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 | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 115 | 104 | 141 | 121 | 95 | 159 | 0 | 90 | 138 | 235 |
N.S. |
1 | 0.90 | 1.23 | 1.05 | 0.83 | 1.38 | 0.00 | 0.78 | 1.20 | 2.04 |
time (sec) |
N/A | 0.269 | 0.080 | 1.207 | 0.031 | 0.138 | 0.000 | 0.195 | 0.179 | 17.275 |
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 | 71 | 66 | 82 | 81 | 51 | 87 | 0 | 59 | 93 | 154 |
N.S. |
1 | 0.93 | 1.15 | 1.14 | 0.72 | 1.23 | 0.00 | 0.83 | 1.31 | 2.17 |
time (sec) |
N/A | 0.241 | 0.156 | 0.621 | 0.031 | 0.092 | 0.000 | 0.166 | 0.191 | 17.046 |
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 | 30 | 29 | 38 | 23 | 25 | 27 | 0 | 28 | 54 | 43 |
N.S. |
1 | 0.97 | 1.27 | 0.77 | 0.83 | 0.90 | 0.00 | 0.93 | 1.80 | 1.43 |
time (sec) |
N/A | 0.212 | 0.021 | 0.299 | 0.027 | 0.149 | 0.000 | 0.134 | 0.184 | 17.265 |
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 | 24 | 24 | 35 | 23 | 22 | 24 | 0 | 23 | 38 | 38 |
N.S. |
1 | 1.00 | 1.46 | 0.96 | 0.92 | 1.00 | 0.00 | 0.96 | 1.58 | 1.58 |
time (sec) |
N/A | 0.207 | 0.021 | 0.200 | 0.034 | 0.093 | 0.000 | 0.119 | 0.158 | 17.348 |
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 | 54 | 48 | 54 | 67 | 45 | 69 | 0 | 46 | 88 | 146 |
N.S. |
1 | 0.89 | 1.00 | 1.24 | 0.83 | 1.28 | 0.00 | 0.85 | 1.63 | 2.70 |
time (sec) |
N/A | 0.235 | 0.038 | 0.565 | 0.030 | 0.092 | 0.000 | 0.129 | 0.190 | 17.329 |
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 | 81 | 69 | 81 | 101 | 69 | 110 | 0 | 70 | 108 | 207 |
N.S. |
1 | 0.85 | 1.00 | 1.25 | 0.85 | 1.36 | 0.00 | 0.86 | 1.33 | 2.56 |
time (sec) |
N/A | 0.244 | 0.052 | 0.997 | 0.034 | 0.099 | 0.000 | 0.138 | 0.179 | 17.410 |
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 | 115 | 97 | 115 | 143 | 91 | 158 | 0 | 92 | 128 | 267 |
N.S. |
1 | 0.84 | 1.00 | 1.24 | 0.79 | 1.37 | 0.00 | 0.80 | 1.11 | 2.32 |
time (sec) |
N/A | 0.269 | 0.087 | 1.929 | 0.027 | 0.095 | 0.000 | 0.147 | 0.182 | 17.915 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 101 | 101 | 110 | 135 | 87 | 116 | 0 | 0 | 381 | 351 |
N.S. |
1 | 1.00 | 1.09 | 1.34 | 0.86 | 1.15 | 0.00 | 0.00 | 3.77 | 3.48 |
time (sec) |
N/A | 0.329 | 0.327 | 1.822 | 0.112 | 0.123 | 0.000 | 0.000 | 0.185 | 20.442 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 72 | 72 | 81 | 98 | 65 | 88 | 0 | 0 | 263 | 231 |
N.S. |
1 | 1.00 | 1.12 | 1.36 | 0.90 | 1.22 | 0.00 | 0.00 | 3.65 | 3.21 |
time (sec) |
N/A | 0.285 | 0.210 | 0.964 | 0.104 | 0.090 | 0.000 | 0.000 | 0.154 | 19.044 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 39 | 48 | 47 | 56 | 39 | 80 | 0 | 1008 | 78 | 111 |
