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 | 36 | 36 | 30 | 25 | 24 | 29 | 34 | 24 | 28 | 25 |
N.S. |
1 | 1.00 | 0.83 | 0.69 | 0.67 | 0.81 | 0.94 | 0.67 | 0.78 | 0.69 |
time (sec) |
N/A | 0.271 | 0.017 | 0.150 | 0.026 | 0.120 | 1.136 | 0.125 | 0.167 | 17.775 |
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 | 36 | 36 | 30 | 25 | 24 | 29 | 34 | 24 | 28 | 25 |
N.S. |
1 | 1.00 | 0.83 | 0.69 | 0.67 | 0.81 | 0.94 | 0.67 | 0.78 | 0.69 |
time (sec) |
N/A | 0.272 | 0.016 | 0.144 | 0.032 | 0.140 | 0.805 | 0.124 | 0.168 | 17.557 |
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 | 36 | 36 | 30 | 25 | 24 | 29 | 34 | 24 | 28 | 25 |
N.S. |
1 | 1.00 | 0.83 | 0.69 | 0.67 | 0.81 | 0.94 | 0.67 | 0.78 | 0.69 |
time (sec) |
N/A | 0.274 | 0.016 | 0.143 | 0.032 | 0.101 | 0.592 | 0.141 | 0.166 | 0.040 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 36 | 30 | 25 | 24 | 29 | 34 | 24 | 28 | 25 |
N.S. |
1 | 1.00 | 0.83 | 0.69 | 0.67 | 0.81 | 0.94 | 0.67 | 0.78 | 0.69 |
time (sec) |
N/A | 0.268 | 0.017 | 0.140 | 0.027 | 0.101 | 0.626 | 0.125 | 0.166 | 17.535 |
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 | 36 | 36 | 30 | 25 | 24 | 29 | 34 | 24 | 28 | 25 |
N.S. |
1 | 1.00 | 0.83 | 0.69 | 0.67 | 0.81 | 0.94 | 0.67 | 0.78 | 0.69 |
time (sec) |
N/A | 0.264 | 0.018 | 0.138 | 0.028 | 0.140 | 0.347 | 0.104 | 0.163 | 0.039 |
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 | 36 | 36 | 30 | 25 | 24 | 29 | 34 | 24 | 28 | 26 |
N.S. |
1 | 1.00 | 0.83 | 0.69 | 0.67 | 0.81 | 0.94 | 0.67 | 0.78 | 0.72 |
time (sec) |
N/A | 0.261 | 0.016 | 0.135 | 0.028 | 0.076 | 0.364 | 0.137 | 0.163 | 0.041 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 36 | 30 | 25 | 24 | 29 | 34 | 24 | 28 | 26 |
N.S. |
1 | 1.00 | 0.83 | 0.69 | 0.67 | 0.81 | 0.94 | 0.67 | 0.78 | 0.72 |
time (sec) |
N/A | 0.261 | 0.016 | 0.125 | 0.026 | 0.107 | 0.402 | 0.142 | 0.174 | 0.041 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 36 | 30 | 25 | 24 | 27 | 34 | 24 | 26 | 26 |
N.S. |
1 | 1.00 | 0.83 | 0.69 | 0.67 | 0.75 | 0.94 | 0.67 | 0.72 | 0.72 |
time (sec) |
N/A | 0.260 | 0.015 | 0.121 | 0.027 | 0.106 | 0.497 | 0.115 | 0.161 | 17.388 |
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 | 51 | 51 | 51 | 36 | 35 | 40 | 49 | 35 | 39 | 35 |
N.S. |
1 | 1.00 | 1.00 | 0.71 | 0.69 | 0.78 | 0.96 | 0.69 | 0.76 | 0.69 |
time (sec) |
N/A | 0.278 | 0.027 | 0.185 | 0.032 | 0.113 | 2.077 | 0.108 | 0.162 | 0.048 |
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 | 51 | 51 | 51 | 36 | 35 | 40 | 49 | 35 | 39 | 35 |
N.S. |
1 | 1.00 | 1.00 | 0.71 | 0.69 | 0.78 | 0.96 | 0.69 | 0.76 | 0.69 |
time (sec) |
N/A | 0.284 | 0.032 | 0.178 | 0.027 | 0.092 | 1.588 | 0.105 | 0.169 | 0.047 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 51 | 51 | 47 | 36 | 35 | 40 | 49 | 35 | 39 | 35 |
N.S. |
1 | 1.00 | 0.92 | 0.71 | 0.69 | 0.78 | 0.96 | 0.69 | 0.76 | 0.69 |
time (sec) |
N/A | 0.288 | 0.019 | 0.176 | 0.028 | 0.143 | 1.151 | 0.108 | 0.164 | 0.047 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 51 | 51 | 41 | 36 | 35 | 40 | 49 | 35 | 39 | 35 |
N.S. |
1 | 1.00 | 0.80 | 0.71 | 0.69 | 0.78 | 0.96 | 0.69 | 0.76 | 0.69 |
time (sec) |
N/A | 0.291 | 0.019 | 0.171 | 0.032 | 0.087 | 1.055 | 0.100 | 0.174 | 0.047 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 51 | 51 | 41 | 36 | 35 | 40 | 49 | 35 | 39 | 35 |
N.S. |
1 | 1.00 | 0.80 | 0.71 | 0.69 | 0.78 | 0.96 | 0.69 | 0.76 | 0.69 |
