Detailed conclusion table per each integral is given by the table below. The elapsed time is in seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2) if the failure was due to an exception being raised, which could indicate a bug in the system. If the failure was due to integral not being evaluated within the time limit, then it is given as F.
In this table, the column N.S.
means normalized size and is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To make the table
fit the page, the name Mathematica
was abbreviated to MMA
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 43 | 20 | 18 | 21 | 21 | 19 | 36 | 26 | 17 |
N.S. |
1 | 2.15 | 1.00 | 0.90 | 1.05 | 1.05 | 0.95 | 1.80 | 1.30 | 0.85 |
time (sec) |
N/A | 0.339 | 0.036 | 0.214 | 0.032 | 0.089 | 0.114 | 0.115 | 0.168 | 3.261 |
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 | 22 | 0 | 24 | 27 | 27 | 27 | 31 | 31 | 21 | 28 |
N.S. |
1 | 0.00 | 1.09 | 1.23 | 1.23 | 1.23 | 1.41 | 1.41 | 0.95 | 1.27 |
time (sec) |
N/A | 0.000 | 0.074 | 0.195 | 0.136 | 0.103 | 0.057 | 0.113 | 0.168 | 3.274 |
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 | 10 | 10 | 11 | 10 | 12 | 8 | 10 | 12 | 12 |
N.S. |
1 | 0.40 | 0.40 | 0.44 | 0.40 | 0.48 | 0.32 | 0.40 | 0.48 | 0.48 |
time (sec) |
N/A | 0.287 | 0.001 | 0.020 | 0.034 | 0.067 | 0.031 | 0.109 | 0.166 | 0.014 |
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 | 24 | 23 | 36 | 25 | 22 | 36 | 28 | 25 |
N.S. |
1 | 0.00 | 0.89 | 0.85 | 1.33 | 0.93 | 0.81 | 1.33 | 1.04 | 0.93 |
time (sec) |
N/A | 0.000 | 1.789 | 0.436 | 0.128 | 0.090 | 0.234 | 0.129 | 0.171 | 3.320 |
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 | 21 | 20 | 24 | 29 | 24 | 25 | 28 | 19 |
N.S. |
1 | 0.00 | 0.84 | 0.80 | 0.96 | 1.16 | 0.96 | 1.00 | 1.12 | 0.76 |
time (sec) |
N/A | 0.000 | 0.313 | 1.198 | 0.084 | 0.083 | 0.093 | 0.130 | 0.173 | 3.187 |
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 | 23 | 23 | 17 | 16 | 16 | 12 | 16 | 26 | 16 |
N.S. |
1 | 1.15 | 1.15 | 0.85 | 0.80 | 0.80 | 0.60 | 0.80 | 1.30 | 0.80 |
time (sec) |
N/A | 0.314 | 0.044 | 0.063 | 0.042 | 0.095 | 0.060 | 0.114 | 0.169 | 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 | 37 | 33 | 35 | 35 | 37 | 40 | 29 | 40 |
N.S. |
1 | 0.00 | 1.54 | 1.38 | 1.46 | 1.46 | 1.54 | 1.67 | 1.21 | 1.67 |
time (sec) |
N/A | 0.000 | 0.090 | 0.312 | 0.062 | 0.085 | 0.176 | 0.119 | 0.163 | 3.169 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | B | A | B | B | F | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 47 | 146 | 25 | 51 | 78 | 0 | 103 | 84 |
N.S. |
1 | 0.00 | 2.04 | 6.35 | 1.09 | 2.22 | 3.39 | 0.00 | 4.48 | 3.65 |
time (sec) |
N/A | 0.000 | 0.276 | 2.560 | 0.070 | 0.111 | 1.928 | 0.000 | 0.345 | 3.355 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 18 | 21 | 20 | 19 | 25 | 20 | 29 | 26 | 19 |
N.S. |
1 | 0.86 | 1.00 | 0.95 | 0.90 | 1.19 | 0.95 | 1.38 | 1.24 | 0.90 |
time (sec) |
N/A | 0.519 | 0.022 | 0.086 | 0.144 | 0.088 | 0.070 | 0.115 | 0.164 | 3.111 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | B | F | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 27 | 22 | 30 | 36 | 34 | 162 | 206 | 30 |
N.S. |
1 | 0.00 | 0.87 | 0.71 | 0.97 | 1.16 | 1.10 | 5.23 | 6.65 | 0.97 |
time (sec) |
N/A | 0.000 | 1.603 | 0.362 | 0.097 | 0.084 | 0.093 | 0.161 | 0.288 | 3.104 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | B | B | B | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 88 | 46 | 219 | 295 | 292 | 205 | 42 | 1870 |
N.S. |
1 | 1.00 | 3.26 | 1.70 | 8.11 | 10.93 | 10.81 | 7.59 | 1.56 | 69.26 |
time (sec) |
N/A | 0.395 | 0.031 | 0.626 | 0.038 | 0.092 | 0.571 | 0.131 | 0.163 | 75.161 |
