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 | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 53 | 53 | 42 | 41 | 41 | 49 | 41 | 53 | 46 |
N.S. |
1 | 1.71 | 1.71 | 1.35 | 1.32 | 1.32 | 1.58 | 1.32 | 1.71 | 1.48 |
time (sec) |
N/A | 0.179 | 0.008 | 0.198 | 0.038 | 0.075 | 0.045 | 0.121 | 0.174 | 3.703 |
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 | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 12 | 12 | 12 | 31 | 11 | 12 | 11 | 14 | 11 |
N.S. |
1 | 0.86 | 0.86 | 0.86 | 2.21 | 0.79 | 0.86 | 0.79 | 1.00 | 0.79 |
time (sec) |
N/A | 0.216 | 0.002 | 0.066 | 0.034 | 0.079 | 0.047 | 0.120 | 0.178 | 0.052 |
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 | 29 | 0 | 27 | 31 | 35 | 30 | 31 | 30 | 31 | 0 |
N.S. |
1 | 0.00 | 0.93 | 1.07 | 1.21 | 1.03 | 1.07 | 1.03 | 1.07 | 0.00 |
time (sec) |
N/A | 0.000 | 1.404 | 0.359 | 0.145 | 0.085 | 0.158 | 0.128 | 1.386 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 13 | 13 | 11 | 10 | 12 | 10 | 14 | 17 | 10 |
N.S. |
1 | 0.72 | 0.72 | 0.61 | 0.56 | 0.67 | 0.56 | 0.78 | 0.94 | 0.56 |
time (sec) |
N/A | 0.142 | 0.006 | 0.065 | 0.042 | 0.091 | 0.053 | 0.123 | 0.174 | 3.729 |
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 | 14 | 13 | 14 | 21 | 13 | 14 | 15 | 12 | 11 |
N.S. |
1 | 0.67 | 0.62 | 0.67 | 1.00 | 0.62 | 0.67 | 0.71 | 0.57 | 0.52 |
time (sec) |
N/A | 0.184 | 0.009 | 0.161 | 0.056 | 0.089 | 0.052 | 0.123 | 0.176 | 3.732 |
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 | 26 | 47 | 24 | 36 | 153 | 27 | 44 | 27 | 28 | 20 |
N.S. |
1 | 1.81 | 0.92 | 1.38 | 5.88 | 1.04 | 1.69 | 1.04 | 1.08 | 0.77 |
time (sec) |
N/A | 0.222 | 1.687 | 0.418 | 0.106 | 0.089 | 0.162 | 0.121 | 0.183 | 0.164 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | B | F | B | B | B | F | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 87 | 104 | 0 | 103 | 104 | 163 | 219 | 338 |
N.S. |
1 | 0.00 | 3.78 | 4.52 | 0.00 | 4.48 | 4.52 | 7.09 | 9.52 | 14.70 |
time (sec) |
N/A | 0.000 | 0.255 | 14.001 | 0.000 | 0.106 | 0.481 | 1.136 | 200.027 | 4.405 |
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 | 33 | 0 | 25 | 26 | 25 | 27 | 26 | 27 | 27 | 0 |
N.S. |
1 | 0.00 | 0.76 | 0.79 | 0.76 | 0.82 | 0.79 | 0.82 | 0.82 | 0.00 |
time (sec) |
N/A | 0.000 | 5.025 | 0.783 | 0.183 | 0.092 | 0.116 | 0.274 | 0.177 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | B | B | B | B | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 109 | 22 | 83 | 262 | 57 | 104 | 130 | 58 | 21 |
N.S. |
1 | 4.36 | 0.88 | 3.32 | 10.48 | 2.28 | 4.16 | 5.20 | 2.32 | 0.84 |
time (sec) |
N/A | 0.830 | 0.624 | 0.930 | 0.049 | 0.085 | 0.193 | 0.120 | 0.175 | 3.897 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | A | B | A | A | B | F | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 0 | 88 | 57 | 83 | 51 | 48 | 96 | 383 | 44 |
N.S. |
1 | 0.00 | 2.67 | 1.73 | 2.52 | 1.55 | 1.45 | 2.91 | 11.61 | 1.33 |
time (sec) |
N/A | 0.000 | 0.145 | 48.092 | 0.083 | 0.090 | 3.311 | 0.156 | 0.197 | 3.985 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 20 | 22 | 85 | 25 | 26 | 45 | 24 | 16 |
N.S. |
1 | 1.00 | 0.91 | 1.00 | 3.86 | 1.14 | 1.18 | 2.05 | 1.09 | 0.73 |
time (sec) |
N/A | 0.259 | 0.009 | 0.244 | 0.093 | 0.079 | 0.172 | 0.121 | 0.164 | 3.695 |
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 | 25 | 69 | 18 | 25 | 17 | 25 | 20 | 24 | 17 | 17 |
N.S. |
1 | 2.76 | 0.72 | 1.00 | 0.68 | 1.00 | 0.80 | 0.96 | 0.68 | 0.68 |
time (sec) |
N/A | 0.242 | 0.017 | 0.690 | 0.207 | 0.078 | 0.062 | 0.128 | 1.037 | 4.287 |
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 | 31 | 20 | 20 | 27 | 27 | 26 | 27 | 28 | 21 |
