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 | B | B | B | B | F | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 28 | 81 | 173 | 78 | 75 | 0 | 56 | 302 |
N.S. |
1 | 0.00 | 1.00 | 2.89 | 6.18 | 2.79 | 2.68 | 0.00 | 2.00 | 10.79 |
time (sec) |
N/A | 0.000 | 0.431 | 17.036 | 0.582 | 0.074 | 0.397 | 0.000 | 0.192 | 2.037 |
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 | 24 | 24 | 22 | 23 | 24 | 24 | 23 | 44 | 24 |
N.S. |
1 | 0.92 | 0.92 | 0.85 | 0.88 | 0.92 | 0.92 | 0.88 | 1.69 | 0.92 |
time (sec) |
N/A | 0.418 | 0.094 | 1.105 | 0.206 | 0.073 | 0.178 | 0.146 | 3.439 | 1.832 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 33 | 34 | 49 | 49 | 31 | 35 | 48 | 32 |
N.S. |
1 | 0.00 | 1.10 | 1.13 | 1.63 | 1.63 | 1.03 | 1.17 | 1.60 | 1.07 |
time (sec) |
N/A | 0.000 | 0.032 | 1.435 | 0.072 | 0.066 | 0.072 | 0.122 | 0.178 | 1.968 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 17 | 17 | 81 | 1368 | 101 | 112 | 112 | 277 | 109 |
N.S. |
1 | 0.89 | 0.89 | 4.26 | 72.00 | 5.32 | 5.89 | 5.89 | 14.58 | 5.74 |
time (sec) |
N/A | 0.788 | 0.022 | 43.239 | 0.144 | 0.069 | 0.228 | 0.143 | 0.176 | 2.076 |
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 | 26 | 26 | 28 | 36 | 41 | 36 | 198 | 28 | 25 |
N.S. |
1 | 0.93 | 0.93 | 1.00 | 1.29 | 1.46 | 1.29 | 7.07 | 1.00 | 0.89 |
time (sec) |
N/A | 3.471 | 0.239 | 0.502 | 0.208 | 0.063 | 0.128 | 0.151 | 0.173 | 0.199 |
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 | 31 | 32 | 23 | 24 | 38 | 20 | 23 | 42 | 22 |
N.S. |
1 | 1.03 | 1.07 | 0.77 | 0.80 | 1.27 | 0.67 | 0.77 | 1.40 | 0.73 |
time (sec) |
N/A | 0.528 | 0.022 | 0.245 | 0.028 | 0.065 | 0.093 | 0.110 | 0.176 | 0.098 |
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 | 38 | 27 | 37 | 38 | 40 | 32 | 40 | 47 | 36 |
N.S. |
1 | 1.36 | 0.96 | 1.32 | 1.36 | 1.43 | 1.14 | 1.43 | 1.68 | 1.29 |
time (sec) |
N/A | 1.032 | 0.138 | 0.887 | 0.074 | 0.082 | 0.196 | 0.141 | 0.192 | 2.180 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 0 | 43 | 29 | 50 | 42 | 27 | 88 | 118 | 187 |
N.S. |
1 | 0.00 | 1.30 | 0.88 | 1.52 | 1.27 | 0.82 | 2.67 | 3.58 | 5.67 |
time (sec) |
N/A | 0.000 | 0.095 | 15.622 | 0.169 | 0.076 | 0.143 | 0.180 | 0.196 | 2.861 |
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 | 18 | 18 | 18 | 15 | 14 | 39 | 14 | 14 | 47 | 14 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 0.78 | 2.17 | 0.78 | 0.78 | 2.61 | 0.78 |
time (sec) |
N/A | 0.458 | 0.038 | 1.461 | 0.054 | 0.064 | 0.083 | 0.119 | 0.189 | 1.828 |
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 | 28 | 30 | 33 | 25 | 79 | 34 | 20 | 40 | 43 | 22 |
N.S. |
1 | 1.07 | 1.18 | 0.89 | 2.82 | 1.21 | 0.71 | 1.43 | 1.54 | 0.79 |
time (sec) |
N/A | 0.961 | 0.041 | 0.344 | 0.159 | 0.069 | 0.109 | 0.116 | 0.177 | 1.821 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 14 | 13 | 12 | 16 | 12 | 12 | 14 | 12 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 0.86 | 1.14 | 0.86 | 0.86 | 1.00 | 0.86 |
time (sec) |
N/A | 0.332 | 0.008 | 0.135 | 0.068 | 0.076 | 0.067 | 0.121 | 0.177 | 1.795 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | B | A | F | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 28 | 28 | 32 | 78 | 22 | 0 | 31 | 25 |
N.S. |
1 | 0.00 | 0.97 | 0.97 | 1.10 | 2.69 | 0.76 | 0.00 | 1.07 | 0.86 |
time (sec) |
N/A | 0.000 | 0.740 | 1.063 | 0.287 | 0.070 | 0.157 | 0.000 | 0.178 | 1.960 |
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 | 25 | 17 | 15 | 25 | 14 | 20 | 14 | 17 | 14 |
N.S. |