time (sec) |
N/A | 0.291 | 0.018 | 0.173 | 0.032 | 0.115 | 0.845 | 0.129 | 0.162 | 0.047 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 51 | 51 | 41 | 36 | 35 | 40 | 49 | 35 | 39 | 35 |
N.S. |
1 | 1.00 | 0.80 | 0.71 | 0.69 | 0.78 | 0.96 | 0.69 | 0.76 | 0.69 |
time (sec) |
N/A | 0.282 | 0.018 | 0.169 | 0.034 | 0.127 | 0.853 | 0.120 | 0.161 | 0.046 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 51 | 51 | 41 | 36 | 35 | 40 | 49 | 35 | 39 | 35 |
N.S. |
1 | 1.00 | 0.80 | 0.71 | 0.69 | 0.78 | 0.96 | 0.69 | 0.76 | 0.69 |
time (sec) |
N/A | 0.279 | 0.020 | 0.167 | 0.028 | 0.090 | 0.925 | 0.104 | 0.170 | 0.050 |
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 | 51 | 51 | 41 | 36 | 35 | 40 | 49 | 35 | 39 | 35 |
N.S. |
1 | 1.00 | 0.80 | 0.71 | 0.69 | 0.78 | 0.96 | 0.69 | 0.76 | 0.69 |
time (sec) |
N/A | 0.283 | 0.018 | 0.168 | 0.028 | 0.157 | 1.125 | 0.115 | 0.163 | 0.047 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 162 | 250 | 129 | 128 | 198 | 177 | 0 | 197 | 158 | 66 |
N.S. |
1 | 1.54 | 0.80 | 0.79 | 1.22 | 1.09 | 0.00 | 1.22 | 0.98 | 0.41 |
time (sec) |
N/A | 0.757 | 0.167 | 0.143 | 0.114 | 0.119 | 0.000 | 0.165 | 0.160 | 0.105 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 159 | 248 | 128 | 125 | 194 | 167 | 0 | 196 | 157 | 67 |
N.S. |
1 | 1.56 | 0.81 | 0.79 | 1.22 | 1.05 | 0.00 | 1.23 | 0.99 | 0.42 |
time (sec) |
N/A | 0.726 | 0.151 | 0.132 | 0.111 | 0.130 | 0.000 | 0.131 | 0.173 | 0.104 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 148 | 231 | 119 | 116 | 186 | 158 | 124 | 178 | 147 | 54 |
N.S. |
1 | 1.56 | 0.80 | 0.78 | 1.26 | 1.07 | 0.84 | 1.20 | 0.99 | 0.36 |
time (sec) |
N/A | 0.697 | 0.132 | 0.134 | 0.117 | 0.149 | 91.921 | 0.159 | 0.165 | 17.649 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 147 | 229 | 118 | 115 | 185 | 117 | 110 | 178 | 145 | 55 |
N.S. |
1 | 1.56 | 0.80 | 0.78 | 1.26 | 0.80 | 0.75 | 1.21 | 0.99 | 0.37 |
time (sec) |
N/A | 0.684 | 0.134 | 0.118 | 0.111 | 0.160 | 46.436 | 0.106 | 0.163 | 18.017 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 137 | 214 | 91 | 106 | 172 | 132 | 104 | 182 | 112 | 38 |
N.S. |
1 | 1.56 | 0.66 | 0.77 | 1.26 | 0.96 | 0.76 | 1.33 | 0.82 | 0.28 |
time (sec) |
N/A | 0.649 | 0.107 | 0.097 | 0.118 | 0.141 | 26.321 | 0.126 | 0.169 | 0.076 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 136 | 214 | 92 | 106 | 172 | 120 | 104 | 182 | 112 | 37 |
N.S. |
1 | 1.57 | 0.68 | 0.78 | 1.26 | 0.88 | 0.76 | 1.34 | 0.82 | 0.27 |
time (sec) |
N/A | 0.635 | 0.112 | 0.096 | 0.111 | 0.128 | 14.133 | 0.129 | 0.168 | 0.087 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 146 | 229 | 117 | 115 | 186 | 140 | 114 | 190 | 155 | 54 |
N.S. |
1 | 1.57 | 0.80 | 0.79 | 1.27 | 0.96 | 0.78 | 1.30 | 1.06 | 0.37 |
time (sec) |
N/A | 0.701 | 0.147 | 0.125 | 0.119 | 0.147 | 7.260 | 0.172 | 0.170 | 17.877 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 149 | 231 | 119 | 116 | 187 | 165 | 128 | 178 | 163 | 53 |
N.S. |
1 | 1.55 | 0.80 | 0.78 | 1.26 | 1.11 | 0.86 | 1.19 | 1.09 | 0.36 |
time (sec) |
N/A | 0.695 | 0.147 | 0.125 | 0.113 | 0.104 | 12.578 | 0.133 | 0.166 | 17.724 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 160 | 248 | 127 | 124 | 198 | 191 | 139 | 200 | 180 | 66 |
N.S. |
1 | 1.55 | 0.79 | 0.78 | 1.24 | 1.19 | 0.87 | 1.25 | 1.12 | 0.41 |
time (sec) |