N.S. |
1 | 1.55 | 1.00 | 1.00 | 1.35 | 1.35 | 1.30 | 1.35 | 1.40 | 1.05 |
time (sec) |
N/A | 0.185 | 0.006 | 0.109 | 0.043 | 0.076 | 0.048 | 0.116 | 0.167 | 0.058 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 42 | 22 | 27 | 0 | 27 | 17 | 39 | 49 | 22 |
N.S. |
1 | 1.68 | 0.88 | 1.08 | 0.00 | 1.08 | 0.68 | 1.56 | 1.96 | 0.88 |
time (sec) |
N/A | 0.555 | 0.077 | 0.465 | 0.000 | 0.095 | 0.095 | 0.121 | 0.182 | 3.698 |
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 | 37 | 16 | 16 | 21 | 21 | 19 | 25 | 21 | 15 |
N.S. |
1 | 2.06 | 0.89 | 0.89 | 1.17 | 1.17 | 1.06 | 1.39 | 1.17 | 0.83 |
time (sec) |
N/A | 0.518 | 0.094 | 0.110 | 0.102 | 0.079 | 0.060 | 0.118 | 0.170 | 3.700 |
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 | 21 | 41 | 30 | 37 | 46 | 52 | 54 | 52 | 44 | 44 |
N.S. |
1 | 1.95 | 1.43 | 1.76 | 2.19 | 2.48 | 2.57 | 2.48 | 2.10 | 2.10 |
time (sec) |
N/A | 2.236 | 0.461 | 0.899 | 0.084 | 0.074 | 0.090 | 0.126 | 0.170 | 3.738 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | A | A | F | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 23 | 34 | 58 | 33 | 31 | 0 | 40 | 62 |
N.S. |
1 | 0.00 | 1.00 | 1.48 | 2.52 | 1.43 | 1.35 | 0.00 | 1.74 | 2.70 |
time (sec) |
N/A | 0.000 | 0.200 | 1.161 | 0.211 | 0.081 | 0.197 | 0.000 | 0.197 | 3.949 |
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 | 3 | 3 | 4 | 3 | 3 | 2 | 3 | 3 | 3 |
N.S. |
1 | 0.20 | 0.20 | 0.27 | 0.20 | 0.20 | 0.13 | 0.20 | 0.20 | 0.20 |
time (sec) |
N/A | 0.121 | 0.000 | 0.017 | 0.023 | 0.061 | 0.015 | 0.115 | 0.161 | 0.012 |
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 | 30 | 0 | 50 | 40 | 61 | 53 | 44 | 66 | 81 | 281 |
N.S. |
1 | 0.00 | 1.67 | 1.33 | 2.03 | 1.77 | 1.47 | 2.20 | 2.70 | 9.37 |
time (sec) |
N/A | 0.000 | 0.164 | 9.463 | 0.083 | 0.079 | 0.211 | 0.206 | 0.160 | 4.618 |
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 | 19 | 15 | 13 | 12 | 12 | 10 | 12 | 13 | 12 |
N.S. |
1 | 0.68 | 0.54 | 0.46 | 0.43 | 0.43 | 0.36 | 0.43 | 0.46 | 0.43 |
time (sec) |
N/A | 0.146 | 0.004 | 0.059 | 0.033 | 0.077 | 0.035 | 0.122 | 0.159 | 3.744 |
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 | 16 | 16 | 16 | 16 | 15 | 15 | 17 | 0 | 17 | 15 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.94 | 0.94 | 1.06 | 0.00 | 1.06 | 0.94 |
time (sec) |
N/A | 0.214 | 0.015 | 0.343 | 0.207 | 0.075 | 0.066 | 0.000 | 0.163 | 4.022 |
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 | 17 | 17 | 17 | 18 | 74 | 74 | 78 | 134 | 93 | 17 |
N.S. |
1 | 1.00 | 1.00 | 1.06 | 4.35 | 4.35 | 4.59 | 7.88 | 5.47 | 1.00 |
time (sec) |
N/A | 0.525 | 0.009 | 0.238 | 0.099 | 0.088 | 0.151 | 0.144 | 0.177 | 4.002 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | A | B | B | B | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 160 | 40 | 144 | 110 | 90 | 139 | 96 | 186 |
N.S. |
1 | 0.00 | 5.00 | 1.25 | 4.50 | 3.44 | 2.81 | 4.34 | 3.00 | 5.81 |
time (sec) |
N/A | 0.000 | 0.350 | 5.893 | 0.421 | 10.602 | 0.675 | 0.492 | 0.182 | 4.368 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | B | B | A | B | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 372 | 29 | 47 | 70 | 63 | 41 | 75 | 40 | 0 |
N.S. |
1 | 12.83 | 1.00 | 1.62 | 2.41 | 2.17 | 1.41 | 2.59 | 1.38 | 0.00 |
time (sec) |
N/A | 5.181 | 0.109 | 0.560 | 0.202 | 0.088 | 0.233 | 0.138 | 0.179 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | A | B | A | B | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 77 | 76 | 52 | 128 | 48 | 53 | 87 | 76 | 65 |
N.S. |
1 | 2.75 | 2.71 | 1.86 | 4.57 | 1.71 | 1.89 | 3.11 | 2.71 | 2.32 |
time (sec) |
