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 | B | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 94 | 24 | 28 | 23 | 27 | 22 | 27 | 28 | 26 |
N.S. |
1 | 3.92 | 1.00 | 1.17 | 0.96 | 1.12 | 0.92 | 1.12 | 1.17 | 1.08 |
time (sec) |
N/A | 0.339 | 0.033 | 0.193 | 0.128 | 0.089 | 0.073 | 0.130 | 0.232 | 2.742 |
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 | 18 | 0 | 16 | 17 | 18 | 18 | 15 | 18 | 16 | 16 |
N.S. |
1 | 0.00 | 0.89 | 0.94 | 1.00 | 1.00 | 0.83 | 1.00 | 0.89 | 0.89 |
time (sec) |
N/A | 0.000 | 0.110 | 24.214 | 0.191 | 0.090 | 0.131 | 0.127 | 0.236 | 3.062 |
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 | 27 | 23 | 27 | 30 | 28 | 26 | 28 | 27 | 31 |
N.S. |
1 | 1.17 | 1.00 | 1.17 | 1.30 | 1.22 | 1.13 | 1.22 | 1.17 | 1.35 |
time (sec) |
N/A | 8.880 | 0.110 | 0.655 | 0.122 | 0.097 | 0.091 | 0.143 | 0.206 | 2.894 |
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 | 15 | 33 | 16 | 17 | 74 | 16 | 14 | 16 | 16 | 16 |
N.S. |
1 | 2.20 | 1.07 | 1.13 | 4.93 | 1.07 | 0.93 | 1.07 | 1.07 | 1.07 |
time (sec) |
N/A | 2.157 | 0.044 | 0.224 | 0.092 | 0.091 | 0.081 | 0.119 | 0.195 | 2.852 |
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 | 16 | 17 | 19 | 19 | 15 | 19 | 16 | 16 |
N.S. |
1 | 0.00 | 1.00 | 1.06 | 1.19 | 1.19 | 0.94 | 1.19 | 1.00 | 1.00 |
time (sec) |
N/A | 0.000 | 0.120 | 0.242 | 0.066 | 0.086 | 0.054 | 0.126 | 0.184 | 0.223 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | B | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 77 | 21 | 21 | 53 | 54 | 116 | 25 | 71 | 78 |
N.S. |
1 | 3.67 | 1.00 | 1.00 | 2.52 | 2.57 | 5.52 | 1.19 | 3.38 | 3.71 |
time (sec) |
N/A | 0.612 | 0.022 | 0.464 | 0.041 | 0.083 | 0.841 | 0.120 | 0.214 | 0.303 |
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 | 36 | 0 | 49 | 35 | 37 | 34 | 34 | 34 | 41 | 69 |
N.S. |
1 | 0.00 | 1.36 | 0.97 | 1.03 | 0.94 | 0.94 | 0.94 | 1.14 | 1.92 |
time (sec) |
N/A | 0.000 | 0.085 | 1.178 | 0.100 | 0.096 | 0.179 | 1.371 | 0.229 | 2.742 |
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 | 29 | 0 | 19 | 19 | 75 | 75 | 37 | 77 | 84 | 0 |
N.S. |
1 | 0.00 | 0.66 | 0.66 | 2.59 | 2.59 | 1.28 | 2.66 | 2.90 | 0.00 |
time (sec) |
N/A | 0.000 | 0.237 | 15.846 | 0.083 | 0.091 | 0.080 | 0.131 | 0.199 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | C | F | A | F(-2) | F | B | B |
verified |
N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 0 | 44 | 224 | 0 | 63 | 0 | 0 | 70 | 37 |
N.S. |
1 | 0.00 | 1.26 | 6.40 | 0.00 | 1.80 | 0.00 | 0.00 | 2.00 | 1.06 |
time (sec) |
N/A | 0.000 | 0.208 | 64.379 | 0.000 | 0.111 | 0.000 | 0.000 | 0.227 | 3.334 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | F | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 31 | 33 | 32 | 36 | 26 | 0 | 40 | 52 |
N.S. |
1 | 0.00 | 1.07 | 1.14 | 1.10 | 1.24 | 0.90 | 0.00 | 1.38 | 1.79 |
time (sec) |
N/A | 0.000 | 4.090 | 2.110 | 0.349 | 0.093 | 0.219 | 0.000 | 0.245 | 2.872 |
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 | 21 | 0 | 20 | 36 | 53 | 34 | 29 | 93 | 37 | 83 |
N.S. |
1 | 0.00 | 0.95 | 1.71 | 2.52 | 1.62 | 1.38 | 4.43 | 1.76 | 3.95 |
time (sec) |
N/A | 0.000 | 5.079 | 0.595 | 0.384 | 0.081 | 0.336 | 0.467 | 0.191 | 2.983 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | F(-2) | B | B | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 50 | 74 | 0 | 86 | 70 | 66 | 126 | 74 |
N.S. |
1 | 0.00 | 1.56 | 2.31 | 0.00 | 2.69 | 2.19 | 2.06 | 3.94 | 2.31 |
time (sec) |
N/A | 0.000 | 1.342 | 7.518 | 0.000 | 0.090 | 0.213 | 0.160 | 0.207 | 2.938 |