N/A | 0.737 | 0.177 | 0.135 | 0.115 | 0.148 | 24.623 | 0.121 | 0.165 | 0.089 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 161 | 250 | 129 | 127 | 201 | 191 | 146 | 192 | 180 | 65 |
N.S. |
1 | 1.55 | 0.80 | 0.79 | 1.25 | 1.19 | 0.91 | 1.19 | 1.12 | 0.40 |
time (sec) |
N/A | 0.723 | 0.178 | 0.136 | 0.113 | 0.106 | 61.568 | 0.131 | 0.177 | 17.721 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 174 | 267 | 140 | 138 | 209 | 202 | 160 | 199 | 191 | 77 |
N.S. |
1 | 1.53 | 0.80 | 0.79 | 1.20 | 1.16 | 0.92 | 1.14 | 1.10 | 0.44 |
time (sec) |
N/A | 0.762 | 0.195 | 0.142 | 0.117 | 0.151 | 143.903 | 0.135 | 0.163 | 0.094 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 190 | 277 | 149 | 147 | 217 | 240 | 0 | 216 | 326 | 92 |
N.S. |
1 | 1.46 | 0.78 | 0.77 | 1.14 | 1.26 | 0.00 | 1.14 | 1.72 | 0.48 |
time (sec) |
N/A | 0.762 | 0.294 | 0.204 | 0.118 | 0.190 | 0.000 | 0.112 | 0.171 | 0.096 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 177 | 260 | 138 | 136 | 207 | 238 | 0 | 196 | 314 | 80 |
N.S. |
1 | 1.47 | 0.78 | 0.77 | 1.17 | 1.34 | 0.00 | 1.11 | 1.77 | 0.45 |
time (sec) |
N/A | 0.748 | 0.293 | 0.195 | 0.117 | 0.159 | 0.000 | 0.164 | 0.166 | 18.518 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 177 | 258 | 138 | 136 | 206 | 209 | 0 | 196 | 313 | 80 |
N.S. |
1 | 1.46 | 0.78 | 0.77 | 1.16 | 1.18 | 0.00 | 1.11 | 1.77 | 0.45 |
time (sec) |
N/A | 0.736 | 0.277 | 0.188 | 0.112 | 0.171 | 0.000 | 0.117 | 0.170 | 18.583 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 165 | 241 | 128 | 124 | 195 | 200 | 0 | 199 | 307 | 64 |
N.S. |
1 | 1.46 | 0.78 | 0.75 | 1.18 | 1.21 | 0.00 | 1.21 | 1.86 | 0.39 |
time (sec) |
N/A | 0.699 | 0.268 | 0.161 | 0.110 | 0.150 | 0.000 | 0.140 | 0.176 | 0.085 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 165 | 241 | 127 | 127 | 195 | 191 | 0 | 199 | 304 | 64 |
N.S. |
1 | 1.46 | 0.77 | 0.77 | 1.18 | 1.16 | 0.00 | 1.21 | 1.84 | 0.39 |
time (sec) |
N/A | 0.689 | 0.264 | 0.132 | 0.118 | 0.159 | 0.000 | 0.108 | 0.173 | 0.093 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 165 | 241 | 128 | 127 | 194 | 204 | 0 | 199 | 305 | 64 |
N.S. |
1 | 1.46 | 0.78 | 0.77 | 1.18 | 1.24 | 0.00 | 1.21 | 1.85 | 0.39 |
time (sec) |
N/A | 0.693 | 0.257 | 0.123 | 0.118 | 0.120 | 0.000 | 0.154 | 0.168 | 0.093 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 165 | 241 | 128 | 124 | 194 | 193 | 0 | 199 | 306 | 64 |
N.S. |
1 | 1.46 | 0.78 | 0.75 | 1.18 | 1.17 | 0.00 | 1.21 | 1.85 | 0.39 |
time (sec) |
N/A | 0.716 | 0.259 | 0.122 | 0.117 | 0.135 | 0.000 | 0.154 | 0.171 | 17.573 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 177 | 258 | 138 | 136 | 208 | 218 | 0 | 210 | 329 | 77 |
N.S. |
1 | 1.46 | 0.78 | 0.77 | 1.18 | 1.23 | 0.00 | 1.19 | 1.86 | 0.44 |
time (sec) |
N/A | 0.736 | 0.307 | 0.175 | 0.117 | 0.155 | 0.000 | 0.178 | 0.166 | 0.089 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 177 | 260 | 138 | 136 | 209 | 244 | 0 | 196 | 336 | 77 |
N.S. |
1 | 1.47 | 0.78 | 0.77 | 1.18 | 1.38 | 0.00 | 1.11 | 1.90 | 0.44 |
time (sec) |
N/A | 0.724 | 0.313 | 0.170 | 0.115 | 0.132 | 0.000 | 0.150 | 0.167 | 17.578 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 190 | 277 | 149 | 145 | 221 | 263 | 0 | 220 | 355 | 87 |
N.S. |
1 | 1.46 | 0.78 | 0.76 | 1.16 | 1.38 | 0.00 | 1.16 | 1.87 | 0.46 |
time (sec) |
N/A | 0.760 | 0.325 | 0.183 | 0.115 | 0.112 | 0.000 | 0.151 | 0.174 | 0.095 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 190 | 279 | 149 | 147 | 224 | 263 | 0 | 212 | 355 | 87 |