N/A | 0.560 | 0.058 | 0.976 | 0.044 | 0.085 | 0.120 | 0.124 | 0.177 | 3.899 |
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 | 23 | 24 | 22 | 24 | 22 | 23 | 24 | 0 | 23 | 23 |
N.S. |
1 | 1.04 | 0.96 | 1.04 | 0.96 | 1.00 | 1.04 | 0.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.456 | 0.113 | 0.570 | 0.175 | 0.091 | 0.174 | 0.000 | 0.174 | 4.184 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | B | B | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 39 | 39 | 76 | 76 | 42 | 46 | 78 | 284 |
N.S. |
1 | 0.00 | 1.44 | 1.44 | 2.81 | 2.81 | 1.56 | 1.70 | 2.89 | 10.52 |
time (sec) |
N/A | 0.000 | 0.039 | 18.533 | 0.082 | 0.081 | 0.065 | 0.132 | 0.170 | 3.996 |
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 | 19 | 18 | 18 | 19 | 20 | 19 | 21 | 17 |
N.S. |
1 | 0.00 | 0.66 | 0.62 | 0.62 | 0.66 | 0.69 | 0.66 | 0.72 | 0.59 |
time (sec) |
N/A | 0.000 | 0.165 | 0.273 | 0.047 | 0.080 | 0.269 | 0.125 | 0.183 | 3.732 |
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 | 5 | 5 | 5 | 5 | 4 | 4 | 3 | 4 | 5 | 4 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.80 | 0.80 | 0.60 | 0.80 | 1.00 | 0.80 |
time (sec) |
N/A | 0.138 | 0.000 | 0.029 | 0.028 | 0.081 | 0.032 | 0.118 | 0.173 | 0.007 |
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 | 10 | 14 | 8 | 7 | 9 | 8 | 7 | 8 | 8 |
N.S. |
1 | 0.67 | 0.93 | 0.53 | 0.47 | 0.60 | 0.53 | 0.47 | 0.53 | 0.53 |
time (sec) |
N/A | 0.129 | 0.000 | 0.028 | 0.042 | 0.067 | 0.022 | 0.121 | 0.181 | 0.002 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 25 | 23 | 26 | 25 | 25 | 20 | 25 | 24 | 24 |
N.S. |
1 | 0.93 | 0.85 | 0.96 | 0.93 | 0.93 | 0.74 | 0.93 | 0.89 | 0.89 |
time (sec) |
N/A | 0.991 | 0.310 | 2.013 | 0.122 | 0.083 | 0.127 | 0.296 | 0.187 | 4.707 |
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 | 34 | 0 | 34 | 32 | 51 | 53 | 34 | 38 | 77 | 45 |
N.S. |
1 | 0.00 | 1.00 | 0.94 | 1.50 | 1.56 | 1.00 | 1.12 | 2.26 | 1.32 |
time (sec) |
N/A | 0.000 | 0.053 | 2.549 | 0.155 | 0.086 | 0.152 | 0.141 | 0.177 | 3.847 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | B | B | B | B | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 38 | 43 | 119 | 119 | 61 | 65 | 130 | 0 |
N.S. |
1 | 0.00 | 1.41 | 1.59 | 4.41 | 4.41 | 2.26 | 2.41 | 4.81 | 0.00 |
time (sec) |
N/A | 0.000 | 0.040 | 15.710 | 0.087 | 0.089 | 0.090 | 0.138 | 0.182 | 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 | 27 | 0 | 26 | 32 | 78 | 29 | 36 | 41 | 30 | 22 |
N.S. |
1 | 0.00 | 0.96 | 1.19 | 2.89 | 1.07 | 1.33 | 1.52 | 1.11 | 0.81 |
time (sec) |
N/A | 0.000 | 0.276 | 15.599 | 0.082 | 0.093 | 116.431 | 0.199 | 0.187 | 4.667 |
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 | 18 | 16 | 18 | 21 | 26 | 21 | 21 | 23 |
N.S. |
1 | 1.00 | 0.90 | 0.80 | 0.90 | 1.05 | 1.30 | 1.05 | 1.05 | 1.15 |
time (sec) |
N/A | 0.228 | 0.028 | 0.117 | 0.030 | 0.092 | 0.087 | 0.123 | 0.166 | 0.262 |
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 | 20 | 18 | 15 | 14 | 14 | 15 | 14 | 14 | 12 |
N.S. |
1 | 0.74 | 0.67 | 0.56 | 0.52 | 0.52 | 0.56 | 0.52 | 0.52 | 0.44 |
time (sec) |
N/A | 0.148 | 0.002 | 0.069 | 0.027 | 0.077 | 0.047 | 0.119 | 0.164 | 3.657 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | B | B | A | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 69 | 18 | 38 | 41 | 36 | 41 | 41 | 34 | 13 |
N.S. |
1 | 3.14 | 0.82 | 1.73 | 1.86 | 1.64 | 1.86 | 1.86 | 1.55 | 0.59 |
time (sec) |
N/A | 0.257 | 0.058 | 1.707 | 0.136 | 0.088 | 0.152 | 0.120 | 0.159 | 3.815 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | A | A | F | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 56 | 23 | 19 | 18 | 34 | 20 | 0 | 26 | 19 |
