 0.099 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | F | A | F(-1) | F | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 79 | 24 | 18 | 0 | 20 | 0 | 0 | 24 | 18 |
N.S. |
1 | 3.04 | 0.92 | 0.69 | 0.00 | 0.77 | 0.00 | 0.00 | 0.92 | 0.69 |
time (sec) |
N/A | 0.328 | 0.057 | 0.887 | 0.000 | 0.086 | 0.000 | 0.000 | 0.169 | 2.954 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | C | A | A | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 28 | 25 | 70 | 41 | 19 | 86 | 38 | 25 |
N.S. |
1 | 0.00 | 0.88 | 0.78 | 2.19 | 1.28 | 0.59 | 2.69 | 1.19 | 0.78 |
time (sec) |
N/A | 0.000 | 0.200 | 4.388 | 0.164 | 0.106 | 0.063 | 0.157 | 0.158 | 3.186 |
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 | 23 | 121 | 85 | 109 | 104 | 104 | 112 | 104 | 119 | 114 |
N.S. |
1 | 5.26 | 3.70 | 4.74 | 4.52 | 4.52 | 4.87 | 4.52 | 5.17 | 4.96 |
time (sec) |
N/A | 0.732 | 0.082 | 1.706 | 0.115 | 0.088 | 0.075 | 0.112 | 0.159 | 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 | 27 | 36 | 36 | 31 | 34 | 32 | 29 | 33 | 34 | 34 |
N.S. |
1 | 1.33 | 1.33 | 1.15 | 1.26 | 1.19 | 1.07 | 1.22 | 1.26 | 1.26 |
time (sec) |
N/A | 0.219 | 0.007 | 0.132 | 0.030 | 0.076 | 0.050 | 0.111 | 0.159 | 3.040 |
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 | 24 | 0 | 36 | 45 | 43 | 21 | 32 | 43 | 44 | 36 |
N.S. |
1 | 0.00 | 1.50 | 1.88 | 1.79 | 0.88 | 1.33 | 1.79 | 1.83 | 1.50 |
time (sec) |
N/A | 0.000 | 0.118 | 1.020 | 0.135 | 0.085 | 0.169 | 0.139 | 0.164 | 3.263 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 29 | 28 | 24 | 23 | 23 | 24 | 24 | 24 | 22 |
N.S. |
1 | 1.26 | 1.22 | 1.04 | 1.00 | 1.00 | 1.04 | 1.04 | 1.04 | 0.96 |
time (sec) |
N/A | 0.404 | 0.017 | 0.284 | 0.095 | 0.104 | 0.130 | 0.113 | 0.160 | 3.101 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F | B | A | F | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 25 | 34 | 0 | 49 | 32 | 0 | 48 | 25 |
N.S. |
1 | 0.00 | 0.96 | 1.31 | 0.00 | 1.88 | 1.23 | 0.00 | 1.85 | 0.96 |
time (sec) |
N/A | 0.000 | 1.253 | 0.138 | 0.000 | 0.088 | 0.171 | 0.000 | 0.215 | 3.174 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | A | A | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 28 | 28 | 110 | 25 | 26 | 49 | 28 | 25 |
N.S. |
1 | 0.00 | 1.22 | 1.22 | 4.78 | 1.09 | 1.13 | 2.13 | 1.22 | 1.09 |
time (sec) |
N/A | 0.000 | 0.103 | 1.586 | 0.148 | 0.088 | 0.151 | 0.197 | 0.157 | 6.602 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | A | B | A | A | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 140 | 55 | 54 | 49 | 46 | 49 | 48 | 86 | 48 |
N.S. |
1 | 6.09 | 2.39 | 2.35 | 2.13 | 2.00 | 2.13 | 2.09 | 3.74 | 2.09 |
time (sec) |
N/A | 10.971 | 0.030 | 0.696 | 0.041 | 0.083 | 1.607 | 0.123 | 0.164 | 0.189 |
