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 | C | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 59 | 65 | 82 | 67 | 64 | 66 | 42 | 65 | 15 | 76 |
N.S. |
1 | 1.10 | 1.39 | 1.14 | 1.08 | 1.12 | 0.71 | 1.10 | 0.25 | 1.29 |
time (sec) |
N/A | 0.178 | 0.051 | 7.806 | 0.104 | 0.064 | 0.421 | 0.183 | 0.156 | 0.257 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | C | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 70 | 76 | 83 | 76 | 66 | 79 | 34 | 67 | 37 | 92 |
N.S. |
1 | 1.09 | 1.19 | 1.09 | 0.94 | 1.13 | 0.49 | 0.96 | 0.53 | 1.31 |
time (sec) |
N/A | 0.187 | 0.077 | 7.841 | 0.103 | 0.063 | 0.611 | 0.121 | 0.162 | 0.206 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | B | C | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 68 | 76 | 68 | 20 | 83 | 146 | 41 | 83 | 15 | 18 |
N.S. |
1 | 1.12 | 1.00 | 0.29 | 1.22 | 2.15 | 0.60 | 1.22 | 0.22 | 0.26 |
time (sec) |
N/A | 0.189 | 0.140 | 3.154 | 0.103 | 1.969 | 0.507 | 0.135 | 0.149 | 0.236 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | C | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 93 | 103 | 82 | 19 | 130 | 102 | 41 | 110 | 46 | 0 |
N.S. |
1 | 1.11 | 0.88 | 0.20 | 1.40 | 1.10 | 0.44 | 1.18 | 0.49 | 0.00 |
time (sec) |
N/A | 0.208 | 0.236 | 2.414 | 0.107 | 0.070 | 0.828 | 0.132 | 0.157 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | C | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 93 | 103 | 82 | 20 | 129 | 102 | 39 | 109 | 46 | 0 |
N.S. |
1 | 1.11 | 0.88 | 0.22 | 1.39 | 1.10 | 0.42 | 1.17 | 0.49 | 0.00 |
time (sec) |
N/A | 0.202 | 0.220 | 2.327 | 0.110 | 0.069 | 0.979 | 0.126 | 0.148 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | A | F | A | F | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 93 | 105 | 137 | 15 | 0 | 99 | 0 | 69 | 39 | 29 |
N.S. |
1 | 1.13 | 1.47 | 0.16 | 0.00 | 1.06 | 0.00 | 0.74 | 0.42 | 0.31 |
time (sec) |
N/A | 0.233 | 0.440 | 2.997 | 0.000 | 0.170 | 0.000 | 0.122 | 0.173 | 0.209 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 126 | 127 | 69 | 51 | 0 | 87 | 0 | 66 | 68 | 27 |
N.S. |
1 | 1.01 | 0.55 | 0.40 | 0.00 | 0.69 | 0.00 | 0.52 | 0.54 | 0.21 |
time (sec) |
N/A | 0.298 | 0.114 | 0.111 | 0.000 | 39.893 | 0.000 | 0.191 | 0.147 | 0.167 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 34 | 41 | 28 | 0 | 49 | 0 | 70 | 31 | 35 |
N.S. |
1 | 1.00 | 1.21 | 0.82 | 0.00 | 1.44 | 0.00 | 2.06 | 0.91 | 1.03 |
time (sec) |
N/A | 0.167 | 0.157 | 0.296 | 0.000 | 0.064 | 0.000 | 0.141 | 0.157 | 0.287 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 67 | 55 | 41 | 0 | 47 | 0 | 49 | 142 | 43 |
N.S. |
1 | 1.16 | 0.95 | 0.71 | 0.00 | 0.81 | 0.00 | 0.84 | 2.45 | 0.74 |
time (sec) |
N/A | 0.198 | 0.070 | 0.349 | 0.000 | 0.063 | 0.000 | 0.126 | 2.646 | 0.172 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 71 | 80 | 57 | 54 | 52 | 81 | 0 | 112 | 19 | 0 |
N.S. |
1 | 1.13 | 0.80 | 0.76 | 0.73 | 1.14 | 0.00 | 1.58 | 0.27 | 0.00 |
time (sec) |
N/A | 0.214 | 0.083 | 0.224 | 0.106 | 0.064 | 0.000 | 0.129 | 0.174 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | B | B | F | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 52 | 27 | 52 | 59 | 0 | 69 | 50 | 49 |
N.S. |
1 | 1.00 | 2.48 | 1.29 | 2.48 | 2.81 | 0.00 | 3.29 | 2.38 | 2.33 |
time (sec) |
N/A | 0.174 | 0.081 | 0.207 | 0.031 | 0.062 | 0.000 | 0.125 | 0.159 | 0.444 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | B | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 17 | 75 | 14 | 13 | 13 | 36 | 13 | 46 | 21 |