N.S. |
1 | 2.43 | 1.00 | 0.83 | 0.78 | 1.48 | 0.87 | 0.00 | 1.13 | 0.83 |
time (sec) |
N/A | 0.294 | 0.029 | 5.414 | 0.219 | 0.096 | 14.823 | 0.000 | 0.161 | 3.850 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | B | A | F | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 37 | 0 | 37 | 48 | 57 | 55 | 53 | 59 | 0 | 63 |
N.S. |
1 | 0.00 | 1.00 | 1.30 | 1.54 | 1.49 | 1.43 | 1.59 | 0.00 | 1.70 |
time (sec) |
N/A | 0.000 | 0.096 | 0.700 | 0.366 | 0.080 | 0.577 | 0.424 | 0.686 | 4.277 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | B | B | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 136 | 40 | 51 | 67 | 43 | 34 | 44 | 86 | 46 |
N.S. |
1 | 6.18 | 1.82 | 2.32 | 3.05 | 1.95 | 1.55 | 2.00 | 3.91 | 2.09 |
time (sec) |
N/A | 0.847 | 0.044 | 0.709 | 0.086 | 0.087 | 0.112 | 0.126 | 0.169 | 0.176 |
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 | 25 | 0 | 28 | 34 | 44 | 35 | 36 | 59 | 34 | 142 |
N.S. |
1 | 0.00 | 1.12 | 1.36 | 1.76 | 1.40 | 1.44 | 2.36 | 1.36 | 5.68 |
time (sec) |
N/A | 0.000 | 0.510 | 1.667 | 0.163 | 0.078 | 0.157 | 0.170 | 0.181 | 4.060 |
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 | 42 | 22 | 21 | 20 | 20 | 22 | 20 | 18 | 16 |
N.S. |
1 | 2.33 | 1.22 | 1.17 | 1.11 | 1.11 | 1.22 | 1.11 | 1.00 | 0.89 |
time (sec) |
N/A | 0.178 | 0.011 | 0.112 | 0.037 | 0.082 | 0.083 | 0.120 | 0.168 | 3.842 |
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 | 26 | 30 | 20 | 23 | 22 | 28 | 20 | 22 | 27 | 20 |
N.S. |
1 | 1.15 | 0.77 | 0.88 | 0.85 | 1.08 | 0.77 | 0.85 | 1.04 | 0.77 |
time (sec) |
N/A | 0.248 | 0.009 | 0.109 | 0.037 | 0.076 | 0.239 | 0.119 | 0.166 | 0.062 |
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 | 17 | 10 | 10 | 11 | 12 | 10 | 7 | 10 | 10 | 10 |
N.S. |
1 | 0.59 | 0.59 | 0.65 | 0.71 | 0.59 | 0.41 | 0.59 | 0.59 | 0.59 |
time (sec) |
N/A | 0.194 | 0.037 | 0.163 | 0.062 | 0.062 | 0.038 | 0.125 | 0.163 | 3.942 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | A | B | A | F(-2) | B | F | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 82 | 45 | 111 | 53 | 0 | 75 | 0 | 0 |
N.S. |
1 | 0.00 | 2.56 | 1.41 | 3.47 | 1.66 | 0.00 | 2.34 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 0.548 | 3.553 | 0.120 | 0.089 | 0.000 | 0.250 | 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 | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 26 | 25 | 60 | 25 | 22 | 52 | 49 | 56 |
N.S. |
1 | 0.00 | 0.93 | 0.89 | 2.14 | 0.89 | 0.79 | 1.86 | 1.75 | 2.00 |
time (sec) |
N/A | 0.000 | 5.171 | 7.852 | 0.260 | 0.081 | 0.645 | 0.209 | 0.187 | 0.486 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | B | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 44 | 29 | 28 | 71 | 43 | 44 | 71 | 84 | 78 |
N.S. |
1 | 1.52 | 1.00 | 0.97 | 2.45 | 1.48 | 1.52 | 2.45 | 2.90 | 2.69 |
time (sec) |
N/A | 2.893 | 2.347 | 0.437 | 0.369 | 0.083 | 0.169 | 0.130 | 200.039 | 4.014 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 57 | 39 | 35 | 27 | 39 | 22 | 0 | 38 | 0 |
N.S. |
1 | 1.97 | 1.34 | 1.21 | 0.93 | 1.34 | 0.76 | 0.00 | 1.31 | 0.00 |
time (sec) |
N/A | 1.077 | 0.153 | 1.039 | 0.098 | 0.082 | 0.118 | 0.000 | 0.182 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | F | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 0 | 24 | 19 | 19 | 19 | 20 | 19 | 82 | 19 |
N.S. |
1 | 0.00 | 1.26 | 1.00 | 1.00 | 1.00 | 1.05 | 1.00 | 4.32 | 1.00 |
time (sec) |
N/A | 0.000 | 0.625 | 0.171 | 0.032 | 0.081 | 0.155 | 0.125 | 0.244 | 4.127 |
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 | 11 | 11 | 11 | 10 | 10 | 12 | 10 | 14 | 10 |
N.S. |
