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 | B | A | B | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 12 | 75 | 83 | 11 | 47 | 10 | 10 | 10 | 10 | 10 |
N.S. |
1 | 6.25 | 6.92 | 0.92 | 3.92 | 0.83 | 0.83 | 0.83 | 0.83 | 0.83 |
time (sec) |
N/A | 0.478 | 0.019 | 0.286 | 0.031 | 0.079 | 0.060 | 0.109 | 0.178 | 2.909 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | B | F(-1) | A | B | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 0 | 33 | 33 | 42 | 72 | 0 | 37 | 36 | 0 |
N.S. |
1 | 0.00 | 1.00 | 1.00 | 1.27 | 2.18 | 0.00 | 1.12 | 1.09 | 0.00 |
time (sec) |
N/A | 0.000 | 5.097 | 40.395 | 0.116 | 0.107 | 0.000 | 0.227 | 0.178 | 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 | 23 | 0 | 22 | 25 | 38 | 25 | 22 | 39 | 25 | 25 |
N.S. |
1 | 0.00 | 0.96 | 1.09 | 1.65 | 1.09 | 0.96 | 1.70 | 1.09 | 1.09 |
time (sec) |
N/A | 0.000 | 0.258 | 3.664 | 0.177 | 0.080 | 0.245 | 0.143 | 0.178 | 2.907 |
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 | 24 | 21 | 17 | 17 | 22 | 20 | 17 | 16 |
N.S. |
1 | 0.00 | 1.41 | 1.24 | 1.00 | 1.00 | 1.29 | 1.18 | 1.00 | 0.94 |
time (sec) |
N/A | 0.000 | 0.099 | 8.167 | 0.062 | 0.093 | 0.140 | 0.132 | 0.193 | 3.035 |
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 | 23 | 21 | 21 | 21 | 27 | 40 | 26 | 0 |
N.S. |
1 | 0.00 | 1.00 | 0.91 | 0.91 | 0.91 | 1.17 | 1.74 | 1.13 | 0.00 |
time (sec) |
N/A | 0.000 | 2.308 | 0.049 | 0.110 | 0.079 | 3.244 | 0.131 | 0.198 | 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 | 27 | 23 | 19 | 13 | 12 | 13 | 12 | 42 | 14 | 12 |
N.S. |
1 | 0.85 | 0.70 | 0.48 | 0.44 | 0.48 | 0.44 | 1.56 | 0.52 | 0.44 |
time (sec) |
N/A | 0.185 | 0.009 | 0.208 | 0.031 | 0.077 | 0.049 | 0.117 | 0.186 | 2.605 |
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 | 24 | 77 | 43 | 33 | 47 | 29 | 37 | 32 | 35 | 34 |
N.S. |
1 | 3.21 | 1.79 | 1.38 | 1.96 | 1.21 | 1.54 | 1.33 | 1.46 | 1.42 |
time (sec) |
N/A | 0.250 | 0.013 | 0.316 | 0.027 | 0.087 | 0.125 | 0.113 | 0.173 | 2.706 |
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 | 28 | 0 | 28 | 26 | 25 | 65 | 22 | 0 | 31 | 26 |
N.S. |
1 | 0.00 | 1.00 | 0.93 | 0.89 | 2.32 | 0.79 | 0.00 | 1.11 | 0.93 |
time (sec) |
N/A | 0.000 | 0.440 | 10.097 | 0.185 | 0.087 | 3.342 | 0.000 | 0.215 | 3.167 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 23 | 24 | 24 | 24 | 24 | 24 | 35 | 0 |
N.S. |
1 | 0.00 | 0.88 | 0.92 | 0.92 | 0.92 | 0.92 | 0.92 | 1.35 | 0.00 |
time (sec) |
N/A | 0.000 | 0.102 | 1.181 | 0.137 | 0.086 | 0.089 | 0.153 | 0.177 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 39 | 29 | 34 | 27 | 30 | 39 | 25 | 70 | 24 |
N.S. |
1 | 1.50 | 1.12 | 1.31 | 1.04 | 1.15 | 1.50 | 0.96 | 2.69 | 0.92 |
time (sec) |
N/A | 0.770 | 0.180 | 0.540 | 0.291 | 0.081 | 0.234 | 0.219 | 200.036 | 2.670 |
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 | 27 | 12 | 12 | 21 | 11 | 10 | 11 | 10 | 9 |
N.S. |
1 | 1.69 | 0.75 | 0.75 | 1.31 | 0.69 | 0.62 | 0.69 | 0.62 | 0.56 |
time (sec) |
N/A | 0.157 | 0.016 | 0.117 | 0.027 | 0.080 | 0.038 | 0.112 | 0.184 | 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 | 24 | 22 | 29 | 27 | 24 | 23 | 27 | 24 | 27 | 23 |
N.S. |
1 | 0.92 | 1.21 | 1.12 | 1.00 | 0.96 | 1.12 | 1.00 | 1.12 | 0.96 |
time (sec) |
N/A | 0.141 | 0.002 | 0.126 | 0.029 | 0.083 | 0.027 | 0.115 | 0.182 | 2.560 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | B | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 43 | 42 | 39 | 39 | 37 | 53 | 47 | 39 |
N.S. |
1 | 0.00 | 1.87 | 1.83 | 1.70 | 1.70 | 1.61 | 2.30 | 2.04 | 1.70 |
time (sec) |