N.S. |
1 | 1.00 | 4.41 | 0.82 | 0.76 | 0.76 | 2.12 | 0.76 | 2.71 | 1.24 |
time (sec) |
N/A | 0.143 | 10.041 | 0.143 | 0.029 | 0.056 | 0.157 | 0.116 | 0.256 | 0.158 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | C | A | F | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 46 | 46 | 40 | 116 | 34 | 35 | 221 | 34 | 52 | 34 |
N.S. |
1 | 1.00 | 0.87 | 2.52 | 0.74 | 0.76 | 4.80 | 0.74 | 1.13 | 0.74 |
time (sec) |
N/A | 0.343 | 0.037 | 0.348 | 0.029 | 0.060 | 3.610 | 0.129 | 0.159 | 0.205 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 78 | 78 | 110 | 93 | 0 | 232 | 0 | 0 | 25 | 0 |
N.S. |
1 | 1.00 | 1.41 | 1.19 | 0.00 | 2.97 | 0.00 | 0.00 | 0.32 | 0.00 |
time (sec) |
N/A | 0.168 | 0.212 | 2.792 | 0.000 | 1.357 | 0.000 | 0.000 | 0.153 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 141 | 146 | 76 | 100 | 0 | 161 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.04 | 0.54 | 0.71 | 0.00 | 1.14 | 0.00 | 0.00 | 0.16 | 0.00 |
time (sec) |
N/A | 0.266 | 0.186 | 2.003 | 0.000 | 2.025 | 0.000 | 0.000 | 0.153 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 63 | 65 | 90 | 29 | 94 | 86 | 71 | 0 | 25 | 0 |
N.S. |
1 | 1.03 | 1.43 | 0.46 | 1.49 | 1.37 | 1.13 | 0.00 | 0.40 | 0.00 |
time (sec) |
N/A | 0.162 | 0.163 | 1.736 | 0.105 | 0.067 | 0.883 | 0.000 | 0.160 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 74 | 79 | 74 | 85 | 0 | 211 | 0 | 0 | 81 | 0 |
N.S. |
1 | 1.07 | 1.00 | 1.15 | 0.00 | 2.85 | 0.00 | 0.00 | 1.09 | 0.00 |
time (sec) |
N/A | 0.191 | 0.252 | 2.458 | 0.000 | 2.981 | 0.000 | 0.000 | 0.162 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 48 | 64 | 26 | 23 | 73 | 40 | 0 | 0 | 34 | 23 |
N.S. |
1 | 1.33 | 0.54 | 0.48 | 1.52 | 0.83 | 0.00 | 0.00 | 0.71 | 0.48 |
time (sec) |
N/A | 0.174 | 0.896 | 0.189 | 0.026 | 0.063 | 0.000 | 0.000 | 0.146 | 0.157 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 90 | 90 | 180 | 2515 | 0 | 458 | 0 | 0 | 62 | 0 |
N.S. |
1 | 1.00 | 2.00 | 27.94 | 0.00 | 5.09 | 0.00 | 0.00 | 0.69 | 0.00 |
time (sec) |
N/A | 0.189 | 0.346 | 11.731 | 0.000 | 4.320 | 0.000 | 0.000 | 0.150 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 23 | 19 | 0 | 18 | 0 | 0 | 50 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 0.00 | 0.78 | 0.00 | 0.00 | 2.17 | 0.00 |
time (sec) |
N/A | 0.181 | 0.004 | 0.589 | 0.000 | 0.086 | 0.000 | 0.000 | 0.160 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 23 | 22 | 0 | 42 | 0 | 0 | 28 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.96 | 0.00 | 1.83 | 0.00 | 0.00 | 1.22 | 0.00 |
time (sec) |
N/A | 0.184 | 0.002 | 0.782 | 0.000 | 0.087 | 0.000 | 0.000 | 0.143 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | B | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 21 | 41 | 18 | 57 | 49 | 14 | 51 | 42 | 17 |
N.S. |
1 | 1.31 | 2.56 | 1.12 | 3.56 | 3.06 | 0.88 | 3.19 | 2.62 | 1.06 |
time (sec) |
N/A | 0.170 | 0.055 | 0.192 | 0.109 | 0.061 | 3.934 | 0.131 | 0.151 | 0.082 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | B | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 19 | 39 | 18 | 57 | 47 | 14 | 51 | 42 | 17 |
N.S. |
1 | 1.19 | 2.44 | 1.12 | 3.56 | 2.94 | 0.88 | 3.19 | 2.62 | 1.06 |
time (sec) |
N/A | 0.171 | 0.056 | 0.207 | 0.106 | 0.062 | 2.154 | 0.116 | 0.153 | 0.133 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 26 | 31 | 0 | 45 | 0 | 0 | 31 | 0 |
N.S. |
1 | 1.00 | 1.00 | 1.19 | 0.00 | 1.73 | 0.00 | 0.00 | 1.19 | 0.00 |
time (sec) |