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 | 25 | 25 | 18 | 22 | 16 | 14 | 16 | 28 | 22 |
N.S. |
1 | 1.25 | 1.25 | 0.90 | 1.10 | 0.80 | 0.70 | 0.80 | 1.40 | 1.10 |
time (sec) |
N/A | 0.459 | 0.357 | 0.153 | 0.126 | 0.090 | 0.113 | 0.117 | 0.168 | 3.457 |
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 | 30 | 30 | 20 | 23 | 20 | 20 | 21 | 21 | 19 |
N.S. |
1 | 1.58 | 1.58 | 1.05 | 1.21 | 1.05 | 1.05 | 1.11 | 1.11 | 1.00 |
time (sec) |
N/A | 0.885 | 1.999 | 0.169 | 0.143 | 0.082 | 0.192 | 0.122 | 0.166 | 3.267 |
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 | 22 | 22 | 22 | 22 | 17 | 22 | 22 | 22 |
N.S. |
1 | 0.00 | 1.16 | 1.16 | 1.16 | 1.16 | 0.89 | 1.16 | 1.16 | 1.16 |
time (sec) |
N/A | 0.000 | 0.139 | 0.135 | 0.060 | 0.071 | 0.064 | 0.114 | 0.166 | 3.151 |
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 | 27 | 16 | 16 | 22 | 14 | 24 | 28 | 14 |
N.S. |
1 | 1.22 | 1.00 | 0.59 | 0.59 | 0.81 | 0.52 | 0.89 | 1.04 | 0.52 |
time (sec) |
N/A | 0.638 | 0.039 | 0.143 | 0.078 | 0.084 | 0.077 | 0.121 | 0.169 | 3.179 |
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 | 30 | 20 | 20 | 25 | 25 | 22 | 25 | 26 | 20 |
N.S. |
1 | 1.76 | 1.18 | 1.18 | 1.47 | 1.47 | 1.29 | 1.47 | 1.53 | 1.18 |
time (sec) |
N/A | 0.194 | 0.002 | 0.036 | 0.026 | 0.073 | 0.025 | 0.111 | 0.177 | 0.025 |
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 | 21 | 33 | 26 | 35 | 33 | 87 | 34 | 20 | 97 | 108 |
N.S. |
1 | 1.57 | 1.24 | 1.67 | 1.57 | 4.14 | 1.62 | 0.95 | 4.62 | 5.14 |
time (sec) |
N/A | 0.616 | 0.023 | 0.133 | 0.032 | 0.082 | 0.250 | 0.112 | 0.178 | 3.285 |
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 | 9 | 9 | 10 | 9 | 9 | 8 | 9 | 7 | 7 |
N.S. |
1 | 0.90 | 0.90 | 1.00 | 0.90 | 0.90 | 0.80 | 0.90 | 0.70 | 0.70 |
time (sec) |
N/A | 0.215 | 0.004 | 0.023 | 0.054 | 0.080 | 0.110 | 0.112 | 0.170 | 3.076 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | A | A | A | A | A | B | B |
verified | N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 0 | 36 | 46 | 46 | 34 | 35 | 37 | 34 |
N.S. |
1 | 0.00 | 0.00 | 1.44 | 1.84 | 1.84 | 1.36 | 1.40 | 1.48 | 1.36 |
time (sec) |
N/A | 0.000 | 0.000 | 0.293 | 0.154 | 0.101 | 0.332 | 0.132 | 0.198 | 3.144 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F | A | A | A | B | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 0 | 21 | 24 | 0 | 23 | 20 | 21 | 24 | 0 |
N.S. |
1 | 0.00 | 1.00 | 1.14 | 0.00 | 1.10 | 0.95 | 1.00 | 1.14 | 0.00 |
time (sec) |
N/A | 0.000 | 0.063 | 0.183 | 0.000 | 0.086 | 0.132 | 0.132 | 0.165 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | F(-2) | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 40 | 23 | 30 | 24 | 20 | 0 | 41 | 22 |
N.S. |
1 | 0.00 | 1.54 | 0.88 | 1.15 | 0.92 | 0.77 | 0.00 | 1.58 | 0.85 |
time (sec) |
N/A | 0.000 | 0.475 | 0.495 | 0.102 | 0.094 | 0.308 | 0.000 | 0.167 | 3.160 |
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 | 30 | 0 | 39 | 35 | 46 | 42 | 37 | 1342 | 54 | 40 |
N.S. |
1 | 0.00 | 1.30 | 1.17 | 1.53 | 1.40 | 1.23 | 44.73 | 1.80 | 1.33 |
time (sec) |
N/A | 0.000 | 0.195 | 0.734 | 0.128 | 0.081 | 0.187 | 0.318 | 24.802 | 3.139 |
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 | 11 | 9 | 9 | 9 | 33 | 8 | 8 | 8 | 10 | 8 |
N.S. |
1 | 0.82 | 0.82 | 0.82 | 3.00 | 0.73 | 0.73 | 0.73 | 0.91 | 0.73 |
time (sec) |
N/A | 0.223 | 0.004 | 0.030 | 0.028 | 0.077 | 0.050 | 0.113 | 0.170 | 3.079 |
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 | 31 | 24 | 25 | 31 | 25 | 20 | 35 | 35 | 18 |
N.S. |
1 | 1.24 | 0.96 | 1.00 | 1.24 | 1.00 | 0.80 | 1.40 | 1.40 | 0.72 |
time (sec) |
N/A | 0.220 | 0.009 | 0.095 | 0.028 | 0.089 | 0.070 | 0.119 | 0.167 | 3.132 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 23 | 27 | 53 | 24 | 20 | 52 | 25 | 54 |
