Detailed conclusion table per each integral is given by the table below. The elapsed time is in seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2) if the failure was due to an exception being raised, which could indicate a bug in the system. If the failure was due to integral not being evaluated within the time limit, then it is given as F.
In this table, the column N.S.
means normalized size and is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To make the table
fit the page, the name Mathematica
was abbreviated to MMA
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | B | B | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 39 | 45 | 43 | 48 | 44 | 49 | 69 | 45 |
N.S. |
1 | 0.00 | 1.77 | 2.05 | 1.95 | 2.18 | 2.00 | 2.23 | 3.14 | 2.05 |
time (sec) |
N/A | 0.000 | 0.242 | 0.172 | 0.084 | 0.084 | 0.226 | 1.378 | 0.165 | 3.580 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | B | A | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 0 | 47 | 30 | 39 | 68 | 37 | 104 | 102 | 44 |
N.S. |
1 | 0.00 | 1.42 | 0.91 | 1.18 | 2.06 | 1.12 | 3.15 | 3.09 | 1.33 |
time (sec) |
N/A | 0.000 | 0.139 | 7.066 | 0.322 | 0.093 | 0.158 | 0.216 | 0.185 | 4.000 |
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 | 28 | 27 | 34 | 27 | 32 | 24 | 92 | 41 | 27 |
N.S. |
1 | 1.00 | 0.96 | 1.21 | 0.96 | 1.14 | 0.86 | 3.29 | 1.46 | 0.96 |
time (sec) |
N/A | 0.273 | 0.160 | 0.144 | 0.099 | 0.075 | 0.149 | 0.138 | 0.175 | 3.572 |
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 | 23 | 23 | 22 | 23 | 19 | 26 | 28 | 26 |
N.S. |
1 | 1.62 | 0.96 | 0.96 | 0.92 | 0.96 | 0.79 | 1.08 | 1.17 | 1.08 |
time (sec) |
N/A | 0.429 | 0.058 | 1.418 | 0.100 | 0.098 | 0.114 | 0.126 | 0.170 | 0.355 |
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 | 30 | 92 | 29 | 28 | 40 | 30 | 20 | 28 | 29 | 30 |
N.S. |
1 | 3.07 | 0.97 | 0.93 | 1.33 | 1.00 | 0.67 | 0.93 | 0.97 | 1.00 |
time (sec) |
N/A | 0.900 | 0.046 | 0.704 | 0.079 | 0.074 | 0.095 | 0.127 | 0.166 | 3.598 |
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 | 18 | 12 | 10 | 9 | 9 | 8 | 11 | 10 | 9 |
N.S. |
1 | 0.95 | 0.63 | 0.53 | 0.47 | 0.47 | 0.42 | 0.58 | 0.53 | 0.47 |
time (sec) |
N/A | 0.167 | 0.005 | 0.066 | 0.032 | 0.080 | 0.042 | 0.118 | 0.172 | 0.043 |
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 | 21 | 27 | 30 | 20 | 19 | 24 | 22 | 0 | 25 | 20 |
N.S. |
1 | 1.29 | 1.43 | 0.95 | 0.90 | 1.14 | 1.05 | 0.00 | 1.19 | 0.95 |
time (sec) |
N/A | 0.472 | 0.226 | 235.725 | 26.082 | 0.086 | 0.109 | 0.000 | 4.584 | 3.617 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | F | A | F(-1) | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 23 | 54 | 0 | 18 | 0 | 18 | 22 | 18 |
N.S. |
1 | 0.00 | 1.00 | 2.35 | 0.00 | 0.78 | 0.00 | 0.78 | 0.96 | 0.78 |
time (sec) |
N/A | 0.000 | 0.219 | 10.459 | 0.000 | 0.085 | 0.000 | 0.133 | 0.177 | 4.360 |
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 | 19 | 0 | 21 | 18 | 36 | 29 | 29 | 36 | 45 | 41 |
N.S. |
1 | 0.00 | 1.11 | 0.95 | 1.89 | 1.53 | 1.53 | 1.89 | 2.37 | 2.16 |
time (sec) |
N/A | 0.000 | 1.083 | 0.136 | 0.174 | 0.081 | 0.133 | 0.135 | 0.202 | 3.585 |
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 | 25 | 33 | 21 | 32 | 0 | 21 | 29 | 29 | 27 | 25 |
N.S. |
1 | 1.32 | 0.84 | 1.28 | 0.00 | 0.84 | 1.16 | 1.16 | 1.08 | 1.00 |
time (sec) |
N/A | 1.319 | 0.147 | 2.678 | 0.000 | 0.077 | 0.154 | 0.134 | 0.175 | 3.656 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | A | B | B | F(-2) | A | B | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 0 | 70 | 47 | 67 | 67 | 0 | 58 | 56 | 0 |
N.S. |
1 | 0.00 | 2.06 | 1.38 | 1.97 | 1.97 | 0.00 | 1.71 | 1.65 | 0.00 |
time (sec) |
