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 | A | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 29 | 37 | 29 | 39 | 27 | 43 | 41 | 38 |
N.S. |
1 | 0.00 | 1.00 | 1.28 | 1.00 | 1.34 | 0.93 | 1.48 | 1.41 | 1.31 |
time (sec) |
N/A | 0.000 | 0.167 | 4.082 | 0.075 | 0.089 | 0.085 | 0.177 | 0.193 | 3.517 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | F | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 31 | 27 | 30 | 27 | 27 | 27 | 1017 | 0 |
N.S. |
1 | 0.00 | 1.00 | 0.87 | 0.97 | 0.87 | 0.87 | 0.87 | 32.81 | 0.00 |
time (sec) |
N/A | 0.000 | 0.163 | 1.036 | 0.211 | 0.119 | 0.213 | 0.514 | 0.332 | 0.000 |
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 | 20 | 38 | 19 | 25 | 49 | 23 | 26 | 33 | 25 | 78 |
N.S. |
1 | 1.90 | 0.95 | 1.25 | 2.45 | 1.15 | 1.30 | 1.65 | 1.25 | 3.90 |
time (sec) |
N/A | 0.263 | 0.041 | 0.425 | 0.032 | 0.125 | 0.086 | 0.117 | 0.200 | 9.391 |
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 | 16 | 14 | 13 | 13 | 12 | 13 | 14 | 13 |
N.S. |
1 | 0.78 | 0.70 | 0.61 | 0.57 | 0.57 | 0.52 | 0.57 | 0.61 | 0.57 |
time (sec) |
N/A | 0.152 | 0.002 | 0.064 | 0.036 | 0.092 | 0.043 | 0.120 | 0.221 | 0.043 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 13 | 5 | 7 | 6 | 7 | 7 | 5 | 7 | 5 | 5 |
N.S. |
1 | 0.38 | 0.54 | 0.46 | 0.54 | 0.54 | 0.38 | 0.54 | 0.38 | 0.38 |
time (sec) |
N/A | 0.130 | 0.000 | 0.021 | 0.030 | 0.076 | 0.017 | 0.119 | 0.195 | 0.026 |
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 | 41 | 39 | 56 | 30 | 37 | 80 | 89 | 41 |
N.S. |
1 | 0.00 | 1.78 | 1.70 | 2.43 | 1.30 | 1.61 | 3.48 | 3.87 | 1.78 |
time (sec) |
N/A | 0.000 | 2.205 | 0.444 | 0.159 | 0.088 | 0.151 | 0.147 | 0.197 | 0.204 |
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 | 16 | 16 | 17 | 15 | 17 | 19 | 16 | 13 |
N.S. |
1 | 0.00 | 0.76 | 0.76 | 0.81 | 0.71 | 0.81 | 0.90 | 0.76 | 0.62 |
time (sec) |
N/A | 0.000 | 0.081 | 0.163 | 0.144 | 0.085 | 0.113 | 0.122 | 0.205 | 3.536 |
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 | 30 | 140 | 50 | 72 | 80 | 68 | 88 | 63 | 129 | 63 |
N.S. |
1 | 4.67 | 1.67 | 2.40 | 2.67 | 2.27 | 2.93 | 2.10 | 4.30 | 2.10 |
time (sec) |
N/A | 0.947 | 0.034 | 1.240 | 0.044 | 0.122 | 1.301 | 0.152 | 0.214 | 3.769 |
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 | 28 | 0 | 33 | 41 | 55 | 55 | 0 | 39 | 63 | 37 |
N.S. |
1 | 0.00 | 1.18 | 1.46 | 1.96 | 1.96 | 0.00 | 1.39 | 2.25 | 1.32 |
time (sec) |
N/A | 0.000 | 0.067 | 13.343 | 0.155 | 0.110 | 0.000 | 0.155 | 0.202 | 3.843 |
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 | 20 | 20 | 22 | 16 | 21 | 19 | 21 | 21 | 21 |
N.S. |
1 | 0.95 | 0.95 | 1.05 | 0.76 | 1.00 | 0.90 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.394 | 0.181 | 0.234 | 0.067 | 0.093 | 0.062 | 0.132 | 0.190 | 3.531 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | B | A | B | B | B | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 47 | 89 | 63 | 60 | 66 | 67 | 63 | 0 |
N.S. |
1 | 0.00 | 1.47 | 2.78 | 1.97 | 1.88 | 2.06 | 2.09 | 1.97 | 0.00 |
time (sec) |
N/A | 0.000 | 0.074 | 0.237 | 0.119 | 0.121 | 0.177 | 4.595 | 0.207 | 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 | 20 | 24 | 24 | 19 | 18 | 20 | 19 | 18 | 20 | 18 |
N.S. |
1 | 1.20 | 1.20 | 0.95 | 0.90 | 1.00 | 0.95 | 0.90 | 1.00 | 0.90 |
time (sec) |
N/A | 0.857 | 0.319 | 0.371 | 0.071 | 0.090 | 0.144 | 0.133 | 0.203 | 0.211 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 53 | 33 | 27 | 51 | 47 | 29 | 47 | 29 | 26 |
N.S. |
1 | 1.66 | 1.03 | 0.84 | 1.59 | 1.47 | 0.91 | 1.47 | 0.91 | 0.81 |