N/A | 0.000 | 3.139 | 5.314 | 0.119 | 0.079 | 0.449 | 0.401 | 0.204 | 2.715 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | B | B | B | F(-1) | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 700 | 711 | 683 | 780 | 666 | 0 | 1412 | 974 | 767 |
N.S. |
1 | 26.92 | 27.35 | 26.27 | 30.00 | 25.62 | 0.00 | 54.31 | 37.46 | 29.50 |
time (sec) |
N/A | 4.962 | 0.553 | 1.796 | 0.080 | 0.094 | 0.000 | 0.133 | 0.179 | 2.859 |
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 | 41 | 41 | 42 | 41 | 39 | 37 | 41 | 41 | 34 |
N.S. |
1 | 1.78 | 1.78 | 1.83 | 1.78 | 1.70 | 1.61 | 1.78 | 1.78 | 1.48 |
time (sec) |
N/A | 0.468 | 0.004 | 0.729 | 0.071 | 0.086 | 0.069 | 0.114 | 0.171 | 2.642 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | B | B | B | B | B | F(-1) |
verified | N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 43 | 274 | 248 | 196 | 243 | 314 | 295 | 0 |
N.S. |
1 | 0.00 | 1.54 | 9.79 | 8.86 | 7.00 | 8.68 | 11.21 | 10.54 | 0.00 |
time (sec) |
N/A | 0.000 | 0.187 | 0.160 | 0.678 | 0.104 | 0.588 | 1.772 | 0.192 | 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 | 3 | 3 | 3 | 3 | 2 | 2 | 2 | 2 | 3 | 2 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.67 | 0.67 | 0.67 | 0.67 | 1.00 | 0.67 |
time (sec) |
N/A | 0.130 | 0.000 | 0.043 | 0.024 | 0.070 | 0.031 | 0.111 | 0.181 | 0.005 |
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 | 25 | 26 | 33 | 24 | 29 | 32 | 34 | 108 |
N.S. |
1 | 0.00 | 0.93 | 0.96 | 1.22 | 0.89 | 1.07 | 1.19 | 1.26 | 4.00 |
time (sec) |
N/A | 0.000 | 1.988 | 17.546 | 0.158 | 0.093 | 0.144 | 0.174 | 0.185 | 2.972 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | A | F | B | F(-1) | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 40 | 0 | 82 | 35 | 0 | 64 | 0 | 272 | 84 | 254 |
N.S. |
1 | 0.00 | 2.05 | 0.88 | 0.00 | 1.60 | 0.00 | 6.80 | 2.10 | 6.35 |
time (sec) |
N/A | 0.000 | 0.316 | 4.514 | 0.000 | 0.089 | 0.000 | 0.353 | 0.225 | 3.233 |
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 | 17 | 15 | 16 | 16 | 14 | 15 | 16 | 16 |
N.S. |
1 | 0.00 | 0.71 | 0.62 | 0.67 | 0.67 | 0.58 | 0.62 | 0.67 | 0.67 |
time (sec) |
N/A | 0.000 | 0.253 | 0.061 | 0.065 | 0.078 | 0.086 | 0.112 | 0.188 | 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 | 16 | 17 | 21 | 15 | 14 | 22 | 10 | 14 | 24 | 14 |
N.S. |
1 | 1.06 | 1.31 | 0.94 | 0.88 | 1.38 | 0.62 | 0.88 | 1.50 | 0.88 |
time (sec) |
N/A | 0.183 | 0.010 | 0.265 | 0.027 | 0.078 | 0.051 | 0.110 | 0.179 | 0.052 |
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 | 10 | 10 | 11 | 10 | 15 | 8 | 11 | 21 | 10 |
N.S. |
1 | 0.50 | 0.50 | 0.55 | 0.50 | 0.75 | 0.40 | 0.55 | 1.05 | 0.50 |
time (sec) |
N/A | 0.193 | 0.005 | 0.047 | 0.023 | 0.068 | 0.040 | 0.110 | 0.172 | 2.998 |
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 | 33 | 32 | 28 | 27 | 28 | 32 | 26 |
N.S. |
1 | 0.00 | 0.94 | 1.00 | 0.97 | 0.85 | 0.82 | 0.85 | 0.97 | 0.79 |
time (sec) |
N/A | 0.000 | 0.224 | 0.830 | 0.177 | 0.092 | 4.946 | 0.150 | 0.175 | 3.285 |
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 | 18 | 23 | 23 | 59 | 57 | 57 | 60 | 122 | 57 | 62 |
N.S. |
1 | 1.28 | 1.28 | 3.28 | 3.17 | 3.17 | 3.33 | 6.78 | 3.17 | 3.44 |
time (sec) |
N/A | 0.527 | 0.020 | 1.364 | 0.084 | 0.090 | 0.513 | 0.212 | 0.177 | 3.202 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | A | A | A | A | F | B | B |
verified | N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 0 | 0 | 17 | 17 | 17 | 20 | 0 | 20 | 17 |
N.S. |
1 | 0.00 | 0.00 | 0.89 | 0.89 | 0.89 | 1.05 | 0.00 | 1.05 | 0.89 |
time (sec) |
N/A | 0.000 | 0.000 | 0.530 | 0.144 | 0.086 | 0.088 | 0.000 | 0.175 | 2.602 |
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 | 10 | 9 | 9 | 8 | 11 | 9 | 9 |