N/A | 0.000 | 19.493 | 1.118 | 0.101 | 0.101 | 0.000 | 0.156 | 0.179 | 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 | 53 | 25 | 20 | 20 | 20 | 22 | 0 | 25 | 21 |
N.S. |
1 | 2.30 | 1.09 | 0.87 | 0.87 | 0.87 | 0.96 | 0.00 | 1.09 | 0.91 |
time (sec) |
N/A | 0.244 | 0.022 | 0.124 | 0.129 | 0.080 | 0.091 | 0.000 | 0.166 | 3.574 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | B | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 20 | 20 | 40 | 63 | 46 | 46 | 315 | 39 | 0 |
N.S. |
1 | 0.87 | 0.87 | 1.74 | 2.74 | 2.00 | 2.00 | 13.70 | 1.70 | 0.00 |
time (sec) |
N/A | 0.621 | 0.251 | 49.716 | 0.122 | 0.081 | 0.204 | 1.346 | 0.194 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | F | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 22 | 34 | 39 | 35 | 36 | 35 | 234 | 37 |
N.S. |
1 | 0.00 | 0.73 | 1.13 | 1.30 | 1.17 | 1.20 | 1.17 | 7.80 | 1.23 |
time (sec) |
N/A | 0.000 | 0.422 | 1.366 | 0.107 | 0.083 | 0.154 | 0.121 | 0.171 | 3.680 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | B | B | B | B | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 10 | 22 | 10 | 20 | 19 | 19 | 17 | 19 | 17 | 9 |
N.S. |
1 | 2.20 | 1.00 | 2.00 | 1.90 | 1.90 | 1.70 | 1.90 | 1.70 | 0.90 |
time (sec) |
N/A | 0.187 | 0.022 | 0.079 | 0.030 | 0.068 | 0.052 | 0.122 | 0.172 | 0.046 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | A | F | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 42 | 34 | 33 | 159 | 96 | 39 | 0 | 116 | 31 |
N.S. |
1 | 1.40 | 1.13 | 1.10 | 5.30 | 3.20 | 1.30 | 0.00 | 3.87 | 1.03 |
time (sec) |
N/A | 10.843 | 0.104 | 35.184 | 0.356 | 0.085 | 0.262 | 0.000 | 0.163 | 3.743 |
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 | 15 | 15 | 11 | 10 | 10 | 12 | 10 | 13 | 10 |
N.S. |
1 | 0.58 | 0.58 | 0.42 | 0.38 | 0.38 | 0.46 | 0.38 | 0.50 | 0.38 |
time (sec) |
N/A | 0.149 | 0.021 | 0.025 | 0.030 | 0.068 | 0.048 | 0.119 | 0.165 | 3.492 |
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 | 32 | 87 | 36 | 35 | 130 | 30 | 39 | 68 | 77 | 76 |
N.S. |
1 | 2.72 | 1.12 | 1.09 | 4.06 | 0.94 | 1.22 | 2.12 | 2.41 | 2.38 |
time (sec) |
N/A | 0.968 | 0.531 | 0.677 | 0.124 | 0.087 | 0.106 | 0.122 | 0.167 | 0.192 |
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 | 14 | 26 | 24 | 21 | 16 | 20 | 22 | 16 | 16 | 20 |
N.S. |
1 | 1.86 | 1.71 | 1.50 | 1.14 | 1.43 | 1.57 | 1.14 | 1.14 | 1.43 |
time (sec) |
N/A | 0.192 | 0.005 | 0.147 | 0.038 | 0.091 | 0.072 | 0.124 | 0.165 | 3.556 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | B | A | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 33 | 28 | 28 | 37 | 67 | 27 | 80 | 39 | 33 |
N.S. |
1 | 1.14 | 0.97 | 0.97 | 1.28 | 2.31 | 0.93 | 2.76 | 1.34 | 1.14 |
time (sec) |
N/A | 0.697 | 0.160 | 0.182 | 0.061 | 0.086 | 0.175 | 0.132 | 0.167 | 3.601 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | B | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 33 | 29 | 47 | 56 | 44 | 49 | 54 | 122 |
N.S. |
1 | 0.00 | 1.03 | 0.91 | 1.47 | 1.75 | 1.38 | 1.53 | 1.69 | 3.81 |
time (sec) |
N/A | 0.000 | 5.060 | 0.211 | 0.100 | 0.081 | 0.166 | 0.130 | 0.165 | 4.097 |
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 | 34 | 0 | 30 | 35 | 34 | 41 | 20 | 0 | 102 | 37 |
N.S. |
1 | 0.00 | 0.88 | 1.03 | 1.00 | 1.21 | 0.59 | 0.00 | 3.00 | 1.09 |
time (sec) |
N/A | 0.000 | 1.389 | 3.632 | 0.265 | 0.089 | 1.229 | 0.000 | 0.179 | 3.609 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 15 | 15 | 14 | 15 | 15 | 12 | 15 | 13 | 14 |
N.S. |
1 | 0.79 | 0.79 | 0.74 | 0.79 | 0.79 | 0.63 | 0.79 | 0.68 | 0.74 |
time (sec) |
N/A | 0.156 | 0.000 | 0.028 | 0.030 | 0.084 | 0.019 | 0.123 | 0.176 | 0.028 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | A | A | A | A | A | F | B |