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 | 26 | 25 | 36 | 27 | 22 | 0 | 29 | 37 |
N.S. |
1 | 0.00 | 1.00 | 0.96 | 1.38 | 1.04 | 0.85 | 0.00 | 1.12 | 1.42 |
time (sec) |
N/A | 0.000 | 0.075 | 0.160 | 0.163 | 0.102 | 0.109 | 0.000 | 0.183 | 2.756 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 23 | 18 | 21 | 0 | 30 | 22 | 50 | 50 | 22 |
N.S. |
1 | 1.28 | 1.00 | 1.17 | 0.00 | 1.67 | 1.22 | 2.78 | 2.78 | 1.22 |
time (sec) |
N/A | 0.591 | 0.026 | 0.164 | 0.000 | 0.088 | 0.084 | 0.125 | 0.208 | 0.113 |
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 | 21 | 257 | 161 | 162 | 240 | 240 | 238 | 163 | 236 | 239 |
N.S. |
1 | 12.24 | 7.67 | 7.71 | 11.43 | 11.43 | 11.33 | 7.76 | 11.24 | 11.38 |
time (sec) |
N/A | 3.777 | 0.035 | 0.148 | 0.059 | 0.104 | 0.205 | 0.121 | 0.186 | 1.838 |
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 | 29 | 30 | 29 | 32 | 24 | 29 | 34 | 25 |
N.S. |
1 | 1.10 | 0.97 | 1.00 | 0.97 | 1.07 | 0.80 | 0.97 | 1.13 | 0.83 |
time (sec) |
N/A | 0.212 | 0.004 | 0.234 | 0.030 | 0.095 | 0.067 | 0.118 | 0.171 | 2.704 |
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 | 21 | 63 | 19 | 17 | 16 | 16 | 20 | 16 | 20 | 16 |
N.S. |
1 | 3.00 | 0.90 | 0.81 | 0.76 | 0.76 | 0.95 | 0.76 | 0.95 | 0.76 |
time (sec) |
N/A | 0.699 | 0.089 | 0.186 | 0.083 | 0.084 | 0.074 | 0.118 | 0.175 | 2.703 |
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 | 29 | 41 | 22 | 23 | 37 | 22 | 24 | 56 | 23 | 22 |
N.S. |
1 | 1.41 | 0.76 | 0.79 | 1.28 | 0.76 | 0.83 | 1.93 | 0.79 | 0.76 |
time (sec) |
N/A | 0.239 | 0.034 | 0.769 | 0.173 | 0.091 | 5.580 | 0.155 | 0.192 | 0.228 |
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 | 19 | 19 | 20 | 19 | 19 | 19 | 20 | 19 | 19 |
N.S. |
1 | 1.12 | 1.12 | 1.18 | 1.12 | 1.12 | 1.12 | 1.18 | 1.12 | 1.12 |
time (sec) |
N/A | 0.191 | 0.004 | 0.042 | 0.030 | 0.075 | 0.055 | 0.125 | 0.173 | 0.091 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | B | B | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 30 | 53 | 58 | 90 | 49 | 56 | 225 | 5211 |
N.S. |
1 | 0.00 | 1.00 | 1.77 | 1.93 | 3.00 | 1.63 | 1.87 | 7.50 | 173.70 |
time (sec) |
N/A | 0.000 | 0.050 | 16.030 | 0.197 | 0.098 | 0.120 | 0.890 | 0.177 | 5.846 |
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 | 8 | 8 | 9 | 8 | 8 | 8 | 9 | 8 | 8 |
N.S. |
1 | 0.80 | 0.80 | 0.90 | 0.80 | 0.80 | 0.80 | 0.90 | 0.80 | 0.80 |
time (sec) |
N/A | 0.270 | 0.013 | 0.076 | 0.033 | 0.074 | 0.087 | 0.126 | 0.216 | 2.969 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-2) | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 25 | 25 | 22 | 26 | 21 | 0 | 0 | 23 | 21 |
N.S. |
1 | 0.93 | 0.93 | 0.81 | 0.96 | 0.78 | 0.00 | 0.00 | 0.85 | 0.78 |
time (sec) |
N/A | 2.023 | 0.587 | 17.866 | 0.183 | 0.095 | 0.000 | 0.000 | 0.180 | 3.102 |
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 | 2 | 2 | 3 | 2 | 2 | 2 | 3 | 2 | 2 |
N.S. |
1 | 0.20 | 0.20 | 0.30 | 0.20 | 0.20 | 0.20 | 0.30 | 0.20 | 0.20 |
time (sec) |
N/A | 0.124 | 0.000 | 0.017 | 0.027 | 0.069 | 0.037 | 0.116 | 0.183 | 0.009 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 24 | 18 | 16 | 23 | 13 | 14 | 17 | 25 | 13 |
N.S. |
1 | 1.14 | 0.86 | 0.76 | 1.10 | 0.62 | 0.67 | 0.81 | 1.19 | 0.62 |
time (sec) |
N/A | 0.208 | 0.040 | 0.171 | 0.060 | 0.080 | 0.056 | 0.122 | 0.200 | 2.723 |
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 | 22 | 19 | 18 | 18 | 22 | 18 | 17 | 16 |
N.S. |
1 | 2.00 | 1.00 | 0.86 | 0.82 | 0.82 | 1.00 | 0.82 | 0.77 | 0.73 |
time (sec) |