N.S. |
1 | 0.69 | 0.69 | 0.77 | 0.69 | 0.69 | 0.62 | 0.85 | 0.69 | 0.69 |
time (sec) |
N/A | 0.152 | 0.003 | 0.115 | 0.024 | 0.075 | 0.047 | 0.115 | 0.174 | 0.026 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | B | B | B | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 32 | 37 | 48 | 50 | 60 | 56 | 56 | 0 |
N.S. |
1 | 0.00 | 1.23 | 1.42 | 1.85 | 1.92 | 2.31 | 2.15 | 2.15 | 0.00 |
time (sec) |
N/A | 0.000 | 0.091 | 0.347 | 0.076 | 0.095 | 0.196 | 0.158 | 0.182 | 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 | 25 | 40 | 30 | 26 | 54 | 33 | 41 | 41 | 45 | 29 |
N.S. |
1 | 1.60 | 1.20 | 1.04 | 2.16 | 1.32 | 1.64 | 1.64 | 1.80 | 1.16 |
time (sec) |
N/A | 0.226 | 0.010 | 0.249 | 0.033 | 0.096 | 0.086 | 0.113 | 0.174 | 2.711 |
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 | 16 | 14 | 11 | 16 | 16 | 17 | 10 | 18 | 10 |
N.S. |
1 | 1.14 | 1.00 | 0.79 | 1.14 | 1.14 | 1.21 | 0.71 | 1.29 | 0.71 |
time (sec) |
N/A | 0.172 | 0.005 | 0.078 | 0.030 | 0.083 | 0.047 | 0.115 | 0.184 | 2.634 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | A | A | A | F(-2) | A | B | B |
verified | N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 0 | 22 | 34 | 21 | 0 | 22 | 27 | 23 |
N.S. |
1 | 0.00 | 0.00 | 0.92 | 1.42 | 0.88 | 0.00 | 0.92 | 1.12 | 0.96 |
time (sec) |
N/A | 0.000 | 0.000 | 153.113 | 0.332 | 0.095 | 0.000 | 0.124 | 0.182 | 3.045 |
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 | 15 | 15 | 13 | 14 | 19 | 19 | 17 | 17 | 12 |
N.S. |
1 | 0.88 | 0.88 | 0.76 | 0.82 | 1.12 | 1.12 | 1.00 | 1.00 | 0.71 |
time (sec) |
N/A | 0.385 | 0.013 | 0.266 | 0.165 | 0.087 | 0.135 | 0.113 | 1.564 | 2.729 |
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 | 19 | 19 | 17 | 16 | 16 | 14 | 16 | 17 | 16 |
N.S. |
1 | 0.90 | 0.90 | 0.81 | 0.76 | 0.76 | 0.67 | 0.76 | 0.81 | 0.76 |
time (sec) |
N/A | 0.377 | 4.325 | 0.345 | 0.163 | 0.093 | 0.134 | 0.114 | 0.195 | 2.670 |
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 | 12 | 12 | 12 | 11 | 11 | 10 | 11 | 12 | 11 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.92 | 0.92 | 0.83 | 0.92 | 1.00 | 0.92 |
time (sec) |
N/A | 0.229 | 0.009 | 0.067 | 0.030 | 0.086 | 0.071 | 0.109 | 0.187 | 2.544 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | F | A | F(-1) | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 52 | 23 | 0 | 20 | 0 | 35 | 39 | 18 |
N.S. |
1 | 1.00 | 2.36 | 1.05 | 0.00 | 0.91 | 0.00 | 1.59 | 1.77 | 0.82 |
time (sec) |
N/A | 0.671 | 0.024 | 4.071 | 0.000 | 0.091 | 0.000 | 0.158 | 0.185 | 2.509 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 79 | 73 | 27 | 33 | 30 | 31 | 33 | 33 | 33 |
N.S. |
1 | 3.29 | 3.04 | 1.12 | 1.38 | 1.25 | 1.29 | 1.38 | 1.38 | 1.38 |
time (sec) |
N/A | 0.476 | 0.064 | 0.464 | 0.194 | 0.077 | 0.165 | 0.154 | 0.206 | 2.955 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F | A | A | F | B | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 43 | 29 | 0 | 37 | 37 | 0 | 39 | 0 |
N.S. |
1 | 0.00 | 1.34 | 0.91 | 0.00 | 1.16 | 1.16 | 0.00 | 1.22 | 0.00 |
time (sec) |
N/A | 0.000 | 0.265 | 0.250 | 0.000 | 0.100 | 5.228 | 0.000 | 0.218 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 39 | 21 | 34 | 23 | 68 | 36 | 69 | 60 | 39 |
N.S. |
1 | 1.86 | 1.00 | 1.62 | 1.10 | 3.24 | 1.71 | 3.29 | 2.86 | 1.86 |
time (sec) |
N/A | 0.212 | 0.009 | 0.150 | 0.106 | 0.079 | 0.068 | 0.128 | 0.184 | 2.658 |
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 | 33 | 33 | 32 | 32 | 29 | 32 | 30 | 32 |
N.S. |
1 | 0.00 | 1.32 | 1.32 | 1.28 | 1.28 | 1.16 | 1.28 | 1.20 | 1.28 |
time (sec) |