verified | N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 0 | 0 | 17 | 23 | 23 | 22 | 23 | 145 | 26 |
N.S. |
1 | 0.00 | 0.00 | 0.89 | 1.21 | 1.21 | 1.16 | 1.21 | 7.63 | 1.37 |
time (sec) |
N/A | 0.000 | 0.000 | 0.201 | 0.037 | 0.081 | 0.127 | 0.131 | 0.234 | 3.778 |
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 | 25 | 39 | 21 | 22 | 37 | 21 | 73 | 39 | 21 | 37 |
N.S. |
1 | 1.56 | 0.84 | 0.88 | 1.48 | 0.84 | 2.92 | 1.56 | 0.84 | 1.48 |
time (sec) |
N/A | 0.213 | 0.005 | 0.112 | 0.038 | 0.082 | 0.444 | 0.118 | 0.170 | 0.114 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | A | B | A | B | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 51 | 57 | 35 | 40 | 32 | 44 | 48 | 66 | 42 |
N.S. |
1 | 2.43 | 2.71 | 1.67 | 1.90 | 1.52 | 2.10 | 2.29 | 3.14 | 2.00 |
time (sec) |
N/A | 0.190 | 0.047 | 0.136 | 0.038 | 0.075 | 0.071 | 0.119 | 0.166 | 0.074 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F | A | A | A | F | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 24 | 23 | 0 | 22 | 27 | 22 | 190 | 27 |
N.S. |
1 | 0.00 | 1.00 | 0.96 | 0.00 | 0.92 | 1.12 | 0.92 | 7.92 | 1.12 |
time (sec) |
N/A | 0.000 | 1.166 | 0.206 | 0.000 | 0.088 | 0.155 | 0.165 | 1.778 | 3.675 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | A | B | F | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 44 | 47 | 759 | 51 | 146 | 0 | 67 | 54 |
N.S. |
1 | 0.00 | 1.57 | 1.68 | 27.11 | 1.82 | 5.21 | 0.00 | 2.39 | 1.93 |
time (sec) |
N/A | 0.000 | 0.211 | 1.633 | 0.180 | 0.092 | 0.780 | 0.000 | 0.174 | 4.433 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | A | A | B | B | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 44 | 25 | 58 | 33 | 20 | 49 | 57 | 0 |
N.S. |
1 | 0.00 | 1.91 | 1.09 | 2.52 | 1.43 | 0.87 | 2.13 | 2.48 | 0.00 |
time (sec) |
N/A | 0.000 | 0.462 | 0.408 | 0.079 | 0.073 | 0.328 | 0.174 | 0.186 | 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 | 23 | 23 | 24 | 23 | 23 | 24 | 23 | 23 | 23 |
N.S. |
1 | 1.28 | 1.28 | 1.33 | 1.28 | 1.28 | 1.33 | 1.28 | 1.28 | 1.28 |
time (sec) |
N/A | 0.144 | 0.000 | 0.075 | 0.035 | 0.074 | 0.047 | 0.115 | 0.171 | 0.074 |
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 | 21 | 18 | 18 | 17 | 17 | 12 | 17 | 15 | 9 |
N.S. |
1 | 1.11 | 0.95 | 0.95 | 0.89 | 0.89 | 0.63 | 0.89 | 0.79 | 0.47 |
time (sec) |
N/A | 0.186 | 0.023 | 0.085 | 0.028 | 0.070 | 0.045 | 0.122 | 0.176 | 3.701 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 39 | 22 | 30 | 29 | 45 | 31 | 52 | 37 | 30 |
N.S. |
1 | 1.44 | 0.81 | 1.11 | 1.07 | 1.67 | 1.15 | 1.93 | 1.37 | 1.11 |
time (sec) |
N/A | 0.220 | 0.015 | 0.181 | 0.034 | 0.083 | 0.095 | 0.120 | 0.171 | 3.857 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | F | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 27 | 23 | 21 | 22 | 20 | 0 | 0 | 32 | 25 |
N.S. |
1 | 1.17 | 1.00 | 0.91 | 0.96 | 0.87 | 0.00 | 0.00 | 1.39 | 1.09 |
time (sec) |
N/A | 1.106 | 0.192 | 0.561 | 0.167 | 0.088 | 0.000 | 0.000 | 0.171 | 3.854 |
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 | 24 | 21 | 21 | 24 | 21 | 17 | 27 | 24 | 19 |
N.S. |
1 | 1.04 | 0.91 | 0.91 | 1.04 | 0.91 | 0.74 | 1.17 | 1.04 | 0.83 |
time (sec) |
N/A | 0.234 | 0.006 | 0.040 | 0.039 | 0.064 | 0.051 | 0.129 | 0.171 | 0.083 |
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 | 37 | 34 | 30 | 32 | 63 | 33 | 36 | 33 |
N.S. |
1 | 0.00 | 1.42 | 1.31 | 1.15 | 1.23 | 2.42 | 1.27 | 1.38 | 1.27 |
time (sec) |
N/A | 0.000 | 1.027 | 0.822 | 0.097 | 0.092 | 0.199 | 0.141 | 0.175 | 4.102 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | B | C | B | B | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 113 | 101 | 99 | 157 | 99 | 102 | 108 | 115 | 92 |