time (sec) |
N/A | 0.531 | 0.040 | 0.405 | 0.035 | 0.120 | 0.102 | 0.121 | 0.223 | 0.106 |
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 | 26 | 0 | 26 | 299 | 47 | 36 | 20 | 38 | 24 | 26 |
N.S. |
1 | 0.00 | 1.00 | 11.50 | 1.81 | 1.38 | 0.77 | 1.46 | 0.92 | 1.00 |
time (sec) |
N/A | 0.000 | 0.117 | 0.016 | 0.168 | 0.099 | 1.028 | 0.213 | 0.236 | 4.189 |
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 | 10 | 10 | 8 | 7 | 7 | 8 | 7 | 8 | 7 |
N.S. |
1 | 1.00 | 1.00 | 0.80 | 0.70 | 0.70 | 0.80 | 0.70 | 0.80 | 0.70 |
time (sec) |
N/A | 0.141 | 0.000 | 0.053 | 0.032 | 0.079 | 0.020 | 0.123 | 0.182 | 0.043 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 49 | 21 | 23 | 28 | 27 | 29 | 30 | 83 | 20 |
N.S. |
1 | 2.13 | 0.91 | 1.00 | 1.22 | 1.17 | 1.26 | 1.30 | 3.61 | 0.87 |
time (sec) |
N/A | 0.336 | 0.020 | 0.492 | 0.036 | 0.084 | 0.652 | 0.122 | 0.187 | 4.279 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | C | B | A | A | F | F | B |
verified | N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 29 | 75 | 116 | 32 | 29 | 0 | 905 | 56 |
N.S. |
1 | 0.00 | 1.04 | 2.68 | 4.14 | 1.14 | 1.04 | 0.00 | 32.32 | 2.00 |
time (sec) |
N/A | 0.000 | 0.177 | 0.158 | 0.109 | 0.105 | 0.582 | 0.000 | 0.297 | 3.827 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | A | A | B | F | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 26 | 27 | 49 | 29 | 24 | 230 | 921 | 0 |
N.S. |
1 | 0.00 | 1.13 | 1.17 | 2.13 | 1.26 | 1.04 | 10.00 | 40.04 | 0.00 |
time (sec) |
N/A | 0.000 | 0.035 | 5.190 | 0.094 | 0.108 | 0.148 | 0.219 | 0.214 | 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 | 7 | 11 | 7 | 7 | 6 | 6 | 7 | 7 | 7 | 6 |
N.S. |
1 | 1.57 | 1.00 | 1.00 | 0.86 | 0.86 | 1.00 | 1.00 | 1.00 | 0.86 |
time (sec) |
N/A | 0.190 | 0.001 | 0.094 | 0.026 | 0.100 | 0.025 | 0.120 | 0.187 | 0.028 |
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 | 21 | 18 | 23 | 23 | 19 | 17 | 18 | 17 |
N.S. |
1 | 0.00 | 1.31 | 1.12 | 1.44 | 1.44 | 1.19 | 1.06 | 1.12 | 1.06 |
time (sec) |
N/A | 0.000 | 0.323 | 0.053 | 0.077 | 0.083 | 0.126 | 0.121 | 0.201 | 0.111 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | B | A | A | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 0 | 32 | 112 | 57 | 44 | 26 | 218 | 54 | 296 |
N.S. |
1 | 0.00 | 0.97 | 3.39 | 1.73 | 1.33 | 0.79 | 6.61 | 1.64 | 8.97 |
time (sec) |
N/A | 0.000 | 0.081 | 1.391 | 0.177 | 0.108 | 0.131 | 0.583 | 0.193 | 3.925 |
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 | 27 | 26 | 17 | 15 | 22 | 14 | 17 | 20 | 16 |
N.S. |
1 | 1.42 | 1.37 | 0.89 | 0.79 | 1.16 | 0.74 | 0.89 | 1.05 | 0.84 |
time (sec) |
N/A | 0.455 | 0.084 | 0.451 | 0.054 | 0.096 | 0.042 | 0.133 | 0.191 | 3.273 |
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 | 27 | 50 | 28 | 17 | 0 | 31 | 29 | 31 | 31 | 17 |
N.S. |
1 | 1.85 | 1.04 | 0.63 | 0.00 | 1.15 | 1.07 | 1.15 | 1.15 | 0.63 |
time (sec) |
N/A | 0.505 | 0.237 | 0.333 | 0.000 | 0.094 | 0.086 | 0.123 | 0.216 | 0.105 |
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 | 12 | 12 | 10 | 12 | 15 | 23 | 14 | 15 | 15 | 11 |
N.S. |
1 | 1.00 | 0.83 | 1.00 | 1.25 | 1.92 | 1.17 | 1.25 | 1.25 | 0.92 |
time (sec) |
N/A | 0.146 | 0.001 | 0.067 | 0.036 | 0.080 | 0.027 | 0.126 | 0.208 | 0.054 |
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 | 36 | 14 | 14 | 13 | 13 | 12 | 13 | 14 | 13 |
N.S. |
1 | 1.64 | 0.64 | 0.64 | 0.59 | 0.59 | 0.55 | 0.59 | 0.64 | 0.59 |
time (sec) |
N/A | 0.231 | 0.019 | 0.085 | 0.098 | 0.094 | 0.106 | 0.120 | 0.195 | 3.362 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 17 | 17 | 15 | 14 | 14 | 14 | 14 | 15 | 14 |