N.S. |
1 | 1.47 | 0.78 | 0.77 | 1.18 | 1.38 | 0.00 | 1.12 | 1.87 | 0.46 |
time (sec) |
N/A | 0.755 | 0.330 | 0.181 | 0.112 | 0.149 | 0.000 | 0.126 | 0.165 | 17.631 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 205 | 296 | 160 | 158 | 232 | 274 | 0 | 219 | 366 | 99 |
N.S. |
1 | 1.44 | 0.78 | 0.77 | 1.13 | 1.34 | 0.00 | 1.07 | 1.79 | 0.48 |
time (sec) |
N/A | 0.786 | 0.361 | 0.188 | 0.113 | 0.146 | 0.000 | 0.158 | 0.170 | 0.109 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 198 | 287 | 149 | 145 | 229 | 275 | 0 | 208 | 484 | 101 |
N.S. |
1 | 1.45 | 0.75 | 0.73 | 1.16 | 1.39 | 0.00 | 1.05 | 2.44 | 0.51 |
time (sec) |
N/A | 0.770 | 0.380 | 0.281 | 0.120 | 0.124 | 0.000 | 0.144 | 0.169 | 17.669 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 186 | 270 | 138 | 136 | 218 | 276 | 0 | 209 | 478 | 87 |
N.S. |
1 | 1.45 | 0.74 | 0.73 | 1.17 | 1.48 | 0.00 | 1.12 | 2.57 | 0.47 |
time (sec) |
N/A | 0.736 | 0.367 | 0.231 | 0.118 | 0.192 | 0.000 | 0.122 | 0.175 | 17.744 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 186 | 270 | 138 | 139 | 218 | 275 | 0 | 209 | 477 | 87 |
N.S. |
1 | 1.45 | 0.74 | 0.75 | 1.17 | 1.48 | 0.00 | 1.12 | 2.56 | 0.47 |
time (sec) |
N/A | 0.742 | 0.374 | 0.229 | 0.110 | 0.160 | 0.000 | 0.116 | 0.171 | 0.096 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 189 | 270 | 136 | 138 | 222 | 289 | 0 | 212 | 478 | 85 |
N.S. |
1 | 1.43 | 0.72 | 0.73 | 1.17 | 1.53 | 0.00 | 1.12 | 2.53 | 0.45 |
time (sec) |
N/A | 0.761 | 0.367 | 0.230 | 0.114 | 0.192 | 0.000 | 0.117 | 0.171 | 17.521 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 189 | 270 | 137 | 138 | 221 | 279 | 0 | 211 | 477 | 85 |
N.S. |
1 | 1.43 | 0.72 | 0.73 | 1.17 | 1.48 | 0.00 | 1.12 | 2.52 | 0.45 |
time (sec) |
N/A | 0.760 | 0.338 | 0.149 | 0.116 | 0.138 | 0.000 | 0.121 | 0.171 | 0.095 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 186 | 270 | 138 | 150 | 217 | 281 | 0 | 209 | 478 | 86 |
N.S. |
1 | 1.45 | 0.74 | 0.81 | 1.17 | 1.51 | 0.00 | 1.12 | 2.57 | 0.46 |
time (sec) |
N/A | 0.765 | 0.245 | 0.135 | 0.116 | 0.196 | 0.000 | 0.113 | 0.167 | 17.573 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 186 | 270 | 138 | 147 | 217 | 268 | 0 | 209 | 477 | 86 |
N.S. |
1 | 1.45 | 0.74 | 0.79 | 1.17 | 1.44 | 0.00 | 1.12 | 2.56 | 0.46 |
time (sec) |
N/A | 0.756 | 0.236 | 0.134 | 0.113 | 0.129 | 0.000 | 0.114 | 0.173 | 0.097 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 198 | 287 | 149 | 145 | 230 | 284 | 0 | 220 | 506 | 99 |
N.S. |
1 | 1.45 | 0.75 | 0.73 | 1.16 | 1.43 | 0.00 | 1.11 | 2.56 | 0.50 |
time (sec) |
N/A | 0.778 | 0.387 | 0.218 | 0.114 | 0.134 | 0.000 | 0.129 | 0.176 | 17.561 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 198 | 289 | 149 | 145 | 231 | 310 | 0 | 208 | 513 | 99 |
N.S. |
1 | 1.46 | 0.75 | 0.73 | 1.17 | 1.57 | 0.00 | 1.05 | 2.59 | 0.50 |
time (sec) |
N/A | 0.765 | 0.386 | 0.217 | 0.112 | 0.129 | 0.000 | 0.132 | 0.171 | 0.119 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 211 | 306 | 160 | 155 | 243 | 329 | 0 | 232 | 532 | 109 |
N.S. |
1 | 1.45 | 0.76 | 0.73 | 1.15 | 1.56 | 0.00 | 1.10 | 2.52 | 0.52 |
time (sec) |
N/A | 0.818 | 0.422 | 0.224 | 0.117 | 0.126 | 0.000 | 0.116 | 0.169 | 17.525 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 211 | 308 | 160 | 155 | 246 | 329 | 0 | 224 | 532 | 109 |
N.S. |