N.S. |
1 | 1.00 | 1.00 | 1.17 | 2.30 | 1.04 | 0.87 | 2.26 | 1.09 | 2.35 |
time (sec) |
N/A | 0.357 | 0.093 | 0.272 | 0.044 | 0.103 | 0.216 | 0.112 | 0.151 | 4.208 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 17 | 17 | 16 | 31 | 27 | 10 | 103 | 19 | 15 |
N.S. |
1 | 1.00 | 1.00 | 0.94 | 1.82 | 1.59 | 0.59 | 6.06 | 1.12 | 0.88 |
time (sec) |
N/A | 0.643 | 0.078 | 0.416 | 0.027 | 0.084 | 0.091 | 0.189 | 0.154 | 3.150 |
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 | 30 | 248 | 28 | 33 | 34 | 34 | 36 | 0 | 43 | 35 |
N.S. |
1 | 8.27 | 0.93 | 1.10 | 1.13 | 1.13 | 1.20 | 0.00 | 1.43 | 1.17 |
time (sec) |
N/A | 2.219 | 0.136 | 1.031 | 0.124 | 0.085 | 4.482 | 0.000 | 0.196 | 0.138 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | B | A | B | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 155 | 62 | 53 | 64 | 51 | 54 | 56 | 69 | 64 |
N.S. |
1 | 5.00 | 2.00 | 1.71 | 2.06 | 1.65 | 1.74 | 1.81 | 2.23 | 2.06 |
time (sec) |
N/A | 3.363 | 5.065 | 9.669 | 0.081 | 0.092 | 0.213 | 0.122 | 0.153 | 3.213 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 18 | 17 | 16 | 16 | 17 | 16 | 17 | 17 |
N.S. |
1 | 1.00 | 1.00 | 0.94 | 0.89 | 0.89 | 0.94 | 0.89 | 0.94 | 0.94 |
time (sec) |
N/A | 0.460 | 0.011 | 0.260 | 0.140 | 0.084 | 0.054 | 0.119 | 0.151 | 3.226 |
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 | 23 | 29 | 25 | 24 | 0 | 23 | 22 | 24 | 22 | 21 |
N.S. |
1 | 1.26 | 1.09 | 1.04 | 0.00 | 1.00 | 0.96 | 1.04 | 0.96 | 0.91 |
time (sec) |
N/A | 0.331 | 0.036 | 0.723 | 0.000 | 0.083 | 0.124 | 0.117 | 0.152 | 3.228 |
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 | 31 | 0 | 44 | 34 | 57 | 35 | 31 | 0 | 46 | 94 |
N.S. |
1 | 0.00 | 1.42 | 1.10 | 1.84 | 1.13 | 1.00 | 0.00 | 1.48 | 3.03 |
time (sec) |
N/A | 0.000 | 2.313 | 0.665 | 0.289 | 0.098 | 0.311 | 0.000 | 0.156 | 3.602 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | B | A | F(-2) | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 33 | 33 | 68 | 63 | 32 | 0 | 153 | 82 |
N.S. |
1 | 0.00 | 1.27 | 1.27 | 2.62 | 2.42 | 1.23 | 0.00 | 5.88 | 3.15 |
time (sec) |
N/A | 0.000 | 0.057 | 1.661 | 0.086 | 0.110 | 0.121 | 0.000 | 0.153 | 3.710 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | F | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 28 | 96 | 0 | 30 | 27 | 47 | 75 | 30 |
N.S. |
1 | 0.00 | 0.97 | 3.31 | 0.00 | 1.03 | 0.93 | 1.62 | 2.59 | 1.03 |
time (sec) |
N/A | 0.000 | 0.646 | 74.093 | 0.000 | 0.097 | 0.408 | 1.381 | 0.182 | 3.347 |
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 | 23 | 20 | 20 | 18 | 0 | 17 | 17 | 17 | 18 | 17 |
N.S. |
1 | 0.87 | 0.87 | 0.78 | 0.00 | 0.74 | 0.74 | 0.74 | 0.78 | 0.74 |
time (sec) |
N/A | 0.607 | 0.037 | 0.352 | 0.000 | 0.093 | 0.132 | 0.114 | 0.149 | 0.143 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 29 | 32 | 35 | 40 | 34 | 32 | 42 | 40 | 37 |
N.S. |
1 | 0.97 | 1.07 | 1.17 | 1.33 | 1.13 | 1.07 | 1.40 | 1.33 | 1.23 |
time (sec) |
N/A | 0.227 | 0.011 | 0.082 | 0.029 | 0.078 | 0.069 | 0.112 | 0.148 | 0.063 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | C | B | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 106 | 24 | 28 | 43 | 39 | 17 | 39 | 34 | 21 |
N.S. |
1 | 4.42 | 1.00 | 1.17 | 1.79 | 1.62 | 0.71 | 1.62 | 1.42 | 0.88 |
time (sec) |
N/A | 0.687 | 0.082 | 4.871 | 0.144 | 0.096 | 0.128 | 0.120 | 0.146 | 3.155 |
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 | 23 | 28 | 28 | 52 | 64 | 54 | 49 | 54 | 132 | 55 |
N.S. |
1 | 1.22 | 1.22 | 2.26 | 2.78 | 2.35 | 2.13 | 2.35 | 5.74 | 2.39 |
time (sec) |
N/A | 1.283 | 0.069 | 0.493 | 0.753 | 0.090 | 0.128 | 0.181 | 0.152 | 3.322 |