N.S. |
1 | 0.68 | 0.68 | 0.60 | 0.56 | 0.56 | 0.56 | 0.56 | 0.60 | 0.56 |
time (sec) |
N/A | 0.916 | 0.108 | 26.407 | 0.200 | 0.106 | 0.338 | 0.124 | 0.220 | 3.556 |
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 | 22 | 105 | 33 | 19 | 28 | 18 | 19 | 28 | 23 | 20 |
N.S. |
1 | 4.77 | 1.50 | 0.86 | 1.27 | 0.82 | 0.86 | 1.27 | 1.05 | 0.91 |
time (sec) |
N/A | 1.294 | 0.288 | 2.930 | 0.192 | 0.101 | 1.425 | 0.129 | 0.231 | 3.532 |
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 | 20 | 20 | 19 | 18 | 18 | 17 | 18 | 20 | 18 |
N.S. |
1 | 0.91 | 0.91 | 0.86 | 0.82 | 0.82 | 0.77 | 0.82 | 0.91 | 0.82 |
time (sec) |
N/A | 0.803 | 0.395 | 0.224 | 0.073 | 0.088 | 0.169 | 0.127 | 0.213 | 0.434 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 13 | 22 | 14 | 13 | 29 | 15 | 20 | 31 | 14 | 12 |
N.S. |
1 | 1.69 | 1.08 | 1.00 | 2.23 | 1.15 | 1.54 | 2.38 | 1.08 | 0.92 |
time (sec) |
N/A | 0.299 | 0.043 | 0.678 | 0.036 | 0.101 | 0.105 | 0.119 | 0.201 | 3.372 |
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 | 16 | 26 | 26 | 17 | 44 | 19 | 15 | 26 | 16 | 16 |
N.S. |
1 | 1.62 | 1.62 | 1.06 | 2.75 | 1.19 | 0.94 | 1.62 | 1.00 | 1.00 |
time (sec) |
N/A | 0.610 | 0.098 | 0.095 | 0.080 | 0.085 | 0.040 | 0.123 | 0.204 | 3.396 |
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 | 26 | 23 | 23 | 40 | 30 | 29 | 31 | 30 | 39 | 0 |
N.S. |
1 | 0.88 | 0.88 | 1.54 | 1.15 | 1.12 | 1.19 | 1.15 | 1.50 | 0.00 |
time (sec) |
N/A | 1.626 | 0.223 | 0.497 | 0.162 | 0.110 | 0.259 | 0.148 | 0.213 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | B | B | B | B | F | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 185 | 30 | 73 | 61 | 71 | 71 | 0 | 149 | 72 |
N.S. |
1 | 7.40 | 1.20 | 2.92 | 2.44 | 2.84 | 2.84 | 0.00 | 5.96 | 2.88 |
time (sec) |
N/A | 40.545 | 0.097 | 2.032 | 0.374 | 0.110 | 1.635 | 0.000 | 200.034 | 3.606 |
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 | 27 | 0 | 48 | 47 | 46 | 40 | 0 | 48 | 56 | 250 |
N.S. |
1 | 0.00 | 1.78 | 1.74 | 1.70 | 1.48 | 0.00 | 1.78 | 2.07 | 9.26 |
time (sec) |
N/A | 0.000 | 0.073 | 1.058 | 0.087 | 0.096 | 0.000 | 0.309 | 0.215 | 8.155 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F(-2) | A | F(-2) | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 0 | 35 | 38 | 0 | 29 | 0 | 59 | 41 | 56 |
N.S. |
1 | 0.00 | 1.06 | 1.15 | 0.00 | 0.88 | 0.00 | 1.79 | 1.24 | 1.70 |
time (sec) |
N/A | 0.000 | 0.292 | 0.099 | 0.000 | 0.091 | 0.000 | 0.175 | 0.189 | 3.891 |
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 | 23 | 23 | 27 | 22 | 21 | 17 | 21 | 23 | 21 |
N.S. |
1 | 0.82 | 0.82 | 0.96 | 0.79 | 0.75 | 0.61 | 0.75 | 0.82 | 0.75 |
time (sec) |
N/A | 0.237 | 0.002 | 0.339 | 0.035 | 0.086 | 0.066 | 0.118 | 0.178 | 3.397 |
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 | 14 | 27 | 19 | 26 | 26 | 20 | 26 | 18 | 21 |
N.S. |
1 | 0.50 | 0.96 | 0.68 | 0.93 | 0.93 | 0.71 | 0.93 | 0.64 | 0.75 |
time (sec) |
N/A | 0.221 | 0.000 | 0.063 | 0.032 | 0.088 | 0.021 | 0.123 | 0.207 | 0.029 |
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 | 25 | 0 | 34 | 33 | 56 | 30 | 37 | 53 | 30 | 32 |
N.S. |
1 | 0.00 | 1.36 | 1.32 | 2.24 | 1.20 | 1.48 | 2.12 | 1.20 | 1.28 |
time (sec) |
N/A | 0.000 | 5.050 | 4.730 | 0.165 | 0.095 | 0.158 | 0.237 | 0.189 | 4.065 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | B | B | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 0 | 51 | 46 | 49 | 60 | 46 | 53 | 73 | 50 |
N.S. |
1 | 0.00 | 1.55 | 1.39 | 1.48 | 1.82 | 1.39 | 1.61 | 2.21 | 1.52 |