1 | 1.00 | 0.68 | 0.60 | 1.00 | 0.56 | 0.80 | 0.56 | 0.68 | 0.56 |
time (sec) |
N/A | 0.350 | 0.046 | 0.155 | 0.054 | 0.072 | 0.059 | 0.113 | 0.191 | 0.062 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | B | B | B | B | B | F | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 0 | 55 | 52 | 110 | 110 | 109 | 128 | 238 | 0 |
N.S. |
1 | 0.00 | 2.62 | 2.48 | 5.24 | 5.24 | 5.19 | 6.10 | 11.33 | 0.00 |
time (sec) |
N/A | 0.000 | 3.282 | 0.446 | 0.139 | 0.067 | 0.169 | 0.530 | 200.028 | 0.000 |
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 | 35 | 138 | 105 | 116 | 119 | 149 | 116 | 114 | 167 | 116 |
N.S. |
1 | 3.94 | 3.00 | 3.31 | 3.40 | 4.26 | 3.31 | 3.26 | 4.77 | 3.31 |
time (sec) |
N/A | 2.031 | 0.053 | 0.648 | 0.029 | 0.079 | 2.288 | 0.118 | 0.184 | 0.304 |
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 | 28 | 27 | 26 | 23 | 25 | 22 | 22 | 0 | 34 | 28 |
N.S. |
1 | 0.96 | 0.93 | 0.82 | 0.89 | 0.79 | 0.79 | 0.00 | 1.21 | 1.00 |
time (sec) |
N/A | 4.366 | 0.093 | 2.106 | 0.115 | 0.070 | 0.260 | 0.000 | 2.439 | 2.303 |
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 | 14 | 14 | 14 | 14 | 13 | 15 | 14 |
N.S. |
1 | 1.00 | 1.00 | 0.82 | 0.82 | 0.82 | 0.82 | 0.76 | 0.88 | 0.82 |
time (sec) |
N/A | 0.189 | 0.005 | 0.462 | 0.031 | 0.063 | 0.042 | 0.110 | 0.178 | 1.875 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | B | B | B | F(-1) | F | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 111 | 35 | 84 | 97 | 216 | 0 | 0 | 150 | 100 |
N.S. |
1 | 3.26 | 1.03 | 2.47 | 2.85 | 6.35 | 0.00 | 0.00 | 4.41 | 2.94 |
time (sec) |
N/A | 7.235 | 0.327 | 37.197 | 0.337 | 0.110 | 0.000 | 0.000 | 2.316 | 2.307 |
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 | 18 | 20 | 17 | 16 | 16 | 15 | 18 | 27 | 16 |
N.S. |
1 | 0.82 | 0.91 | 0.77 | 0.73 | 0.73 | 0.68 | 0.82 | 1.23 | 0.73 |
time (sec) |
N/A | 0.229 | 0.005 | 0.063 | 0.026 | 0.072 | 0.049 | 0.116 | 0.181 | 1.754 |
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 | 12 | 12 | 12 | 12 | 0 | 11 | 10 | 11 | 12 | 11 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.00 | 0.92 | 0.83 | 0.92 | 1.00 | 0.92 |
time (sec) |
N/A | 0.413 | 0.054 | 0.291 | 0.000 | 0.068 | 0.072 | 0.113 | 0.176 | 1.781 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | B | B | B | B | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 125 | 39 | 46 | 60 | 53 | 56 | 53 | 73 | 0 |
N.S. |
1 | 4.17 | 1.30 | 1.53 | 2.00 | 1.77 | 1.87 | 1.77 | 2.43 | 0.00 |
time (sec) |
N/A | 0.577 | 0.100 | 0.496 | 0.110 | 0.073 | 17.304 | 0.198 | 0.334 | 0.000 |
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 | 39 | 0 | 33 | 37 | 124 | 38 | 32 | 91 | 43 | 0 |
N.S. |
1 | 0.00 | 0.85 | 0.95 | 3.18 | 0.97 | 0.82 | 2.33 | 1.10 | 0.00 |
time (sec) |
N/A | 0.000 | 0.057 | 9.980 | 0.357 | 0.062 | 0.238 | 0.487 | 0.232 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 20 | 24 | 20 | 23 | 27 | 24 | 27 | 43 | 27 |
N.S. |
1 | 1.05 | 1.26 | 1.05 | 1.21 | 1.42 | 1.26 | 1.42 | 2.26 | 1.42 |
time (sec) |
N/A | 0.593 | 0.072 | 0.494 | 0.123 | 0.062 | 0.075 | 0.121 | 3.953 | 1.768 |
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 | 21 | 21 | 18 | 24 | 17 | 14 | 19 | 21 | 18 |
N.S. |
1 | 0.84 | 0.84 | 0.72 | 0.96 | 0.68 | 0.56 | 0.76 | 0.84 | 0.72 |
time (sec) |
N/A | 1.405 | 0.056 | 0.342 | 0.151 | 0.068 | 0.061 | 0.108 | 0.175 | 0.134 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 30 | 21 | 23 | 24 | 19 | 26 | 30 | 27 |
N.S. |
1 | 0.00 | 1.00 | 0.70 | 0.77 | 0.80 | 0.63 | 0.87 | 1.00 | 0.90 |
time (sec) |