N/A | 0.000 | 0.021 | 0.448 | 0.035 | 0.080 | 8.231 | 0.137 | 0.178 | 0.139 |
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 | 22 | 26 | 25 | 22 | 20 | 22 | 27 | 19 |
N.S. |
1 | 0.00 | 0.76 | 0.90 | 0.86 | 0.76 | 0.69 | 0.76 | 0.93 | 0.66 |
time (sec) |
N/A | 0.000 | 0.175 | 0.270 | 0.097 | 0.075 | 0.082 | 0.124 | 1.638 | 2.574 |
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 | 38 | 25 | 24 | 27 | 27 | 27 | 27 | 24 | 19 |
N.S. |
1 | 1.65 | 1.09 | 1.04 | 1.17 | 1.17 | 1.17 | 1.17 | 1.04 | 0.83 |
time (sec) |
N/A | 0.232 | 0.007 | 0.165 | 0.030 | 0.081 | 0.162 | 0.113 | 0.177 | 0.072 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
verified | N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 30 | 25 | 22 | 18 | 18 | 0 | 31 | 20 | 35 |
N.S. |
1 | 1.11 | 0.93 | 0.81 | 0.67 | 0.67 | 0.00 | 1.15 | 0.74 | 1.30 |
time (sec) |
N/A | 0.314 | 0.140 | 0.264 | 0.034 | 0.084 | 0.000 | 0.582 | 0.210 | 2.814 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | F | F | F(-2) | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 101 | 26 | 0 | 0 | 0 | 0 | 0 | 262 | 0 |
N.S. |
1 | 3.88 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 10.08 | 0.00 |
time (sec) |
N/A | 0.428 | 0.091 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.290 | 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 | 28 | 0 | 49 | 29 | 113 | 29 | 32 | 45 | 31 | 27 |
N.S. |
1 | 0.00 | 1.75 | 1.04 | 4.04 | 1.04 | 1.14 | 1.61 | 1.11 | 0.96 |
time (sec) |
N/A | 0.000 | 0.064 | 0.271 | 0.040 | 0.084 | 0.128 | 0.112 | 0.172 | 2.385 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F | B | A | F | F | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 0 | 16 | 20 | 0 | 35 | 19 | 0 | 118 | 0 |
N.S. |
1 | 0.00 | 1.00 | 1.25 | 0.00 | 2.19 | 1.19 | 0.00 | 7.38 | 0.00 |
time (sec) |
N/A | 0.000 | 0.999 | 0.316 | 0.000 | 0.094 | 0.188 | 0.000 | 0.189 | 0.000 |
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 | 22 | 23 | 61 | 61 | 31 | 61 | 87 | 44 |
N.S. |
1 | 0.00 | 0.88 | 0.92 | 2.44 | 2.44 | 1.24 | 2.44 | 3.48 | 1.76 |
time (sec) |
N/A | 0.000 | 0.034 | 0.343 | 0.076 | 0.082 | 0.079 | 0.136 | 0.276 | 2.806 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | B | B | B | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 52 | 55 | 49 | 49 | 68 | 56 | 70 | 0 |
N.S. |
1 | 0.00 | 1.73 | 1.83 | 1.63 | 1.63 | 2.27 | 1.87 | 2.33 | 0.00 |
time (sec) |
N/A | 0.000 | 0.056 | 0.425 | 0.188 | 0.096 | 0.290 | 0.223 | 0.184 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | C | B | A | F(-2) | B | B | B |
verified | N/A | N/A | N/A | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 0 | 2291 | 75 | 36 | 0 | 143 | 35 | 35 |
N.S. |
1 | 0.00 | 0.00 | 79.00 | 2.59 | 1.24 | 0.00 | 4.93 | 1.21 | 1.21 |
time (sec) |
N/A | 0.000 | 0.000 | 2.497 | 0.190 | 0.091 | 0.000 | 0.789 | 0.181 | 3.079 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | F(-1) | A | B | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 0 | 23 | 26 | 20 | 28 | 0 | 28 | 22 | 0 |
N.S. |
1 | 0.00 | 1.21 | 1.37 | 1.05 | 1.47 | 0.00 | 1.47 | 1.16 | 0.00 |
time (sec) |
N/A | 0.000 | 1.153 | 0.828 | 0.148 | 0.083 | 0.000 | 0.126 | 0.178 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | A | F(-2) | A | A | F | F | B |
verified | N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 0 | 36 | 0 | 36 | 37 | 0 | 0 | 48 |
N.S. |
1 | 0.00 | 0.00 | 1.38 | 0.00 | 1.38 | 1.42 | 0.00 | 0.00 | 1.85 |
time (sec) |
N/A | 0.000 | 0.000 | 108.617 | 0.000 | 0.096 | 1.568 | 0.000 | 4.623 | 3.061 |
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 | 15 | 15 | 16 | 15 | 15 | 14 | 15 | 15 | 15 |
N.S. |