N/A | 0.189 | 0.161 | 1.165 | 0.000 | 0.087 | 0.000 | 0.000 | 0.156 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 15 | 14 | 0 | 13 | 0 | 0 | 64 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 0.00 | 0.87 | 0.00 | 0.00 | 4.27 | 0.00 |
time (sec) |
N/A | 0.180 | 0.127 | 0.959 | 0.000 | 0.086 | 0.000 | 0.000 | 0.158 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 16 | 15 | 22 | 14 | 0 | 0 | 13 | 14 |
N.S. |
1 | 1.00 | 1.00 | 0.94 | 1.38 | 0.88 | 0.00 | 0.00 | 0.81 | 0.88 |
time (sec) |
N/A | 0.154 | 0.266 | 0.426 | 0.073 | 0.062 | 0.000 | 0.000 | 0.159 | 0.032 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 74 | 74 | 65 | 78 | 0 | 252 | 0 | 0 | 44 | 0 |
N.S. |
1 | 1.00 | 0.88 | 1.05 | 0.00 | 3.41 | 0.00 | 0.00 | 0.59 | 0.00 |
time (sec) |
N/A | 0.312 | 0.569 | 2.405 | 0.000 | 0.190 | 0.000 | 0.000 | 180.009 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 96 | 0 | 0 | 62 | 0 | 0 | 56 | 0 |
N.S. |
1 | 1.00 | 4.36 | 0.00 | 0.00 | 2.82 | 0.00 | 0.00 | 2.55 | 0.00 |
time (sec) |
N/A | 0.195 | 0.234 | 0.000 | 0.000 | 0.391 | 0.000 | 0.000 | 0.185 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 26 | 0 | 0 | 0 | 0 | 0 | 67 | 0 |
N.S. |
1 | 1.00 | 1.08 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 2.79 | 0.00 |
time (sec) |
N/A | 0.203 | 0.124 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.174 | 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 | 14 | 14 | 14 | 11 | 10 | 10 | 10 | 10 | 10 | 10 |
N.S. |
1 | 1.00 | 1.00 | 0.79 | 0.71 | 0.71 | 0.71 | 0.71 | 0.71 | 0.71 |
time (sec) |
N/A | 0.164 | 0.001 | 0.152 | 0.024 | 0.066 | 0.017 | 0.121 | 0.137 | 0.017 |
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 | 11 | 11 | 11 | 11 | 9 | 10 | 8 | 9 | 12 | 9 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.82 | 0.91 | 0.73 | 0.82 | 1.09 | 0.82 |
time (sec) |
N/A | 0.171 | 0.000 | 0.360 | 0.025 | 0.067 | 0.019 | 0.119 | 0.150 | 0.019 |
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 | 29 | 22 | 17 | 16 | 19 | 24 | 16 | 18 | 16 |
N.S. |
1 | 1.21 | 0.92 | 0.71 | 0.67 | 0.79 | 1.00 | 0.67 | 0.75 | 0.67 |
time (sec) |
N/A | 0.193 | 0.001 | 0.459 | 0.029 | 0.071 | 0.018 | 0.116 | 0.154 | 0.018 |
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 | 44 | 30 | 23 | 24 | 25 | 36 | 22 | 26 | 22 |
N.S. |
1 | 1.29 | 0.88 | 0.68 | 0.71 | 0.74 | 1.06 | 0.65 | 0.76 | 0.65 |
time (sec) |
N/A | 0.246 | 0.002 | 1.049 | 0.029 | 0.071 | 0.025 | 0.109 | 0.156 | 0.021 |
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 | 44 | 59 | 38 | 29 | 30 | 31 | 48 | 28 | 34 | 28 |
N.S. |
1 | 1.34 | 0.86 | 0.66 | 0.68 | 0.70 | 1.09 | 0.64 | 0.77 | 0.64 |
time (sec) |
N/A | 0.286 | 0.007 | 1.978 | 0.031 | 0.075 | 0.018 | 0.113 | 0.153 | 0.016 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 47 | 21 | 15 | 23 | 37 | 99 | 14 | 42 | 20 |
N.S. |
1 | 2.35 | 1.05 | 0.75 | 1.15 | 1.85 | 4.95 | 0.70 | 2.10 | 1.00 |
time (sec) |
N/A | 0.210 | 0.033 | 0.544 | 0.031 | 0.073 | 0.125 | 0.121 | 0.155 | 0.152 |
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 | 33 | 31 | 22 | 23 | 22 | 39 | 23 | 22 | 22 |
N.S. |
1 | 1.06 | 1.00 | 0.71 | 0.74 | 0.71 | 1.26 | 0.74 | 0.71 | 0.71 |
time (sec) |
N/A | 0.177 | 0.034 | 1.099 | 0.025 | 0.068 | 0.081 | 0.157 | 0.163 | 0.058 |
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 | 21 | 27 | 18 | 20 | 37 | 32 | 20 | 22 | 27 |
N.S. |
1 | 1.00 | 1.29 | 0.86 | 0.95 | 1.76 | 1.52 | 0.95 | 1.05 | 1.29 |
time (sec) |
N/A | 0.172 | 0.007 | 0.200 | 0.029 | 0.060 | 0.021 | 0.120 | 0.165 | 0.121 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 46 | 95 | 32 | 54 | 93 | 60 | 112 | 38 | 44 |