N.S. |
1 | 4.52 | 4.04 | 3.96 | 6.28 | 3.96 | 4.08 | 4.32 | 4.60 | 3.68 |
time (sec) |
N/A | 0.551 | 0.552 | 4.010 | 0.076 | 0.085 | 0.112 | 0.128 | 0.176 | 3.865 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | B | C | B | B | C | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 191 | 46 | 116 | 228 | 89 | 134 | 238 | 129 | 91 |
N.S. |
1 | 7.35 | 1.77 | 4.46 | 8.77 | 3.42 | 5.15 | 9.15 | 4.96 | 3.50 |
time (sec) |
N/A | 1.294 | 0.096 | 92.511 | 0.203 | 0.092 | 4.057 | 0.193 | 3.818 | 4.931 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | B | A | B | F | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 28 | 24 | 72 | 72 | 34 | 72 | 172 | 23 |
N.S. |
1 | 0.00 | 1.08 | 0.92 | 2.77 | 2.77 | 1.31 | 2.77 | 6.62 | 0.88 |
time (sec) |
N/A | 0.000 | 0.055 | 52.695 | 0.178 | 0.084 | 0.159 | 4.118 | 200.020 | 3.880 |
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 | 32 | 0 | 26 | 33 | 61 | 38 | 36 | 46 | 75 | 0 |
N.S. |
1 | 0.00 | 0.81 | 1.03 | 1.91 | 1.19 | 1.12 | 1.44 | 2.34 | 0.00 |
time (sec) |
N/A | 0.000 | 0.158 | 0.045 | 0.313 | 0.089 | 9.502 | 0.874 | 0.180 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | A | A | A | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 272 | 27 | 29 | 29 | 31 | 27 | 34 | 31 | 0 |
N.S. |
1 | 10.07 | 1.00 | 1.07 | 1.07 | 1.15 | 1.00 | 1.26 | 1.15 | 0.00 |
time (sec) |
N/A | 3.820 | 0.180 | 2.694 | 0.100 | 0.085 | 0.129 | 0.148 | 0.162 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | A | B | B | B | F | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 65 | 30 | 75 | 52 | 56 | 0 | 106 | 85 |
N.S. |
1 | 0.00 | 2.41 | 1.11 | 2.78 | 1.93 | 2.07 | 0.00 | 3.93 | 3.15 |
time (sec) |
N/A | 0.000 | 0.243 | 11.355 | 0.340 | 0.089 | 0.410 | 0.000 | 1.051 | 4.128 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | C | B | B | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 38 | 76 | 49 | 200 | 51 | 51 | 148 | 45 | 106 |
N.S. |
1 | 1.52 | 3.04 | 1.96 | 8.00 | 2.04 | 2.04 | 5.92 | 1.80 | 4.24 |
time (sec) |
N/A | 0.523 | 0.613 | 0.532 | 0.216 | 0.087 | 0.074 | 0.140 | 0.190 | 0.256 |
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 | 25 | 21 | 17 | 16 | 16 | 15 | 16 | 19 | 16 |
N.S. |
1 | 1.14 | 0.95 | 0.77 | 0.73 | 0.73 | 0.68 | 0.73 | 0.86 | 0.73 |
time (sec) |
N/A | 0.176 | 0.020 | 0.092 | 0.032 | 0.079 | 0.123 | 0.118 | 0.181 | 3.636 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 0 | 19 | 18 | 29 | 30 | 17 | 17 | 36 | 32 |
N.S. |
1 | 0.00 | 1.00 | 0.95 | 1.53 | 1.58 | 0.89 | 0.89 | 1.89 | 1.68 |
time (sec) |
N/A | 0.000 | 0.121 | 0.581 | 0.150 | 0.090 | 0.077 | 0.136 | 0.197 | 4.173 |
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 | 20 | 0 | 19 | 16 | 16 | 21 | 17 | 16 | 18 | 21 |
N.S. |
1 | 0.00 | 0.95 | 0.80 | 0.80 | 1.05 | 0.85 | 0.80 | 0.90 | 1.05 |
time (sec) |
N/A | 0.000 | 0.023 | 0.297 | 0.084 | 0.072 | 0.106 | 0.129 | 0.190 | 4.069 |
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 | 22 | 27 | 27 | 17 | 20 | 16 | 17 | 18 | 17 | 16 |
N.S. |
1 | 1.23 | 1.23 | 0.77 | 0.91 | 0.73 | 0.77 | 0.82 | 0.77 | 0.73 |
time (sec) |
N/A | 0.779 | 0.096 | 0.285 | 0.143 | 0.101 | 0.103 | 0.124 | 0.193 | 3.878 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 26 | 25 | 38 | 26 | 42 | 24 | 24 | 0 |
N.S. |
1 | 0.00 | 1.00 | 0.96 | 1.46 | 1.00 | 1.62 | 0.92 | 0.92 | 0.00 |
time (sec) |
N/A | 0.000 | 0.156 | 3.193 | 0.177 | 0.082 | 0.174 | 0.356 | 0.194 | 0.000 |
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 | 27 | 0 | 27 | 22 | 100 | 24 | 24 | 86 | 24 | 23 |
N.S. |
1 | 0.00 | 1.00 | 0.81 | 3.70 | 0.89 | 0.89 | 3.19 | 0.89 | 0.85 |
time (sec) |