1 | 1.15 | 1.15 | 1.23 | 1.15 | 1.15 | 1.08 | 1.15 | 1.15 | 1.15 |
time (sec) |
N/A | 0.445 | 0.305 | 0.195 | 0.056 | 0.083 | 0.096 | 0.128 | 0.196 | 0.197 |
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 | 19 | 17 | 13 | 12 | 12 | 15 | 12 | 15 | 12 |
N.S. |
1 | 1.00 | 0.89 | 0.68 | 0.63 | 0.63 | 0.79 | 0.63 | 0.79 | 0.63 |
time (sec) |
N/A | 0.169 | 0.007 | 0.139 | 0.030 | 0.088 | 0.052 | 0.114 | 0.208 | 2.820 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | B | B | A | B | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 60 | 61 | 54 | 66 | 52 | 54 | 61 | 55 | 49 |
N.S. |
1 | 2.40 | 2.44 | 2.16 | 2.64 | 2.08 | 2.16 | 2.44 | 2.20 | 1.96 |
time (sec) |
N/A | 0.216 | 0.016 | 0.385 | 0.026 | 0.084 | 0.078 | 0.117 | 0.239 | 2.702 |
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 | 21 | 18 | 14 | 19 | 16 | 20 | 19 | 20 | 17 |
N.S. |
1 | 1.17 | 1.00 | 0.78 | 1.06 | 0.89 | 1.11 | 1.06 | 1.11 | 0.94 |
time (sec) |
N/A | 0.310 | 0.187 | 0.516 | 0.157 | 0.078 | 0.190 | 0.124 | 0.247 | 2.527 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | B | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 30 | 30 | 53 | 33 | 52 | 61 | 63 | 57 | 52 |
N.S. |
1 | 1.20 | 1.20 | 2.12 | 1.32 | 2.08 | 2.44 | 2.52 | 2.28 | 2.08 |
time (sec) |
N/A | 0.923 | 0.052 | 30.283 | 0.192 | 0.090 | 6.047 | 3.269 | 0.195 | 2.904 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | F(-2) | F | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 33 | 27 | 26 | 26 | 0 | 0 | 30 | 21 |
N.S. |
1 | 0.00 | 1.14 | 0.93 | 0.90 | 0.90 | 0.00 | 0.00 | 1.03 | 0.72 |
time (sec) |
N/A | 0.000 | 0.963 | 0.914 | 0.096 | 0.091 | 0.000 | 0.000 | 0.191 | 2.503 |
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 | 22 | 26 | 25 | 25 | 0 | 29 | 25 | 20 |
N.S. |
1 | 0.00 | 0.92 | 1.08 | 1.04 | 1.04 | 0.00 | 1.21 | 1.04 | 0.83 |
time (sec) |
N/A | 0.000 | 0.336 | 81.512 | 0.104 | 0.091 | 0.000 | 0.128 | 0.186 | 2.683 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | C | A | A | A | B | B | F(-1) |
verified | N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 62 | 33 | 2626 | 43 | 37 | 32 | 54 | 57 | 0 |
N.S. |
1 | 2.14 | 1.14 | 90.55 | 1.48 | 1.28 | 1.10 | 1.86 | 1.97 | 0.00 |
time (sec) |
N/A | 14.214 | 0.110 | 0.095 | 0.131 | 0.106 | 0.659 | 0.279 | 0.210 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | B | B | F | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 0 | 26 | 67 | 146 | 63 | 70 | 0 | 107 | 213 |
N.S. |
1 | 0.00 | 1.24 | 3.19 | 6.95 | 3.00 | 3.33 | 0.00 | 5.10 | 10.14 |
time (sec) |
N/A | 0.000 | 0.101 | 1.898 | 1.948 | 0.098 | 1.642 | 0.000 | 0.240 | 3.074 |
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 | 23 | 40 | 40 | 22 | 40 | 66 | 39 |
N.S. |
1 | 0.00 | 1.00 | 0.82 | 1.43 | 1.43 | 0.79 | 1.43 | 2.36 | 1.39 |
time (sec) |
N/A | 0.000 | 0.243 | 0.427 | 0.140 | 0.080 | 0.078 | 0.143 | 0.243 | 2.560 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 27 | 27 | 30 | 29 | 31 | 60 | 29 | 31 | 47 |
N.S. |
1 | 0.96 | 0.96 | 1.07 | 1.04 | 1.11 | 2.14 | 1.04 | 1.11 | 1.68 |
time (sec) |
N/A | 0.166 | 0.006 | 0.407 | 0.039 | 0.085 | 0.064 | 0.108 | 0.189 | 0.055 |
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 | 25 | 22 | 23 | 35 | 35 | 17 | 35 | 41 | 21 |
N.S. |
1 | 0.89 | 0.79 | 0.82 | 1.25 | 1.25 | 0.61 | 1.25 | 1.46 | 0.75 |
time (sec) |
N/A | 0.914 | 0.154 | 0.154 | 0.142 | 0.083 | 0.120 | 0.362 | 0.182 | 2.401 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | B | B | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 21 | 32 | 61 | 61 | 63 | 61 | 64 | 71 |
N.S. |
1 | 0.00 | 0.91 | 1.39 | 2.65 | 2.65 | 2.74 | 2.65 | 2.78 | 3.09 |