N.S. |
1 | 1.28 | 2.64 | 0.89 | 1.50 | 2.58 | 1.67 | 3.11 | 1.06 | 1.22 |
time (sec) |
N/A | 0.307 | 0.010 | 0.241 | 0.031 | 0.070 | 0.070 | 0.120 | 0.159 | 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 | 41 | 41 | 41 | 37 | 33 | 40 | 66 | 33 | 72 | 51 |
N.S. |
1 | 1.00 | 1.00 | 0.90 | 0.80 | 0.98 | 1.61 | 0.80 | 1.76 | 1.24 |
time (sec) |
N/A | 0.193 | 0.007 | 0.567 | 0.026 | 0.069 | 0.022 | 0.126 | 0.156 | 0.129 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 40 | 40 | 40 | 40 | 51 | 70 | 388 | 53 | 97 | 35 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 1.28 | 1.75 | 9.70 | 1.32 | 2.42 | 0.88 |
time (sec) |
N/A | 0.223 | 0.010 | 0.377 | 0.030 | 0.074 | 0.477 | 0.135 | 0.148 | 0.348 |
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 | 22 | 24 | 19 | 18 | 18 | 31 | 18 | 18 | 18 |
N.S. |
1 | 1.00 | 1.09 | 0.86 | 0.82 | 0.82 | 1.41 | 0.82 | 0.82 | 0.82 |
time (sec) |
N/A | 0.241 | 0.001 | 0.034 | 0.106 | 0.067 | 0.026 | 0.126 | 0.145 | 0.021 |
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 | 20 | 20 | 16 | 26 | 22 | 40 | 19 | 37 | 36 | 26 |
N.S. |
1 | 1.00 | 0.80 | 1.30 | 1.10 | 2.00 | 0.95 | 1.85 | 1.80 | 1.30 |
time (sec) |
N/A | 0.250 | 0.006 | 0.059 | 0.024 | 0.070 | 0.042 | 0.124 | 0.154 | 0.146 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 32 | 40 | 25 | 30 | 70 | 20 | 53 | 24 | 24 |
N.S. |
1 | 1.00 | 1.25 | 0.78 | 0.94 | 2.19 | 0.62 | 1.66 | 0.75 | 0.75 |
time (sec) |
N/A | 0.219 | 0.016 | 0.092 | 0.104 | 0.073 | 0.070 | 0.141 | 0.155 | 0.053 |
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 | 56 | 76 | 46 | 35 | 24 | 37 | 56 | 34 | 42 | 38 |
N.S. |
1 | 1.36 | 0.82 | 0.62 | 0.43 | 0.66 | 1.00 | 0.61 | 0.75 | 0.68 |
time (sec) |
N/A | 0.401 | 0.026 | 8.766 | 0.026 | 0.072 | 0.029 | 0.116 | 0.157 | 0.024 |
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 | 33 | 55 | 26 | 25 | 25 | 27 | 25 | 54 | 25 |
N.S. |
1 | 1.00 | 1.67 | 0.79 | 0.76 | 0.76 | 0.82 | 0.76 | 1.64 | 0.76 |
time (sec) |
N/A | 0.193 | 0.063 | 55.436 | 0.023 | 0.076 | 0.023 | 0.109 | 0.150 | 0.117 |
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 | 46 | 48 | 46 | 37 | 40 | 38 | 44 | 42 | 58 | 36 |
N.S. |
1 | 1.04 | 1.00 | 0.80 | 0.87 | 0.83 | 0.96 | 0.91 | 1.26 | 0.78 |
time (sec) |
N/A | 0.203 | 0.009 | 4.425 | 0.024 | 0.087 | 0.040 | 0.123 | 0.161 | 0.023 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 41 | 41 | 53 | 38 | 37 | 55 | 44 | 26 | 56 | 27 |
N.S. |
1 | 1.00 | 1.29 | 0.93 | 0.90 | 1.34 | 1.07 | 0.63 | 1.37 | 0.66 |
time (sec) |
N/A | 0.204 | 0.031 | 0.660 | 0.031 | 0.066 | 0.028 | 0.122 | 0.158 | 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 | 24 | 29 | 14 | 11 | 10 | 19 | 14 | 10 | 18 | 18 |
N.S. |
1 | 1.21 | 0.58 | 0.46 | 0.42 | 0.79 | 0.58 | 0.42 | 0.75 | 0.75 |
time (sec) |
N/A | 0.209 | 0.001 | 0.378 | 0.024 | 0.072 | 0.023 | 0.111 | 0.153 | 0.025 |
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 | 46 | 61 | 22 | 17 | 16 | 31 | 31 | 16 | 34 | 32 |
N.S. |
1 | 1.33 | 0.48 | 0.37 | 0.35 | 0.67 | 0.67 | 0.35 | 0.74 | 0.70 |
time (sec) |
N/A | 0.334 | 0.001 | 2.480 | 0.024 | 0.069 | 0.021 | 0.122 | 0.163 | 0.022 |
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 | 68 | 93 | 30 | 23 | 24 | 43 | 46 | 22 | 50 | 44 |
N.S. |
1 | 1.37 | 0.44 | 0.34 | 0.35 | 0.63 | 0.68 | 0.32 | 0.74 | 0.65 |
time (sec) |
N/A | 0.474 | 0.008 | 28.368 | 0.026 | 0.075 | 0.023 | 0.134 | 0.154 | 0.016 |