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 | 24 | 24 | 24 | 24 | 22 | 24 | 24 | 24 |
N.S. |
1 | 0.00 | 0.89 | 0.89 | 0.89 | 0.89 | 0.81 | 0.89 | 0.89 | 0.89 |
time (sec) |
N/A | 0.000 | 0.231 | 0.162 | 0.068 | 0.091 | 0.081 | 0.118 | 0.152 | 3.160 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F(-2) | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 27 | 34 | 0 | 33 | 34 | 23 | 37 | 25 |
N.S. |
1 | 0.00 | 1.00 | 1.26 | 0.00 | 1.22 | 1.26 | 0.85 | 1.37 | 0.93 |
time (sec) |
N/A | 0.000 | 0.114 | 9.662 | 0.000 | 0.096 | 0.462 | 0.305 | 0.191 | 3.269 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | A | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 48 | 30 | 30 | 0 | 29 | 26 | 51 | 32 | 28 |
N.S. |
1 | 1.85 | 1.15 | 1.15 | 0.00 | 1.12 | 1.00 | 1.96 | 1.23 | 1.08 |
time (sec) |
N/A | 0.240 | 0.100 | 0.116 | 0.000 | 0.090 | 1.783 | 0.121 | 0.154 | 3.112 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 7 | 5 | 5 | 6 | 5 | 5 | 5 | 5 | 5 | 5 |
N.S. |
1 | 0.71 | 0.71 | 0.86 | 0.71 | 0.71 | 0.71 | 0.71 | 0.71 | 0.71 |
time (sec) |
N/A | 0.154 | 0.001 | 0.015 | 0.030 | 0.094 | 0.049 | 0.113 | 0.152 | 3.075 |
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 | 21 | 18 | 19 | 19 | 15 | 21 | 21 | 21 |
N.S. |
1 | 0.00 | 1.11 | 0.95 | 1.00 | 1.00 | 0.79 | 1.11 | 1.11 | 1.11 |
time (sec) |
N/A | 0.000 | 0.065 | 0.084 | 0.137 | 0.090 | 0.084 | 0.116 | 0.149 | 3.126 |
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 | 28 | 41 | 23 | 27 | 0 | 22 | 26 | 23 | 28 | 27 |
N.S. |
1 | 1.46 | 0.82 | 0.96 | 0.00 | 0.79 | 0.93 | 0.82 | 1.00 | 0.96 |
time (sec) |
N/A | 1.434 | 1.148 | 0.261 | 0.000 | 0.102 | 0.076 | 0.110 | 0.149 | 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 | 19 | 10 | 10 | 11 | 10 | 10 | 8 | 11 | 10 | 10 |
N.S. |
1 | 0.53 | 0.53 | 0.58 | 0.53 | 0.53 | 0.42 | 0.58 | 0.53 | 0.53 |
time (sec) |
N/A | 0.245 | 0.002 | 0.026 | 0.028 | 0.073 | 0.032 | 0.116 | 0.150 | 0.018 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | A | B | A | A | B | B | B |
verified | N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 0 | 28 | 47 | 27 | 27 | 59 | 28 | 27 |
N.S. |
1 | 0.00 | 0.00 | 1.27 | 2.14 | 1.23 | 1.23 | 2.68 | 1.27 | 1.23 |
time (sec) |
N/A | 0.000 | 0.000 | 0.786 | 0.144 | 0.090 | 0.182 | 0.598 | 0.152 | 3.273 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | B | B | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 0 | 39 | 51 | 50 | 50 | 49 | 160 | 54 | 0 |
N.S. |
1 | 0.00 | 1.18 | 1.55 | 1.52 | 1.52 | 1.48 | 4.85 | 1.64 | 0.00 |
time (sec) |
N/A | 0.000 | 0.187 | 115.075 | 0.221 | 0.093 | 1.554 | 0.585 | 0.185 | 0.000 |
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 | 16 | 19 | 15 | 0 | 22 | 15 | 19 |
N.S. |
1 | 0.00 | 0.92 | 0.67 | 0.79 | 0.62 | 0.00 | 0.92 | 0.62 | 0.79 |
time (sec) |
N/A | 0.000 | 0.129 | 0.263 | 0.149 | 0.084 | 0.000 | 0.124 | 0.150 | 3.399 |
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 | 16 | 19 | 21 | 17 | 15 | 17 | 16 | 17 |
N.S. |
1 | 0.00 | 0.80 | 0.95 | 1.05 | 0.85 | 0.75 | 0.85 | 0.80 | 0.85 |
time (sec) |
N/A | 0.000 | 0.112 | 0.577 | 0.103 | 0.091 | 10.575 | 0.187 | 0.148 | 3.161 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | A | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 40 | 37 | 37 | 408 | 61 | 39 | 147 | 61 | 43 |
N.S. |
1 | 1.48 | 1.37 | 1.37 | 15.11 | 2.26 | 1.44 | 5.44 | 2.26 | 1.59 |
time (sec) |
N/A | 1.276 | 0.055 | 0.408 | 0.097 | 0.094 | 0.115 | 0.164 | 0.150 | 0.094 |
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 | 13 | 13 | 16 | 13 | 15 | 15 | 13 | 17 | 17 |
N.S. |
1 | 0.54 | 0.54 | 0.67 | 0.54 | 0.62 | 0.62 | 0.54 | 0.71 | 0.71 |