time (sec) |
N/A | 0.000 | 2.335 | 0.523 | 0.082 | 0.079 | 0.113 | 0.127 | 0.180 | 4.559 |
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 | 20 | 20 | 29 | 29 | 14 | 19 | 29 | 90 |
N.S. |
1 | 0.00 | 0.87 | 0.87 | 1.26 | 1.26 | 0.61 | 0.83 | 1.26 | 3.91 |
time (sec) |
N/A | 0.000 | 0.188 | 1.647 | 0.071 | 0.081 | 0.195 | 0.200 | 0.207 | 2.520 |
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 | 38 | 36 | 35 | 35 | 31 | 35 | 36 | 216 |
N.S. |
1 | 0.00 | 1.06 | 1.00 | 0.97 | 0.97 | 0.86 | 0.97 | 1.00 | 6.00 |
time (sec) |
N/A | 0.000 | 0.069 | 18.675 | 0.228 | 0.098 | 0.217 | 0.360 | 0.214 | 2.592 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 23 | 25 | 18 | 22 | 22 | 15 | 22 | 19 | 24 |
N.S. |
1 | 0.68 | 0.74 | 0.53 | 0.65 | 0.65 | 0.44 | 0.65 | 0.56 | 0.71 |
time (sec) |
N/A | 0.158 | 0.002 | 0.053 | 0.024 | 0.076 | 0.020 | 0.113 | 0.188 | 0.275 |
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 | 11 | 9 | 9 | 9 | 9 | 7 | 9 | 8 | 8 |
N.S. |
1 | 0.69 | 0.56 | 0.56 | 0.56 | 0.56 | 0.44 | 0.56 | 0.50 | 0.50 |
time (sec) |
N/A | 0.131 | 0.000 | 0.023 | 0.027 | 0.064 | 0.015 | 0.106 | 0.183 | 0.016 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | A | A | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 62 | 21 | 20 | 24 | 27 | 20 | 54 | 38 | 25 |
N.S. |
1 | 2.30 | 0.78 | 0.74 | 0.89 | 1.00 | 0.74 | 2.00 | 1.41 | 0.93 |
time (sec) |
N/A | 0.339 | 0.018 | 0.229 | 0.035 | 0.086 | 0.416 | 0.120 | 0.195 | 2.602 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | C | A | B | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 27 | 27 | 56 | 69 | 46 | 53 | 88 | 39 | 38 |
N.S. |
1 | 0.96 | 0.96 | 2.00 | 2.46 | 1.64 | 1.89 | 3.14 | 1.39 | 1.36 |
time (sec) |
N/A | 0.519 | 0.017 | 0.564 | 0.137 | 0.093 | 0.176 | 0.128 | 0.190 | 2.778 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | B | B | B | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 96 | 28 | 35 | 57 | 72 | 53 | 72 | 59 | 169 |
N.S. |
1 | 4.17 | 1.22 | 1.52 | 2.48 | 3.13 | 2.30 | 3.13 | 2.57 | 7.35 |
time (sec) |
N/A | 1.619 | 5.051 | 40.233 | 0.087 | 0.090 | 0.152 | 0.146 | 0.172 | 2.692 |
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 | 29 | 28 | 27 | 27 | 24 | 27 | 26 | 25 |
N.S. |
1 | 1.64 | 1.32 | 1.27 | 1.23 | 1.23 | 1.09 | 1.23 | 1.18 | 1.14 |
time (sec) |
N/A | 0.180 | 0.013 | 0.222 | 0.025 | 0.103 | 0.063 | 0.110 | 0.179 | 0.040 |
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 | 19 | 16 | 15 | 17 | 17 | 17 | 21 | 17 |
N.S. |
1 | 1.05 | 1.00 | 0.84 | 0.79 | 0.89 | 0.89 | 0.89 | 1.11 | 0.89 |
time (sec) |
N/A | 0.167 | 0.052 | 0.148 | 0.029 | 0.085 | 0.056 | 0.107 | 0.179 | 0.063 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | C | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 18 | 17 | 18 | 28 | 17 | 14 | 45 | 17 | 17 |
N.S. |
1 | 0.95 | 0.89 | 0.95 | 1.47 | 0.89 | 0.74 | 2.37 | 0.89 | 0.89 |
time (sec) |
N/A | 0.387 | 0.046 | 0.378 | 0.058 | 0.084 | 0.112 | 0.122 | 0.186 | 2.671 |
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 | 38 | 14 | 19 | 30 | 17 | 15 | 18 | 21 | 13 |
N.S. |
1 | 1.81 | 0.67 | 0.90 | 1.43 | 0.81 | 0.71 | 0.86 | 1.00 | 0.62 |
time (sec) |
N/A | 0.220 | 0.060 | 0.147 | 0.026 | 0.080 | 0.047 | 0.111 | 0.184 | 0.041 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 6 | 3 | 3 | 4 | 3 | 3 | 2 | 3 | 3 | 3 |
N.S. |
1 | 0.50 | 0.50 | 0.67 | 0.50 | 0.50 | 0.33 | 0.50 | 0.50 | 0.50 |
time (sec) |
N/A | 0.117 | 0.000 | 0.019 | 0.024 | 0.070 | 0.015 | 0.108 | 0.184 | 0.009 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | A | A | B | F | B |