N/A | 0.000 | 1.877 | 0.256 | 0.070 | 0.068 | 0.222 | 0.119 | 0.178 | 1.868 |
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 | 18 | 18 | 14 | 0 | 13 | 14 | 13 | 14 | 12 |
N.S. |
1 | 0.75 | 0.75 | 0.58 | 0.00 | 0.54 | 0.58 | 0.54 | 0.58 | 0.50 |
time (sec) |
N/A | 0.215 | 0.020 | 0.523 | 0.000 | 0.070 | 0.097 | 0.120 | 0.178 | 1.768 |
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 | 17 | 20 | 15 | 12 | 14 | 15 | 14 | 13 | 14 |
N.S. |
1 | 0.85 | 1.00 | 0.75 | 0.60 | 0.70 | 0.75 | 0.70 | 0.65 | 0.70 |
time (sec) |
N/A | 0.279 | 0.003 | 0.319 | 0.053 | 0.066 | 0.077 | 0.120 | 0.182 | 1.696 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | C | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 22 | 21 | 52 | 21 | 19 | 21 | 20 | 28 |
N.S. |
1 | 0.00 | 0.92 | 0.88 | 2.17 | 0.88 | 0.79 | 0.88 | 0.83 | 1.17 |
time (sec) |
N/A | 0.000 | 0.064 | 0.158 | 0.072 | 0.072 | 0.054 | 0.115 | 0.193 | 1.667 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | B | B | A | B | F | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 39 | 83 | 77 | 82 | 41 | 94 | 1367 | 45 |
N.S. |
1 | 0.00 | 1.39 | 2.96 | 2.75 | 2.93 | 1.46 | 3.36 | 48.82 | 1.61 |
time (sec) |
N/A | 0.000 | 0.064 | 31.954 | 0.258 | 0.073 | 0.317 | 2.008 | 0.280 | 2.037 |
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 | 15 | 19 | 15 | 14 | 14 | 14 | 14 | 15 | 14 |
N.S. |
1 | 0.62 | 0.79 | 0.62 | 0.58 | 0.58 | 0.58 | 0.58 | 0.62 | 0.58 |
time (sec) |
N/A | 0.318 | 0.006 | 0.263 | 0.031 | 0.058 | 0.071 | 0.118 | 0.187 | 1.707 |
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 | 3 | 3 | 4 | 3 | 3 | 2 | 3 | 3 | 3 |
N.S. |
1 | 0.17 | 0.17 | 0.22 | 0.17 | 0.17 | 0.11 | 0.17 | 0.17 | 0.17 |
time (sec) |
N/A | 0.174 | 0.001 | 0.038 | 0.023 | 0.055 | 0.026 | 0.118 | 0.191 | 0.014 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 45 | 28 | 27 | 28 | 30 | 26 | 30 | 48 | 26 |
N.S. |
1 | 1.73 | 1.08 | 1.04 | 1.08 | 1.15 | 1.00 | 1.15 | 1.85 | 1.00 |
time (sec) |
N/A | 0.588 | 0.016 | 0.283 | 0.027 | 0.062 | 0.410 | 0.116 | 0.190 | 1.776 |
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 | 14 | 15 | 15 | 15 | 15 | 28 | 14 | 14 |
N.S. |
1 | 0.00 | 0.82 | 0.88 | 0.88 | 0.88 | 0.88 | 1.65 | 0.82 | 0.82 |
time (sec) |
N/A | 0.000 | 0.078 | 1.801 | 0.065 | 0.069 | 0.141 | 0.123 | 0.199 | 1.918 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | A | A | A | B | B | B | F(-1) |
verified | N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 0 | 46 | 39 | 40 | 58 | 63 | 42 | 0 |
N.S. |
1 | 0.00 | 0.00 | 1.70 | 1.44 | 1.48 | 2.15 | 2.33 | 1.56 | 0.00 |
time (sec) |
N/A | 0.000 | 0.000 | 2.054 | 0.149 | 0.073 | 0.090 | 0.136 | 0.213 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | B | B | B | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 41 | 46 | 48 | 48 | 73 | 89 | 50 | 49 |
N.S. |
1 | 0.00 | 1.71 | 1.92 | 2.00 | 2.00 | 3.04 | 3.71 | 2.08 | 2.04 |
time (sec) |
N/A | 0.000 | 0.243 | 9.217 | 0.077 | 0.068 | 0.168 | 0.136 | 0.192 | 1.858 |
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 | 16 | 16 | 17 | 22 | 16 | 15 | 25 | 22 | 14 |
N.S. |
1 | 0.80 | 0.80 | 0.85 | 1.10 | 0.80 | 0.75 | 1.25 | 1.10 | 0.70 |
time (sec) |
N/A | 0.246 | 0.007 | 0.294 | 0.031 | 0.063 | 0.047 | 0.109 | 0.185 | 0.056 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 43 | 36 | 31 | 0 | 32 | 32 | 46 | 53 | 47 |
N.S. |
1 | 1.43 | 1.20 | 1.03 | 0.00 | 1.07 | 1.07 | 1.53 | 1.77 | 1.57 |
time (sec) |