1 | 1.46 | 0.76 | 0.73 | 1.17 | 1.56 | 0.00 | 1.06 | 2.52 | 0.52 |
time (sec) |
N/A | 0.803 | 0.406 | 0.222 | 0.114 | 0.243 | 0.000 | 0.145 | 0.175 | 0.134 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 226 | 325 | 171 | 167 | 254 | 340 | 0 | 231 | 543 | 121 |
N.S. |
1 | 1.44 | 0.76 | 0.74 | 1.12 | 1.50 | 0.00 | 1.02 | 2.40 | 0.54 |
time (sec) |
N/A | 0.832 | 0.441 | 0.232 | 0.118 | 0.164 | 0.000 | 0.149 | 0.174 | 0.140 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 226 | 327 | 171 | 167 | 257 | 340 | 0 | 243 | 543 | 121 |
N.S. |
1 | 1.45 | 0.76 | 0.74 | 1.14 | 1.50 | 0.00 | 1.08 | 2.40 | 0.54 |
time (sec) |
N/A | 0.823 | 0.441 | 0.231 | 0.117 | 0.269 | 0.000 | 0.146 | 0.173 | 18.412 |
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 | 119 | 137 | 121 | 100 | 121 | 188 | 0 | 101 | 99 | 105 |
N.S. |
1 | 1.15 | 1.02 | 0.84 | 1.02 | 1.58 | 0.00 | 0.85 | 0.83 | 0.88 |
time (sec) |
N/A | 0.463 | 0.343 | 0.271 | 0.037 | 0.192 | 0.000 | 0.169 | 0.167 | 18.192 |
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 | 91 | 103 | 110 | 90 | 97 | 167 | 0 | 85 | 80 | 77 |
N.S. |
1 | 1.13 | 1.21 | 0.99 | 1.07 | 1.84 | 0.00 | 0.93 | 0.88 | 0.85 |
time (sec) |
N/A | 0.420 | 0.255 | 0.172 | 0.036 | 0.221 | 0.000 | 0.136 | 0.165 | 17.970 |
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 | 68 | 72 | 97 | 77 | 73 | 140 | 0 | 69 | 60 | 64 |
N.S. |
1 | 1.06 | 1.43 | 1.13 | 1.07 | 2.06 | 0.00 | 1.01 | 0.88 | 0.94 |
time (sec) |
N/A | 0.345 | 0.218 | 0.150 | 0.034 | 0.117 | 0.000 | 0.150 | 0.249 | 17.996 |
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 | 52 | 64 | 63 | 49 | 115 | 0 | 52 | 40 | 50 |
N.S. |
1 | 0.95 | 1.16 | 1.15 | 0.89 | 2.09 | 0.00 | 0.95 | 0.73 | 0.91 |
time (sec) |
N/A | 0.348 | 0.053 | 0.138 | 0.034 | 0.224 | 0.000 | 0.135 | 0.228 | 18.422 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 52 | 57 | 68 | 65 | 51 | 115 | 0 | 61 | 43 | 0 |
N.S. |
1 | 1.10 | 1.31 | 1.25 | 0.98 | 2.21 | 0.00 | 1.17 | 0.83 | 0.00 |
time (sec) |
N/A | 0.350 | 0.060 | 0.150 | 0.034 | 0.122 | 0.000 | 0.151 | 0.232 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 25 | 29 | 41 | 28 | 0 | 63 | 42 | 28 |
N.S. |
1 | 1.00 | 1.00 | 1.16 | 1.64 | 1.12 | 0.00 | 2.52 | 1.68 | 1.12 |
time (sec) |
N/A | 0.261 | 0.048 | 0.133 | 0.036 | 0.098 | 0.000 | 0.144 | 0.262 | 18.323 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 52 | 52 | 46 | 37 | 65 | 42 | 0 | 120 | 63 | 41 |
N.S. |
1 | 1.00 | 0.88 | 0.71 | 1.25 | 0.81 | 0.00 | 2.31 | 1.21 | 0.79 |
time (sec) |
N/A | 0.309 | 0.059 | 0.147 | 0.033 | 0.174 | 0.000 | 0.183 | 0.245 | 18.566 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 80 | 86 | 57 | 48 | 89 | 53 | 0 | 148 | 82 | 89 |
N.S. |
1 | 1.08 | 0.71 | 0.60 | 1.11 | 0.66 | 0.00 | 1.85 | 1.02 | 1.11 |
time (sec) |
N/A | 0.367 | 0.068 | 0.170 | 0.046 | 0.239 | 0.000 | 0.170 | 0.241 | 18.669 |
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 | 108 | 120 | 68 | 61 | 113 | 64 | 0 | 178 | 101 | 113 |
N.S. |
1 | 1.11 | 0.63 | 0.56 | 1.05 | 0.59 | 0.00 | 1.65 | 0.94 | 1.05 |
time (sec) |
N/A | 0.430 | 0.071 | 0.200 | 0.038 | 0.197 | 0.000 | 0.189 | 0.265 | 18.822 |
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 | 136 | 154 | 79 | 72 | 137 | 75 | 0 | 206 | 120 | 137 |
N.S. |
1 | 1.13 | 0.58 | 0.53 | 1.01 | 0.55 | 0.00 | 1.51 | 0.88 | 1.01 |
time (sec) |
N/A | 0.507 | 0.082 | 0.230 | 0.038 | 0.253 | 0.000 | 0.133 | 0.252 | 19.057 |