time (sec) |
N/A | 0.000 | 0.128 | 3.312 | 0.444 | 0.108 | 0.476 | 0.379 | 0.188 | 4.026 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 19 | 15 | 18 | 17 | 14 | 18 | 19 | 18 |
N.S. |
1 | 0.00 | 0.83 | 0.65 | 0.78 | 0.74 | 0.61 | 0.78 | 0.83 | 0.78 |
time (sec) |
N/A | 0.000 | 0.227 | 0.054 | 0.076 | 0.085 | 0.099 | 0.130 | 0.177 | 3.427 |
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 | 21 | 86 | 21 | 27 | 76 | 27 | 27 | 62 | 21 | 20 |
N.S. |
1 | 4.10 | 1.00 | 1.29 | 3.62 | 1.29 | 1.29 | 2.95 | 1.00 | 0.95 |
time (sec) |
N/A | 0.316 | 0.034 | 0.474 | 0.035 | 0.114 | 0.080 | 0.128 | 0.171 | 3.300 |
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 | 21 | 21 | 20 | 24 | 24 | 22 | 24 | 27 | 25 |
N.S. |
1 | 0.88 | 0.88 | 0.83 | 1.00 | 1.00 | 0.92 | 1.00 | 1.12 | 1.04 |
time (sec) |
N/A | 0.574 | 1.164 | 0.140 | 0.077 | 0.102 | 0.067 | 0.145 | 0.248 | 3.565 |
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 | 11 | 11 | 12 | 11 | 11 | 10 | 11 | 10 | 10 |
N.S. |
1 | 0.65 | 0.65 | 0.71 | 0.65 | 0.65 | 0.59 | 0.65 | 0.59 | 0.59 |
time (sec) |
N/A | 0.146 | 0.002 | 0.074 | 0.026 | 0.084 | 0.043 | 0.125 | 0.184 | 3.403 |
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 | 7 | 7 | 8 | 7 | 7 | 5 | 7 | 7 | 7 |
N.S. |
1 | 0.58 | 0.58 | 0.67 | 0.58 | 0.58 | 0.42 | 0.58 | 0.58 | 0.58 |
time (sec) |
N/A | 0.140 | 0.000 | 0.032 | 0.025 | 0.087 | 0.022 | 0.123 | 0.180 | 3.334 |
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 | 81 | 64 | 73 | 78 | 54 | 65 | 71 | 78 | 65 |
N.S. |
1 | 2.70 | 2.13 | 2.43 | 2.60 | 1.80 | 2.17 | 2.37 | 2.60 | 2.17 |
time (sec) |
N/A | 0.509 | 0.111 | 1.352 | 0.061 | 0.090 | 0.197 | 0.123 | 0.182 | 3.419 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F | B | B | F | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 34 | 57 | 0 | 66 | 61 | 0 | 108 | 29 |
N.S. |
1 | 0.00 | 1.06 | 1.78 | 0.00 | 2.06 | 1.91 | 0.00 | 3.38 | 0.91 |
time (sec) |
N/A | 0.000 | 6.748 | 0.749 | 0.000 | 0.103 | 0.255 | 0.000 | 0.240 | 0.464 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | F | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 40 | 29 | 34 | 34 | 26 | 38 | 507 | 0 |
N.S. |
1 | 0.00 | 1.60 | 1.16 | 1.36 | 1.36 | 1.04 | 1.52 | 20.28 | 0.00 |
time (sec) |
N/A | 0.000 | 0.183 | 0.490 | 0.072 | 0.098 | 0.247 | 0.151 | 0.190 | 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 | 17 | 14 | 15 | 12 | 12 | 11 | 12 | 12 | 14 | 12 |
N.S. |
1 | 0.82 | 0.88 | 0.71 | 0.71 | 0.65 | 0.71 | 0.71 | 0.82 | 0.71 |
time (sec) |
N/A | 0.327 | 0.048 | 0.155 | 0.095 | 0.091 | 0.056 | 0.115 | 0.749 | 3.306 |
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 | 14 | 14 | 15 | 14 | 20 | 14 | 14 | 20 | 14 |
N.S. |
1 | 0.54 | 0.54 | 0.58 | 0.54 | 0.77 | 0.54 | 0.54 | 0.77 | 0.54 |
time (sec) |
N/A | 0.286 | 0.004 | 0.091 | 0.032 | 0.086 | 0.046 | 0.124 | 0.182 | 3.335 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 18 | 15 | 14 | 14 | 12 | 14 | 18 | 15 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 0.78 | 0.78 | 0.67 | 0.78 | 1.00 | 0.83 |
time (sec) |
N/A | 0.153 | 0.012 | 0.088 | 0.030 | 0.090 | 0.063 | 0.124 | 0.176 | 0.058 |
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 | 28 | 0 | 38 | 34 | 53 | 30 | 32 | 52 | 42 | 31 |
N.S. |
1 | 0.00 | 1.36 | 1.21 | 1.89 | 1.07 | 1.14 | 1.86 | 1.50 | 1.11 |
time (sec) |
N/A | 0.000 | 0.127 | 0.654 | 0.164 | 0.096 | 0.213 | 0.139 | 0.189 | 3.701 |
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 | 9 | 9 | 8 | 7 | 7 | 7 | 7 | 9 | 7 |
N.S. |
1 | 0.64 | 0.64 | 0.57 | 0.50 | 0.50 | 0.50 | 0.50 | 0.64 | 0.50 |