N/A | 0.000 | 0.207 | 2.392 | 0.074 | 0.087 | 0.294 | 0.145 | 0.198 | 4.596 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 19 | 16 | 18 | 14 | 12 | 18 | 19 | 14 |
N.S. |
1 | 1.00 | 1.19 | 1.00 | 1.12 | 0.88 | 0.75 | 1.12 | 1.19 | 0.88 |
time (sec) |
N/A | 0.177 | 0.006 | 0.088 | 0.028 | 0.101 | 0.059 | 0.115 | 0.183 | 3.783 |
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 | 18 | 14 | 14 | 17 | 19 | 14 | 17 | 20 | 13 |
N.S. |
1 | 0.78 | 0.61 | 0.61 | 0.74 | 0.83 | 0.61 | 0.74 | 0.87 | 0.57 |
time (sec) |
N/A | 0.162 | 0.002 | 0.054 | 0.033 | 0.071 | 0.046 | 0.119 | 0.187 | 3.824 |
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 | 22 | 44 | 19 | 22 | 0 | 18 | 24 | 22 | 34 | 0 |
N.S. |
1 | 2.00 | 0.86 | 1.00 | 0.00 | 0.82 | 1.09 | 1.00 | 1.55 | 0.00 |
time (sec) |
N/A | 0.305 | 0.206 | 4.135 | 0.000 | 0.096 | 5.024 | 0.121 | 0.180 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 17 | 34 | 18 | 17 | 17 | 17 | 0 | 17 | 17 |
N.S. |
1 | 0.55 | 1.10 | 0.58 | 0.55 | 0.55 | 0.55 | 0.00 | 0.55 | 0.55 |
time (sec) |
N/A | 0.573 | 0.081 | 2.089 | 0.155 | 0.092 | 0.108 | 0.000 | 0.179 | 4.215 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 27 | 27 | 26 | 25 | 25 | 20 | 25 | 25 | 25 |
N.S. |
1 | 0.93 | 0.93 | 0.90 | 0.86 | 0.86 | 0.69 | 0.86 | 0.86 | 0.86 |
time (sec) |
N/A | 0.727 | 0.028 | 0.618 | 0.072 | 0.082 | 0.177 | 0.150 | 0.190 | 3.869 |
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 | 21 | 25 | 21 | 38 | 24 | 36 | 36 | 42 | 43 | 37 |
N.S. |
1 | 1.19 | 1.00 | 1.81 | 1.14 | 1.71 | 1.71 | 2.00 | 2.05 | 1.76 |
time (sec) |
N/A | 0.900 | 0.052 | 5.409 | 0.226 | 0.084 | 0.257 | 1.200 | 0.195 | 3.943 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 34 | 49 | 37 | 26 | 36 | 27 | 26 | 35 | 30 |
N.S. |
1 | 1.42 | 2.04 | 1.54 | 1.08 | 1.50 | 1.12 | 1.08 | 1.46 | 1.25 |
time (sec) |
N/A | 0.284 | 0.023 | 0.272 | 0.029 | 0.080 | 0.153 | 0.114 | 0.191 | 0.181 |
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 | 22 | 21 | 19 | 22 | 23 | 23 | 26 | 23 | 19 | 28 |
N.S. |
1 | 0.95 | 0.86 | 1.00 | 1.05 | 1.05 | 1.18 | 1.05 | 0.86 | 1.27 |
time (sec) |
N/A | 0.210 | 0.008 | 0.140 | 0.037 | 0.067 | 0.536 | 0.126 | 0.184 | 0.103 |
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 | 16 | 13 | 11 | 11 | 11 | 14 | 11 | 16 | 13 |
N.S. |
1 | 1.23 | 1.00 | 0.85 | 0.85 | 0.85 | 1.08 | 0.85 | 1.23 | 1.00 |
time (sec) |
N/A | 0.201 | 0.014 | 0.082 | 0.031 | 0.080 | 0.046 | 0.123 | 0.182 | 3.765 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | F(-1) | B | B | B | F | B | B |
verified | N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 176 | 0 | 917 | 179 | 187 | 0 | 292 | 1097 |
N.S. |
1 | 0.00 | 5.68 | 0.00 | 29.58 | 5.77 | 6.03 | 0.00 | 9.42 | 35.39 |
time (sec) |
N/A | 0.000 | 1.078 | 0.000 | 15.935 | 0.102 | 6.380 | 0.000 | 0.401 | 5.594 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | A | A | A | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 92 | 21 | 19 | 24 | 20 | 19 | 69 | 19 | 21 |
N.S. |
1 | 4.00 | 0.91 | 0.83 | 1.04 | 0.87 | 0.83 | 3.00 | 0.83 | 0.91 |
time (sec) |
N/A | 1.642 | 0.090 | 0.900 | 0.151 | 0.084 | 0.347 | 0.151 | 0.181 | 4.277 |
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 | 27 | 21 | 21 | 18 | 24 | 17 | 22 | 17 | 17 | 17 |
N.S. |
1 | 0.78 | 0.78 | 0.67 | 0.89 | 0.63 | 0.81 | 0.63 | 0.63 | 0.63 |
time (sec) |
N/A | 0.193 | 0.003 | 0.030 | 0.078 | 0.078 | 0.051 | 0.134 | 0.178 | 4.016 |
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 | 32 | 0 | 29 | 36 | 0 | 41 | 26 | 0 | 46 | 29 |
N.S. |
1 | 0.00 | 0.91 | 1.12 | 0.00 | 1.28 | 0.81 | 0.00 | 1.44 | 0.91 |
time (sec) |