1 | 0.73 | 0.73 | 0.73 | 0.67 | 0.67 | 0.80 | 0.67 | 0.93 | 0.67 |
time (sec) |
N/A | 0.162 | 0.010 | 0.041 | 0.034 | 0.078 | 0.046 | 0.127 | 0.170 | 0.025 |
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 | 21 | 93 | 194 | 194 | 92 | 212 | 226 | 0 |
N.S. |
1 | 0.00 | 0.91 | 4.04 | 8.43 | 8.43 | 4.00 | 9.22 | 9.83 | 0.00 |
time (sec) |
N/A | 0.000 | 0.063 | 0.120 | 0.113 | 0.092 | 0.181 | 0.160 | 0.165 | 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 | 23 | 19 | 20 | 20 | 26 | 26 | 22 | 20 | 20 | 20 |
N.S. |
1 | 0.83 | 0.87 | 0.87 | 1.13 | 1.13 | 0.96 | 0.87 | 0.87 | 0.87 |
time (sec) |
N/A | 0.559 | 0.142 | 0.293 | 0.088 | 0.094 | 0.169 | 0.125 | 0.163 | 4.136 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | B | A | A | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 55 | 40 | 35 | 50 | 33 | 36 | 45 | 34 | 31 |
N.S. |
1 | 2.75 | 2.00 | 1.75 | 2.50 | 1.65 | 1.80 | 2.25 | 1.70 | 1.55 |
time (sec) |
N/A | 0.187 | 0.005 | 0.156 | 0.026 | 0.099 | 0.068 | 0.118 | 0.168 | 4.106 |
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 | 28 | 28 | 22 | 20 | 28 | 27 | 20 | 29 | 21 |
N.S. |
1 | 1.12 | 1.12 | 0.88 | 0.80 | 1.12 | 1.08 | 0.80 | 1.16 | 0.84 |
time (sec) |
N/A | 0.165 | 0.017 | 0.109 | 0.035 | 0.089 | 0.066 | 0.118 | 0.187 | 0.123 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 12 | 21 | 12 | 12 | 23 | 12 | 10 | 11 | 12 | 9 |
N.S. |
1 | 1.75 | 1.00 | 1.00 | 1.92 | 1.00 | 0.83 | 0.92 | 1.00 | 0.75 |
time (sec) |
N/A | 0.174 | 0.020 | 0.077 | 0.034 | 0.084 | 0.047 | 0.121 | 0.177 | 4.018 |
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 | 21 | 21 | 21 | 27 | 30 | 23 | 19 | 23 | 24 | 0 |
N.S. |
1 | 1.00 | 1.00 | 1.29 | 1.43 | 1.10 | 0.90 | 1.10 | 1.14 | 0.00 |
time (sec) |
N/A | 0.611 | 0.042 | 0.710 | 0.165 | 0.100 | 0.149 | 0.168 | 0.173 | 0.000 |
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 | 48 | 15 | 45 | 45 | 48 | 51 | 48 | 67 | 16 |
N.S. |
1 | 2.29 | 0.71 | 2.14 | 2.14 | 2.29 | 2.43 | 2.29 | 3.19 | 0.76 |
time (sec) |
N/A | 0.211 | 0.011 | 0.136 | 0.114 | 0.072 | 0.087 | 0.122 | 0.205 | 0.072 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 25 | 25 | 29 | 31 | 28 | 26 | 28 | 28 | 25 |
N.S. |
1 | 0.78 | 0.78 | 0.91 | 0.97 | 0.88 | 0.81 | 0.88 | 0.88 | 0.78 |
time (sec) |
N/A | 0.529 | 0.298 | 0.349 | 0.160 | 0.074 | 0.217 | 0.150 | 0.180 | 4.525 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | C | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 39 | 65 | 43 | 66 | 42 | 41 | 48 | 35 | 41 |
N.S. |
1 | 1.56 | 2.60 | 1.72 | 2.64 | 1.68 | 1.64 | 1.92 | 1.40 | 1.64 |
time (sec) |
N/A | 0.720 | 0.135 | 0.811 | 0.095 | 0.082 | 0.188 | 0.136 | 0.184 | 4.323 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | F | B | B | B | F | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 26 | 52 | 0 | 56 | 54 | 64 | 1274 | 60 |
N.S. |
1 | 0.00 | 1.04 | 2.08 | 0.00 | 2.24 | 2.16 | 2.56 | 50.96 | 2.40 |
time (sec) |
N/A | 0.000 | 5.156 | 0.471 | 0.000 | 0.089 | 0.315 | 0.186 | 1.359 | 4.474 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | B | B | B | B | F(-1) | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 123 | 88 | 60 | 54 | 97 | 58 | 0 | 161 | 0 |
N.S. |
1 | 4.39 | 3.14 | 2.14 | 1.93 | 3.46 | 2.07 | 0.00 | 5.75 | 0.00 |
time (sec) |
N/A | 10.299 | 0.388 | 2.245 | 0.051 | 0.100 | 4.092 | 0.000 | 0.186 | 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 | 27 | 0 | 18 | 17 | 16 | 16 | 15 | 16 | 24 | 17 |
N.S. |
1 | 0.00 | 0.67 | 0.63 | 0.59 | 0.59 | 0.56 | 0.59 | 0.89 | 0.63 |
time (sec) |