time (sec) |
N/A | 0.150 | 0.002 | 0.030 | 0.040 | 0.075 | 0.045 | 0.114 | 0.149 | 0.023 |
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 | 25 | 25 | 24 | 23 | 23 | 24 | 23 | 27 | 23 |
N.S. |
1 | 1.39 | 1.39 | 1.33 | 1.28 | 1.28 | 1.33 | 1.28 | 1.50 | 1.28 |
time (sec) |
N/A | 0.368 | 0.012 | 0.170 | 0.035 | 0.088 | 0.056 | 0.109 | 0.143 | 3.138 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | F | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 23 | 22 | 35 | 40 | 22 | 0 | 40 | 22 |
N.S. |
1 | 0.00 | 0.96 | 0.92 | 1.46 | 1.67 | 0.92 | 0.00 | 1.67 | 0.92 |
time (sec) |
N/A | 0.000 | 0.181 | 11.070 | 0.094 | 0.097 | 1.472 | 0.000 | 0.148 | 3.190 |
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 | 29 | 0 | 29 | 36 | 58 | 35 | 31 | 121 | 36 | 36 |
N.S. |
1 | 0.00 | 1.00 | 1.24 | 2.00 | 1.21 | 1.07 | 4.17 | 1.24 | 1.24 |
time (sec) |
N/A | 0.000 | 0.092 | 0.117 | 0.159 | 0.076 | 0.096 | 0.203 | 0.148 | 3.442 |
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 | 27 | 27 | 25 | 22 | 21 | 24 | 19 | 21 | 37 | 0 |
N.S. |
1 | 1.00 | 0.93 | 0.81 | 0.78 | 0.89 | 0.70 | 0.78 | 1.37 | 0.00 |
time (sec) |
N/A | 3.890 | 0.482 | 1.206 | 0.154 | 0.098 | 0.132 | 0.130 | 0.156 | 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 | 12 | 12 | 13 | 12 | 12 | 10 | 14 | 12 | 12 |
N.S. |
1 | 0.63 | 0.63 | 0.68 | 0.63 | 0.63 | 0.53 | 0.74 | 0.63 | 0.63 |
time (sec) |
N/A | 0.287 | 0.003 | 0.035 | 0.023 | 0.086 | 0.054 | 0.112 | 0.152 | 3.115 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | A | B | B | B | B | B | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 84 | 22 | 179 | 179 | 88 | 248 | 268 | 0 |
N.S. |
1 | 0.00 | 3.82 | 1.00 | 8.14 | 8.14 | 4.00 | 11.27 | 12.18 | 0.00 |
time (sec) |
N/A | 0.000 | 4.089 | 2.189 | 0.098 | 0.093 | 0.212 | 0.199 | 0.217 | 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 | 23 | 248 | 38 | 63 | 107 | 112 | 122 | 55 | 147 | 92 |
N.S. |
1 | 10.78 | 1.65 | 2.74 | 4.65 | 4.87 | 5.30 | 2.39 | 6.39 | 4.00 |
time (sec) |
N/A | 1.047 | 0.033 | 1.174 | 0.054 | 0.099 | 6.129 | 0.153 | 0.198 | 0.299 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 22 | 22 | 23 | 40 | 21 | 24 | 21 | 25 | 20 |
N.S. |
1 | 0.88 | 0.88 | 0.92 | 1.60 | 0.84 | 0.96 | 0.84 | 1.00 | 0.80 |
time (sec) |
N/A | 0.195 | 0.008 | 0.128 | 0.144 | 0.082 | 0.083 | 0.116 | 0.156 | 0.054 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 24 | 24 | 24 | 23 | 26 | 19 | 26 | 27 | 23 |
N.S. |
1 | 0.73 | 0.73 | 0.73 | 0.70 | 0.79 | 0.58 | 0.79 | 0.82 | 0.70 |
time (sec) |
N/A | 0.199 | 0.013 | 0.183 | 0.039 | 0.095 | 0.061 | 0.114 | 0.150 | 0.036 |
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 | 11 | 14 | 11 | 11 | 26 | 10 | 7 | 23 | 11 | 10 |
N.S. |
1 | 1.27 | 1.00 | 1.00 | 2.36 | 0.91 | 0.64 | 2.09 | 1.00 | 0.91 |
time (sec) |
N/A | 0.177 | 0.005 | 0.072 | 0.063 | 0.082 | 0.063 | 0.128 | 0.157 | 3.095 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | B | A | A | B | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 53 | 39 | 33 | 57 | 40 | 32 | 53 | 54 | 0 |
N.S. |
1 | 2.12 | 1.56 | 1.32 | 2.28 | 1.60 | 1.28 | 2.12 | 2.16 | 0.00 |
time (sec) |
N/A | 0.895 | 0.304 | 1.137 | 0.173 | 0.090 | 1.280 | 0.128 | 0.147 | 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 | 20 | 18 | 16 | 15 | 15 | 15 | 15 | 26 | 17 |
N.S. |
1 | 1.11 | 1.00 | 0.89 | 0.83 | 0.83 | 0.83 | 0.83 | 1.44 | 0.94 |
time (sec) |
N/A | 0.525 | 0.098 | 0.115 | 0.108 | 0.080 | 0.053 | 0.107 | 0.147 | 3.153 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | C | A | A | F(-2) | B | F | B |
verified | N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 0 | 49 | 566 | 46 | 49 | 0 | 81 | 0 | 51 |