N.S. |
1 | 1.23 | 1.21 | 1.44 | 1.00 | 2.05 | 0.00 | 25.85 | 2.00 | 2.85 |
time (sec) |
N/A | 0.422 | 0.169 | 0.596 | 0.105 | 0.081 | 0.000 | 0.747 | 0.162 | 17.370 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 41 | 41 | 75 | 49 | 54 | 84 | 0 | 108 | 70 | 108 |
N.S. |
1 | 1.00 | 1.83 | 1.20 | 1.32 | 2.05 | 0.00 | 2.63 | 1.71 | 2.63 |
time (sec) |
N/A | 0.246 | 0.124 | 0.290 | 0.107 | 0.095 | 0.000 | 0.131 | 0.157 | 17.212 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 78 | 82 | 125 | 86 | 92 | 160 | 0 | 141 | 96 | 228 |
N.S. |
1 | 1.05 | 1.60 | 1.10 | 1.18 | 2.05 | 0.00 | 1.81 | 1.23 | 2.92 |
time (sec) |
N/A | 0.296 | 0.237 | 0.569 | 0.113 | 0.167 | 0.000 | 0.154 | 0.183 | 17.181 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 117 | 122 | 164 | 129 | 125 | 222 | 0 | 199 | 138 | 291 |
N.S. |
1 | 1.04 | 1.40 | 1.10 | 1.07 | 1.90 | 0.00 | 1.70 | 1.18 | 2.49 |
time (sec) |
N/A | 0.328 | 0.266 | 1.199 | 0.113 | 0.096 | 0.000 | 0.170 | 0.195 | 17.153 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 119 | 108 | 75 | 195 | 96 | 168 | 0 | 85 | 413 | 283 |
N.S. |
1 | 0.91 | 0.63 | 1.64 | 0.81 | 1.41 | 0.00 | 0.71 | 3.47 | 2.38 |
time (sec) |
N/A | 0.281 | 0.299 | 3.557 | 0.033 | 0.106 | 0.000 | 0.229 | 0.194 | 17.349 |
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 | 72 | 65 | 54 | 50 | 58 | 90 | 0 | 60 | 228 | 204 |
N.S. |
1 | 0.90 | 0.75 | 0.69 | 0.81 | 1.25 | 0.00 | 0.83 | 3.17 | 2.83 |
time (sec) |
N/A | 0.252 | 0.120 | 1.664 | 0.033 | 0.093 | 0.000 | 0.185 | 0.183 | 17.607 |
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 | 48 | 40 | 70 | 43 | 45 | 0 | 50 | 82 | 178 |
N.S. |
1 | 0.92 | 0.77 | 1.35 | 0.83 | 0.87 | 0.00 | 0.96 | 1.58 | 3.42 |
time (sec) |
N/A | 0.231 | 0.043 | 0.870 | 0.034 | 0.133 | 0.000 | 0.127 | 0.170 | 17.187 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 30 | 28 | 94 | 53 | 76 | 0 | 53 | 54 | 56 |
N.S. |
1 | 1.00 | 0.93 | 3.13 | 1.77 | 2.53 | 0.00 | 1.77 | 1.80 | 1.87 |
time (sec) |
N/A | 0.214 | 0.052 | 0.936 | 0.030 | 0.139 | 0.000 | 0.131 | 0.155 | 17.240 |
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 | 132 | 114 | 86 | 228 | 107 | 206 | 0 | 108 | 130 | 392 |
N.S. |
1 | 0.86 | 0.65 | 1.73 | 0.81 | 1.56 | 0.00 | 0.82 | 0.98 | 2.97 |
time (sec) |
N/A | 0.276 | 0.246 | 3.930 | 0.030 | 0.118 | 0.000 | 0.153 | 0.172 | 20.306 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 141 | 149 | 174 | 188 | 152 | 152 | 0 | 0 | 423 | 392 |
N.S. |
1 | 1.06 | 1.23 | 1.33 | 1.08 | 1.08 | 0.00 | 0.00 | 3.00 | 2.78 |