time (sec) |
N/A | 0.177 | 0.007 | 0.053 | 0.035 | 0.102 | 0.059 | 0.115 | 0.176 | 0.059 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | F | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 25 | 25 | 24 | 24 | 22 | 24 | 201 | 0 |
N.S. |
1 | 0.00 | 1.00 | 1.00 | 0.96 | 0.96 | 0.88 | 0.96 | 8.04 | 0.00 |
time (sec) |
N/A | 0.000 | 0.193 | 0.271 | 0.166 | 0.091 | 0.073 | 0.170 | 0.207 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | A | A | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 67 | 21 | 31 | 31 | 15 | 42 | 44 | 20 |
N.S. |
1 | 0.00 | 2.39 | 0.75 | 1.11 | 1.11 | 0.54 | 1.50 | 1.57 | 0.71 |
time (sec) |
N/A | 0.000 | 2.063 | 0.059 | 0.097 | 0.106 | 0.126 | 0.153 | 0.177 | 3.438 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | C | B | A | B | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 26 | 44256 | 145 | 52 | 71 | 284 | 29 | 70 |
N.S. |
1 | 0.00 | 0.93 | 1580.57 | 5.18 | 1.86 | 2.54 | 10.14 | 1.04 | 2.50 |
time (sec) |
N/A | 0.000 | 0.283 | 1.562 | 0.196 | 0.110 | 0.172 | 0.180 | 0.176 | 3.705 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | B | B | A | A | F | F | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 114 | 206 | 96 | 32 | 32 | 0 | 181 | 57 |
N.S. |
1 | 0.00 | 3.93 | 7.10 | 3.31 | 1.10 | 1.10 | 0.00 | 6.24 | 1.97 |
time (sec) |
N/A | 0.000 | 0.077 | 0.377 | 0.044 | 0.087 | 0.129 | 0.000 | 0.185 | 3.563 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 32 | 27 | 23 | 24 | 25 | 20 | 26 | 30 | 20 |
N.S. |
1 | 1.45 | 1.23 | 1.05 | 1.09 | 1.14 | 0.91 | 1.18 | 1.36 | 0.91 |
time (sec) |
N/A | 0.272 | 0.009 | 0.212 | 0.030 | 0.091 | 0.170 | 0.117 | 0.177 | 0.099 |
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 | 24 | 0 | 38 | 31 | 21 | 29 | 26 | 65 | 41 | 52 |
N.S. |
1 | 0.00 | 1.58 | 1.29 | 0.88 | 1.21 | 1.08 | 2.71 | 1.71 | 2.17 |
time (sec) |
N/A | 0.000 | 0.405 | 0.386 | 0.228 | 0.081 | 0.097 | 0.145 | 0.177 | 3.370 |
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 | 15 | 13 | 13 | 9 | 8 | 8 | 10 | 0 | 13 | 8 |
N.S. |
1 | 0.87 | 0.87 | 0.60 | 0.53 | 0.53 | 0.67 | 0.00 | 0.87 | 0.53 |
time (sec) |
N/A | 0.321 | 0.027 | 0.123 | 0.041 | 0.083 | 0.107 | 0.000 | 0.182 | 0.077 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | A | F | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 28 | 23 | 24 | 0 | 36 | 20 | 0 | 70 | 22 |
N.S. |
1 | 1.22 | 1.00 | 1.04 | 0.00 | 1.57 | 0.87 | 0.00 | 3.04 | 0.96 |
time (sec) |
N/A | 0.747 | 0.631 | 2.043 | 0.000 | 0.088 | 0.234 | 0.000 | 54.374 | 3.419 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 31 | 21 | 26 | 97 | 25 | 26 | 74 | 24 | 23 |
N.S. |
1 | 1.41 | 0.95 | 1.18 | 4.41 | 1.14 | 1.18 | 3.36 | 1.09 | 1.05 |
time (sec) |
N/A | 0.485 | 0.042 | 0.738 | 0.035 | 0.089 | 0.140 | 0.121 | 0.191 | 3.425 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 26 | 24 | 0 | 23 | 22 | 43 | 28 | 23 |
N.S. |
1 | 0.00 | 0.96 | 0.89 | 0.00 | 0.85 | 0.81 | 1.59 | 1.04 | 0.85 |
time (sec) |
N/A | 0.000 | 2.708 | 0.442 | 0.000 | 0.095 | 2.863 | 0.142 | 0.202 | 3.481 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | A | A | F(-1) | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 65 | 21 | 20 | 19 | 19 | 19 | 0 | 22 | 19 |
N.S. |
1 | 2.83 | 0.91 | 0.87 | 0.83 | 0.83 | 0.83 | 0.00 | 0.96 | 0.83 |
time (sec) |
N/A | 0.670 | 0.146 | 0.489 | 0.090 | 0.092 | 0.114 | 0.000 | 0.237 | 3.484 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | B | B | B | F(-2) | F | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 37 | 0 | 53 | 107 | 222 | 115 | 114 | 0 | 322 | 419 |