N/A | 0.508 | 0.102 | 0.561 | 0.000 | 0.069 | 0.165 | 0.119 | 0.177 | 1.842 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 25 | 33 | 22 | 25 | 25 | 24 | 27 | 25 | 23 |
N.S. |
1 | 1.47 | 1.94 | 1.29 | 1.47 | 1.47 | 1.41 | 1.59 | 1.47 | 1.35 |
time (sec) |
N/A | 0.333 | 0.009 | 0.062 | 0.113 | 0.067 | 0.077 | 0.118 | 0.181 | 1.766 |
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 | 42 | 23 | 30 | 33 | 23 | 20 | 41 | 72 | 25 |
N.S. |
1 | 1.40 | 0.77 | 1.00 | 1.10 | 0.77 | 0.67 | 1.37 | 2.40 | 0.83 |
time (sec) |
N/A | 1.469 | 8.169 | 0.387 | 0.144 | 0.074 | 0.148 | 0.135 | 0.175 | 1.976 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | F(-2) | A | F(-2) | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 81 | 20 | 18 | 0 | 19 | 0 | 19 | 18 | 17 |
N.S. |
1 | 3.38 | 0.83 | 0.75 | 0.00 | 0.79 | 0.00 | 0.79 | 0.75 | 0.71 |
time (sec) |
N/A | 0.887 | 0.135 | 0.773 | 0.000 | 0.067 | 0.000 | 0.135 | 0.185 | 1.902 |
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 | 28 | 38 | 29 | 34 | 27 | 32 | 31 | 0 | 36 | 28 |
N.S. |
1 | 1.36 | 1.04 | 1.21 | 0.96 | 1.14 | 1.11 | 0.00 | 1.29 | 1.00 |
time (sec) |
N/A | 0.431 | 0.675 | 1.341 | 0.196 | 0.067 | 0.260 | 0.000 | 0.195 | 2.051 |
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 | 22 | 22 | 24 | 21 | 22 | 23 | 23 | 21 |
N.S. |
1 | 1.20 | 1.10 | 1.10 | 1.20 | 1.05 | 1.10 | 1.15 | 1.15 | 1.05 |
time (sec) |
N/A | 0.432 | 0.007 | 0.145 | 0.031 | 0.057 | 0.254 | 0.121 | 0.184 | 0.160 |
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 | 44 | 29 | 24 | 0 | 26 | 20 | 26 | 40 | 24 |
N.S. |
1 | 1.63 | 1.07 | 0.89 | 0.00 | 0.96 | 0.74 | 0.96 | 1.48 | 0.89 |
time (sec) |
N/A | 0.420 | 0.058 | 0.365 | 0.000 | 0.068 | 0.125 | 0.119 | 0.177 | 1.831 |
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 | 25 | 25 | 23 | 23 | 23 | 22 | 19 | 0 | 23 | 22 |
N.S. |
1 | 1.00 | 0.92 | 0.92 | 0.92 | 0.88 | 0.76 | 0.00 | 0.92 | 0.88 |
time (sec) |
N/A | 0.470 | 0.287 | 11.845 | 0.049 | 0.071 | 0.229 | 0.000 | 0.174 | 24.551 |
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 | 16 | 17 | 17 | 15 | 17 | 17 | 17 |
N.S. |
1 | 1.00 | 1.00 | 0.94 | 1.00 | 1.00 | 0.88 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.259 | 0.004 | 2.646 | 0.040 | 0.056 | 0.045 | 0.112 | 0.173 | 0.049 |
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 | 11 | 30 | 30 | 31 | 30 | 29 | 29 | 29 | 30 | 11 |
N.S. |
1 | 2.73 | 2.73 | 2.82 | 2.73 | 2.64 | 2.64 | 2.64 | 2.73 | 1.00 |
time (sec) |
N/A | 0.361 | 0.003 | 0.451 | 0.028 | 0.065 | 0.063 | 0.122 | 0.183 | 1.968 |
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 | 17 | 0 | 18 | 15 | 14 | 20 | 10 | 33 | 17 | 15 |
N.S. |
1 | 0.00 | 1.06 | 0.88 | 0.82 | 1.18 | 0.59 | 1.94 | 1.00 | 0.88 |
time (sec) |
N/A | 0.000 | 0.126 | 0.439 | 0.064 | 0.080 | 0.090 | 0.117 | 0.192 | 1.920 |
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 | 26 | 17 | 13 | 17 | 14 | 13 | 14 | 14 |
N.S. |
1 | 1.00 | 1.44 | 0.94 | 0.72 | 0.94 | 0.78 | 0.72 | 0.78 | 0.78 |
time (sec) |
N/A | 0.143 | 0.000 | 0.237 | 0.036 | 0.062 | 0.028 | 0.108 | 0.181 | 0.039 |
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 | 20 | 24 | 24 | 27 | 26 | 26 | 24 | 26 | 25 | 0 |
N.S. |
1 | 1.20 | 1.20 | 1.35 | 1.30 | 1.30 | 1.20 | 1.30 | 1.25 | 0.00 |
time (sec) |
N/A | 0.538 | 0.019 | 0.885 | 0.160 | 0.064 | 0.100 | 0.124 | 0.192 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 43 | 35 | 30 | 41 | 36 | 27 | 40 | 36 | 30 |
N.S. |
1 | 1.59 | 1.30 | 1.11 | 1.52 | 1.33 | 1.00 | 1.48 | 1.33 | 1.11 |
time (sec) |
N/A | 0.501 | 0.095 | 0.026 | 0.054 | 0.068 | 0.096 | 0.113 | 0.171 | 1.879 |