N/A | 0.000 | 0.230 | 0.187 | 0.059 | 0.070 | 0.080 | 0.120 | 0.181 | 0.244 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | C | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 47 | 47 | 40 | 39 | 68 | 48 | 315 | 55 | 45 |
N.S. |
1 | 1.52 | 1.52 | 1.29 | 1.26 | 2.19 | 1.55 | 10.16 | 1.77 | 1.45 |
time (sec) |
N/A | 0.651 | 1.071 | 0.403 | 0.032 | 0.091 | 0.077 | 0.151 | 0.182 | 3.954 |
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 | 23 | 15 | 12 | 13 | 13 | 12 | 13 | 13 | 13 |
N.S. |
1 | 1.53 | 1.00 | 0.80 | 0.87 | 0.87 | 0.80 | 0.87 | 0.87 | 0.87 |
time (sec) |
N/A | 0.561 | 0.153 | 0.161 | 0.141 | 0.080 | 0.062 | 0.117 | 0.172 | 3.844 |
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 | 27 | 0 | 33 | 28 | 27 | 29 | 29 | 29 | 29 | 27 |
N.S. |
1 | 0.00 | 1.22 | 1.04 | 1.00 | 1.07 | 1.07 | 1.07 | 1.07 | 1.00 |
time (sec) |
N/A | 0.000 | 0.250 | 0.225 | 0.092 | 0.089 | 0.107 | 0.122 | 0.174 | 3.835 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | F(-1) | F | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 0 | 21 | 18 | 23 | 16 | 0 | 0 | 19 | 17 |
N.S. |
1 | 0.00 | 1.00 | 0.86 | 1.10 | 0.76 | 0.00 | 0.00 | 0.90 | 0.81 |
time (sec) |
N/A | 0.000 | 0.422 | 25.037 | 0.270 | 0.093 | 0.000 | 0.000 | 0.181 | 3.948 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | B | B | B | B | F(-1) | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 124 | 61 | 78 | 70 | 70 | 0 | 97 | 72 |
N.S. |
1 | 0.00 | 4.13 | 2.03 | 2.60 | 2.33 | 2.33 | 0.00 | 3.23 | 2.40 |
time (sec) |
N/A | 0.000 | 1.226 | 27.625 | 0.121 | 0.088 | 0.503 | 0.000 | 0.218 | 3.978 |
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 | 20 | 19 | 32 | 28 | 15 | 18 | 59 | 37 |
N.S. |
1 | 0.00 | 1.00 | 0.95 | 1.60 | 1.40 | 0.75 | 0.90 | 2.95 | 1.85 |
time (sec) |
N/A | 0.000 | 0.135 | 0.505 | 0.161 | 0.085 | 0.065 | 0.122 | 0.183 | 3.820 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | B | A | A | B | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 1653 | 28 | 30 | 898 | 42 | 26 | 53 | 59 | 0 |
N.S. |
1 | 61.22 | 1.04 | 1.11 | 33.26 | 1.56 | 0.96 | 1.96 | 2.19 | 0.00 |
time (sec) |
N/A | 15.838 | 5.044 | 3.399 | 0.198 | 0.095 | 0.151 | 0.135 | 0.175 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 19 | 19 | 10 | 11 | 11 | 8 | 13 | 11 | 8 |
N.S. |
1 | 1.12 | 1.12 | 0.59 | 0.65 | 0.65 | 0.47 | 0.76 | 0.65 | 0.47 |
time (sec) |
N/A | 0.155 | 0.003 | 0.082 | 0.029 | 0.072 | 0.042 | 0.116 | 0.192 | 3.763 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 43 | 38 | 35 | 37 | 37 | 39 | 37 | 41 | 36 |
N.S. |
1 | 1.65 | 1.46 | 1.35 | 1.42 | 1.42 | 1.50 | 1.42 | 1.58 | 1.38 |
time (sec) |
N/A | 0.179 | 0.010 | 0.066 | 0.042 | 0.081 | 0.024 | 0.116 | 0.173 | 0.059 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | A | A | F | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 0 | 38 | 32 | 161 | 33 | 32 | 0 | 82 | 48 |
N.S. |
1 | 0.00 | 1.15 | 0.97 | 4.88 | 1.00 | 0.97 | 0.00 | 2.48 | 1.45 |
time (sec) |
N/A | 0.000 | 0.394 | 6.086 | 0.224 | 0.086 | 0.371 | 0.000 | 11.905 | 4.178 |
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 | 25 | 53 | 27 | 25 | 42 | 44 | 27 | 27 |
N.S. |
1 | 0.00 | 0.86 | 1.83 | 0.93 | 0.86 | 1.45 | 1.52 | 0.93 | 0.93 |
time (sec) |
N/A | 0.000 | 0.039 | 0.609 | 0.154 | 0.086 | 0.401 | 0.187 | 0.205 | 3.980 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 15 | 15 | 17 | 17 | 16 | 14 | 47 | 17 | 17 |
N.S. |
1 | 0.71 | 0.71 | 0.81 | 0.81 | 0.76 | 0.67 | 2.24 | 0.81 | 0.81 |
time (sec) |
N/A | 0.390 | 0.043 | 0.161 | 0.154 | 0.073 | 0.104 | 0.125 | 0.195 | 4.157 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F | A | A | F | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 0 | 21 | 20 | 0 | 31 | 20 | 0 | 31 | 30 |