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 | 78 | 84 | 57 | 50 | 46 | 53 | 0 | 60 | 45 | 53 |
N.S. |
1 | 1.08 | 0.73 | 0.64 | 0.59 | 0.68 | 0.00 | 0.77 | 0.58 | 0.68 |
time (sec) |
N/A | 0.352 | 0.030 | 0.670 | 0.042 | 0.110 | 0.000 | 0.151 | 0.214 | 17.945 |
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 | 52 | 52 | 45 | 39 | 34 | 41 | 0 | 44 | 33 | 41 |
N.S. |
1 | 1.00 | 0.87 | 0.75 | 0.65 | 0.79 | 0.00 | 0.85 | 0.63 | 0.79 |
time (sec) |
N/A | 0.298 | 0.025 | 0.552 | 0.037 | 0.139 | 0.000 | 0.132 | 0.177 | 17.921 |
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 | 25 | 25 | 25 | 29 | 14 | 28 | 0 | 27 | 20 | 29 |
N.S. |
1 | 1.00 | 1.00 | 1.16 | 0.56 | 1.12 | 0.00 | 1.08 | 0.80 | 1.16 |
time (sec) |
N/A | 0.239 | 0.005 | 0.474 | 0.039 | 0.145 | 0.000 | 0.137 | 0.168 | 18.031 |
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 | 50 | 50 | 60 | 65 | 0 | 112 | 0 | 69 | 60 | 68 |
N.S. |
1 | 1.00 | 1.20 | 1.30 | 0.00 | 2.24 | 0.00 | 1.38 | 1.20 | 1.36 |
time (sec) |
N/A | 0.308 | 0.048 | 0.538 | 0.000 | 0.208 | 0.000 | 0.116 | 0.170 | 18.164 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 56 | 56 | 63 | 74 | 0 | 129 | 0 | 47 | 79 | 0 |
N.S. |
1 | 1.00 | 1.12 | 1.32 | 0.00 | 2.30 | 0.00 | 0.84 | 1.41 | 0.00 |
time (sec) |
N/A | 0.293 | 0.088 | 0.651 | 0.000 | 0.216 | 0.000 | 0.115 | 0.175 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 84 | 87 | 91 | 88 | 0 | 154 | 0 | 78 | 100 | 0 |
N.S. |
1 | 1.04 | 1.08 | 1.05 | 0.00 | 1.83 | 0.00 | 0.93 | 1.19 | 0.00 |
time (sec) |
N/A | 0.371 | 0.109 | 0.794 | 0.000 | 0.098 | 0.000 | 0.133 | 0.175 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 112 | 121 | 103 | 100 | 0 | 180 | 0 | 88 | 120 | 0 |
N.S. |
1 | 1.08 | 0.92 | 0.89 | 0.00 | 1.61 | 0.00 | 0.79 | 1.07 | 0.00 |
time (sec) |
N/A | 0.440 | 0.122 | 0.973 | 0.000 | 0.114 | 0.000 | 0.144 | 0.186 | 0.000 |
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 | 124 | 144 | 132 | 111 | 142 | 210 | 0 | 115 | 118 | 134 |
N.S. |
1 | 1.16 | 1.06 | 0.90 | 1.15 | 1.69 | 0.00 | 0.93 | 0.95 | 1.08 |
time (sec) |
N/A | 0.448 | 0.452 | 0.214 | 0.039 | 0.124 | 0.000 | 0.138 | 0.170 | 18.330 |
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 | 101 | 113 | 121 | 100 | 118 | 189 | 0 | 99 | 99 | 99 |
N.S. |
1 | 1.12 | 1.20 | 0.99 | 1.17 | 1.87 | 0.00 | 0.98 | 0.98 | 0.98 |
time (sec) |
N/A | 0.393 | 0.337 | 0.186 | 0.036 | 0.143 | 0.000 | 0.121 | 0.175 | 18.904 |
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 | 88 | 97 | 110 | 90 | 91 | 166 | 255 | 84 | 80 | 0 |
N.S. |
1 | 1.10 | 1.25 | 1.02 | 1.03 | 1.89 | 2.90 | 0.95 | 0.91 | 0.00 |
time (sec) |
N/A | 0.386 | 0.291 | 0.168 | 0.037 | 0.201 | 1.888 | 0.141 | 0.174 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 80 | 80 | 74 | 76 | 70 | 145 | 0 | 68 | 61 | 0 |
N.S. |
1 | 1.00 | 0.92 | 0.95 | 0.88 | 1.81 | 0.00 | 0.85 | 0.76 | 0.00 |
time (sec) |
N/A | 0.378 | 0.073 | 0.152 | 0.038 | 0.193 | 0.000 | 0.131 | 0.166 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 77 | 88 | 77 | 71 | 139 | 0 | 79 | 62 | 0 |
N.S. |
1 | 1.00 | 1.14 | 1.00 | 0.92 | 1.81 | 0.00 | 1.03 | 0.81 | 0.00 |
time (sec) |
N/A | 0.384 | 0.140 | 0.173 | 0.038 | 0.116 | 0.000 | 0.166 | 0.172 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 75 | 82 | 85 | 73 | 89 | 135 | 0 | 122 | 58 | 0 |
N.S. |
1 | 1.09 | 1.13 | 0.97 | 1.19 | 1.80 | 0.00 | 1.63 | 0.77 | 0.00 |
time (sec) |