time (sec) |
N/A | 0.404 | 1.910 | 5.245 | 0.111 | 0.086 | 0.000 | 0.000 | 0.165 | 20.306 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 120 | 128 | 159 | 132 | 120 | 196 | 0 | 0 | 232 | 287 |
N.S. |
1 | 1.07 | 1.32 | 1.10 | 1.00 | 1.63 | 0.00 | 0.00 | 1.93 | 2.39 |
time (sec) |
N/A | 0.625 | 2.208 | 2.728 | 0.110 | 0.117 | 0.000 | 0.000 | 0.158 | 19.657 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 71 | 63 | 120 | 79 | 84 | 125 | 0 | 5370 | 87 | 213 |
N.S. |
1 | 0.89 | 1.69 | 1.11 | 1.18 | 1.76 | 0.00 | 75.63 | 1.23 | 3.00 |
time (sec) |
N/A | 0.288 | 0.814 | 1.493 | 0.118 | 0.088 | 0.000 | 6.659 | 0.153 | 18.629 |
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 | 45 | 45 | 34 | 32 | 47 | 41 | 78 | 38 | 36 | 123 |
N.S. |
1 | 1.00 | 0.76 | 0.71 | 1.04 | 0.91 | 1.73 | 0.84 | 0.80 | 2.73 |
time (sec) |
N/A | 0.199 | 0.089 | 0.599 | 0.034 | 0.079 | 0.089 | 0.112 | 0.175 | 17.861 |
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 | 74 | 78 | 94 | 80 | 79 | 105 | 0 | 143 | 90 | 201 |
N.S. |
1 | 1.05 | 1.27 | 1.08 | 1.07 | 1.42 | 0.00 | 1.93 | 1.22 | 2.72 |
time (sec) |
N/A | 0.305 | 6.100 | 0.538 | 0.114 | 0.128 | 0.000 | 0.144 | 0.233 | 17.801 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 98 | 102 | 191 | 146 | 139 | 192 | 0 | 209 | 129 | 293 |
N.S. |
1 | 1.04 | 1.95 | 1.49 | 1.42 | 1.96 | 0.00 | 2.13 | 1.32 | 2.99 |
time (sec) |
N/A | 0.370 | 11.010 | 1.329 | 0.118 | 0.106 | 0.000 | 0.175 | 0.191 | 17.723 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 160 | 143 | 99 | 260 | 133 | 240 | 0 | 114 | 645 | 398 |
N.S. |
1 | 0.89 | 0.62 | 1.62 | 0.83 | 1.50 | 0.00 | 0.71 | 4.03 | 2.49 |
time (sec) |
N/A | 0.316 | 0.483 | 18.802 | 0.035 | 0.103 | 0.000 | 0.350 | 0.193 | 17.778 |
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 | 81 | 66 | 60 | 72 | 104 | 0 | 89 | 243 | 262 |
N.S. |
1 | 0.89 | 0.73 | 0.66 | 0.79 | 1.14 | 0.00 | 0.98 | 2.67 | 2.88 |
time (sec) |
N/A | 0.267 | 0.189 | 5.906 | 0.032 | 0.121 | 0.000 | 0.233 | 0.185 | 18.150 |
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 | 70 | 63 | 52 | 108 | 57 | 61 | 0 | 71 | 94 | 281 |
N.S. |
1 | 0.90 | 0.74 | 1.54 | 0.81 | 0.87 | 0.00 | 1.01 | 1.34 | 4.01 |
time (sec) |
N/A | 0.241 | 0.053 | 3.314 | 0.028 | 0.094 | 0.000 | 0.147 | 0.193 | 18.018 |
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 | 98 | 86 | 66 | 116 | 80 | 118 | 0 | 81 | 110 | 253 |
N.S. |
1 | 0.88 | 0.67 | 1.18 | 0.82 | 1.20 | 0.00 | 0.83 | 1.12 | 2.58 |
time (sec) |