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 | 90 | 125 | 38 | 68 | 30 | 55 | 61 | 28 | 66 | 56 |
N.S. |
1 | 1.39 | 0.42 | 0.76 | 0.33 | 0.61 | 0.68 | 0.31 | 0.73 | 0.62 |
time (sec) |
N/A | 0.643 | 0.025 | 0.094 | 0.032 | 0.084 | 0.023 | 0.123 | 0.154 | 0.018 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 68 | 68 | 58 | 0 | 0 | 0 | 0 | 0 | 15 | 52 |
N.S. |
1 | 1.00 | 0.85 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.22 | 0.76 |
time (sec) |
N/A | 0.208 | 0.045 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.150 | 0.420 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 32 | 47 | 25 | 41 | 71 | 54 | 132 | 85 | 24 |
N.S. |
1 | 1.00 | 1.47 | 0.78 | 1.28 | 2.22 | 1.69 | 4.12 | 2.66 | 0.75 |
time (sec) |
N/A | 0.191 | 0.023 | 0.269 | 0.030 | 0.073 | 0.520 | 0.144 | 0.159 | 0.173 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 8 | 8 | 8 | 7 | 6 | 14 | 17 | 6 | 18 | 6 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 0.75 | 1.75 | 2.12 | 0.75 | 2.25 | 0.75 |
time (sec) |
N/A | 0.168 | 0.002 | 0.192 | 0.028 | 0.067 | 0.020 | 0.120 | 0.156 | 0.017 |
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 | 11 | 11 | 11 | 10 | 14 | 22 | 15 | 14 | 12 | 11 |
N.S. |
1 | 1.00 | 1.00 | 0.91 | 1.27 | 2.00 | 1.36 | 1.27 | 1.09 | 1.00 |
time (sec) |
N/A | 0.181 | 0.001 | 0.129 | 0.029 | 0.066 | 0.036 | 0.119 | 0.160 | 0.187 |
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 | 8 | 8 | 8 | 7 | 6 | 6 | 7 | 6 | 6 | 6 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 0.75 | 0.75 | 0.88 | 0.75 | 0.75 | 0.75 |
time (sec) |
N/A | 0.162 | 0.001 | 0.320 | 0.025 | 0.065 | 0.022 | 0.128 | 0.148 | 0.211 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 31 | 71 | 36 | 38 | 68 | 41 | 47 | 29 | 24 |
N.S. |
1 | 1.19 | 2.73 | 1.38 | 1.46 | 2.62 | 1.58 | 1.81 | 1.12 | 0.92 |
time (sec) |
N/A | 0.271 | 0.021 | 0.148 | 0.025 | 0.073 | 0.064 | 0.122 | 0.151 | 0.187 |
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 | 17 | 17 | 17 | 22 | 14 | 30 | 15 | 14 | 17 | 13 |
N.S. |
1 | 1.00 | 1.00 | 1.29 | 0.82 | 1.76 | 0.88 | 0.82 | 1.00 | 0.76 |
time (sec) |
N/A | 0.197 | 0.001 | 0.250 | 0.029 | 0.062 | 0.039 | 0.121 | 0.157 | 0.133 |
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 | 31 | 24 | 20 | 19 | 20 | 39 | 20 | 21 | 22 |
N.S. |
1 | 1.00 | 0.77 | 0.65 | 0.61 | 0.65 | 1.26 | 0.65 | 0.68 | 0.71 |
time (sec) |
N/A | 0.190 | 0.050 | 0.220 | 0.031 | 0.077 | 8.016 | 0.122 | 0.152 | 0.634 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 22 | 14 | 13 | 27 | 0 | 13 | 26 | 32 |
N.S. |
1 | 1.00 | 1.05 | 0.67 | 0.62 | 1.29 | 0.00 | 0.62 | 1.24 | 1.52 |
time (sec) |
N/A | 0.184 | 0.039 | 0.168 | 0.024 | 0.083 | 0.000 | 0.117 | 0.156 | 0.666 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 48 | 95 | 52 | 54 | 93 | 56 | 44 | 38 | 57 |
N.S. |
1 | 1.26 | 2.50 | 1.37 | 1.42 | 2.45 | 1.47 | 1.16 | 1.00 | 1.50 |
time (sec) |
N/A | 0.351 | 0.022 | 0.221 | 0.026 | 0.075 | 0.070 | 0.120 | 0.163 | 0.171 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 76 | 77 | 74 | 76 | 74 | 82 | 0 | 95 | 163 | 75 |
N.S. |
1 | 1.01 | 0.97 | 1.00 | 0.97 | 1.08 | 0.00 | 1.25 | 2.14 | 0.99 |
time (sec) |
N/A | 0.325 | 0.020 | 0.552 | 0.029 | 0.076 | 0.000 | 0.178 | 0.157 | 3.909 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 88 | 100 | 127 | 76 | 115 | 178 | 100 | 149 | 428 | 133 |
N.S. |
1 | 1.14 | 1.44 | 0.86 | 1.31 | 2.02 | 1.14 | 1.69 | 4.86 | 1.51 |
time (sec) |
N/A | 0.759 | 2.374 | 66.764 | 0.110 | 0.106 | 147.341 | 0.131 | 0.177 | 0.231 |