N.S. |
1 | 0.00 | 1.43 | 2.89 | 6.00 | 3.11 | 3.08 | 0.00 | 8.70 | 11.32 |
time (sec) |
N/A | 0.000 | 0.390 | 71.497 | 50.277 | 0.099 | 46.060 | 0.000 | 200.016 | 4.299 |
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 | 44 | 20 | 24 | 19 | 23 | 20 | 23 | 35 | 21 |
N.S. |
1 | 2.00 | 0.91 | 1.09 | 0.86 | 1.05 | 0.91 | 1.05 | 1.59 | 0.95 |
time (sec) |
N/A | 0.284 | 0.032 | 0.373 | 0.107 | 0.085 | 0.087 | 0.120 | 0.188 | 3.313 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 22 | 18 | 29 | 41 | 47 | 42 | 41 | 88 | 39 |
N.S. |
1 | 0.96 | 0.78 | 1.26 | 1.78 | 2.04 | 1.83 | 1.78 | 3.83 | 1.70 |
time (sec) |
N/A | 0.364 | 0.014 | 0.175 | 0.035 | 0.089 | 0.186 | 0.113 | 0.211 | 0.218 |
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 | 23 | 0 | 0 | 22 | 27 | 23 | 19 | 23 | 80 | 80 |
N.S. |
1 | 0.00 | 0.00 | 0.96 | 1.17 | 1.00 | 0.83 | 1.00 | 3.48 | 3.48 |
time (sec) |
N/A | 0.000 | 0.000 | 0.540 | 0.169 | 0.100 | 0.121 | 0.181 | 200.033 | 3.540 |
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 | 25 | 26 | 26 | 25 | 66 | 24 | 24 | 42 | 24 | 24 |
N.S. |
1 | 1.04 | 1.04 | 1.00 | 2.64 | 0.96 | 0.96 | 1.68 | 0.96 | 0.96 |
time (sec) |
N/A | 0.386 | 0.016 | 1.065 | 0.062 | 0.104 | 0.102 | 0.118 | 0.252 | 3.364 |
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 | 27 | 27 | 21 | 20 | 20 | 29 | 20 | 22 | 20 |
N.S. |
1 | 0.90 | 0.90 | 0.70 | 0.67 | 0.67 | 0.97 | 0.67 | 0.73 | 0.67 |
time (sec) |
N/A | 0.251 | 0.004 | 0.064 | 0.035 | 0.100 | 0.035 | 0.109 | 0.326 | 0.119 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | A | B | A | A | A | F | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 60 | 21 | 53 | 33 | 34 | 33 | 157 | 36 |
N.S. |
1 | 0.00 | 2.40 | 0.84 | 2.12 | 1.32 | 1.36 | 1.32 | 6.28 | 1.44 |
time (sec) |
N/A | 0.000 | 0.206 | 0.525 | 0.130 | 0.095 | 0.180 | 0.580 | 200.034 | 0.166 |
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 | 25 | 0 | 24 | 14 | 17 | 14 | 14 | 17 | 295 | 16 |
N.S. |
1 | 0.00 | 0.96 | 0.56 | 0.68 | 0.56 | 0.56 | 0.68 | 11.80 | 0.64 |
time (sec) |
N/A | 0.000 | 0.727 | 4.432 | 0.409 | 0.113 | 0.379 | 0.128 | 0.310 | 3.914 |
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 | 19 | 19 | 25 | 19 | 17 | 17 | 17 | 0 | 17 | 16 |
N.S. |
1 | 1.00 | 1.32 | 1.00 | 0.89 | 0.89 | 0.89 | 0.00 | 0.89 | 0.84 |
time (sec) |
N/A | 0.655 | 0.436 | 22.503 | 0.176 | 0.092 | 1.914 | 0.000 | 0.177 | 3.426 |
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 | 20 | 33 | 14 | 15 | 69 | 19 | 17 | 19 | 19 | 14 |
N.S. |
1 | 1.65 | 0.70 | 0.75 | 3.45 | 0.95 | 0.85 | 0.95 | 0.95 | 0.70 |
time (sec) |
N/A | 0.961 | 0.047 | 0.289 | 0.103 | 0.104 | 0.083 | 0.108 | 0.173 | 3.301 |
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 | 19 | 22 | 18 | 19 | 18 | 20 | 15 | 40 | 20 | 18 |
N.S. |
1 | 1.16 | 0.95 | 1.00 | 0.95 | 1.05 | 0.79 | 2.11 | 1.05 | 0.95 |
time (sec) |
N/A | 0.323 | 0.013 | 0.300 | 0.033 | 0.084 | 0.070 | 0.138 | 0.172 | 3.317 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 19 | 19 | 19 | 18 | 22 | 15 | 22 | 24 | 18 |
N.S. |
1 | 0.79 | 0.79 | 0.79 | 0.75 | 0.92 | 0.62 | 0.92 | 1.00 | 0.75 |
time (sec) |
N/A | 0.331 | 0.025 | 0.193 | 0.037 | 0.104 | 0.052 | 0.122 | 0.182 | 3.323 |
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 | 31 | 32 | 163 | 33 | 32 | 58 | 40 | 35 |
N.S. |
1 | 0.00 | 1.15 | 1.19 | 6.04 | 1.22 | 1.19 | 2.15 | 1.48 | 1.30 |
time (sec) |
N/A | 0.000 | 0.054 | 2.480 | 0.330 | 0.100 | 0.484 | 0.146 | 0.179 | 0.400 |