N/A | 0.260 | 0.148 | 1.899 | 0.032 | 0.098 | 0.000 | 0.139 | 0.169 | 17.692 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 180 | 188 | 243 | 195 | 209 | 289 | 0 | 0 | 433 | 438 |
N.S. |
1 | 1.04 | 1.35 | 1.08 | 1.16 | 1.61 | 0.00 | 0.00 | 2.41 | 2.43 |
time (sec) |
N/A | 1.079 | 11.024 | 14.475 | 0.117 | 0.136 | 0.000 | 0.000 | 0.157 | 20.645 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | B | F | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 119 | 123 | 177 | 149 | 165 | 220 | 0 | 0 | 242 | 371 |
N.S. |
1 | 1.03 | 1.49 | 1.25 | 1.39 | 1.85 | 0.00 | 0.00 | 2.03 | 3.12 |
time (sec) |
N/A | 0.401 | 7.802 | 8.326 | 0.116 | 0.116 | 0.000 | 0.000 | 0.185 | 20.176 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 89 | 83 | 115 | 98 | 117 | 154 | 0 | 0 | 97 | 288 |
N.S. |
1 | 0.93 | 1.29 | 1.10 | 1.31 | 1.73 | 0.00 | 0.00 | 1.09 | 3.24 |
time (sec) |
N/A | 0.318 | 6.051 | 4.850 | 0.120 | 0.097 | 0.000 | 0.000 | 0.169 | 19.910 |
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 | 63 | 63 | 44 | 43 | 72 | 54 | 121 | 55 | 52 | 156 |
N.S. |
1 | 1.00 | 0.70 | 0.68 | 1.14 | 0.86 | 1.92 | 0.87 | 0.83 | 2.48 |
time (sec) |
N/A | 0.256 | 0.211 | 9.454 | 0.042 | 0.093 | 0.123 | 0.121 | 0.153 | 18.970 |
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 | 92 | 96 | 106 | 94 | 93 | 121 | 0 | 162 | 107 | 264 |
N.S. |
1 | 1.04 | 1.15 | 1.02 | 1.01 | 1.32 | 0.00 | 1.76 | 1.16 | 2.87 |
time (sec) |
N/A | 0.337 | 6.734 | 1.632 | 0.113 | 0.147 | 0.000 | 0.161 | 0.171 | 17.447 |
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 | 129 | 113 | 83 | 83 | 109 | 154 | 0 | 118 | 436 | 379 |
N.S. |
1 | 0.88 | 0.64 | 0.64 | 0.84 | 1.19 | 0.00 | 0.91 | 3.38 | 2.94 |
time (sec) |
N/A | 0.298 | 0.444 | 35.269 | 0.035 | 0.134 | 0.000 | 0.369 | 0.174 | 18.637 |
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 | 107 | 94 | 76 | 70 | 85 | 116 | 0 | 105 | 253 | 320 |
N.S. |
1 | 0.88 | 0.71 | 0.65 | 0.79 | 1.08 | 0.00 | 0.98 | 2.36 | 2.99 |
time (sec) |
N/A | 0.275 | 0.181 | 22.782 | 0.044 | 0.091 | 0.000 | 0.283 | 0.160 | 18.249 |
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 | 88 | 78 | 62 | 59 | 70 | 74 | 0 | 87 | 104 | 131 |
N.S. |
1 | 0.89 | 0.70 | 0.67 | 0.80 | 0.84 | 0.00 | 0.99 | 1.18 | 1.49 |
time (sec) |
N/A | 0.250 | 0.084 | 16.150 | 0.033 | 0.092 | 0.000 | 0.149 | 0.162 | 17.566 |
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 | 102 | 90 | 68 | 129 | 82 | 131 | 0 | 83 | 110 | 298 |
N.S. |
1 | 0.88 | 0.67 | 1.26 | 0.80 | 1.28 | 0.00 | 0.81 | 1.08 | 2.92 |
time (sec) |