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 | 16 | 54 | 16 | 15 | 14 | 14 | 14 | 0 | 16 | 14 |
N.S. |
1 | 3.38 | 1.00 | 0.94 | 0.88 | 0.88 | 0.88 | 0.00 | 1.00 | 0.88 |
time (sec) |
N/A | 0.197 | 0.015 | 0.569 | 0.068 | 0.092 | 1.625 | 0.000 | 0.162 | 3.114 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 10 | 17 | 10 | 11 | 17 | 10 | 7 | 10 | 13 | 10 |
N.S. |
1 | 1.70 | 1.00 | 1.10 | 1.70 | 1.00 | 0.70 | 1.00 | 1.30 | 1.00 |
time (sec) |
N/A | 0.428 | 0.023 | 0.239 | 0.061 | 0.100 | 0.036 | 0.113 | 0.162 | 3.109 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | A | A | B | B | B | B | B |
verified | N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 0 | 26 | 43 | 51 | 46 | 149 | 59 | 120 |
N.S. |
1 | 0.00 | 0.00 | 0.96 | 1.59 | 1.89 | 1.70 | 5.52 | 2.19 | 4.44 |
time (sec) |
N/A | 0.000 | 0.000 | 9.180 | 0.446 | 0.089 | 0.771 | 0.320 | 0.633 | 3.476 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 8 | 8 | 9 | 8 | 8 | 5 | 9 | 8 | 8 |
N.S. |
1 | 0.38 | 0.38 | 0.43 | 0.38 | 0.38 | 0.24 | 0.43 | 0.38 | 0.38 |
time (sec) |
N/A | 0.151 | 0.001 | 0.033 | 0.038 | 0.078 | 0.028 | 0.106 | 0.157 | 0.011 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | B | B | A | B | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 115 | 70 | 51 | 117 | 46 | 53 | 122 | 56 | 49 |
N.S. |
1 | 4.60 | 2.80 | 2.04 | 4.68 | 1.84 | 2.12 | 4.88 | 2.24 | 1.96 |
time (sec) |
N/A | 0.438 | 0.023 | 0.776 | 0.035 | 0.080 | 0.093 | 0.115 | 0.160 | 3.169 |
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 | 16 | 14 | 15 | 15 | 14 | 15 | 26 | 13 |
N.S. |
1 | 0.76 | 0.76 | 0.67 | 0.71 | 0.71 | 0.67 | 0.71 | 1.24 | 0.62 |
time (sec) |
N/A | 0.673 | 0.142 | 0.259 | 0.063 | 0.089 | 0.063 | 0.110 | 0.160 | 0.078 |
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 | 28 | 0 | 28 | 260 | 27 | 25 | 22 | 25 | 92 | 24 |
N.S. |
1 | 0.00 | 1.00 | 9.29 | 0.96 | 0.89 | 0.79 | 0.89 | 3.29 | 0.86 |
time (sec) |
N/A | 0.000 | 0.164 | 225.491 | 0.198 | 0.110 | 0.966 | 0.201 | 0.200 | 3.239 |
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 | 25 | 0 | 24 | 24 | 74 | 74 | 37 | 78 | 78 | 191 |
N.S. |
1 | 0.00 | 0.96 | 0.96 | 2.96 | 2.96 | 1.48 | 3.12 | 3.12 | 7.64 |
time (sec) |
N/A | 0.000 | 0.157 | 51.191 | 0.221 | 0.096 | 0.182 | 0.274 | 0.195 | 3.348 |
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 | 14 | 14 | 16 | 14 | 15 | 15 | 16 | 15 | 14 |
N.S. |
1 | 0.70 | 0.70 | 0.80 | 0.70 | 0.75 | 0.75 | 0.80 | 0.75 | 0.70 |
time (sec) |
N/A | 0.162 | 0.005 | 0.085 | 0.027 | 0.081 | 0.043 | 0.113 | 0.157 | 0.024 |
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 | 27 | 36 | 36 | 15 | 22 | 36 | 28 |
N.S. |