N.S. |
1 | 0.00 | 1.48 | 17.15 | 1.39 | 1.48 | 0.00 | 2.45 | 0.00 | 1.55 |
time (sec) |
N/A | 0.000 | 0.125 | 0.200 | 0.290 | 0.099 | 0.000 | 1.729 | 8.635 | 4.441 |
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 | 24 | 64 | 64 | 59 | 104 | 48 | 46 | 58 | 59 | 54 |
N.S. |
1 | 2.67 | 2.67 | 2.46 | 4.33 | 2.00 | 1.92 | 2.42 | 2.46 | 2.25 |
time (sec) |
N/A | 0.481 | 0.015 | 0.690 | 0.033 | 0.082 | 0.095 | 0.116 | 0.180 | 3.152 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | A | F(-1) | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 37 | 115 | 30 | 29 | 28 | 30 | 0 | 29 | 32 | 26 |
N.S. |
1 | 3.11 | 0.81 | 0.78 | 0.76 | 0.81 | 0.00 | 0.78 | 0.86 | 0.70 |
time (sec) |
N/A | 0.409 | 0.016 | 0.218 | 0.102 | 0.081 | 0.000 | 0.122 | 1.232 | 3.149 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 25 | 46 | 24 | 56 | 23 | 19 | 23 | 83 | 23 |
N.S. |
1 | 0.96 | 1.77 | 0.92 | 2.15 | 0.88 | 0.73 | 0.88 | 3.19 | 0.88 |
time (sec) |
N/A | 1.059 | 0.126 | 2.763 | 0.212 | 0.085 | 0.336 | 0.761 | 0.184 | 4.608 |
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 | 22 | 22 | 19 | 18 | 23 | 19 | 23 | 27 | 21 |
N.S. |
1 | 1.16 | 1.16 | 1.00 | 0.95 | 1.21 | 1.00 | 1.21 | 1.42 | 1.11 |
time (sec) |
N/A | 0.307 | 0.267 | 0.109 | 0.119 | 0.096 | 0.109 | 0.114 | 0.183 | 0.067 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | B | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 0 | 18 | 18 | 16 | 16 | 26 | 17 | 20 | 31 |
N.S. |
1 | 0.00 | 1.00 | 1.00 | 0.89 | 0.89 | 1.44 | 0.94 | 1.11 | 1.72 |
time (sec) |
N/A | 0.000 | 0.380 | 0.060 | 0.073 | 0.093 | 0.109 | 0.125 | 0.174 | 0.070 |
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 | 12 | 12 | 12 | 11 | 11 | 10 | 11 | 12 | 11 |
N.S. |
1 | 0.86 | 0.86 | 0.86 | 0.79 | 0.79 | 0.71 | 0.79 | 0.86 | 0.79 |
time (sec) |
N/A | 0.272 | 0.008 | 0.167 | 0.026 | 0.077 | 0.063 | 0.114 | 0.174 | 3.330 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | F | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 25 | 22 | 21 | 23 | 19 | 0 | 31 | 21 |
N.S. |
1 | 0.00 | 0.83 | 0.73 | 0.70 | 0.77 | 0.63 | 0.00 | 1.03 | 0.70 |
time (sec) |
N/A | 0.000 | 0.112 | 0.161 | 0.194 | 0.100 | 0.133 | 0.000 | 0.176 | 0.077 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | A | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 36 | 48 | 89 | 66 | 31 | 104 | 93 | 38 |
N.S. |
1 | 1.00 | 1.29 | 1.71 | 3.18 | 2.36 | 1.11 | 3.71 | 3.32 | 1.36 |
time (sec) |
N/A | 1.267 | 1.041 | 75.605 | 0.146 | 0.102 | 0.113 | 0.118 | 0.174 | 3.303 |
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 | 9 | 7 | 7 | 7 | 6 | 6 | 5 | 6 | 7 | 6 |
N.S. |
1 | 0.78 | 0.78 | 0.78 | 0.67 | 0.67 | 0.56 | 0.67 | 0.78 | 0.67 |
time (sec) |
N/A | 0.143 | 0.001 | 0.017 | 0.032 | 0.082 | 0.033 | 0.111 | 0.170 | 0.009 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | B | A | B | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 51 | 27 | 19 | 43 | 38 | 73 | 50 | 18 | 51 |
N.S. |
1 | 2.12 | 1.12 | 0.79 | 1.79 | 1.58 | 3.04 | 2.08 | 0.75 | 2.12 |
time (sec) |
N/A | 0.280 | 0.010 | 0.089 | 0.030 | 0.088 | 0.145 | 0.114 | 0.169 | 3.134 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 31 | 24 | 20 | 16 | 16 | 22 | 16 | 14 | 12 |
N.S. |
1 | 2.07 | 1.60 | 1.33 | 1.07 | 1.07 | 1.47 | 1.07 | 0.93 | 0.80 |
time (sec) |
N/A | 0.277 | 0.006 | 0.113 | 0.032 | 0.097 | 0.060 | 0.113 | 0.165 | 0.038 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 18 | 19 | 18 | 21 | 19 | 18 | 18 | 22 |
N.S. |
1 | 1.00 | 1.00 | 1.06 | 1.00 | 1.17 | 1.06 | 1.00 | 1.00 | 1.22 |
time (sec) |
N/A | 0.298 | 0.002 | 0.113 | 0.028 | 0.076 | 0.059 | 0.114 | 0.165 | 3.025 |