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 | 13 | 13 | 14 | 13 | 15 | 10 | 13 | 15 | 16 |
N.S. |
1 | 0.81 | 0.81 | 0.88 | 0.81 | 0.94 | 0.62 | 0.81 | 0.94 | 1.00 |
time (sec) |
N/A | 0.189 | 0.004 | 0.155 | 0.028 | 0.064 | 0.054 | 0.109 | 0.178 | 1.856 |
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 | 27 | 104 | 96 | 107 | 201 | 253 | 202 | 181 | 429 | 67153 |
N.S. |
1 | 3.85 | 3.56 | 3.96 | 7.44 | 9.37 | 7.48 | 6.70 | 15.89 | 2487.15 |
time (sec) |
N/A | 1.060 | 0.176 | 0.907 | 0.046 | 0.070 | 6.485 | 0.133 | 0.185 | 17.892 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | B | C | B | B | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 163 | 26 | 152 | 385 | 156 | 153 | 164 | 178 | 156 |
N.S. |
1 | 6.79 | 1.08 | 6.33 | 16.04 | 6.50 | 6.38 | 6.83 | 7.42 | 6.50 |
time (sec) |
N/A | 1.495 | 3.163 | 0.158 | 0.160 | 0.079 | 0.362 | 0.127 | 0.207 | 2.315 |
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 | 20 | 20 | 19 | 18 | 18 | 17 | 18 | 25 | 19 |
N.S. |
1 | 1.00 | 1.00 | 0.95 | 0.90 | 0.90 | 0.85 | 0.90 | 1.25 | 0.95 |
time (sec) |
N/A | 0.288 | 0.672 | 0.101 | 0.159 | 0.068 | 0.131 | 0.126 | 0.202 | 0.106 |
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 | 28 | 71 | 59 | 57 | 67 | 98 | 66 | 51 | 112 | 66 |
N.S. |
1 | 2.54 | 2.11 | 2.04 | 2.39 | 3.50 | 2.36 | 1.82 | 4.00 | 2.36 |
time (sec) |
N/A | 0.373 | 0.028 | 0.188 | 0.047 | 0.061 | 0.208 | 0.114 | 0.188 | 0.143 |
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 | 25 | 40 | 28 | 34 | 34 | 38 | 37 | 38 |
N.S. |
1 | 0.00 | 1.04 | 1.67 | 1.17 | 1.42 | 1.42 | 1.58 | 1.54 | 1.58 |
time (sec) |
N/A | 0.000 | 0.025 | 30.889 | 0.170 | 0.074 | 1.502 | 0.205 | 0.190 | 3.386 |
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 | 27 | 18 | 14 | 23 | 21 | 14 | 16 | 23 | 13 |
N.S. |
1 | 1.35 | 0.90 | 0.70 | 1.15 | 1.05 | 0.70 | 0.80 | 1.15 | 0.65 |
time (sec) |
N/A | 0.358 | 0.029 | 0.132 | 0.029 | 0.066 | 0.060 | 0.113 | 0.188 | 0.069 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | A | B | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 24 | 47 | 123 | 46 | 42 | 46 | 48 | 116 |
N.S. |
1 | 0.00 | 0.92 | 1.81 | 4.73 | 1.77 | 1.62 | 1.77 | 1.85 | 4.46 |
time (sec) |
N/A | 0.000 | 0.515 | 4.809 | 0.233 | 0.067 | 0.144 | 0.280 | 0.199 | 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 | 18 | 29 | 27 | 18 | 17 | 17 | 19 | 17 | 51 | 17 |
N.S. |
1 | 1.61 | 1.50 | 1.00 | 0.94 | 0.94 | 1.06 | 0.94 | 2.83 | 0.94 |
time (sec) |
N/A | 0.285 | 0.031 | 0.085 | 0.036 | 0.071 | 0.078 | 0.118 | 0.182 | 0.092 |
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 | 22 | 18 | 18 | 18 | 15 | 15 | 112 | 16 | 16 | 15 |
N.S. |
1 | 0.82 | 0.82 | 0.82 | 0.68 | 0.68 | 5.09 | 0.73 | 0.73 | 0.68 |
time (sec) |
N/A | 0.161 | 0.005 | 0.257 | 0.033 | 0.061 | 1.737 | 0.123 | 0.181 | 0.096 |
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 | 15 | 15 | 17 | 17 | 14 | 17 | 32 | 17 |
N.S. |
1 | 0.95 | 0.79 | 0.79 | 0.89 | 0.89 | 0.74 | 0.89 | 1.68 | 0.89 |
time (sec) |
N/A | 0.505 | 0.311 | 0.191 | 0.099 | 0.074 | 0.086 | 0.113 | 0.174 | 1.861 |
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 | 22 | 29 | 26 | 30 | 29 | 29 | 29 | 46 | 36 | 19 |
N.S. |
1 | 1.32 | 1.18 | 1.36 | 1.32 | 1.32 | 1.32 | 2.09 | 1.64 | 0.86 |
time (sec) |
N/A | 0.190 | 0.027 | 0.227 | 0.035 | 0.066 | 0.115 | 0.117 | 0.188 | 0.084 |
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 | 30 | 0 | 29 | 34 | 35 | 33 | 41 | 35 | 30 | 0 |
N.S. |