1 | 0.00 | 1.00 | 1.17 | 1.57 | 1.57 | 0.65 | 0.96 | 1.57 | 1.22 |
time (sec) |
N/A | 0.000 | 0.101 | 0.728 | 0.060 | 0.084 | 0.060 | 0.121 | 0.159 | 3.049 |
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 | 31 | 93 | 26 | 25 | 52 | 24 | 24 | 0 | 43 | 25 |
N.S. |
1 | 3.00 | 0.84 | 0.81 | 1.68 | 0.77 | 0.77 | 0.00 | 1.39 | 0.81 |
time (sec) |
N/A | 2.411 | 0.041 | 3.793 | 0.213 | 0.091 | 11.324 | 0.000 | 0.166 | 3.643 |
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 | 27 | 27 | 23 | 46 | 27 | 20 | 31 | 49 | 30 |
N.S. |
1 | 1.12 | 1.12 | 0.96 | 1.92 | 1.12 | 0.83 | 1.29 | 2.04 | 1.25 |
time (sec) |
N/A | 0.284 | 0.104 | 0.380 | 0.062 | 0.091 | 0.059 | 0.111 | 0.161 | 0.040 |
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 | 19 | 0 | 19 | 16 | 0 | 27 | 19 | 0 | 28 | 22 |
N.S. |
1 | 0.00 | 1.00 | 0.84 | 0.00 | 1.42 | 1.00 | 0.00 | 1.47 | 1.16 |
time (sec) |
N/A | 0.000 | 0.205 | 0.216 | 0.000 | 0.087 | 0.120 | 0.000 | 0.169 | 3.003 |
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 | 24 | 20 | 21 | 20 | 20 | 19 | 20 | 21 | 19 |
N.S. |
1 | 1.60 | 1.33 | 1.40 | 1.33 | 1.33 | 1.27 | 1.33 | 1.40 | 1.27 |
time (sec) |
N/A | 0.143 | 0.003 | 0.130 | 0.033 | 0.078 | 0.023 | 0.114 | 0.172 | 0.124 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 7 | 13 | 5 | 5 | 9 | 4 | 3 | 4 | 5 | 4 |
N.S. |
1 | 1.86 | 0.71 | 0.71 | 1.29 | 0.57 | 0.43 | 0.57 | 0.71 | 0.57 |
time (sec) |
N/A | 0.171 | 0.001 | 0.037 | 0.031 | 0.074 | 0.031 | 0.112 | 0.171 | 0.009 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | A | A | A | A | A | F | F(-1) |
verified | N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 0 | 40 | 54 | 38 | 36 | 38 | 419 | 0 |
N.S. |
1 | 0.00 | 0.00 | 1.29 | 1.74 | 1.23 | 1.16 | 1.23 | 13.52 | 0.00 |
time (sec) |
N/A | 0.000 | 0.000 | 0.358 | 0.072 | 0.092 | 0.154 | 0.171 | 0.207 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | B | B | B | B | F(-2) | F | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 74 | 199 | 217 | 195 | 201 | 0 | 503 | 1346 |
N.S. |
1 | 0.00 | 2.74 | 7.37 | 8.04 | 7.22 | 7.44 | 0.00 | 18.63 | 49.85 |
time (sec) |
N/A | 0.000 | 4.240 | 29.145 | 2.377 | 0.109 | 37.225 | 0.000 | 200.028 | 4.218 |
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 | 29 | 0 | 24 | 26 | 26 | 24 | 41 | 23 | 50 | 21 |
N.S. |
1 | 0.00 | 0.83 | 0.90 | 0.90 | 0.83 | 1.41 | 0.79 | 1.72 | 0.72 |
time (sec) |
N/A | 0.000 | 0.041 | 3.139 | 0.179 | 0.092 | 0.701 | 0.298 | 0.169 | 3.132 |
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 | 22 | 18 | 18 | 19 | 25 | 18 | 14 | 284 | 18 | 18 |
N.S. |
1 | 0.82 | 0.82 | 0.86 | 1.14 | 0.82 | 0.64 | 12.91 | 0.82 | 0.82 |
time (sec) |
N/A | 0.418 | 0.017 | 5.043 | 0.155 | 0.075 | 0.081 | 0.212 | 0.158 | 3.196 |