N/A | 0.199 | 0.047 | 0.535 | 0.041 | 0.088 | 0.105 | 0.118 | 0.202 | 2.869 |
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 | 23 | 0 | 46 | 35 | 37 | 38 | 36 | 62 | 67 | 58 |
N.S. |
1 | 0.00 | 2.00 | 1.52 | 1.61 | 1.65 | 1.57 | 2.70 | 2.91 | 2.52 |
time (sec) |
N/A | 0.000 | 2.702 | 0.286 | 0.128 | 0.088 | 0.124 | 0.153 | 0.225 | 2.933 |
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 | 23 | 0 | 24 | 31 | 34 | 28 | 22 | 28 | 46 | 0 |
N.S. |
1 | 0.00 | 1.04 | 1.35 | 1.48 | 1.22 | 0.96 | 1.22 | 2.00 | 0.00 |
time (sec) |
N/A | 0.000 | 0.048 | 0.753 | 0.115 | 0.084 | 0.227 | 0.436 | 0.215 | 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 | 22 | 19 | 17 | 16 | 17 | 16 | 15 | 17 | 25 | 18 |
N.S. |
1 | 0.86 | 0.77 | 0.73 | 0.77 | 0.73 | 0.68 | 0.77 | 1.14 | 0.82 |
time (sec) |
N/A | 0.165 | 0.020 | 0.063 | 0.043 | 0.091 | 0.040 | 0.124 | 0.185 | 2.792 |
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 | 22 | 51 | 51 | 51 | 58 | 47 | 44 | 48 | 51 | 51 |
N.S. |
1 | 2.32 | 2.32 | 2.32 | 2.64 | 2.14 | 2.00 | 2.18 | 2.32 | 2.32 |
time (sec) |
N/A | 0.264 | 0.009 | 0.765 | 0.036 | 0.082 | 0.087 | 0.123 | 0.188 | 2.830 |
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 | 15 | 15 | 12 | 11 | 20 | 14 | 11 | 13 | 11 |
N.S. |
1 | 1.00 | 1.00 | 0.80 | 0.73 | 1.33 | 0.93 | 0.73 | 0.87 | 0.73 |
time (sec) |
N/A | 0.253 | 0.016 | 0.062 | 0.027 | 0.090 | 0.066 | 0.121 | 0.221 | 0.084 |
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 | 23 | 0 | 25 | 22 | 34 | 24 | 22 | 0 | 312 | 28 |
N.S. |
1 | 0.00 | 1.09 | 0.96 | 1.48 | 1.04 | 0.96 | 0.00 | 13.57 | 1.22 |
time (sec) |
N/A | 0.000 | 10.237 | 0.495 | 0.100 | 0.080 | 0.108 | 0.000 | 0.855 | 0.723 |
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 | 33 | 752 | 38 | 40 | 54 | 32 | 32 | 91 | 84 | 46 |
N.S. |
1 | 22.79 | 1.15 | 1.21 | 1.64 | 0.97 | 0.97 | 2.76 | 2.55 | 1.39 |
time (sec) |
N/A | 7.625 | 0.055 | 54.266 | 0.184 | 0.089 | 0.364 | 0.138 | 0.190 | 3.260 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | F(-1) | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 36 | 40 | 50 | 41 | 0 | 42 | 77 | 44 |
N.S. |
1 | 0.00 | 1.16 | 1.29 | 1.61 | 1.32 | 0.00 | 1.35 | 2.48 | 1.42 |
time (sec) |
N/A | 0.000 | 0.060 | 1.450 | 0.319 | 0.078 | 0.000 | 0.411 | 0.196 | 5.540 |
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 | 24 | 59 | 51 | 55 | 65 | 60 | 53 | 63 | 68 | 52 |
N.S. |
1 | 2.46 | 2.12 | 2.29 | 2.71 | 2.50 | 2.21 | 2.62 | 2.83 | 2.17 |
time (sec) |
N/A | 0.562 | 3.626 | 1.015 | 0.072 | 0.091 | 0.072 | 0.128 | 0.186 | 0.088 |
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 | 4 | 4 | 5 | 4 | 4 | 3 | 5 | 4 | 4 |
N.S. |
1 | 0.25 | 0.25 | 0.31 | 0.25 | 0.25 | 0.19 | 0.31 | 0.25 | 0.25 |
time (sec) |
N/A | 0.209 | 0.000 | 0.020 | 0.030 | 0.071 | 0.017 | 0.120 | 0.208 | 0.009 |
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 | 28 | 31 | 31 | 36 | 32 | 44 | 29 | 39 |
N.S. |
1 | 0.00 | 1.00 | 1.11 | 1.11 | 1.29 | 1.14 | 1.57 | 1.04 | 1.39 |
time (sec) |
N/A | 0.000 | 3.220 | 0.633 | 0.083 | 0.096 | 0.164 | 0.141 | 0.184 | 0.470 |
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 | 39 | 0 | 38 | 31 | 57 | 56 | 27 | 60 | 444 | 0 |
N.S. |
1 | 0.00 | 0.97 | 0.79 | 1.46 | 1.44 | 0.69 | 1.54 | 11.38 | 0.00 |
time (sec) |
N/A | 0.000 | 0.079 | 1.122 | 0.080 | 0.100 | 0.163 | 0.186 | 0.206 | 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 | 22 | 0 | 20 | 16 | 58 | 15 | 20 | 15 | 18 | 15 |
N.S. |
1 | 0.00 | 0.91 | 0.73 | 2.64 | 0.68 | 0.91 | 0.68 | 0.82 | 0.68 |