1 | 0.00 | 0.97 | 1.13 | 1.17 | 1.10 | 1.37 | 1.17 | 1.00 | 0.00 |
time (sec) |
N/A | 0.000 | 0.079 | 22.927 | 0.092 | 0.073 | 0.352 | 0.212 | 0.202 | 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 | 30 | 37 | 28 | 27 | 27 | 27 | 22 | 22 | 26 | 26 |
N.S. |
1 | 1.23 | 0.93 | 0.90 | 0.90 | 0.90 | 0.73 | 0.73 | 0.87 | 0.87 |
time (sec) |
N/A | 2.203 | 0.145 | 0.651 | 0.532 | 0.066 | 0.122 | 0.123 | 0.196 | 0.285 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | A | A | A | B | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 50 | 50 | 48 | 44 | 44 | 46 | 44 | 47 | 48 |
N.S. |
1 | 2.17 | 2.17 | 2.09 | 1.91 | 1.91 | 2.00 | 1.91 | 2.04 | 2.09 |
time (sec) |
N/A | 0.203 | 0.010 | 0.128 | 0.029 | 0.055 | 0.026 | 0.105 | 0.193 | 0.033 |
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 | 23 | 27 | 22 | 26 | 24 | 29 | 61 | 25 | 29 | 21 |
N.S. |
1 | 1.17 | 0.96 | 1.13 | 1.04 | 1.26 | 2.65 | 1.09 | 1.26 | 0.91 |
time (sec) |
N/A | 0.203 | 0.003 | 0.117 | 0.030 | 0.060 | 0.123 | 0.110 | 0.179 | 0.055 |
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 | 28 | 936 | 25 | 31 | 763 | 22 | 31 | 27 | 25 | 24 |
N.S. |
1 | 33.43 | 0.89 | 1.11 | 27.25 | 0.79 | 1.11 | 0.96 | 0.89 | 0.86 |
time (sec) |
N/A | 2.207 | 0.374 | 0.593 | 1.094 | 0.065 | 0.147 | 0.152 | 0.185 | 2.115 |
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 | 38 | 23 | 20 | 20 | 21 | 36 | 21 | 21 | 19 |
N.S. |
1 | 1.41 | 0.85 | 0.74 | 0.74 | 0.78 | 1.33 | 0.78 | 0.78 | 0.70 |
time (sec) |
N/A | 1.406 | 0.108 | 0.271 | 0.073 | 0.075 | 0.080 | 0.104 | 0.181 | 2.151 |
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 | 15 | 0 | 18 | 19 | 18 | 16 | 19 | 18 | 19 | 18 |
N.S. |
1 | 0.00 | 1.20 | 1.27 | 1.20 | 1.07 | 1.27 | 1.20 | 1.27 | 1.20 |
time (sec) |
N/A | 0.000 | 0.004 | 0.069 | 0.028 | 0.066 | 0.063 | 0.115 | 0.188 | 0.047 |
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 | 18 | 12 | 13 | 12 | 16 | 10 | 12 | 16 | 12 |
N.S. |
1 | 0.82 | 0.55 | 0.59 | 0.55 | 0.73 | 0.45 | 0.55 | 0.73 | 0.55 |
time (sec) |
N/A | 0.533 | 0.004 | 0.104 | 0.041 | 0.062 | 0.047 | 0.115 | 0.184 | 1.855 |
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 | 16 | 15 | 14 | 17 | 13 | 14 | 17 | 13 | 13 |
N.S. |
1 | 0.94 | 0.88 | 0.82 | 1.00 | 0.76 | 0.82 | 1.00 | 0.76 | 0.76 |
time (sec) |
N/A | 0.251 | 0.151 | 0.828 | 0.164 | 0.066 | 0.274 | 0.138 | 0.180 | 2.611 |
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 | 22 | 26 | 23 | 21 | 19 | 25 | 26 | 21 |
N.S. |
1 | 0.00 | 0.92 | 1.08 | 0.96 | 0.88 | 0.79 | 1.04 | 1.08 | 0.88 |
time (sec) |
N/A | 0.000 | 0.180 | 0.565 | 0.073 | 0.066 | 0.150 | 0.146 | 0.196 | 2.556 |
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 | 39 | 39 | 36 | 37 | 37 | 36 | 40 | 48 | 35 |
N.S. |
1 | 1.44 | 1.44 | 1.33 | 1.37 | 1.37 | 1.33 | 1.48 | 1.78 | 1.30 |
time (sec) |
N/A | 0.427 | 0.014 | 0.085 | 0.030 | 0.065 | 0.115 | 0.113 | 0.203 | 0.163 |
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 | 21 | 23 | 22 | 21 | 38 | 19 | 22 | 40 | 21 |
N.S. |
1 | 0.72 | 0.79 | 0.76 | 0.72 | 1.31 | 0.66 | 0.76 | 1.38 | 0.72 |
time (sec) |
N/A | 0.304 | 0.013 | 0.055 | 0.037 | 0.060 | 0.059 | 0.110 | 0.194 | 1.844 |
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 | 34 | 34 | 47 | 33 | 27 | 39 | 34 | 33 |
N.S. |
1 | 0.00 | 1.10 | 1.10 | 1.52 | 1.06 | 0.87 | 1.26 | 1.10 | 1.06 |
time (sec) |
N/A | 0.000 | 0.215 | 1.369 | 0.181 | 0.067 | 0.166 | 0.224 | 0.188 | 2.451 |
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 | 28 | 27 | 29 | 29 | 19 | 26 | 29 | 29 |