N/A | 0.265 | 0.177 | 5.481 | 0.033 | 0.122 | 0.000 | 0.135 | 0.155 | 17.700 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 143 | 126 | 252 | 166 | 238 | 247 | 0 | 0 | 252 | 437 |
N.S. |
1 | 0.88 | 1.76 | 1.16 | 1.66 | 1.73 | 0.00 | 0.00 | 1.76 | 3.06 |
time (sec) |
N/A | 0.412 | 7.713 | 28.142 | 0.109 | 0.128 | 0.000 | 0.000 | 0.175 | 20.681 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 113 | 117 | 125 | 115 | 181 | 179 | 0 | 0 | 107 | 363 |
N.S. |
1 | 1.04 | 1.11 | 1.02 | 1.60 | 1.58 | 0.00 | 0.00 | 0.95 | 3.21 |
time (sec) |
N/A | 0.376 | 6.955 | 19.928 | 0.118 | 0.107 | 0.000 | 0.000 | 0.222 | 20.328 |
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 | 87 | 87 | 57 | 56 | 108 | 70 | 224 | 72 | 68 | 237 |
N.S. |
1 | 1.00 | 0.66 | 0.64 | 1.24 | 0.80 | 2.57 | 0.83 | 0.78 | 2.72 |
time (sec) |
N/A | 0.288 | 4.609 | 11.990 | 0.035 | 0.085 | 0.180 | 0.110 | 0.201 | 18.903 |
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 | 116 | 120 | 136 | 136 | 117 | 135 | 0 | 194 | 123 | 295 |
N.S. |
1 | 1.03 | 1.17 | 1.17 | 1.01 | 1.16 | 0.00 | 1.67 | 1.06 | 2.54 |
time (sec) |
N/A | 0.370 | 12.381 | 5.099 | 0.127 | 0.132 | 0.000 | 0.167 | 0.196 | 17.901 |
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 | 140 | 144 | 209 | 222 | 218 | 219 | 0 | 274 | 161 | 384 |
N.S. |
1 | 1.03 | 1.49 | 1.59 | 1.56 | 1.56 | 0.00 | 1.96 | 1.15 | 2.74 |
time (sec) |
N/A | 0.448 | 11.511 | 5.682 | 0.118 | 0.108 | 0.000 | 0.222 | 0.186 | 17.893 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 198 | 202 | 283 | 304 | 313 | 291 | 0 | 339 | 193 | 454 |
N.S. |
1 | 1.02 | 1.43 | 1.54 | 1.58 | 1.47 | 0.00 | 1.71 | 0.97 | 2.29 |
time (sec) |
N/A | 0.638 | 7.920 | 11.255 | 0.122 | 0.135 | 0.000 | 0.280 | 0.190 | 17.928 |
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 | 130 | 136 | 101 | 115 | 175 | 167 | 0 | 125 | 470 | 388 |
N.S. |
1 | 1.05 | 0.78 | 0.88 | 1.35 | 1.28 | 0.00 | 0.96 | 3.62 | 2.98 |
time (sec) |
N/A | 0.779 | 1.119 | 1.366 | 0.037 | 0.101 | 0.000 | 0.169 | 0.190 | 20.807 |
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 | 110 | 84 | 91 | 130 | 147 | 0 | 105 | 340 | 281 |
N.S. |
1 | 1.04 | 0.79 | 0.86 | 1.23 | 1.39 | 0.00 | 0.99 | 3.21 | 2.65 |
time (sec) |
N/A | 0.616 | 0.371 | 0.731 | 0.032 | 0.123 | 0.000 | 0.152 | 0.205 | 20.217 |
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 | 82 | 84 | 54 | 67 | 89 | 125 | 0 | 83 | 214 | 172 |
N.S. |
1 | 1.02 | 0.66 | 0.82 | 1.09 | 1.52 | 0.00 | 1.01 | 2.61 | 2.10 |
time (sec) |
N/A | 0.511 | 0.186 | 0.424 | 0.030 | 0.123 | 0.000 | 0.151 | 0.195 | 18.852 |
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 | 37 | 58 | 28 | 43 | 47 | 58 | 0 | 55 | 85 | 61 |