time (sec) |
N/A | 0.000 | 0.077 | 0.105 | 0.160 | 0.082 | 0.094 | 0.125 | 0.187 | 2.889 |
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 | 24 | 0 | 24 | 27 | 18 | 28 | 0 | 24 | 39 | 22 |
N.S. |
1 | 0.00 | 1.00 | 1.12 | 0.75 | 1.17 | 0.00 | 1.00 | 1.62 | 0.92 |
time (sec) |
N/A | 0.000 | 0.623 | 0.967 | 0.228 | 0.099 | 0.000 | 0.154 | 0.199 | 3.059 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 10 | 10 | 10 | 48 | 9 | 8 | 9 | 12 | 9 |
N.S. |
1 | 0.48 | 0.48 | 0.48 | 2.29 | 0.43 | 0.38 | 0.43 | 0.57 | 0.43 |
time (sec) |
N/A | 0.300 | 0.005 | 0.069 | 0.065 | 0.073 | 0.048 | 0.133 | 0.201 | 2.760 |
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 | 24 | 27 | 26 | 25 | 20 | 24 | 27 | 22 |
N.S. |
1 | 1.04 | 1.04 | 1.17 | 1.13 | 1.09 | 0.87 | 1.04 | 1.17 | 0.96 |
time (sec) |
N/A | 0.678 | 0.212 | 0.409 | 0.156 | 0.094 | 0.084 | 0.123 | 0.211 | 2.882 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | B | A | F | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 0 | 40 | 39 | 40 | 132 | 41 | 0 | 109 | 47 |
N.S. |
1 | 0.00 | 1.18 | 1.15 | 1.18 | 3.88 | 1.21 | 0.00 | 3.21 | 1.38 |
time (sec) |
N/A | 0.000 | 0.301 | 39.438 | 0.737 | 0.100 | 1.024 | 0.000 | 200.040 | 3.258 |
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 | 13 | 13 | 12 | 13 | 13 | 12 | 13 | 25 | 13 |
N.S. |
1 | 0.65 | 0.65 | 0.60 | 0.65 | 0.65 | 0.60 | 0.65 | 1.25 | 0.65 |
time (sec) |
N/A | 0.284 | 0.004 | 0.182 | 0.028 | 0.077 | 0.088 | 0.129 | 0.232 | 0.064 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 16 | 16 | 15 | 17 | 14 | 15 | 14 | 14 | 14 |
N.S. |
1 | 0.73 | 0.73 | 0.68 | 0.77 | 0.64 | 0.68 | 0.64 | 0.64 | 0.64 |
time (sec) |
N/A | 0.434 | 0.043 | 0.054 | 0.147 | 0.080 | 0.097 | 0.125 | 0.224 | 2.934 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 27 | 32 | 32 | 31 | 27 | 33 | 31 | 31 |
N.S. |
1 | 0.00 | 1.04 | 1.23 | 1.23 | 1.19 | 1.04 | 1.27 | 1.19 | 1.19 |
time (sec) |
N/A | 0.000 | 0.048 | 2.186 | 0.082 | 0.087 | 0.200 | 0.190 | 0.239 | 2.984 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | B | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 33 | 105 | 206 | 54 | 51 | 54 | 54 | 54 |
N.S. |
1 | 0.00 | 1.10 | 3.50 | 6.87 | 1.80 | 1.70 | 1.80 | 1.80 | 1.80 |
time (sec) |
N/A | 0.000 | 0.043 | 17.597 | 0.101 | 0.087 | 0.317 | 0.175 | 0.251 | 3.254 |
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 | 27 | 0 | 36 | 29 | 32 | 26 | 22 | 36 | 42 | 0 |
N.S. |
1 | 0.00 | 1.33 | 1.07 | 1.19 | 0.96 | 0.81 | 1.33 | 1.56 | 0.00 |
time (sec) |
N/A | 0.000 | 0.330 | 0.612 | 0.163 | 0.092 | 0.108 | 0.200 | 0.279 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | B | B | B | A | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 40 | 54 | 10769 | 88 | 83 | 44 | 735 | 35 |
N.S. |
1 | 0.00 | 1.60 | 2.16 | 430.76 | 3.52 | 3.32 | 1.76 | 29.40 | 1.40 |
time (sec) |
N/A | 0.000 | 0.025 | 1.227 | 2.698 | 0.089 | 1.987 | 0.138 | 0.276 | 0.260 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | F | A | A | F(-1) | F | F | B |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 0 | 0 | 20 | 20 | 0 | 0 | 304 | 564 |
N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.65 | 0.65 | 0.00 | 0.00 | 9.81 | 18.19 |
time (sec) |
N/A | 0.000 | 0.000 | 0.000 | 0.098 | 0.106 | 0.000 | 0.000 | 0.235 | 3.611 |
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 | 33 | 36 | 29 | 28 | 30 | 35 | 32 | 29 | 34 | 29 |
N.S. |
1 | 1.09 | 0.88 | 0.85 | 0.91 | 1.06 | 0.97 | 0.88 | 1.03 | 0.88 |
time (sec) |