N.S. |
1 | 0.00 | 1.08 | 1.04 | 1.12 | 1.12 | 0.73 | 1.00 | 1.12 | 1.12 |
time (sec) |
N/A | 0.000 | 0.191 | 0.344 | 0.067 | 0.067 | 0.099 | 0.134 | 0.182 | 1.934 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | B | F(-2) | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 25 | 25 | 81 | 102 | 0 | 104 | 112 | 79 |
N.S. |
1 | 0.00 | 0.89 | 0.89 | 2.89 | 3.64 | 0.00 | 3.71 | 4.00 | 2.82 |
time (sec) |
N/A | 0.000 | 0.174 | 14.388 | 0.170 | 0.081 | 0.000 | 0.936 | 0.199 | 2.869 |
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 | 21 | 23 | 23 | 19 | 23 | 18 | 20 | 18 | 193 | 18 |
N.S. |
1 | 1.10 | 1.10 | 0.90 | 1.10 | 0.86 | 0.95 | 0.86 | 9.19 | 0.86 |
time (sec) |
N/A | 0.502 | 0.139 | 0.192 | 0.160 | 0.071 | 0.169 | 0.150 | 0.200 | 0.231 |
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 | 17 | 0 | 17 | 14 | 13 | 46 | 14 | 0 | 147 | 14 |
N.S. |
1 | 0.00 | 1.00 | 0.82 | 0.76 | 2.71 | 0.82 | 0.00 | 8.65 | 0.82 |
time (sec) |
N/A | 0.000 | 0.527 | 0.429 | 0.155 | 0.066 | 1.002 | 0.000 | 0.271 | 2.046 |
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 | 35 | 29 | 25 | 26 | 31 | 31 | 21 | 29 | 25 |
N.S. |
1 | 1.30 | 1.07 | 0.93 | 0.96 | 1.15 | 1.15 | 0.78 | 1.07 | 0.93 |
time (sec) |
N/A | 0.223 | 0.008 | 0.066 | 0.031 | 0.060 | 0.111 | 0.128 | 0.193 | 1.895 |
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 | 19 | 19 | 19 | 19 | 75 | 21 | 15 | 19 | 19 | 18 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 3.95 | 1.11 | 0.79 | 1.00 | 1.00 | 0.95 |
time (sec) |
N/A | 0.205 | 0.014 | 0.086 | 0.166 | 0.068 | 0.076 | 0.121 | 0.180 | 1.901 |
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 | 31 | 30 | 33 | 32 | 43 | 39 | 38 | 46 | 36 |
N.S. |
1 | 1.07 | 1.03 | 1.14 | 1.10 | 1.48 | 1.34 | 1.31 | 1.59 | 1.24 |
time (sec) |
N/A | 0.225 | 0.008 | 0.069 | 0.032 | 0.069 | 0.084 | 0.117 | 0.177 | 0.074 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | B | F | A | A | A | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 56 | 26 | 84 | 0 | 23 | 36 | 37 | 26 | 0 |
N.S. |
1 | 2.15 | 1.00 | 3.23 | 0.00 | 0.88 | 1.38 | 1.42 | 1.00 | 0.00 |
time (sec) |
N/A | 0.869 | 0.208 | 0.089 | 0.000 | 0.071 | 0.215 | 0.129 | 1.047 | 0.000 |
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 | 21 | 0 | 21 | 35 | 32 | 38 | 32 | 32 | 36 | 35 |
N.S. |
1 | 0.00 | 1.00 | 1.67 | 1.52 | 1.81 | 1.52 | 1.52 | 1.71 | 1.67 |
time (sec) |
N/A | 0.000 | 1.006 | 0.862 | 0.219 | 0.069 | 0.216 | 0.160 | 0.176 | 2.027 |
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 | 39 | 323 | 1272 | 532 | 648 | 668 | 728 | 785 | 1300 | 655 |
N.S. |
1 | 8.28 | 32.62 | 13.64 | 16.62 | 17.13 | 18.67 | 20.13 | 33.33 | 16.79 |
time (sec) |
N/A | 3.065 | 0.875 | 1.630 | 0.065 | 0.084 | 30.213 | 0.162 | 2.186 | 3.236 |
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 | 30 | 38 | 38 | 31 | 70 | 29 | 26 | 33 | 81 | 31 |
N.S. |
1 | 1.27 | 1.27 | 1.03 | 2.33 | 0.97 | 0.87 | 1.10 | 2.70 | 1.03 |
time (sec) |
N/A | 1.622 | 0.078 | 0.586 | 0.562 | 0.065 | 0.123 | 0.131 | 0.178 | 2.167 |
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 | 31 | 0 | 28 | 33 | 27 | 31 | 24 | 31 | 128 | 27 |
N.S. |
1 | 0.00 | 0.90 | 1.06 | 0.87 | 1.00 | 0.77 | 1.00 | 4.13 | 0.87 |
time (sec) |
N/A | 0.000 | 0.084 | 0.247 | 0.112 | 0.071 | 0.150 | 0.218 | 96.331 | 2.078 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 9 | 9 | 9 | 7 | 6 | 6 | 7 | 6 | 7 | 6 |
N.S. |
1 | 1.00 | 1.00 | 0.78 | 0.67 | 0.67 | 0.78 | 0.67 | 0.78 | 0.67 |