N/A | 0.000 | 0.255 | 0.028 | 0.000 | 0.092 | 38.217 | 0.000 | 0.277 | 4.170 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F | A | B | A | F | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 44 | 41 | 0 | 36 | 37 | 38 | 86 | 44 |
N.S. |
1 | 0.00 | 1.83 | 1.71 | 0.00 | 1.50 | 1.54 | 1.58 | 3.58 | 1.83 |
time (sec) |
N/A | 0.000 | 0.074 | 0.300 | 0.000 | 0.079 | 0.209 | 0.263 | 56.778 | 3.977 |
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 | 18 | 0 | 20 | 20 | 50 | 50 | 19 | 56 | 60 | 19 |
N.S. |
1 | 0.00 | 1.11 | 1.11 | 2.78 | 2.78 | 1.06 | 3.11 | 3.33 | 1.06 |
time (sec) |
N/A | 0.000 | 1.786 | 0.805 | 0.039 | 0.091 | 0.083 | 0.124 | 0.195 | 0.158 |
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 | 16 | 12 | 13 | 15 | 20 | 15 | 12 | 16 | 14 |
N.S. |
1 | 0.89 | 0.67 | 0.72 | 0.83 | 1.11 | 0.83 | 0.67 | 0.89 | 0.78 |
time (sec) |
N/A | 0.172 | 0.003 | 0.053 | 0.035 | 0.093 | 0.052 | 0.126 | 0.191 | 3.852 |
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 | 14 | 14 | 13 | 12 | 14 | 13 | 13 |
N.S. |
1 | 1.00 | 1.00 | 1.08 | 1.08 | 1.00 | 0.92 | 1.08 | 1.00 | 1.00 |
time (sec) |
N/A | 0.366 | 0.094 | 0.214 | 0.068 | 0.082 | 0.082 | 0.120 | 0.187 | 3.948 |
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 | 18 | 18 | 19 | 24 | 15 | 20 | 18 | 18 | 18 |
N.S. |
1 | 0.95 | 0.95 | 1.00 | 1.26 | 0.79 | 1.05 | 0.95 | 0.95 | 0.95 |
time (sec) |
N/A | 0.317 | 0.118 | 0.170 | 0.148 | 0.099 | 0.088 | 0.123 | 0.183 | 3.948 |
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 | 35 | 39 | 30 | 42 | 41 | 39 | 35 | 34 | 34 |
N.S. |
1 | 1.21 | 1.34 | 1.03 | 1.45 | 1.41 | 1.34 | 1.21 | 1.17 | 1.17 |
time (sec) |
N/A | 0.418 | 0.052 | 0.273 | 0.064 | 0.095 | 0.054 | 0.125 | 0.183 | 3.835 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 22 | 22 | 22 | 21 | 19 | 21 | 22 | 21 |
N.S. |
1 | 0.00 | 1.00 | 1.00 | 1.00 | 0.95 | 0.86 | 0.95 | 1.00 | 0.95 |
time (sec) |
N/A | 0.000 | 0.385 | 0.299 | 0.168 | 0.105 | 0.128 | 0.144 | 0.361 | 4.247 |
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 | 20 | 0 | 24 | 25 | 27 | 27 | 0 | 24 | 31 | 24 |
N.S. |
1 | 0.00 | 1.20 | 1.25 | 1.35 | 1.35 | 0.00 | 1.20 | 1.55 | 1.20 |
time (sec) |
N/A | 0.000 | 0.592 | 0.812 | 0.060 | 0.108 | 0.000 | 0.265 | 0.192 | 3.914 |
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 | 26 | 24 | 25 | 35 | 24 | 25 | 29 | 26 |
N.S. |
1 | 0.00 | 1.08 | 1.00 | 1.04 | 1.46 | 1.00 | 1.04 | 1.21 | 1.08 |
time (sec) |
N/A | 0.000 | 0.258 | 0.540 | 0.366 | 0.086 | 0.148 | 0.149 | 0.199 | 4.822 |
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 | 25 | 0 | 26 | 25 | 28 | 28 | 22 | 0 | 36 | 27 |
N.S. |
1 | 0.00 | 1.04 | 1.00 | 1.12 | 1.12 | 0.88 | 0.00 | 1.44 | 1.08 |
time (sec) |
N/A | 0.000 | 5.040 | 0.339 | 0.095 | 0.089 | 0.123 | 0.000 | 0.192 | 3.845 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | F | F | A | A | F(-1) | B | B |
verified | N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 25 | 0 | 0 | 35 | 34 | 0 | 45 | 37 |
N.S. |
1 | 0.00 | 0.89 | 0.00 | 0.00 | 1.25 | 1.21 | 0.00 | 1.61 | 1.32 |
time (sec) |
N/A | 0.000 | 0.080 | 0.000 | 0.000 | 0.094 | 2.393 | 0.000 | 0.192 | 5.241 |
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 | 14 | 9 | 9 | 12 | 8 | 7 | 8 | 10 | 8 |
N.S. |
1 | 1.27 | 0.82 | 0.82 | 1.09 | 0.73 | 0.64 | 0.73 | 0.91 | 0.73 |
time (sec) |
N/A | 0.149 | 0.010 | 0.033 | 0.033 | 0.079 | 0.034 | 0.112 | 0.188 | 3.725 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 18 | 18 | 17 | 23 | 16 | 17 | 23 | 28 | 0 |
N.S. |
1 | 0.72 | 0.72 | 0.68 | 0.92 | 0.64 | 0.68 | 0.92 | 1.12 | 0.00 |
time (sec) |
N/A | 0.474 | 0.021 | 10.698 | 0.139 | 0.084 | 0.135 | 0.278 | 0.205 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 18 | 18 | 15 | 0 | 14 | 10 | 37 | 16 | 14 |
N.S. |