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 | 12 | 12 | 11 | 14 | 14 | 14 | 14 | 17 | 14 |
N.S. |
1 | 0.92 | 0.92 | 0.85 | 1.08 | 1.08 | 1.08 | 1.08 | 1.31 | 1.08 |
time (sec) |
N/A | 0.318 | 0.035 | 0.119 | 0.025 | 0.088 | 0.060 | 0.113 | 0.166 | 3.001 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | A | B | B | B | F | F | B |
verified | N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 0 | 36 | 226 | 218 | 70 | 0 | 0 | 221 |
N.S. |
1 | 0.00 | 0.00 | 1.38 | 8.69 | 8.38 | 2.69 | 0.00 | 0.00 | 8.50 |
time (sec) |
N/A | 0.000 | 0.000 | 9.148 | 3.750 | 0.104 | 2.045 | 0.000 | 18.194 | 6.711 |
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 | 14 | 18 | 18 | 17 | 0 | 16 | 22 | 16 | 14 | 13 |
N.S. |
1 | 1.29 | 1.29 | 1.21 | 0.00 | 1.14 | 1.57 | 1.14 | 1.00 | 0.93 |
time (sec) |
N/A | 0.254 | 0.017 | 0.254 | 0.000 | 0.103 | 0.112 | 0.113 | 0.160 | 3.060 |
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 | 46 | 22 | 40 | 24 | 20 | 21 | 44 | 23 |
N.S. |
1 | 0.00 | 1.70 | 0.81 | 1.48 | 0.89 | 0.74 | 0.78 | 1.63 | 0.85 |
time (sec) |
N/A | 0.000 | 1.430 | 0.160 | 0.073 | 0.088 | 0.112 | 0.119 | 0.162 | 3.080 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | A | A | A | A | A | B | B |
verified | N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 0 | 0 | 17 | 16 | 16 | 15 | 16 | 16 | 16 |
N.S. |
1 | 0.00 | 0.00 | 1.06 | 1.00 | 1.00 | 0.94 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.000 | 0.000 | 2.510 | 0.086 | 0.087 | 0.487 | 0.197 | 0.152 | 3.344 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | B | B | F | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 28 | 37 | 29 | 29 | 58 | 83 | 373 | 0 |
N.S. |
1 | 0.00 | 1.00 | 1.32 | 1.04 | 1.04 | 2.07 | 2.96 | 13.32 | 0.00 |
time (sec) |
N/A | 0.000 | 0.156 | 0.493 | 0.091 | 0.084 | 0.196 | 0.276 | 0.164 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | A | A | A | A | F(-1) | B | F(-1) |
verified | N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 0 | 54 | 61 | 50 | 26 | 0 | 67 | 0 |
N.S. |
1 | 0.00 | 0.00 | 1.69 | 1.91 | 1.56 | 0.81 | 0.00 | 2.09 | 0.00 |
time (sec) |
N/A | 0.000 | 0.000 | 7.407 | 0.089 | 0.093 | 0.578 | 0.000 | 3.315 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | A | F(-1) | F | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 70 | 26 | 23 | 19 | 24 | 0 | 0 | 24 | 35 |
N.S. |
1 | 3.04 | 1.13 | 1.00 | 0.83 | 1.04 | 0.00 | 0.00 | 1.04 | 1.52 |
time (sec) |
N/A | 0.855 | 0.078 | 0.626 | 0.103 | 0.081 | 0.000 | 0.000 | 0.163 | 3.472 |
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 | 15 | 21 | 15 | 15 | 64 | 17 | 14 | 17 | 15 | 14 |
N.S. |
1 | 1.40 | 1.00 | 1.00 | 4.27 | 1.13 | 0.93 | 1.13 | 1.00 | 0.93 |
time (sec) |
N/A | 0.305 | 0.030 | 0.045 | 0.035 | 0.073 | 0.040 | 0.110 | 0.158 | 3.245 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | B | B | B | B | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 153 | 49 | 51 | 96 | 48 | 70 | 48 | 86 | 27 |
N.S. |
1 | 7.65 | 2.45 | 2.55 | 4.80 | 2.40 | 3.50 | 2.40 | 4.30 | 1.35 |
time (sec) |
N/A | 0.377 | 0.051 | 0.320 | 0.120 | 0.078 | 0.086 | 0.118 | 0.153 | 0.127 |
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 | 38 | 0 | 44 | 34 | 105 | 136 | 58 | 14409 | 142 | 102 |
N.S. |
1 | 0.00 | 1.16 | 0.89 | 2.76 | 3.58 | 1.53 | 379.18 | 3.74 | 2.68 |
time (sec) |
N/A | 0.000 | 0.303 | 3.165 | 0.163 | 0.105 | 0.182 | 1.666 | 0.452 | 3.430 |
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 | 19 | 21 | 22 | 20 | 32 | 20 | 21 | 20 |
N.S. |
1 | 1.00 | 1.00 | 1.11 | 1.16 | 1.05 | 1.68 | 1.05 | 1.11 | 1.05 |
time (sec) |