time (sec) |
N/A | 0.155 | 0.012 | 0.078 | 0.028 | 0.066 | 0.051 | 0.113 | 0.179 | 0.064 |
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 | 22 | 32 | 35 | 31 | 31 | 31 | 34 | 28 | 21 | 28 |
N.S. |
1 | 1.45 | 1.59 | 1.41 | 1.41 | 1.41 | 1.55 | 1.27 | 0.95 | 1.27 |
time (sec) |
N/A | 0.184 | 0.006 | 0.323 | 0.025 | 0.067 | 0.228 | 0.111 | 0.168 | 0.188 |
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 | 22 | 0 | 21 | 31 | 25 | 21 | 24 | 38 | 25 | 19 |
N.S. |
1 | 0.00 | 0.95 | 1.41 | 1.14 | 0.95 | 1.09 | 1.73 | 1.14 | 0.86 |
time (sec) |
N/A | 0.000 | 0.686 | 0.174 | 0.170 | 0.065 | 0.148 | 0.117 | 0.173 | 1.893 |
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 | 18 | 18 | 18 | 17 | 17 | 15 | 17 | 32 | 18 |
N.S. |
1 | 0.82 | 0.82 | 0.82 | 0.77 | 0.77 | 0.68 | 0.77 | 1.45 | 0.82 |
time (sec) |
N/A | 0.159 | 0.024 | 0.086 | 0.032 | 0.068 | 0.059 | 0.107 | 0.165 | 0.097 |
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 | 25 | 26 | 34 | 25 | 24 | 31 | 52 | 29 |
N.S. |
1 | 0.00 | 0.69 | 0.72 | 0.94 | 0.69 | 0.67 | 0.86 | 1.44 | 0.81 |
time (sec) |
N/A | 0.000 | 0.078 | 0.170 | 0.106 | 0.070 | 0.141 | 0.130 | 0.189 | 2.099 |
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 | 11 | 10 | 10 | 8 | 16 | 23 | 10 |
N.S. |
1 | 1.00 | 1.00 | 0.85 | 0.77 | 0.77 | 0.62 | 1.23 | 1.77 | 0.77 |
time (sec) |
N/A | 0.167 | 0.006 | 0.123 | 0.030 | 0.060 | 0.078 | 0.110 | 0.178 | 1.870 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F(-1) | C | A | A | F(-1) | F | B | B |
verified | N/A | N/A | N/A | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 0 | 152 | 42 | 40 | 0 | 0 | 40 | 40 |
N.S. |
1 | 0.00 | 0.00 | 4.90 | 1.35 | 1.29 | 0.00 | 0.00 | 1.29 | 1.29 |
time (sec) |
N/A | 0.000 | 0.000 | 0.227 | 0.241 | 0.076 | 0.000 | 0.000 | 0.185 | 3.952 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | B | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 45 | 41 | 32 | 40 | 39 | 44 | 40 | 36 | 23 |
N.S. |
1 | 1.88 | 1.71 | 1.33 | 1.67 | 1.62 | 1.83 | 1.67 | 1.50 | 0.96 |
time (sec) |
N/A | 0.177 | 0.002 | 0.090 | 0.025 | 0.059 | 0.045 | 0.111 | 0.177 | 1.863 |
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 | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 22 | 22 | 19 | 93 | 18 | 20 | 18 | 29 | 20 |
N.S. |
1 | 0.81 | 0.81 | 0.70 | 3.44 | 0.67 | 0.74 | 0.67 | 1.07 | 0.74 |
time (sec) |
N/A | 0.304 | 0.027 | 0.129 | 0.157 | 0.069 | 0.104 | 0.123 | 0.189 | 0.100 |
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 | 22 | 50 | 29 | 29 | 53 | 59 | 60 | 53 | 50 | 42 |
N.S. |
1 | 2.27 | 1.32 | 1.32 | 2.41 | 2.68 | 2.73 | 2.41 | 2.27 | 1.91 |
time (sec) |
N/A | 0.183 | 0.003 | 0.102 | 0.029 | 0.065 | 0.043 | 0.114 | 0.203 | 0.086 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 10 | 8 | 8 | 9 | 8 | 8 | 5 | 8 | 8 | 8 |
N.S. |
1 | 0.80 | 0.80 | 0.90 | 0.80 | 0.80 | 0.50 | 0.80 | 0.80 | 0.80 |
time (sec) |
N/A | 0.186 | 0.003 | 0.098 | 0.026 | 0.055 | 0.043 | 0.116 | 0.194 | 0.107 |
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 | 17 | 17 | 18 | 17 | 15 | 15 | 16 | 15 | 15 |
N.S. |
1 | 0.63 | 0.63 | 0.67 | 0.63 | 0.56 | 0.56 | 0.59 | 0.56 | 0.56 |
time (sec) |
N/A | 0.191 | 0.004 | 0.164 | 0.027 | 0.062 | 0.066 | 0.115 | 0.188 | 2.141 |
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 | 24 | 30 | 30 | 19 | 42 | 18 | 24 | 18 | 20 | 18 |
N.S. |
1 | 1.25 | 1.25 | 0.79 | 1.75 | 0.75 | 1.00 | 0.75 | 0.83 | 0.75 |
time (sec) |
N/A | 0.599 | 0.045 | 0.548 | 0.181 | 0.067 | 0.516 | 0.276 | 0.200 | 5.669 |