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 | 24 | 24 | 20 | 25 | 19 | 19 | 28 | 26 | 19 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 1.04 | 0.79 | 0.79 | 1.17 | 1.08 | 0.79 |
time (sec) |
N/A | 0.253 | 0.008 | 0.170 | 0.033 | 0.082 | 0.063 | 0.129 | 0.177 | 0.086 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F(-2) | A | F(-2) | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 0 | 16 | 16 | 0 | 15 | 0 | 17 | 20 | 15 |
N.S. |
1 | 0.00 | 0.89 | 0.89 | 0.00 | 0.83 | 0.00 | 0.94 | 1.11 | 0.83 |
time (sec) |
N/A | 0.000 | 0.270 | 0.717 | 0.000 | 0.098 | 0.000 | 0.120 | 0.175 | 3.529 |
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 | 19 | 34 | 32 | 28 | 26 | 26 | 29 | 0 | 47 | 35 |
N.S. |
1 | 1.79 | 1.68 | 1.47 | 1.37 | 1.37 | 1.53 | 0.00 | 2.47 | 1.84 |
time (sec) |
N/A | 0.377 | 0.041 | 0.162 | 0.038 | 0.096 | 1.832 | 0.000 | 0.179 | 0.104 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 12 | 6 | 6 | 7 | 6 | 6 | 5 | 7 | 6 | 6 |
N.S. |
1 | 0.50 | 0.50 | 0.58 | 0.50 | 0.50 | 0.42 | 0.58 | 0.50 | 0.50 |
time (sec) |
N/A | 0.202 | 0.001 | 0.039 | 0.032 | 0.086 | 0.022 | 0.125 | 0.181 | 3.352 |
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 | 25 | 22 | 23 | 19 | 22 | 17 | 17 | 17 | 20 | 17 |
N.S. |
1 | 0.88 | 0.92 | 0.76 | 0.88 | 0.68 | 0.68 | 0.68 | 0.80 | 0.68 |
time (sec) |
N/A | 0.284 | 0.012 | 0.172 | 0.063 | 0.124 | 0.060 | 0.125 | 0.183 | 0.059 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | B | F | B | B | F | B | F(-1) |
verified | N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 0 | 77 | 0 | 64 | 97 | 0 | 71 | 0 |
N.S. |
1 | 0.00 | 0.00 | 2.41 | 0.00 | 2.00 | 3.03 | 0.00 | 2.22 | 0.00 |
time (sec) |
N/A | 0.000 | 0.000 | 6.977 | 0.000 | 0.147 | 0.305 | 0.000 | 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 | 17 | 26 | 19 | 19 | 18 | 18 | 15 | 18 | 20 | 18 |
N.S. |
1 | 1.53 | 1.12 | 1.12 | 1.06 | 1.06 | 0.88 | 1.06 | 1.18 | 1.06 |
time (sec) |
N/A | 0.306 | 0.158 | 0.171 | 0.155 | 0.094 | 0.055 | 0.170 | 0.183 | 3.347 |
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 | 29 | 30 | 32 | 30 | 31 | 31 | 34 | 34 | 24 |
N.S. |
1 | 0.97 | 1.00 | 1.07 | 1.00 | 1.03 | 1.03 | 1.13 | 1.13 | 0.80 |
time (sec) |
N/A | 0.202 | 0.012 | 0.101 | 0.032 | 0.075 | 0.270 | 0.118 | 0.176 | 0.059 |
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 | 22 | 22 | 23 | 30 | 27 | 20 | 22 | 27 | 21 |
N.S. |
1 | 0.88 | 0.88 | 0.92 | 1.20 | 1.08 | 0.80 | 0.88 | 1.08 | 0.84 |
time (sec) |
N/A | 0.233 | 0.004 | 0.332 | 0.033 | 0.083 | 0.058 | 0.123 | 0.172 | 3.355 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 33 | 34 | 27 | 24 | 41 | 24 | 25 | 47 | 24 |
N.S. |
1 | 1.10 | 1.13 | 0.90 | 0.80 | 1.37 | 0.80 | 0.83 | 1.57 | 0.80 |
time (sec) |
N/A | 0.244 | 0.012 | 0.138 | 0.027 | 0.095 | 0.214 | 0.120 | 0.175 | 3.569 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 26 | 26 | 30 | 30 | 24 | 30 | 35 | 25 |
N.S. |
1 | 0.00 | 0.84 | 0.84 | 0.97 | 0.97 | 0.77 | 0.97 | 1.13 | 0.81 |
time (sec) |
N/A | 0.000 | 0.015 | 0.163 | 0.027 | 0.093 | 0.755 | 0.126 | 0.173 | 0.116 |
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 | 16 | 17 | 16 | 14 | 14 | 15 | 14 | 11 |
N.S. |
1 | 1.23 | 1.23 | 1.31 | 1.23 | 1.08 | 1.08 | 1.15 | 1.08 | 0.85 |
time (sec) |
N/A | 0.208 | 0.004 | 0.193 | 0.046 | 0.087 | 0.064 | 0.115 | 0.173 | 3.468 |
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 | 24 | 0 | 26 | 27 | 31 | 31 | 204 | 31 | 26 | 181 |
N.S. |
1 | 0.00 | 1.08 | 1.12 | 1.29 | 1.29 | 8.50 | 1.29 | 1.08 | 7.54 |
time (sec) |