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 | 70 | 76 | 74 | 46 | 54 | 54 | 148 | 54 | 59 | 94 |
N.S. |
1 | 1.09 | 1.06 | 0.66 | 0.77 | 0.77 | 2.11 | 0.77 | 0.84 | 1.34 |
time (sec) |
N/A | 0.332 | 0.196 | 97.490 | 0.025 | 0.071 | 0.194 | 0.129 | 0.162 | 0.229 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 33 | 55 | 33 | 36 | 71 | 39 | 75 | 62 | 75 |
N.S. |
1 | 1.00 | 1.67 | 1.00 | 1.09 | 2.15 | 1.18 | 2.27 | 1.88 | 2.27 |
time (sec) |
N/A | 0.366 | 0.027 | 0.174 | 0.103 | 0.073 | 0.204 | 0.126 | 0.154 | 0.306 |
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 | 16 | 18 | 20 | 21 | 14 | 26 | 24 | 14 | 996 | 26 |
N.S. |
1 | 1.12 | 1.25 | 1.31 | 0.88 | 1.62 | 1.50 | 0.88 | 62.25 | 1.62 |
time (sec) |
N/A | 0.223 | 0.024 | 53.108 | 0.106 | 0.070 | 6.770 | 0.123 | 0.199 | 0.184 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | A | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 12 | 22 | 21 | 27 | 24 | 23 | 11 | 10 |
N.S. |
1 | 1.00 | 1.00 | 1.83 | 1.75 | 2.25 | 2.00 | 1.92 | 0.92 | 0.83 |
time (sec) |
N/A | 0.204 | 0.009 | 0.611 | 0.030 | 0.076 | 0.462 | 0.115 | 0.159 | 0.157 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 17 | 17 | 14 | 13 | 18 | 20 | 13 | 17 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.82 | 0.76 | 1.06 | 1.18 | 0.76 | 1.00 | 0.76 |
time (sec) |
N/A | 0.166 | 0.004 | 0.459 | 0.024 | 0.071 | 0.122 | 0.115 | 0.147 | 0.119 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | B | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 45 | 26 | 31 | 54 | 43 | 75 | 38 | 11 | 33 |
N.S. |
1 | 1.73 | 1.00 | 1.19 | 2.08 | 1.65 | 2.88 | 1.46 | 0.42 | 1.27 |
time (sec) |
N/A | 0.212 | 0.037 | 52.809 | 0.032 | 0.072 | 6.774 | 0.120 | 0.167 | 0.145 |
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 | 38 | 38 | 38 | 29 | 30 | 31 | 139 | 28 | 102 | 36 |
N.S. |
1 | 1.00 | 1.00 | 0.76 | 0.79 | 0.82 | 3.66 | 0.74 | 2.68 | 0.95 |
time (sec) |
N/A | 0.204 | 0.009 | 2.030 | 0.033 | 0.072 | 1.237 | 0.113 | 0.156 | 0.171 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | B | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 42 | 20 | 35 | 33 | 43 | 22 | 21 | 11 | 21 |
N.S. |
1 | 2.10 | 1.00 | 1.75 | 1.65 | 2.15 | 1.10 | 1.05 | 0.55 | 1.05 |
time (sec) |
N/A | 0.240 | 0.009 | 30.076 | 0.026 | 0.079 | 8.518 | 0.133 | 0.157 | 0.142 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 12 | 16 | 12 | 19 | 19 | 25 | 14 | 13 | 150 | 35 |
N.S. |
1 | 1.33 | 1.00 | 1.58 | 1.58 | 2.08 | 1.17 | 1.08 | 12.50 | 2.92 |
time (sec) |
N/A | 0.197 | 0.009 | 2.505 | 0.029 | 0.075 | 2.200 | 0.125 | 0.159 | 0.178 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 64 | 41 | 39 | 35 | 208 | 64 | 0 | 75 | 47 | 47 |
N.S. |
1 | 0.64 | 0.61 | 0.55 | 3.25 | 1.00 | 0.00 | 1.17 | 0.73 | 0.73 |
time (sec) |
N/A | 0.264 | 0.041 | 0.420 | 0.124 | 0.086 | 0.000 | 0.137 | 0.161 | 0.199 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | A | F | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 11 | 21 | 17 | 27 | 92 | 17 | 0 | 24 | 17 | 25 |
N.S. |
1 | 1.91 | 1.55 | 2.45 | 8.36 | 1.55 | 0.00 | 2.18 | 1.55 | 2.27 |
time (sec) |
N/A | 0.195 | 0.010 | 0.969 | 0.032 | 0.073 | 0.000 | 0.122 | 0.149 | 0.370 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 7 | 11 | 7 | 12 | 9 | 11 | 0 | 9 | 18 | 5 |
N.S. |
1 | 1.57 | 1.00 | 1.71 | 1.29 | 1.57 | 0.00 | 1.29 | 2.57 | 0.71 |
time (sec) |
N/A | 0.223 | 0.081 | 15.192 | 0.110 | 0.076 | 0.000 | 0.119 | 0.153 | 0.154 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 53 | 34 | 33 | 43 | 27 | 38 | 107 | 78 | 278 | 23 |