N.S. |
1 | 0.00 | 1.00 | 0.95 | 0.00 | 1.48 | 0.95 | 0.00 | 1.48 | 1.43 |
time (sec) |
N/A | 0.000 | 0.547 | 0.272 | 0.000 | 0.112 | 0.134 | 0.000 | 0.194 | 3.790 |
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 | 201 | 47 | 39 | 49 | 37 | 44 | 37 | 111 | 41 |
N.S. |
1 | 7.18 | 1.68 | 1.39 | 1.75 | 1.32 | 1.57 | 1.32 | 3.96 | 1.46 |
time (sec) |
N/A | 0.586 | 0.080 | 0.781 | 0.191 | 0.089 | 0.082 | 0.126 | 0.209 | 0.249 |
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 | 22 | 45 | 26 | 23 | 71 | 21 | 22 | 26 | 25 | 22 |
N.S. |
1 | 2.05 | 1.18 | 1.05 | 3.23 | 0.95 | 1.00 | 1.18 | 1.14 | 1.00 |
time (sec) |
N/A | 0.272 | 0.132 | 0.076 | 0.032 | 0.079 | 0.055 | 0.130 | 0.190 | 3.638 |
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 | 8 | 8 | 8 | 7 | 7 | 5 | 7 | 8 | 7 |
N.S. |
1 | 0.47 | 0.47 | 0.47 | 0.41 | 0.41 | 0.29 | 0.41 | 0.47 | 0.41 |
time (sec) |
N/A | 0.153 | 0.002 | 0.052 | 0.041 | 0.076 | 0.033 | 0.119 | 0.179 | 0.034 |
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 | 29 | 27 | 29 | 26 | 24 | 26 | 30 | 26 |
N.S. |
1 | 0.00 | 1.21 | 1.12 | 1.21 | 1.08 | 1.00 | 1.08 | 1.25 | 1.08 |
time (sec) |
N/A | 0.000 | 2.372 | 1.631 | 0.189 | 0.092 | 0.380 | 0.196 | 2.046 | 3.811 |
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 | 19 | 20 | 25 | 27 | 24 | 27 | 20 | 27 |
N.S. |
1 | 0.00 | 0.68 | 0.71 | 0.89 | 0.96 | 0.86 | 0.96 | 0.71 | 0.96 |
time (sec) |
N/A | 0.000 | 0.393 | 1.183 | 0.157 | 0.078 | 0.062 | 0.127 | 0.192 | 0.197 |
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 | 24 | 0 | 24 | 22 | 18 | 49 | 17 | 0 | 30 | 18 |
N.S. |
1 | 0.00 | 1.00 | 0.92 | 0.75 | 2.04 | 0.71 | 0.00 | 1.25 | 0.75 |
time (sec) |
N/A | 0.000 | 0.208 | 0.250 | 0.215 | 0.103 | 0.191 | 0.000 | 0.188 | 3.973 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 0 | 19 | 17 | 19 | 16 | 19 | 16 | 33 | 20 |
N.S. |
1 | 0.00 | 1.00 | 0.89 | 1.00 | 0.84 | 1.00 | 0.84 | 1.74 | 1.05 |
time (sec) |
N/A | 0.000 | 0.447 | 1.538 | 0.240 | 0.079 | 0.185 | 0.214 | 0.187 | 3.887 |
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 | 17 | 16 | 20 | 19 | 20 | 20 | 16 |
N.S. |
1 | 1.00 | 1.00 | 0.85 | 0.80 | 1.00 | 0.95 | 1.00 | 1.00 | 0.80 |
time (sec) |
N/A | 0.367 | 0.147 | 0.276 | 0.077 | 0.095 | 0.121 | 0.135 | 0.188 | 3.810 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 27 | 43 | 19 | 33 | 17 | 114 | 33 | 78 | 18 |
N.S. |
1 | 1.08 | 1.72 | 0.76 | 1.32 | 0.68 | 4.56 | 1.32 | 3.12 | 0.72 |
time (sec) |
N/A | 0.171 | 0.009 | 0.196 | 0.034 | 0.069 | 0.167 | 0.127 | 0.203 | 0.143 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | B | C | B | B | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 122 | 122 | 100 | 325 | 107 | 129 | 154 | 166 | 151 |
N.S. |
1 | 4.88 | 4.88 | 4.00 | 13.00 | 4.28 | 5.16 | 6.16 | 6.64 | 6.04 |
time (sec) |
N/A | 0.654 | 10.326 | 33.362 | 0.231 | 0.087 | 0.183 | 0.131 | 0.206 | 3.894 |
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 | 30 | 0 | 25 | 21 | 24 | 19 | 26 | 0 | 622 | 23 |
N.S. |
1 | 0.00 | 0.83 | 0.70 | 0.80 | 0.63 | 0.87 | 0.00 | 20.73 | 0.77 |
time (sec) |
N/A | 0.000 | 0.047 | 0.697 | 0.180 | 0.077 | 0.242 | 0.000 | 1.255 | 5.232 |
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 | 25 | 0 | 24 | 49 | 59 | 43 | 42 | 43 | 45 | 55 |
N.S. |
1 | 0.00 | 0.96 | 1.96 | 2.36 | 1.72 | 1.68 | 1.72 | 1.80 | 2.20 |
time (sec) |
N/A | 0.000 | 0.207 | 63.362 | 0.169 | 0.088 | 0.205 | 0.264 | 0.191 | 3.928 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | F | A | A | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 150 | 23 | 40 | 0 | 36 | 37 | 70 | 49 | 47 |