N/A | 0.383 | 0.082 | 0.174 | 0.040 | 0.096 | 0.000 | 0.263 | 0.168 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 25 | 29 | 81 | 39 | 0 | 92 | 63 | 30 |
N.S. |
1 | 1.00 | 1.00 | 1.16 | 3.24 | 1.56 | 0.00 | 3.68 | 2.52 | 1.20 |
time (sec) |
N/A | 0.252 | 0.063 | 0.148 | 0.045 | 0.096 | 0.000 | 0.163 | 0.170 | 20.172 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 52 | 52 | 35 | 39 | 105 | 53 | 0 | 178 | 82 | 87 |
N.S. |
1 | 1.00 | 0.67 | 0.75 | 2.02 | 1.02 | 0.00 | 3.42 | 1.58 | 1.67 |
time (sec) |
N/A | 0.302 | 0.074 | 0.167 | 0.040 | 0.113 | 0.000 | 0.196 | 0.179 | 20.259 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 80 | 86 | 46 | 50 | 129 | 64 | 0 | 206 | 101 | 111 |
N.S. |
1 | 1.08 | 0.58 | 0.62 | 1.61 | 0.80 | 0.00 | 2.58 | 1.26 | 1.39 |
time (sec) |
N/A | 0.372 | 0.080 | 0.197 | 0.038 | 0.166 | 0.000 | 0.185 | 0.173 | 19.308 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 108 | 120 | 57 | 61 | 153 | 75 | 0 | 236 | 120 | 135 |
N.S. |
1 | 1.11 | 0.53 | 0.56 | 1.42 | 0.69 | 0.00 | 2.19 | 1.11 | 1.25 |
time (sec) |
N/A | 0.441 | 0.090 | 0.246 | 0.039 | 0.245 | 0.000 | 0.196 | 0.173 | 19.780 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 136 | 154 | 68 | 72 | 177 | 86 | 0 | 264 | 139 | 159 |
N.S. |
1 | 1.13 | 0.50 | 0.53 | 1.30 | 0.63 | 0.00 | 1.94 | 1.02 | 1.17 |
time (sec) |
N/A | 0.510 | 0.099 | 0.346 | 0.040 | 0.123 | 0.000 | 0.150 | 0.186 | 19.865 |
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 | 134 | 152 | 68 | 72 | 79 | 86 | 0 | 92 | 78 | 73 |
N.S. |
1 | 1.13 | 0.51 | 0.54 | 0.59 | 0.64 | 0.00 | 0.69 | 0.58 | 0.54 |
time (sec) |
N/A | 0.508 | 0.037 | 0.819 | 0.038 | 0.120 | 0.000 | 0.127 | 0.167 | 18.540 |
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 | 106 | 118 | 57 | 61 | 68 | 75 | 0 | 76 | 67 | 62 |
N.S. |
1 | 1.11 | 0.54 | 0.58 | 0.64 | 0.71 | 0.00 | 0.72 | 0.63 | 0.58 |
time (sec) |
N/A | 0.433 | 0.038 | 0.671 | 0.040 | 0.233 | 0.000 | 0.153 | 0.176 | 17.804 |
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 | 80 | 86 | 46 | 50 | 57 | 64 | 0 | 60 | 56 | 51 |
N.S. |
1 | 1.08 | 0.58 | 0.62 | 0.71 | 0.80 | 0.00 | 0.75 | 0.70 | 0.64 |
time (sec) |
N/A | 0.363 | 0.032 | 0.569 | 0.041 | 0.114 | 0.000 | 0.141 | 0.170 | 18.714 |
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 | 52 | 52 | 35 | 39 | 45 | 52 | 0 | 44 | 44 | 40 |
N.S. |
1 | 1.00 | 0.67 | 0.75 | 0.87 | 1.00 | 0.00 | 0.85 | 0.85 | 0.77 |
time (sec) |
N/A | 0.292 | 0.029 | 0.493 | 0.036 | 0.095 | 0.000 | 0.120 | 0.171 | 19.480 |
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 | 25 | 25 | 25 | 29 | 32 | 39 | 0 | 27 | 31 | 30 |
N.S. |
1 | 1.00 | 1.00 | 1.16 | 1.28 | 1.56 | 0.00 | 1.08 | 1.24 | 1.20 |
time (sec) |
N/A | 0.249 | 0.006 | 0.553 | 0.039 | 0.088 | 0.000 | 0.132 | 0.174 | 18.927 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 73 | 75 | 76 | 78 | 0 | 135 | 0 | 89 | 79 | 0 |
N.S. |
1 | 1.03 | 1.04 | 1.07 | 0.00 | 1.85 | 0.00 | 1.22 | 1.08 | 0.00 |
time (sec) |
N/A | 0.361 | 0.058 | 0.646 | 0.000 | 0.100 | 0.000 | 0.162 | 0.168 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 79 | 78 | 83 | 88 | 0 | 142 | 0 | 63 | 91 | 0 |
N.S. |
1 | 0.99 | 1.05 | 1.11 | 0.00 | 1.80 | 0.00 | 0.80 | 1.15 | 0.00 |
time (sec) |
N/A | 0.362 | 0.080 | 0.794 | 0.000 | 0.102 | 0.000 | 0.151 | 0.175 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 81 | 84 | 92 | 86 | 0 | 159 | 0 | 76 | 101 | 0 |