N/A | 0.224 | 0.005 | 0.098 | 0.028 | 0.079 | 0.169 | 0.120 | 0.220 | 0.068 |
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 | 20 | 464 | 93 | 200 | 559 | 187 | 282 | 694 | 222 | 22 |
N.S. |
1 | 23.20 | 4.65 | 10.00 | 27.95 | 9.35 | 14.10 | 34.70 | 11.10 | 1.10 |
time (sec) |
N/A | 0.798 | 0.109 | 6.585 | 0.036 | 0.106 | 0.210 | 0.133 | 0.240 | 3.186 |
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 | 14 | 14 | 13 | 12 | 12 | 12 | 12 | 10 | 10 |
N.S. |
1 | 1.17 | 1.17 | 1.08 | 1.00 | 1.00 | 1.00 | 1.00 | 0.83 | 0.83 |
time (sec) |
N/A | 0.151 | 0.002 | 0.042 | 0.029 | 0.091 | 0.042 | 0.124 | 0.221 | 2.757 |
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 | 44 | 33 | 36 | 31 | 37 | 44 | 27 | 43 | 32 |
N.S. |
1 | 1.83 | 1.38 | 1.50 | 1.29 | 1.54 | 1.83 | 1.12 | 1.79 | 1.33 |
time (sec) |
N/A | 0.272 | 0.013 | 0.123 | 0.030 | 0.069 | 0.221 | 0.122 | 0.222 | 2.782 |
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 | 29 | 30 | 65 | 46 | 26 | 46 | 45 | 95 |
N.S. |
1 | 0.00 | 1.16 | 1.20 | 2.60 | 1.84 | 1.04 | 1.84 | 1.80 | 3.80 |
time (sec) |
N/A | 0.000 | 0.152 | 2.560 | 0.160 | 0.089 | 0.072 | 0.216 | 0.225 | 3.067 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | C | C | A | A | A | B | F(-1) |
verified |
N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 89 | 151 | 37 | 32 | 27 | 35 | 33 | 0 |
N.S. |
1 | 0.00 | 2.78 | 4.72 | 1.16 | 1.00 | 0.84 | 1.09 | 1.03 | 0.00 |
time (sec) |
N/A | 0.000 | 0.100 | 0.513 | 0.187 | 0.095 | 1.788 | 0.486 | 0.238 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | C | B | B | B | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 0 | 55 | 52 | 99 | 62 | 54 | 90 | 97 | 0 |
N.S. |
1 | 0.00 | 1.57 | 1.49 | 2.83 | 1.77 | 1.54 | 2.57 | 2.77 | 0.00 |
time (sec) |
N/A | 0.000 | 0.146 | 56.361 | 0.546 | 0.106 | 0.426 | 18.381 | 0.289 | 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 | 32 | 0 | 19 | 16 | 23 | 23 | 20 | 15 | 16 | 15 |
N.S. |
1 | 0.00 | 0.59 | 0.50 | 0.72 | 0.72 | 0.62 | 0.47 | 0.50 | 0.47 |
time (sec) |
N/A | 0.000 | 0.129 | 0.046 | 0.064 | 0.101 | 0.091 | 0.126 | 0.240 | 0.085 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 28 | 69 | 27 | 25 | 28 | 29 | 47 | 31 | 22 |
N.S. |
1 | 1.33 | 3.29 | 1.29 | 1.19 | 1.33 | 1.38 | 2.24 | 1.48 | 1.05 |
time (sec) |
N/A | 0.276 | 0.036 | 0.221 | 0.035 | 0.083 | 0.070 | 0.131 | 0.238 | 3.085 |
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 | 31 | 0 | 59 | 50 | 48 | 38 | 37 | 47 | 57 | 0 |
N.S. |
1 | 0.00 | 1.90 | 1.61 | 1.55 | 1.23 | 1.19 | 1.52 | 1.84 | 0.00 |
time (sec) |
N/A | 0.000 | 0.749 | 2.729 | 0.264 | 0.086 | 0.168 | 0.172 | 0.233 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | B | B | B | F(-1) | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 0 | 61 | 143 | 221 | 141 | 82 | 0 | 446 | 0 |
N.S. |
1 | 0.00 | 1.74 | 4.09 | 6.31 | 4.03 | 2.34 | 0.00 | 12.74 | 0.00 |
time (sec) |
N/A | 0.000 | 0.154 | 68.441 | 0.296 | 0.094 | 21.948 | 0.000 | 200.031 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | A | B | B | A | B | F | B |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 0 | 33 | 74 | 63 | 31 | 513 | 1172 | 214 |
N.S. |
1 | 0.00 | 0.00 | 1.03 | 2.31 | 1.97 | 0.97 | 16.03 | 36.62 | 6.69 |
time (sec) |
N/A | 0.000 | 0.000 | 18.035 | 0.230 | 0.088 | 0.319 | 0.490 | 0.766 | 3.399 |
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 | 20 | 0 | 26 | 24 | 37 | 37 | 42 | 37 | 38 | 23 |
N.S. |
1 | 0.00 | 1.30 | 1.20 | 1.85 | 1.85 | 2.10 | 1.85 | 1.90 | 1.15 |
time (sec) |
N/A | 0.000 | 0.065 | 0.635 | 0.072 | 0.078 | 0.060 | 0.120 | 0.443 | 3.407 |