N.S. |
1 | 5.17 | 0.79 | 1.38 | 0.00 | 1.24 | 1.28 | 2.41 | 1.69 | 1.62 |
time (sec) |
N/A | 0.757 | 0.071 | 0.589 | 0.000 | 0.090 | 0.546 | 0.180 | 0.969 | 4.196 |
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 | 25 | 53 | 22 | 25 | 28 | 23 | 27 | 0 | 25 | 20 |
N.S. |
1 | 2.12 | 0.88 | 1.00 | 1.12 | 0.92 | 1.08 | 0.00 | 1.00 | 0.80 |
time (sec) |
N/A | 0.984 | 0.392 | 3.473 | 0.179 | 0.101 | 0.203 | 0.000 | 0.205 | 3.956 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | F | A | A | F(-1) | A | F | F(-1) |
verified | N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 0 | 0 | 32 | 27 | 0 | 31 | 246 | 0 |
N.S. |
1 | 0.00 | 0.00 | 0.00 | 1.33 | 1.12 | 0.00 | 1.29 | 10.25 | 0.00 |
time (sec) |
N/A | 0.000 | 0.000 | 0.000 | 0.201 | 0.088 | 0.000 | 2.927 | 200.028 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 34 | 18 | 33 | 84 | 32 | 31 | 32 | 27 | 23 |
N.S. |
1 | 1.89 | 1.00 | 1.83 | 4.67 | 1.78 | 1.72 | 1.78 | 1.50 | 1.28 |
time (sec) |
N/A | 0.395 | 0.036 | 0.243 | 0.032 | 0.099 | 0.095 | 0.137 | 0.174 | 3.847 |
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 | 26 | 26 | 23 | 22 | 22 | 22 | 22 | 25 | 22 |
N.S. |
1 | 0.79 | 0.79 | 0.70 | 0.67 | 0.67 | 0.67 | 0.67 | 0.76 | 0.67 |
time (sec) |
N/A | 0.154 | 0.006 | 0.119 | 0.035 | 0.083 | 0.038 | 0.120 | 0.178 | 0.065 |
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 | 14 | 15 | 11 | 22 | 20 | 16 | 13 | 17 |
N.S. |
1 | 0.95 | 0.74 | 0.79 | 0.58 | 1.16 | 1.05 | 0.84 | 0.68 | 0.89 |
time (sec) |
N/A | 0.171 | 0.005 | 0.112 | 0.039 | 0.078 | 0.057 | 0.116 | 0.181 | 3.731 |
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 | 11 | 11 | 10 | 11 | 11 | 8 | 11 | 12 | 12 |
N.S. |
1 | 1.22 | 1.22 | 1.11 | 1.22 | 1.22 | 0.89 | 1.22 | 1.33 | 1.33 |
time (sec) |
N/A | 0.140 | 0.000 | 0.031 | 0.029 | 0.073 | 0.020 | 0.120 | 0.188 | 0.020 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | A | A | A | A | B | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 0 | 52 | 68 | 47 | 51 | 26 | 30 | 129 | 0 |
N.S. |
1 | 0.00 | 1.44 | 1.89 | 1.31 | 1.42 | 0.72 | 0.83 | 3.58 | 0.00 |
time (sec) |
N/A | 0.000 | 0.032 | 0.687 | 0.093 | 0.088 | 0.149 | 0.136 | 0.194 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | B | A | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 38 | 25 | 37 | 0 | 39 | 48 | 36 | 41 | 0 |
N.S. |
1 | 2.00 | 1.32 | 1.95 | 0.00 | 2.05 | 2.53 | 1.89 | 2.16 | 0.00 |
time (sec) |
N/A | 3.251 | 0.047 | 0.039 | 0.000 | 0.085 | 7.985 | 0.125 | 0.189 | 0.000 |
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 | 23 | 68 | 23 | 17 | 22 | 16 | 19 | 52 | 19 | 18 |
N.S. |
1 | 2.96 | 1.00 | 0.74 | 0.96 | 0.70 | 0.83 | 2.26 | 0.83 | 0.78 |
time (sec) |
N/A | 0.787 | 0.464 | 0.125 | 0.088 | 0.077 | 0.052 | 0.121 | 0.182 | 3.766 |
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 | 21 | 36 | 21 | 19 | 36 | 17 | 20 | 18 | 20 | 18 |
N.S. |
1 | 1.71 | 1.00 | 0.90 | 1.71 | 0.81 | 0.95 | 0.86 | 0.95 | 0.86 |
time (sec) |
N/A | 0.205 | 0.025 | 0.060 | 0.035 | 0.081 | 0.057 | 0.125 | 0.171 | 0.067 |
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 | 18 | 16 | 18 | 21 | 19 | 15 | 19 | 20 | 22 |
N.S. |
1 | 0.86 | 0.76 | 0.86 | 1.00 | 0.90 | 0.71 | 0.90 | 0.95 | 1.05 |
time (sec) |
N/A | 0.194 | 0.058 | 0.161 | 0.060 | 0.089 | 0.051 | 0.129 | 0.173 | 3.742 |
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 | 22 | 32 | 26 | 30 | 60 | 29 | 27 | 29 | 28 | 29 |
N.S. |
1 | 1.45 | 1.18 | 1.36 | 2.73 | 1.32 | 1.23 | 1.32 | 1.27 | 1.32 |
time (sec) |
N/A | 0.202 | 0.007 | 0.214 | 0.033 | 0.082 | 0.066 | 0.123 | 0.200 | 3.764 |