N.S. |
1 | 1.04 | 1.14 | 1.06 | 0.00 | 1.96 | 0.00 | 0.94 | 1.25 | 0.00 |
time (sec) |
N/A | 0.367 | 0.101 | 0.964 | 0.000 | 0.151 | 0.000 | 0.148 | 0.175 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 109 | 115 | 104 | 100 | 0 | 180 | 0 | 88 | 120 | 0 |
N.S. |
1 | 1.06 | 0.95 | 0.92 | 0.00 | 1.65 | 0.00 | 0.81 | 1.10 | 0.00 |
time (sec) |
N/A | 0.429 | 0.110 | 1.189 | 0.000 | 0.110 | 0.000 | 0.177 | 0.184 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 137 | 149 | 114 | 111 | 0 | 202 | 0 | 119 | 139 | 0 |
N.S. |
1 | 1.09 | 0.83 | 0.81 | 0.00 | 1.47 | 0.00 | 0.87 | 1.01 | 0.00 |
time (sec) |
N/A | 0.505 | 0.141 | 1.484 | 0.000 | 0.112 | 0.000 | 0.200 | 0.201 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 165 | 183 | 126 | 122 | 0 | 224 | 0 | 120 | 158 | 0 |
N.S. |
1 | 1.11 | 0.76 | 0.74 | 0.00 | 1.36 | 0.00 | 0.73 | 0.96 | 0.00 |
time (sec) |
N/A | 0.573 | 0.160 | 1.826 | 0.000 | 0.108 | 0.000 | 0.191 | 0.218 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 114 | 125 | 110 | 89 | 100 | 166 | 0 | 97 | 80 | 0 |
N.S. |
1 | 1.10 | 0.96 | 0.78 | 0.88 | 1.46 | 0.00 | 0.85 | 0.70 | 0.00 |
time (sec) |
N/A | 0.449 | 0.222 | 0.195 | 0.036 | 0.094 | 0.000 | 0.157 | 0.185 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 86 | 91 | 99 | 85 | 76 | 145 | 0 | 79 | 61 | 0 |
N.S. |
1 | 1.06 | 1.15 | 0.99 | 0.88 | 1.69 | 0.00 | 0.92 | 0.71 | 0.00 |
time (sec) |
N/A | 0.377 | 0.159 | 0.161 | 0.039 | 0.088 | 0.000 | 0.169 | 0.172 | 0.000 |
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 | 58 | 57 | 83 | 63 | 52 | 114 | 0 | 59 | 41 | 53 |
N.S. |
1 | 0.98 | 1.43 | 1.09 | 0.90 | 1.97 | 0.00 | 1.02 | 0.71 | 0.91 |
time (sec) |
N/A | 0.321 | 0.121 | 0.148 | 0.037 | 0.077 | 0.000 | 0.120 | 0.169 | 18.363 |
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 | 31 | 31 | 52 | 42 | 32 | 74 | 0 | 38 | 25 | 33 |
N.S. |
1 | 1.00 | 1.68 | 1.35 | 1.03 | 2.39 | 0.00 | 1.23 | 0.81 | 1.06 |
time (sec) |
N/A | 0.272 | 0.010 | 0.132 | 0.036 | 0.098 | 0.000 | 0.120 | 0.177 | 18.377 |
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 | 23 | 23 | 23 | 22 | 21 | 21 | 0 | 34 | 23 | 21 |
N.S. |
1 | 1.00 | 1.00 | 0.96 | 0.91 | 0.91 | 0.00 | 1.48 | 1.00 | 0.91 |
time (sec) |
N/A | 0.243 | 0.032 | 0.129 | 0.036 | 0.077 | 0.000 | 0.133 | 0.172 | 17.277 |
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 | 52 | 52 | 35 | 30 | 44 | 31 | 0 | 59 | 42 | 29 |
N.S. |
1 | 1.00 | 0.67 | 0.58 | 0.85 | 0.60 | 0.00 | 1.13 | 0.81 | 0.56 |
time (sec) |
N/A | 0.297 | 0.047 | 0.138 | 0.040 | 0.071 | 0.000 | 0.138 | 0.173 | 17.597 |
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 | 80 | 86 | 46 | 43 | 68 | 42 | 0 | 81 | 63 | 42 |
N.S. |
1 | 1.08 | 0.58 | 0.54 | 0.85 | 0.52 | 0.00 | 1.01 | 0.79 | 0.52 |
time (sec) |
N/A | 0.358 | 0.054 | 0.154 | 0.048 | 0.080 | 0.000 | 0.128 | 0.172 | 17.969 |
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 | 108 | 120 | 57 | 54 | 92 | 53 | 0 | 107 | 82 | 92 |
N.S. |
1 | 1.11 | 0.53 | 0.50 | 0.85 | 0.49 | 0.00 | 0.99 | 0.76 | 0.85 |
time (sec) |
N/A | 0.432 | 0.060 | 0.181 | 0.041 | 0.078 | 0.000 | 0.161 | 0.177 | 18.059 |
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 | 106 | 118 | 57 | 54 | 57 | 53 | 0 | 79 | 45 | 53 |
N.S. |
1 | 1.11 | 0.54 | 0.51 | 0.54 | 0.50 | 0.00 | 0.75 | 0.42 | 0.50 |
time (sec) |
N/A | 0.428 | 0.031 | 0.955 | 0.038 | 0.074 | 0.000 | 0.128 | 0.180 | 17.686 |