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 | 15 | 15 | 12 | 15 | 11 | 10 | 15 | 11 | 12 |
N.S. |
1 | 0.83 | 0.83 | 0.67 | 0.83 | 0.61 | 0.56 | 0.83 | 0.61 | 0.67 |
time (sec) |
N/A | 0.179 | 0.001 | 0.082 | 0.036 | 0.089 | 0.048 | 0.114 | 0.465 | 2.938 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 32 | 24 | 26 | 37 | 25 | 24 | 0 | 46 | 20 |
N.S. |
1 | 1.28 | 0.96 | 1.04 | 1.48 | 1.00 | 0.96 | 0.00 | 1.84 | 0.80 |
time (sec) |
N/A | 0.625 | 0.166 | 0.166 | 0.141 | 0.080 | 0.089 | 0.000 | 200.024 | 3.089 |
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 | 13 | 23 | 14 | 15 | 15 | 26 | 15 | 15 | 11 |
N.S. |
1 | 0.57 | 1.00 | 0.61 | 0.65 | 0.65 | 1.13 | 0.65 | 0.65 | 0.48 |
time (sec) |
N/A | 0.159 | 0.006 | 0.140 | 0.033 | 0.066 | 0.126 | 0.113 | 0.182 | 0.099 |
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 | 33 | 0 | 31 | 38 | 46 | 46 | 32 | 53 | 156 | 41 |
N.S. |
1 | 0.00 | 0.94 | 1.15 | 1.39 | 1.39 | 0.97 | 1.61 | 4.73 | 1.24 |
time (sec) |
N/A | 0.000 | 0.074 | 0.680 | 0.123 | 0.097 | 0.143 | 0.199 | 0.195 | 3.189 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 33 | 29 | 33 | 98 | 41 | 42 | 41 | 37 | 32 |
N.S. |
1 | 1.32 | 1.16 | 1.32 | 3.92 | 1.64 | 1.68 | 1.64 | 1.48 | 1.28 |
time (sec) |
N/A | 0.246 | 0.005 | 0.333 | 0.154 | 0.086 | 0.098 | 0.116 | 0.170 | 2.922 |
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 | 31 | 33 | 27 | 26 | 26 | 19 | 26 | 27 | 26 |
N.S. |
1 | 1.19 | 1.27 | 1.04 | 1.00 | 1.00 | 0.73 | 1.00 | 1.04 | 1.00 |
time (sec) |
N/A | 0.902 | 1.146 | 0.125 | 0.076 | 0.089 | 0.077 | 0.115 | 0.195 | 0.103 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | A | A | A | A | A | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 71 | 30 | 30 | 31 | 26 | 37 | 782 | 0 |
N.S. |
1 | 0.00 | 2.22 | 0.94 | 0.94 | 0.97 | 0.81 | 1.16 | 24.44 | 0.00 |
time (sec) |
N/A | 0.000 | 1.280 | 0.796 | 0.157 | 0.086 | 0.084 | 0.276 | 0.204 | 0.000 |
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 | 17 | 46 | 36 | 37 | 40 | 33 | 32 | 40 | 29 | 11 |
N.S. |
1 | 2.71 | 2.12 | 2.18 | 2.35 | 1.94 | 1.88 | 2.35 | 1.71 | 0.65 |
time (sec) |
N/A | 0.312 | 0.006 | 0.210 | 0.035 | 0.080 | 0.058 | 0.116 | 0.182 | 3.071 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | F(-2) | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 542 | 36 | 34 | 0 | 37 | 32 | 37 | 36 | 22 |
N.S. |
1 | 25.81 | 1.71 | 1.62 | 0.00 | 1.76 | 1.52 | 1.76 | 1.71 | 1.05 |
time (sec) |
N/A | 8.988 | 5.027 | 4.194 | 0.000 | 0.080 | 0.100 | 0.637 | 0.191 | 0.404 |
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 | 20 | 24 | 16 | 15 | 22 | 12 | 15 | 26 | 15 |
N.S. |
1 | 0.83 | 1.00 | 0.67 | 0.62 | 0.92 | 0.50 | 0.62 | 1.08 | 0.62 |
time (sec) |
N/A | 0.246 | 0.012 | 0.146 | 0.035 | 0.076 | 0.065 | 0.119 | 0.186 | 0.090 |
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 | 25 | 109 | 58 | 57 | 112 | 71 | 60 | 79 | 87 | 58 |
N.S. |
1 | 4.36 | 2.32 | 2.28 | 4.48 | 2.84 | 2.40 | 3.16 | 3.48 | 2.32 |
time (sec) |
N/A | 0.447 | 1.289 | 1.439 | 0.052 | 0.086 | 0.134 | 0.127 | 0.189 | 2.981 |
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 | 22 | 15 | 12 | 17 | 11 | 14 | 11 | 12 | 11 |
N.S. |
1 | 0.81 | 0.56 | 0.44 | 0.63 | 0.41 | 0.52 | 0.41 | 0.44 | 0.41 |
time (sec) |
N/A | 0.171 | 0.006 | 0.096 | 0.036 | 0.083 | 0.058 | 0.118 | 0.187 | 2.929 |
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 | 17 | 17 | 18 | 18 | 29 | 17 | 18 | 17 | 18 |
N.S. |
1 | 1.00 | 1.00 | 1.06 | 1.06 | 1.71 | 1.00 | 1.06 | 1.00 | 1.06 |