verified | N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 32 | 35 | 63 | 32 | 29 | 65 | 137 | 65 |
N.S. |
1 | 0.00 | 1.00 | 1.09 | 1.97 | 1.00 | 0.91 | 2.03 | 4.28 | 2.03 |
time (sec) |
N/A | 0.000 | 0.558 | 3.287 | 0.163 | 0.089 | 0.236 | 0.122 | 0.192 | 2.605 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 22 | 20 | 23 | 46 | 56 | 27 | 55 | 60 | 22 |
N.S. |
1 | 0.88 | 0.80 | 0.92 | 1.84 | 2.24 | 1.08 | 2.20 | 2.40 | 0.88 |
time (sec) |
N/A | 0.637 | 0.167 | 1.618 | 0.061 | 0.087 | 0.066 | 0.121 | 0.197 | 2.681 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | A | B | B | A | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 59 | 28 | 57 | 67 | 20 | 71 | 85 | 30 |
N.S. |
1 | 0.00 | 2.46 | 1.17 | 2.38 | 2.79 | 0.83 | 2.96 | 3.54 | 1.25 |
time (sec) |
N/A | 0.000 | 0.768 | 0.488 | 0.079 | 0.086 | 0.070 | 0.125 | 0.193 | 2.558 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | A | A | F | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 104 | 22 | 19 | 30 | 30 | 27 | 0 | 37 | 32 |
N.S. |
1 | 3.59 | 0.76 | 0.66 | 1.03 | 1.03 | 0.93 | 0.00 | 1.28 | 1.10 |
time (sec) |
N/A | 0.577 | 0.185 | 0.203 | 0.124 | 0.083 | 0.113 | 0.000 | 0.314 | 0.135 |
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 | 25 | 12 | 17 | 16 | 16 | 27 | 16 | 12 | 12 |
N.S. |
1 | 1.56 | 0.75 | 1.06 | 1.00 | 1.00 | 1.69 | 1.00 | 0.75 | 0.75 |
time (sec) |
N/A | 0.342 | 0.027 | 0.210 | 0.056 | 0.078 | 0.206 | 0.116 | 0.190 | 2.515 |
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 | 18 | 48 | 25 | 29 | 23 | 23 | 27 | 29 | 44 | 36 |
N.S. |
1 | 2.67 | 1.39 | 1.61 | 1.28 | 1.28 | 1.50 | 1.61 | 2.44 | 2.00 |
time (sec) |
N/A | 0.215 | 0.078 | 0.178 | 0.025 | 0.095 | 0.053 | 0.108 | 0.188 | 2.575 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | B | A | B | B | B | F | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 207 | 128 | 49 | 46 | 46 | 126 | 0 | 35 | 22 |
N.S. |
1 | 6.68 | 4.13 | 1.58 | 1.48 | 1.48 | 4.06 | 0.00 | 1.13 | 0.71 |
time (sec) |
N/A | 1.761 | 0.098 | 1.221 | 0.100 | 0.081 | 0.368 | 0.000 | 0.179 | 0.232 |
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 | 11 | 11 | 11 | 10 | 10 | 8 | 10 | 16 | 11 |
N.S. |
1 | 0.48 | 0.48 | 0.48 | 0.43 | 0.43 | 0.35 | 0.43 | 0.70 | 0.48 |
time (sec) |
N/A | 0.145 | 0.011 | 0.071 | 0.024 | 0.077 | 0.039 | 0.118 | 0.183 | 0.030 |
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 | 26 | 31 | 45 | 27 | 26 | 26 | 26 | 156 | 25 | 25 |
N.S. |
1 | 1.19 | 1.73 | 1.04 | 1.00 | 1.00 | 1.00 | 6.00 | 0.96 | 0.96 |
time (sec) |
N/A | 0.209 | 0.014 | 0.343 | 0.031 | 0.089 | 0.082 | 0.114 | 0.185 | 2.572 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 28 | 29 | 24 | 23 | 23 | 26 | 23 | 22 | 20 |
N.S. |
1 | 1.08 | 1.12 | 0.92 | 0.88 | 0.88 | 1.00 | 0.88 | 0.85 | 0.77 |
time (sec) |
N/A | 0.195 | 0.016 | 0.142 | 0.025 | 0.083 | 0.051 | 0.110 | 0.197 | 2.441 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 16 | 16 | 15 | 16 | 16 | 12 | 16 | 14 | 14 |
N.S. |
1 | 0.80 | 0.80 | 0.75 | 0.80 | 0.80 | 0.60 | 0.80 | 0.70 | 0.70 |
time (sec) |
N/A | 0.146 | 0.000 | 0.089 | 0.023 | 0.088 | 0.017 | 0.114 | 0.214 | 0.017 |
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 | 28 | 0 | 32 | 30 | 44 | 44 | 24 | 44 | 126 | 29 |
N.S. |
1 | 0.00 | 1.14 | 1.07 | 1.57 | 1.57 | 0.86 | 1.57 | 4.50 | 1.04 |
time (sec) |
N/A | 0.000 | 10.048 | 1.043 | 0.074 | 0.094 | 0.097 | 0.168 | 200.021 | 2.442 |
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 | 31 | 16 | 16 | 23 | 13 | 19 | 15 | 19 | 19 |
N.S. |
1 | 1.94 | 1.00 | 1.00 | 1.44 | 0.81 | 1.19 | 0.94 | 1.19 | 1.19 |
time (sec) |