N.S. |
1 | 0.64 | 0.62 | 0.81 | 0.51 | 0.72 | 2.02 | 1.47 | 5.25 | 0.43 |
time (sec) |
N/A | 0.203 | 0.055 | 0.642 | 0.107 | 0.081 | 4.460 | 0.126 | 0.168 | 0.144 |
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 | 33 | 55 | 22 | 20 | 39 | 66 | 39 | 37 | 27 | 17 |
N.S. |
1 | 1.67 | 0.67 | 0.61 | 1.18 | 2.00 | 1.18 | 1.12 | 0.82 | 0.52 |
time (sec) |
N/A | 0.223 | 0.039 | 0.190 | 0.103 | 0.071 | 0.248 | 0.142 | 0.153 | 0.153 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 9 | 9 | 8 | 7 | 21 | 219 | 20 | 20 | 16 |
N.S. |
1 | 0.33 | 0.33 | 0.30 | 0.26 | 0.78 | 8.11 | 0.74 | 0.74 | 0.59 |
time (sec) |
N/A | 0.185 | 0.068 | 0.509 | 0.110 | 0.070 | 4.463 | 0.123 | 0.153 | 0.159 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 43 | 41 | 31 | 28 | 46 | 102 | 29 | 117 | 38 |
N.S. |
1 | 1.54 | 1.46 | 1.11 | 1.00 | 1.64 | 3.64 | 1.04 | 4.18 | 1.36 |
time (sec) |
N/A | 0.230 | 0.029 | 0.287 | 0.103 | 0.069 | 0.214 | 0.122 | 0.148 | 0.177 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 67 | 45 | 58 | 39 | 38 | 61 | 0 | 78 | 21 | 120 |
N.S. |
1 | 0.67 | 0.87 | 0.58 | 0.57 | 0.91 | 0.00 | 1.16 | 0.31 | 1.79 |
time (sec) |
N/A | 0.216 | 0.131 | 0.326 | 0.111 | 0.072 | 0.000 | 0.124 | 0.149 | 0.248 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 55 | 37 | 54 | 29 | 28 | 58 | 0 | 61 | 100 | 77 |
N.S. |
1 | 0.67 | 0.98 | 0.53 | 0.51 | 1.05 | 0.00 | 1.11 | 1.82 | 1.40 |
time (sec) |
N/A | 0.191 | 1.090 | 0.219 | 0.105 | 0.072 | 0.000 | 0.122 | 0.152 | 0.220 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 42 | 52 | 58 | 45 | 44 | 77 | 252 | 39 | 104 | 48 |
N.S. |
1 | 1.24 | 1.38 | 1.07 | 1.05 | 1.83 | 6.00 | 0.93 | 2.48 | 1.14 |
time (sec) |
N/A | 0.433 | 1.182 | 0.186 | 0.102 | 0.070 | 0.227 | 0.124 | 0.147 | 0.161 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | B | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 9 | 9 | 9 | 20 | 0 | 19 | 76 | 21 | 13 | 7 |
N.S. |
1 | 1.00 | 1.00 | 2.22 | 0.00 | 2.11 | 8.44 | 2.33 | 1.44 | 0.78 |
time (sec) |
N/A | 0.185 | 0.006 | 1.152 | 0.000 | 0.076 | 1.518 | 0.122 | 0.159 | 0.201 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | B | B | F | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 35 | 13 | 129 | 33 | 0 | 49 | 11 | 12 |
N.S. |
1 | 1.00 | 2.33 | 0.87 | 8.60 | 2.20 | 0.00 | 3.27 | 0.73 | 0.80 |
time (sec) |
N/A | 0.182 | 0.056 | 0.586 | 0.118 | 0.076 | 0.000 | 0.135 | 0.158 | 0.069 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 15 | 28 | 21 | 128 | 26 | 22 | 20 | 13 | 9 |
N.S. |
1 | 0.88 | 1.65 | 1.24 | 7.53 | 1.53 | 1.29 | 1.18 | 0.76 | 0.53 |
time (sec) |
N/A | 0.209 | 0.020 | 1.158 | 0.114 | 0.078 | 0.414 | 0.128 | 0.155 | 0.136 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 27 | 21 | 18 | 81 | 19 | 0 | 24 | 13 | 15 |
N.S. |
1 | 1.29 | 1.00 | 0.86 | 3.86 | 0.90 | 0.00 | 1.14 | 0.62 | 0.71 |
time (sec) |
N/A | 0.216 | 0.013 | 2.746 | 0.105 | 0.078 | 0.000 | 0.132 | 0.158 | 0.065 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | B | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 27 | 21 | 27 | 129 | 19 | 17 | 24 | 11 | 17 |
N.S. |
1 | 1.29 | 1.00 | 1.29 | 6.14 | 0.90 | 0.81 | 1.14 | 0.52 | 0.81 |
time (sec) |
N/A | 0.190 | 0.007 | 0.431 | 0.109 | 0.077 | 0.428 | 0.121 | 0.147 | 0.052 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | B | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 26 | 28 | 171 | 50 | 294 | 48 | 11 | 27 |
N.S. |