time (sec) |
N/A | 0.251 | 0.156 | 0.118 | 0.034 | 0.099 | 0.091 | 0.121 | 0.198 | 3.115 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | A | F(-1) | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 41 | 40 | 62 | 40 | 0 | 64 | 46 | 39 |
N.S. |
1 | 0.00 | 1.71 | 1.67 | 2.58 | 1.67 | 0.00 | 2.67 | 1.92 | 1.62 |
time (sec) |
N/A | 0.000 | 0.110 | 0.927 | 0.160 | 0.090 | 0.000 | 0.155 | 0.192 | 3.166 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | B | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 52 | 21 | 34 | 51 | 33 | 42 | 33 | 36 | 33 |
N.S. |
1 | 2.17 | 0.88 | 1.42 | 2.12 | 1.38 | 1.75 | 1.38 | 1.50 | 1.38 |
time (sec) |
N/A | 0.705 | 0.382 | 0.350 | 0.097 | 0.088 | 11.379 | 0.128 | 0.207 | 3.043 |
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 | 15 | 15 | 15 | 12 | 15 | 19 | 14 |
N.S. |
1 | 0.00 | 0.76 | 0.71 | 0.71 | 0.71 | 0.57 | 0.71 | 0.90 | 0.67 |
time (sec) |
N/A | 0.000 | 0.183 | 1.213 | 0.076 | 0.097 | 0.074 | 0.117 | 0.197 | 0.085 |
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 | 17 | 20 | 15 | 14 | 18 | 15 | 14 | 18 | 14 |
N.S. |
1 | 0.71 | 0.83 | 0.62 | 0.58 | 0.75 | 0.62 | 0.58 | 0.75 | 0.58 |
time (sec) |
N/A | 0.186 | 0.003 | 0.086 | 0.030 | 0.075 | 0.065 | 0.121 | 0.183 | 2.845 |
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 | 26 | 20 | 32 | 15 | 70 | 26 | 17 | 31 | 20 | 20 |
N.S. |
1 | 0.77 | 1.23 | 0.58 | 2.69 | 1.00 | 0.65 | 1.19 | 0.77 | 0.77 |
time (sec) |
N/A | 0.354 | 0.053 | 0.346 | 0.116 | 0.090 | 0.096 | 0.121 | 0.185 | 3.056 |
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 | 21 | 23 | 22 | 22 | 19 | 22 | 21 | 22 |
N.S. |
1 | 0.95 | 0.95 | 1.05 | 1.00 | 1.00 | 0.86 | 1.00 | 0.95 | 1.00 |
time (sec) |
N/A | 0.548 | 0.147 | 0.668 | 0.077 | 0.097 | 0.236 | 0.141 | 0.190 | 3.415 |
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 | 45 | 30 | 27 | 27 | 27 | 27 | 27 | 34 | 28 |
N.S. |
1 | 1.50 | 1.00 | 0.90 | 0.90 | 0.90 | 0.90 | 0.90 | 1.13 | 0.93 |
time (sec) |
N/A | 0.353 | 0.017 | 0.365 | 0.044 | 0.080 | 0.322 | 0.120 | 0.200 | 0.204 |
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 | 20 | 20 | 19 | 18 | 18 | 17 | 18 | 20 | 18 |
N.S. |
1 | 0.83 | 0.83 | 0.79 | 0.75 | 0.75 | 0.71 | 0.75 | 0.83 | 0.75 |
time (sec) |
N/A | 0.205 | 0.009 | 0.262 | 0.031 | 0.087 | 0.112 | 0.115 | 0.185 | 3.009 |
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 | 23 | 0 | 25 | 26 | 19 | 25 | 26 | 37 | 89 | 19 |
N.S. |
1 | 0.00 | 1.09 | 1.13 | 0.83 | 1.09 | 1.13 | 1.61 | 3.87 | 0.83 |
time (sec) |
N/A | 0.000 | 0.324 | 0.183 | 0.240 | 0.087 | 0.125 | 0.123 | 0.195 | 2.963 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | C | B | A | A | C | F | B |
verified |
N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 26 | 569 | 105 | 24 | 20 | 60 | 217 | 28 |
N.S. |
1 | 0.00 | 1.00 | 21.88 | 4.04 | 0.92 | 0.77 | 2.31 | 8.35 | 1.08 |
time (sec) |
N/A | 0.000 | 0.172 | 4.397 | 0.155 | 0.107 | 0.369 | 0.171 | 0.606 | 3.148 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | B | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 243 | 29 | 34 | 50 | 43 | 51 | 109 | 50 | 50 |
N.S. |
1 | 8.68 | 1.04 | 1.21 | 1.79 | 1.54 | 1.82 | 3.89 | 1.79 | 1.79 |
time (sec) |
N/A | 0.577 | 0.035 | 0.830 | 0.042 | 0.089 | 2.392 | 0.130 | 0.203 | 0.282 |
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 | 25 | 18 | 20 | 25 | 19 | 19 | 44 | 22 | 17 |
N.S. |
1 | 0.93 | 0.67 | 0.74 | 0.93 | 0.70 | 0.70 | 1.63 | 0.81 | 0.63 |
time (sec) |