N.S. |
1 | 1.57 | 0.76 | 1.16 | 1.27 | 1.57 | 0.00 | 1.49 | 2.30 | 1.65 |
time (sec) |
N/A | 0.395 | 0.041 | 0.307 | 0.032 | 0.086 | 0.000 | 0.123 | 0.172 | 17.311 |
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 | 32 | 34 | 32 | 27 | 31 | 28 | 0 | 34 | 32 | 32 |
N.S. |
1 | 1.06 | 1.00 | 0.84 | 0.97 | 0.88 | 0.00 | 1.06 | 1.00 | 1.00 |
time (sec) |
N/A | 0.215 | 0.022 | 0.288 | 0.033 | 0.114 | 0.000 | 0.122 | 0.178 | 17.714 |
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 | 32 | 32 | 24 | 27 | 26 | 30 | 0 | 26 | 34 | 23 |
N.S. |
1 | 1.00 | 0.75 | 0.84 | 0.81 | 0.94 | 0.00 | 0.81 | 1.06 | 0.72 |
time (sec) |
N/A | 0.311 | 0.037 | 0.536 | 0.050 | 0.073 | 0.000 | 0.123 | 0.175 | 17.673 |
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 | 51 | 47 | 30 | 49 | 46 | 63 | 0 | 46 | 56 | 45 |
N.S. |
1 | 0.92 | 0.59 | 0.96 | 0.90 | 1.24 | 0.00 | 0.90 | 1.10 | 0.88 |
time (sec) |
N/A | 0.400 | 0.058 | 1.086 | 0.027 | 0.080 | 0.000 | 0.136 | 0.162 | 17.744 |
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 | 57 | 61 | 67 | 66 | 96 | 0 | 66 | 76 | 63 |
N.S. |
1 | 0.84 | 0.90 | 0.99 | 0.97 | 1.41 | 0.00 | 0.97 | 1.12 | 0.93 |
time (sec) |
N/A | 0.411 | 0.158 | 2.249 | 0.036 | 0.137 | 0.000 | 0.136 | 0.156 | 17.881 |
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 | 84 | 67 | 77 | 87 | 86 | 127 | 0 | 86 | 96 | 83 |
N.S. |
1 | 0.80 | 0.92 | 1.04 | 1.02 | 1.51 | 0.00 | 1.02 | 1.14 | 0.99 |
time (sec) |
N/A | 0.420 | 0.219 | 4.900 | 0.026 | 0.115 | 0.000 | 0.136 | 0.160 | 17.893 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | B | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 84 | 68 | 146 | 166 | 338 | 95 | 0 | 172 | 598 | 99 |
N.S. |
1 | 0.81 | 1.74 | 1.98 | 4.02 | 1.13 | 0.00 | 2.05 | 7.12 | 1.18 |
time (sec) |
N/A | 0.378 | 1.152 | 0.993 | 0.045 | 0.088 | 0.000 | 0.230 | 0.165 | 18.898 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | B | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 69 | 58 | 106 | 120 | 214 | 75 | 0 | 120 | 302 | 73 |
N.S. |
1 | 0.84 | 1.54 | 1.74 | 3.10 | 1.09 | 0.00 | 1.74 | 4.38 | 1.06 |
time (sec) |
N/A | 0.373 | 0.926 | 0.530 | 0.039 | 0.083 | 0.000 | 0.207 | 0.173 | 17.809 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 50 | 48 | 106 | 70 | 90 | 47 | 0 | 68 | 102 | 47 |
N.S. |
1 | 0.96 | 2.12 | 1.40 | 1.80 | 0.94 | 0.00 | 1.36 | 2.04 | 0.94 |
time (sec) |
N/A | 0.363 | 0.719 | 0.326 | 0.043 | 0.128 | 0.000 | 0.191 | 0.160 | 17.395 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 48 | 22 | 27 | 42 | 27 | 21 | 30 | 21 |