N/A | 0.547 | 0.033 | 0.198 | 0.069 | 0.083 | 0.066 | 0.129 | 0.199 | 3.427 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | A | A | A | A | A | F | B |
verified | N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 0 | 25 | 25 | 24 | 20 | 20 | 56 | 35 |
N.S. |
1 | 0.00 | 0.00 | 0.93 | 0.93 | 0.89 | 0.74 | 0.74 | 2.07 | 1.30 |
time (sec) |
N/A | 0.000 | 0.000 | 24.875 | 0.155 | 0.092 | 0.071 | 0.133 | 200.009 | 3.323 |
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 | 33 | 24 | 39 | 114 | 31 | 26 | 24 | 31 | 31 |
N.S. |
1 | 1.38 | 1.00 | 1.62 | 4.75 | 1.29 | 1.08 | 1.00 | 1.29 | 1.29 |
time (sec) |
N/A | 0.577 | 0.140 | 0.355 | 0.115 | 0.090 | 0.088 | 0.113 | 0.155 | 3.472 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 22 | 16 | 15 | 14 | 25 | 14 | 66 | 16 | 14 |
N.S. |
1 | 1.16 | 0.84 | 0.79 | 0.74 | 1.32 | 0.74 | 3.47 | 0.84 | 0.74 |
time (sec) |
N/A | 0.188 | 0.009 | 0.100 | 0.033 | 0.084 | 0.054 | 0.120 | 0.152 | 3.286 |
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 | 19 | 39 | 15 | 15 | 27 | 27 | 27 | 12 | 30 | 28 |
N.S. |
1 | 2.05 | 0.79 | 0.79 | 1.42 | 1.42 | 1.42 | 0.63 | 1.58 | 1.47 |
time (sec) |
N/A | 0.213 | 0.005 | 0.040 | 0.045 | 0.082 | 0.092 | 0.114 | 0.151 | 3.198 |
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 | 18 | 16 | 14 | 13 | 22 | 14 | 15 | 18 | 13 |
N.S. |
1 | 0.60 | 0.53 | 0.47 | 0.43 | 0.73 | 0.47 | 0.50 | 0.60 | 0.43 |
time (sec) |
N/A | 0.240 | 0.025 | 0.069 | 0.030 | 0.074 | 0.097 | 0.114 | 0.150 | 0.075 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 13 | 13 | 12 | 11 | 11 | 12 | 19 | 13 | 11 |
N.S. |
1 | 0.65 | 0.65 | 0.60 | 0.55 | 0.55 | 0.60 | 0.95 | 0.65 | 0.55 |
time (sec) |
N/A | 0.306 | 0.040 | 0.071 | 0.087 | 0.085 | 0.058 | 0.112 | 0.152 | 3.137 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 20 | 18 | 14 | 15 | 16 | 12 | 15 | 17 | 12 |
N.S. |
1 | 0.83 | 0.75 | 0.58 | 0.62 | 0.67 | 0.50 | 0.62 | 0.71 | 0.50 |
time (sec) |
N/A | 0.154 | 0.003 | 0.045 | 0.029 | 0.072 | 0.045 | 0.108 | 0.155 | 3.174 |
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 | 24 | 22 | 31 | 31 | 30 | 32 | 29 | 56 | 78 | 35 |
N.S. |
1 | 0.92 | 1.29 | 1.29 | 1.25 | 1.33 | 1.21 | 2.33 | 3.25 | 1.46 |
time (sec) |
N/A | 1.493 | 0.213 | 0.375 | 2.514 | 0.090 | 0.163 | 0.196 | 1.703 | 3.312 |
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 | 35 | 23 | 23 | 22 | 21 | 35 | 20 | 21 | 23 | 21 |
N.S. |
1 | 0.66 | 0.66 | 0.63 | 0.60 | 1.00 | 0.57 | 0.60 | 0.66 | 0.60 |
time (sec) |
N/A | 0.815 | 0.036 | 0.221 | 0.063 | 0.086 | 0.087 | 0.136 | 0.173 | 3.277 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | B | B | B | B | B | F | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 125 | 66 | 512 | 105 | 104 | 357 | 178 | 75 |
N.S. |
1 | 0.00 | 4.46 | 2.36 | 18.29 | 3.75 | 3.71 | 12.75 | 6.36 | 2.68 |
time (sec) |
N/A | 0.000 | 0.038 | 0.552 | 0.042 | 0.078 | 0.176 | 0.127 | 0.170 | 3.484 |
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 | 19 | 47 | 34 | 34 | 37 | 37 | 32 | 37 | 42 | 30 |
N.S. |
1 | 2.47 | 1.79 | 1.79 | 1.95 | 1.95 | 1.68 | 1.95 | 2.21 | 1.58 |
time (sec) |
N/A | 0.316 | 0.015 | 0.074 | 0.026 | 0.071 | 0.022 | 0.106 | 0.161 | 0.051 |
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 | 28 | 0 | 41 | 56 | 82 | 82 | 209 | 283 | 100 | 0 |
N.S. |
1 | 0.00 | 1.46 | 2.00 | 2.93 | 2.93 | 7.46 | 10.11 | 3.57 | 0.00 |
time (sec) |
N/A | 0.000 | 0.050 | 3.728 | 0.091 | 0.102 | 0.340 | 0.150 | 0.162 | 0.000 |
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 | 27 | 0 | 24 | 25 | 38 | 38 | 19 | 67 | 51 | 45 |
N.S. |
1 | 0.00 | 0.89 | 0.93 | 1.41 | 1.41 | 0.70 | 2.48 | 1.89 | 1.67 |
time (sec) |
N/A | 0.000 | 0.190 | 2.418 | 0.069 | 0.084 | 0.070 | 0.110 | 0.162 | 0.182 |