N/A | 0.000 | 1.503 | 3.969 | 0.075 | 0.089 | 0.261 | 0.133 | 0.179 | 3.974 |
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 | 35 | 37 | 24 | 29 | 38 | 29 | 29 | 19 | 27 |
N.S. |
1 | 1.35 | 1.42 | 0.92 | 1.12 | 1.46 | 1.12 | 1.12 | 0.73 | 1.04 |
time (sec) |
N/A | 8.948 | 0.015 | 0.251 | 0.033 | 0.107 | 0.154 | 0.113 | 0.168 | 0.123 |
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 | 40 | 36 | 34 | 33 | 33 | 34 | 33 | 36 | 37 |
N.S. |
1 | 1.38 | 1.24 | 1.17 | 1.14 | 1.14 | 1.17 | 1.14 | 1.24 | 1.28 |
time (sec) |
N/A | 1.282 | 0.097 | 0.179 | 0.035 | 0.092 | 0.081 | 0.116 | 0.893 | 3.550 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | F(-2) | B | F | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 0 | 64 | 58 | 62 | 57 | 0 | 111 | 0 | 528 |
N.S. |
1 | 0.00 | 1.78 | 1.61 | 1.72 | 1.58 | 0.00 | 3.08 | 0.00 | 14.67 |
time (sec) |
N/A | 0.000 | 0.175 | 67.720 | 0.203 | 0.100 | 0.000 | 0.838 | 0.740 | 5.017 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | B | B | B | B | B | F | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 0 | 376 | 675 | 663 | 412 | 350 | 626 | 0 | 291 |
N.S. |
1 | 0.00 | 10.74 | 19.29 | 18.94 | 11.77 | 10.00 | 17.89 | 0.00 | 8.31 |
time (sec) |
N/A | 0.000 | 0.339 | 103.621 | 0.228 | 0.120 | 3.634 | 0.161 | 0.252 | 4.601 |
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 | 8 | 8 | 9 | 12 | 8 | 5 | 9 | 8 | 8 |
N.S. |
1 | 0.53 | 0.53 | 0.60 | 0.80 | 0.53 | 0.33 | 0.60 | 0.53 | 0.53 |
time (sec) |
N/A | 0.248 | 0.001 | 0.036 | 0.032 | 0.099 | 0.026 | 0.125 | 0.177 | 0.025 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | C | B | B | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 48 | 29 | 155 | 467 | 128 | 201 | 219 | 166 | 159 |
N.S. |
1 | 2.00 | 1.21 | 6.46 | 19.46 | 5.33 | 8.38 | 9.12 | 6.92 | 6.62 |
time (sec) |
N/A | 1.881 | 0.080 | 0.400 | 0.094 | 0.104 | 0.179 | 0.134 | 0.194 | 3.654 |
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 | 23 | 22 | 24 | 29 | 26 | 20 | 38 | 22 |
N.S. |
1 | 1.08 | 0.96 | 0.92 | 1.00 | 1.21 | 1.08 | 0.83 | 1.58 | 0.92 |
time (sec) |
N/A | 0.265 | 0.055 | 0.174 | 0.027 | 0.100 | 0.136 | 0.120 | 0.182 | 0.113 |
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 | 18 | 18 | 20 | 56 | 17 | 15 | 17 | 21 | 17 |
N.S. |
1 | 1.00 | 1.00 | 1.11 | 3.11 | 0.94 | 0.83 | 0.94 | 1.17 | 0.94 |
time (sec) |
N/A | 1.195 | 0.364 | 1.608 | 0.218 | 0.098 | 0.470 | 0.125 | 0.178 | 4.248 |
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 | 16 | 21 | 13 | 13 | 49 | 15 | 12 | 15 | 14 | 12 |
N.S. |
1 | 1.31 | 0.81 | 0.81 | 3.06 | 0.94 | 0.75 | 0.94 | 0.88 | 0.75 |
time (sec) |
N/A | 0.260 | 0.027 | 0.051 | 0.037 | 0.094 | 0.047 | 0.119 | 0.177 | 0.040 |
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 | 31 | 116 | 28 | 31 | 37 | 32 | 26 | 277 | 31 | 78 |
N.S. |
1 | 3.74 | 0.90 | 1.00 | 1.19 | 1.03 | 0.84 | 8.94 | 1.00 | 2.52 |
time (sec) |
N/A | 1.605 | 5.046 | 1.383 | 0.230 | 0.105 | 0.124 | 0.194 | 0.177 | 4.340 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | A | A | B | A | B | F | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 901 | 29 | 47 | 82 | 22 | 304 | 131 | 27 |
N.S. |
1 | 0.00 | 32.18 | 1.04 | 1.68 | 2.93 | 0.79 | 10.86 | 4.68 | 0.96 |
time (sec) |
N/A | 0.000 | 0.551 | 0.789 | 0.087 | 0.109 | 0.104 | 0.157 | 155.963 | 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 | 36 | 53 | 53 | 48 | 45 | 43 | 41 | 45 | 46 | 42 |
N.S. |
1 | 1.47 | 1.47 | 1.33 | 1.25 | 1.19 | 1.14 | 1.25 | 1.28 | 1.17 |
time (sec) |
N/A | 0.260 | 0.045 | 0.986 | 0.045 | 0.100 | 0.125 | 0.128 | 0.181 | 3.430 |