N/A | 0.237 | 0.134 | 0.177 | 0.196 | 0.081 | 0.086 | 0.126 | 0.199 | 2.943 |
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 | 9 | 9 | 8 | 7 | 9 | 8 | 22 | 9 | 9 |
N.S. |
1 | 0.69 | 0.69 | 0.62 | 0.54 | 0.69 | 0.62 | 1.69 | 0.69 | 0.69 |
time (sec) |
N/A | 0.163 | 0.019 | 0.035 | 0.032 | 0.079 | 0.054 | 0.120 | 0.209 | 3.040 |
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 | 24 | 29 | 37 | 38 | 24 | 43 | 29 | 181 |
N.S. |
1 | 0.00 | 0.96 | 1.16 | 1.48 | 1.52 | 0.96 | 1.72 | 1.16 | 7.24 |
time (sec) |
N/A | 0.000 | 0.127 | 47.230 | 0.174 | 0.085 | 0.093 | 0.181 | 0.193 | 3.735 |
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 | 24 | 22 | 29 | 21 | 27 | 28 | 21 | 21 |
N.S. |
1 | 0.00 | 1.04 | 0.96 | 1.26 | 0.91 | 1.17 | 1.22 | 0.91 | 0.91 |
time (sec) |
N/A | 0.000 | 0.233 | 1.945 | 0.149 | 0.092 | 0.236 | 0.130 | 0.183 | 3.274 |
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 | 31 | 0 | 38 | 46 | 37 | 43 | 36 | 43 | 44 | 0 |
N.S. |
1 | 0.00 | 1.23 | 1.48 | 1.19 | 1.39 | 1.16 | 1.39 | 1.42 | 0.00 |
time (sec) |
N/A | 0.000 | 0.091 | 2.017 | 0.099 | 0.092 | 0.404 | 0.140 | 0.195 | 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 | 19 | 98 | 14 | 15 | 20 | 14 | 14 | 20 | 20 | 14 |
N.S. |
1 | 5.16 | 0.74 | 0.79 | 1.05 | 0.74 | 0.74 | 1.05 | 1.05 | 0.74 |
time (sec) |
N/A | 0.831 | 0.043 | 0.288 | 0.080 | 0.101 | 0.080 | 0.126 | 0.179 | 0.130 |
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 | 16 | 0 | 16 | 17 | 16 | 16 | 14 | 24 | 487 | 956 |
N.S. |
1 | 0.00 | 1.00 | 1.06 | 1.00 | 1.00 | 0.88 | 1.50 | 30.44 | 59.75 |
time (sec) |
N/A | 0.000 | 0.172 | 3.412 | 0.081 | 0.081 | 0.076 | 0.135 | 0.226 | 3.577 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 28 | 28 | 42 | 44 | 44 | 49 | 53 | 59 | 37 |
N.S. |
1 | 1.22 | 1.22 | 1.83 | 1.91 | 1.91 | 2.13 | 2.30 | 2.57 | 1.61 |
time (sec) |
N/A | 0.611 | 0.025 | 0.723 | 0.088 | 0.101 | 2.543 | 0.135 | 0.188 | 2.938 |
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 | 21 | 0 | 21 | 31 | 31 | 55 | 17 | 99 | 22 | 18 |
N.S. |
1 | 0.00 | 1.00 | 1.48 | 1.48 | 2.62 | 0.81 | 4.71 | 1.05 | 0.86 |
time (sec) |
N/A | 0.000 | 0.209 | 0.358 | 0.120 | 0.093 | 0.337 | 0.182 | 0.192 | 3.769 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 96 | 26 | 36 | 42 | 46 | 46 | 37 | 48 | 35 |
N.S. |
1 | 4.57 | 1.24 | 1.71 | 2.00 | 2.19 | 2.19 | 1.76 | 2.29 | 1.67 |
time (sec) |
N/A | 0.286 | 0.006 | 0.163 | 0.037 | 0.092 | 0.117 | 0.119 | 0.194 | 2.850 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 27 | 20 | 20 | 32 | 22 | 20 | 25 | 19 |
N.S. |
1 | 0.00 | 1.00 | 0.74 | 0.74 | 1.19 | 0.81 | 0.74 | 0.93 | 0.70 |
time (sec) |
N/A | 0.000 | 0.038 | 0.059 | 0.032 | 0.094 | 0.115 | 0.123 | 0.180 | 0.101 |
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 | 22 | 17 | 16 | 16 | 17 | 35 | 18 | 16 |
N.S. |
1 | 0.00 | 1.05 | 0.81 | 0.76 | 0.76 | 0.81 | 1.67 | 0.86 | 0.76 |
time (sec) |
N/A | 0.000 | 0.160 | 0.105 | 0.070 | 0.089 | 0.111 | 0.117 | 0.197 | 2.909 |
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 | 13 | 13 | 14 | 14 | 14 | 12 | 14 | 13 | 77 |
N.S. |
1 | 0.93 | 0.93 | 1.00 | 1.00 | 1.00 | 0.86 | 1.00 | 0.93 | 5.50 |
time (sec) |
N/A | 0.424 | 0.057 | 0.247 | 0.064 | 0.084 | 0.079 | 0.130 | 0.176 | 0.310 |
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 | 15 | 38 | 15 | 13 | 12 | 12 | 12 | 12 | 13 | 12 |
N.S. |
1 | 2.53 | 1.00 | 0.87 | 0.80 | 0.80 | 0.80 | 0.80 | 0.87 | 0.80 |
time (sec) |
N/A | 0.356 | 0.009 | 0.266 | 0.100 | 0.086 | 0.221 | 0.127 | 0.170 | 3.022 |