1 | 1.00 | 1.00 | 1.08 | 6.58 | 1.92 | 11.31 | 1.85 | 0.42 | 1.04 |
time (sec) |
N/A | 0.197 | 0.018 | 0.355 | 0.127 | 0.078 | 3.069 | 0.123 | 0.150 | 0.258 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | B | B | B | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 25 | 70 | 28 | 171 | 50 | 294 | 48 | 13 | 27 |
N.S. |
1 | 0.96 | 2.69 | 1.08 | 6.58 | 1.92 | 11.31 | 1.85 | 0.50 | 1.04 |
time (sec) |
N/A | 0.208 | 0.044 | 0.678 | 0.119 | 0.078 | 6.635 | 0.129 | 0.149 | 0.165 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 25 | 22 | 0 | 34 | 0 | 17 | 9 | 21 |
N.S. |
1 | 1.00 | 1.56 | 1.38 | 0.00 | 2.12 | 0.00 | 1.06 | 0.56 | 1.31 |
time (sec) |
N/A | 0.165 | 0.010 | 0.361 | 0.000 | 0.068 | 0.000 | 0.116 | 0.151 | 0.124 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 17 | 27 | 31 | 0 | 35 | 0 | 29 | 11 | 23 |
N.S. |
1 | 1.00 | 1.59 | 1.82 | 0.00 | 2.06 | 0.00 | 1.71 | 0.65 | 1.35 |
time (sec) |
N/A | 0.168 | 0.010 | 0.352 | 0.000 | 0.067 | 0.000 | 0.122 | 0.154 | 0.125 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | B | F | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 16 | 9 | 41 | 55 | 0 | 25 | 18 | 13 |
N.S. |
1 | 1.00 | 0.59 | 0.33 | 1.52 | 2.04 | 0.00 | 0.93 | 0.67 | 0.48 |
time (sec) |
N/A | 0.175 | 0.008 | 0.161 | 0.150 | 0.077 | 0.000 | 0.122 | 0.156 | 0.031 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 30 | 19 | 17 | 101 | 58 | 0 | 57 | 22 | 28 |
N.S. |
1 | 1.00 | 0.63 | 0.57 | 3.37 | 1.93 | 0.00 | 1.90 | 0.73 | 0.93 |
time (sec) |
N/A | 0.183 | 0.013 | 0.224 | 0.153 | 0.071 | 0.000 | 0.241 | 0.149 | 0.136 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 53 | 53 | 61 | 52 | 433 | 107 | 0 | 100 | 28 | 0 |
N.S. |
1 | 1.00 | 1.15 | 0.98 | 8.17 | 2.02 | 0.00 | 1.89 | 0.53 | 0.00 |
time (sec) |
N/A | 0.248 | 0.123 | 0.261 | 0.163 | 0.073 | 0.000 | 0.136 | 0.146 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 73 | 73 | 76 | 47 | 0 | 71 | 0 | 72 | 48 | 0 |
N.S. |
1 | 1.00 | 1.04 | 0.64 | 0.00 | 0.97 | 0.00 | 0.99 | 0.66 | 0.00 |
time (sec) |
N/A | 0.291 | 0.657 | 0.352 | 0.000 | 0.068 | 0.000 | 0.132 | 0.152 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 55 | 43 | 36 | 42 | 43 | 40 | 230 | 43 | 66 | 0 |
N.S. |
1 | 0.78 | 0.65 | 0.76 | 0.78 | 0.73 | 4.18 | 0.78 | 1.20 | 0.00 |
time (sec) |
N/A | 0.401 | 0.055 | 0.658 | 0.030 | 0.078 | 22.274 | 0.126 | 0.151 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 98 | 110 | 40 | 49 | 80 | 70 | 0 | 80 | 5 | 65 |
N.S. |
1 | 1.12 | 0.41 | 0.50 | 0.82 | 0.71 | 0.00 | 0.82 | 0.05 | 0.66 |
time (sec) |
N/A | 0.311 | 0.032 | 0.116 | 0.106 | 0.072 | 0.000 | 0.119 | 0.146 | 0.172 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 57 | 45 | 69 | 53 | 52 | 54 | 0 | 52 | 8 | 67 |
N.S. |
1 | 0.79 | 1.21 | 0.93 | 0.91 | 0.95 | 0.00 | 0.91 | 0.14 | 1.18 |
time (sec) |
N/A | 0.261 | 0.041 | 0.129 | 0.105 | 0.072 | 0.000 | 0.174 | 0.145 | 0.390 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | B | B | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 87 | 92 | 73 | 130 | 3213 | 170 | 0 | 0 | 103 | 63 |
N.S. |
1 | 1.06 | 0.84 | 1.49 | 36.93 | 1.95 | 0.00 | 0.00 | 1.18 | 0.72 |
time (sec) |
N/A | 0.420 | 0.074 | 0.305 | 0.369 | 0.094 | 0.000 | 0.000 | 0.146 | 0.346 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 40 | 40 | 30 | 31 | 30 | 82 | 0 | 31 | 80 | 105 |
N.S. |
1 | 1.00 | 0.75 | 0.78 | 0.75 | 2.05 | 0.00 | 0.78 | 2.00 | 2.62 |
time (sec) |
N/A | 0.320 | 5.124 | 0.568 | 0.030 | 0.082 | 0.000 | 0.133 | 0.147 | 0.790 |