1 | 0.62 | 0.62 | 0.52 | 0.00 | 0.48 | 0.34 | 1.28 | 0.55 | 0.48 |
time (sec) |
N/A | 0.172 | 0.052 | 0.083 | 0.000 | 0.074 | 0.075 | 0.118 | 0.230 | 0.057 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | F | F(-2) | B | F(-1) | F | B | F(-1) |
verified | N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 0 | 20 | 0 | 0 | 42 | 0 | 0 | 22 | 0 |
N.S. |
1 | 0.00 | 1.00 | 0.00 | 0.00 | 2.10 | 0.00 | 0.00 | 1.10 | 0.00 |
time (sec) |
N/A | 0.000 | 0.033 | 0.000 | 0.000 | 0.084 | 0.000 | 0.000 | 0.196 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 24 | 24 | 21 | 22 | 27 | 22 | 25 | 51 | 23 |
N.S. |
1 | 1.09 | 1.09 | 0.95 | 1.00 | 1.23 | 1.00 | 1.14 | 2.32 | 1.05 |
time (sec) |
N/A | 0.239 | 0.227 | 0.159 | 0.122 | 0.077 | 0.113 | 0.117 | 200.011 | 3.597 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 27 | 23 | 20 | 19 | 28 | 20 | 28 | 30 | 19 |
N.S. |
1 | 1.12 | 0.96 | 0.83 | 0.79 | 1.17 | 0.83 | 1.17 | 1.25 | 0.79 |
time (sec) |
N/A | 0.217 | 0.013 | 0.317 | 0.040 | 0.085 | 0.092 | 0.113 | 0.162 | 3.587 |
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 | 17 | 15 | 21 | 16 | 15 | 16 | 25 | 16 |
N.S. |
1 | 0.00 | 1.00 | 0.88 | 1.24 | 0.94 | 0.88 | 0.94 | 1.47 | 0.94 |
time (sec) |
N/A | 0.000 | 0.233 | 0.826 | 0.089 | 0.091 | 3.371 | 0.169 | 0.174 | 3.914 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | B | A | F(-2) | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 26 | 66 | 61 | 34 | 0 | 51 | 37 | 63 |
N.S. |
1 | 0.00 | 0.93 | 2.36 | 2.18 | 1.21 | 0.00 | 1.82 | 1.32 | 2.25 |
time (sec) |
N/A | 0.000 | 0.091 | 129.413 | 0.196 | 0.104 | 0.000 | 0.254 | 0.179 | 4.132 |
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 | 33 | 30 | 32 | 45 | 32 | 0 | 35 | 50 |
N.S. |
1 | 0.00 | 1.27 | 1.15 | 1.23 | 1.73 | 1.23 | 0.00 | 1.35 | 1.92 |
time (sec) |
N/A | 0.000 | 2.413 | 0.493 | 0.120 | 0.087 | 0.116 | 0.000 | 0.169 | 4.144 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | B | A | B | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 27 | 25 | 44 | 44 | 80 | 45 | 47 | 0 |
N.S. |
1 | 0.00 | 0.84 | 0.78 | 1.38 | 1.38 | 2.50 | 1.41 | 1.47 | 0.00 |
time (sec) |
N/A | 0.000 | 0.263 | 2.294 | 0.078 | 0.079 | 0.184 | 0.127 | 0.172 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | A | B | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 21 | 39 | 20 | 23 | 23 | 76 | 62 | 23 | 55 |
N.S. |
1 | 1.11 | 2.05 | 1.05 | 1.21 | 1.21 | 4.00 | 3.26 | 1.21 | 2.89 |
time (sec) |
N/A | 0.248 | 0.091 | 0.122 | 0.036 | 0.082 | 0.163 | 0.114 | 0.166 | 0.159 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 21 | 21 | 20 | 31 | 20 | 23 | 39 | 20 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.95 | 1.48 | 0.95 | 1.10 | 1.86 | 0.95 |
time (sec) |
N/A | 0.261 | 0.018 | 0.117 | 0.035 | 0.097 | 0.098 | 0.113 | 0.171 | 0.116 |
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 | 32 | 0 | 38 | 36 | 45 | 33 | 36 | 0 | 1543 | 52 |
N.S. |
1 | 0.00 | 1.19 | 1.12 | 1.41 | 1.03 | 1.12 | 0.00 | 48.22 | 1.62 |
time (sec) |
N/A | 0.000 | 0.257 | 4.388 | 0.989 | 0.084 | 8.151 | 0.000 | 3.715 | 3.880 |
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 | 32 | 32 | 35 | 32 | 56 | 32 | 27 | 140 | 36 | 32 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 1.75 | 1.00 | 0.84 | 4.38 | 1.12 | 1.00 |
time (sec) |
N/A | 0.454 | 0.050 | 0.345 | 0.080 | 0.096 | 0.175 | 0.128 | 0.160 | 3.578 |
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 | 25 | 0 | 35 | 23 | 35 | 28 | 22 | 63 | 57 | 23 |
N.S. |
1 | 0.00 | 1.40 | 0.92 | 1.40 | 1.12 | 0.88 | 2.52 | 2.28 | 0.92 |
time (sec) |
N/A | 0.000 | 0.630 | 0.208 | 0.153 | 0.085 | 0.078 | 0.140 | 0.165 | 3.787 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | F(-1) | F | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 38 | 24 | 31 | 24 | 29 | 0 | 98 | 22 |