N/A | 0.198 | 0.017 | 0.063 | 0.027 | 0.081 | 0.048 | 0.107 | 0.187 | 0.036 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | B | F(-2) | B | F(-2) | B | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 146 | 62 | 65 | 0 | 57 | 0 | 95 | 230 | 78 |
N.S. |
1 | 4.71 | 2.00 | 2.10 | 0.00 | 1.84 | 0.00 | 3.06 | 7.42 | 2.52 |
time (sec) |
N/A | 4.147 | 0.285 | 0.071 | 0.000 | 0.085 | 0.000 | 0.460 | 165.680 | 2.665 |
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 | 22 | 21 | 21 | 19 | 21 | 21 | 1429 |
N.S. |
1 | 0.00 | 0.83 | 0.96 | 0.91 | 0.91 | 0.83 | 0.91 | 0.91 | 62.13 |
time (sec) |
N/A | 0.000 | 0.028 | 0.171 | 0.026 | 0.081 | 1.109 | 0.153 | 0.229 | 8.822 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 0 | 21 | 19 | 24 | 22 | 17 | 19 | 26 | 22 |
N.S. |
1 | 0.00 | 1.05 | 0.95 | 1.20 | 1.10 | 0.85 | 0.95 | 1.30 | 1.10 |
time (sec) |
N/A | 0.000 | 0.128 | 0.345 | 0.080 | 0.087 | 0.105 | 0.122 | 0.193 | 2.700 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 31 | 29 | 23 | 19 | 70 | 24 | 70 | 31 | 21 |
N.S. |
1 | 1.15 | 1.07 | 0.85 | 0.70 | 2.59 | 0.89 | 2.59 | 1.15 | 0.78 |
time (sec) |
N/A | 0.274 | 0.085 | 0.103 | 0.028 | 0.108 | 0.109 | 0.125 | 0.212 | 2.815 |
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 | 33 | 0 | 47 | 388 | 947 | 281 | 63 | 0 | 62 | 361 |
N.S. |
1 | 0.00 | 1.42 | 11.76 | 28.70 | 8.52 | 1.91 | 0.00 | 1.88 | 10.94 |
time (sec) |
N/A | 0.000 | 0.258 | 9.031 | 5.135 | 0.126 | 4.830 | 0.000 | 0.243 | 4.095 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 33 | 22 | 20 | 19 | 26 | 19 | 19 | 22 | 19 |
N.S. |
1 | 1.22 | 0.81 | 0.74 | 0.70 | 0.96 | 0.70 | 0.70 | 0.81 | 0.70 |
time (sec) |
N/A | 0.284 | 0.010 | 0.739 | 0.057 | 0.091 | 0.081 | 0.116 | 0.199 | 2.536 |
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 | 49 | 21 | 23 | 19 | 20 | 22 | 21 | 22 | 21 |
N.S. |
1 | 2.04 | 0.88 | 0.96 | 0.79 | 0.83 | 0.92 | 0.88 | 0.92 | 0.88 |
time (sec) |
N/A | 0.781 | 0.171 | 7.350 | 0.081 | 0.101 | 3.072 | 0.132 | 0.224 | 3.016 |
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 | 17 | 17 | 15 | 19 | 17 | 19 | 17 | 15 |
N.S. |
1 | 0.00 | 0.94 | 0.94 | 0.83 | 1.06 | 0.94 | 1.06 | 0.94 | 0.83 |
time (sec) |
N/A | 0.000 | 0.125 | 0.329 | 0.090 | 0.087 | 0.239 | 0.124 | 0.200 | 2.926 |
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 | 26 | 33 | 30 | 40 | 36 | 25 | 29 | 34 |
N.S. |
1 | 0.00 | 1.00 | 1.27 | 1.15 | 1.54 | 1.38 | 0.96 | 1.12 | 1.31 |
time (sec) |
N/A | 0.000 | 0.150 | 7.474 | 0.068 | 0.097 | 0.210 | 0.159 | 0.205 | 3.085 |
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 | 20 | 23 | 45 | 45 | 14 | 51 | 43 | 22 |
N.S. |
1 | 0.00 | 0.91 | 1.05 | 2.05 | 2.05 | 0.64 | 2.32 | 1.95 | 1.00 |
time (sec) |
N/A | 0.000 | 2.364 | 0.243 | 0.080 | 0.105 | 0.074 | 0.123 | 0.187 | 2.736 |
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 | 22 | 0 | 22 | 32 | 21 | 21 | 17 | 42 | 23 | 0 |
N.S. |
1 | 0.00 | 1.00 | 1.45 | 0.95 | 0.95 | 0.77 | 1.91 | 1.05 | 0.00 |
time (sec) |
N/A | 0.000 | 5.055 | 17.507 | 0.137 | 0.099 | 0.464 | 0.136 | 0.196 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 29 | 27 | 20 | 33 | 27 | 27 | 27 | 20 | 19 |
N.S. |
1 | 1.38 | 1.29 | 0.95 | 1.57 | 1.29 | 1.29 | 1.29 | 0.95 | 0.90 |
time (sec) |
N/A | 0.799 | 0.111 | 0.936 | 0.137 | 0.085 | 0.079 | 0.119 | 0.209 | 2.776 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | B | B | B | B | B | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 40 | 54 | 78 | 74 | 87 | 116 | 90 | 0 |
N.S. |
1 | 0.00 | 1.74 | 2.35 | 3.39 | 3.22 | 3.78 | 5.04 | 3.91 | 0.00 |
time (sec) |
N/A | 0.000 | 3.570 | 0.761 | 0.091 | 0.085 | 0.116 | 0.140 | 0.208 | 0.000 |