N.S. |
1 | 0.00 | 1.73 | 1.09 | 1.41 | 1.09 | 1.32 | 0.00 | 4.45 | 1.00 |
time (sec) |
N/A | 0.000 | 1.226 | 0.192 | 0.151 | 0.089 | 0.103 | 0.000 | 0.167 | 3.518 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | A | A | F | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 169 | 33 | 31 | 31 | 35 | 36 | 0 | 114 | 29 |
N.S. |
1 | 5.45 | 1.06 | 1.00 | 1.00 | 1.13 | 1.16 | 0.00 | 3.68 | 0.94 |
time (sec) |
N/A | 1.195 | 0.115 | 10.298 | 0.116 | 0.112 | 0.395 | 0.000 | 200.142 | 3.763 |
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 | 34 | 16 | 15 | 17 | 17 | 15 | 18 | 16 |
N.S. |
1 | 1.05 | 1.55 | 0.73 | 0.68 | 0.77 | 0.77 | 0.68 | 0.82 | 0.73 |
time (sec) |
N/A | 0.136 | 0.000 | 0.023 | 0.026 | 0.075 | 0.016 | 0.112 | 0.186 | 0.002 |
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 | 33 | 33 | 32 | 29 | 32 | 27 | 34 | 33 | 32 |
N.S. |
1 | 1.22 | 1.22 | 1.19 | 1.07 | 1.19 | 1.00 | 1.26 | 1.22 | 1.19 |
time (sec) |
N/A | 0.722 | 0.017 | 0.127 | 0.034 | 0.083 | 2.571 | 0.125 | 0.206 | 3.880 |
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 | 17 | 17 | 16 | 14 | 28 | 13 | 14 | 13 | 15 | 13 |
N.S. |
1 | 1.00 | 0.94 | 0.82 | 1.65 | 0.76 | 0.82 | 0.76 | 0.88 | 0.76 |
time (sec) |
N/A | 0.156 | 0.005 | 0.147 | 0.111 | 0.092 | 0.049 | 0.115 | 0.185 | 4.149 |
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 | 17 | 13 | 11 | 10 | 10 | 10 | 10 | 11 | 10 |
N.S. |
1 | 0.94 | 0.72 | 0.61 | 0.56 | 0.56 | 0.56 | 0.56 | 0.61 | 0.56 |
time (sec) |
N/A | 0.164 | 0.006 | 0.065 | 0.034 | 0.084 | 0.054 | 0.119 | 0.204 | 3.456 |
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 | 7 | 7 | 8 | 7 | 7 | 5 | 7 | 7 | 7 |
N.S. |
1 | 0.39 | 0.39 | 0.44 | 0.39 | 0.39 | 0.28 | 0.39 | 0.39 | 0.39 |
time (sec) |
N/A | 0.135 | 0.000 | 0.016 | 0.040 | 0.071 | 0.017 | 0.118 | 0.172 | 0.023 |
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 | 34 | 29 | 26 | 27 | 35 | 16 | 22 | 41 | 38 | 15 |
N.S. |
1 | 0.85 | 0.76 | 0.79 | 1.03 | 0.47 | 0.65 | 1.21 | 1.12 | 0.44 |
time (sec) |
N/A | 0.329 | 0.023 | 0.200 | 0.165 | 0.092 | 0.088 | 0.132 | 0.185 | 3.616 |
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 | 15 | 19 | 15 | 13 | 24 | 11 | 12 | 15 | 13 | 13 |
N.S. |
1 | 1.27 | 1.00 | 0.87 | 1.60 | 0.73 | 0.80 | 1.00 | 0.87 | 0.87 |
time (sec) |
N/A | 0.309 | 0.019 | 0.108 | 0.079 | 0.078 | 0.065 | 0.126 | 0.188 | 0.097 |
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 | 28 | 0 | 28 | 21 | 36 | 26 | 97 | 57 | 32 | 22 |
N.S. |
1 | 0.00 | 1.00 | 0.75 | 1.29 | 0.93 | 3.46 | 2.04 | 1.14 | 0.79 |
time (sec) |
N/A | 0.000 | 1.884 | 0.428 | 0.099 | 0.090 | 0.147 | 0.125 | 0.188 | 3.564 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | F | F | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 0 | 40 | 53 | 38 | 53 | 51 | 0 | 0 | 0 |
N.S. |
1 | 0.00 | 1.14 | 1.51 | 1.09 | 1.51 | 1.46 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 0.048 | 91.431 | 0.603 | 0.097 | 3.528 | 0.000 | 0.288 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | B | B | B | B | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 514 | 28 | 142 | 357 | 125 | 631 | 140 | 153 | 210 |
N.S. |
1 | 19.04 | 1.04 | 5.26 | 13.22 | 4.63 | 23.37 | 5.19 | 5.67 | 7.78 |
time (sec) |
N/A | 3.738 | 12.536 | 7.098 | 0.093 | 0.082 | 0.274 | 0.132 | 0.195 | 0.458 |
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 | 24 | 27 | 27 | 25 | 0 | 24 | 24 | 30 | 22 | 24 |
N.S. |
1 | 1.12 | 1.12 | 1.04 | 0.00 | 1.00 | 1.00 | 1.25 | 0.92 | 1.00 |
time (sec) |
N/A | 0.384 | 0.063 | 0.184 | 0.000 | 0.092 | 0.202 | 0.136 | 0.207 | 3.567 |