N.S. |
1 | 1.00 | 2.09 | 0.96 | 1.17 | 1.83 | 1.17 | 0.91 | 1.30 | 0.91 |
time (sec) |
N/A | 0.184 | 0.032 | 0.136 | 0.028 | 0.101 | 0.382 | 0.122 | 0.174 | 17.571 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | B | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 69 | 44 | 70 | 62 | 0 | 65 | 42 | 25 |
N.S. |
1 | 1.00 | 2.38 | 1.52 | 2.41 | 2.14 | 0.00 | 2.24 | 1.45 | 0.86 |
time (sec) |
N/A | 0.307 | 0.811 | 0.401 | 0.035 | 0.087 | 0.000 | 0.143 | 0.208 | 17.335 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | B | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 58 | 124 | 94 | 155 | 111 | 0 | 127 | 75 | 115 |
N.S. |
1 | 1.00 | 2.14 | 1.62 | 2.67 | 1.91 | 0.00 | 2.19 | 1.29 | 1.98 |
time (sec) |
N/A | 0.427 | 1.214 | 0.770 | 0.036 | 0.095 | 0.000 | 0.151 | 0.165 | 17.495 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | C | B | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 82 | 84 | 189 | 134 | 234 | 155 | 0 | 187 | 107 | 183 |
N.S. |
1 | 1.02 | 2.30 | 1.63 | 2.85 | 1.89 | 0.00 | 2.28 | 1.30 | 2.23 |
time (sec) |
N/A | 0.532 | 1.591 | 1.522 | 0.037 | 0.121 | 0.000 | 0.166 | 0.170 | 17.905 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | C | B | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 106 | 110 | 284 | 168 | 315 | 198 | 0 | 244 | 139 | 387 |
N.S. |
1 | 1.04 | 2.68 | 1.58 | 2.97 | 1.87 | 0.00 | 2.30 | 1.31 | 3.65 |
time (sec) |
N/A | 0.649 | 2.669 | 3.209 | 0.046 | 0.125 | 0.000 | 0.180 | 0.172 | 18.688 |
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 | 189 | 164 | 112 | 127 | 202 | 218 | 0 | 135 | 482 | 444 |
N.S. |
1 | 0.87 | 0.59 | 0.67 | 1.07 | 1.15 | 0.00 | 0.71 | 2.55 | 2.35 |
time (sec) |
N/A | 0.351 | 2.033 | 3.822 | 0.037 | 0.110 | 0.000 | 0.172 | 0.200 | 20.590 |
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 | 146 | 127 | 91 | 103 | 167 | 198 | 0 | 115 | 408 | 361 |
N.S. |
1 | 0.87 | 0.62 | 0.71 | 1.14 | 1.36 | 0.00 | 0.79 | 2.79 | 2.47 |
time (sec) |
N/A | 0.315 | 0.505 | 1.793 | 0.035 | 0.101 | 0.000 | 0.155 | 0.174 | 20.472 |
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 | 104 | 91 | 70 | 79 | 110 | 178 | 0 | 95 | 226 | 240 |
N.S. |
1 | 0.88 | 0.67 | 0.76 | 1.06 | 1.71 | 0.00 | 0.91 | 2.17 | 2.31 |
time (sec) |
N/A | 0.280 | 0.332 | 0.875 | 0.027 | 0.145 | 0.000 | 0.142 | 0.178 | 19.981 |
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 | 60 | 54 | 36 | 55 | 70 | 104 | 0 | 95 | 150 | 116 |
N.S. |
1 | 0.90 | 0.60 | 0.92 | 1.17 | 1.73 | 0.00 | 1.58 | 2.50 | 1.93 |
time (sec) |
N/A | 0.247 | 0.098 | 0.673 | 0.035 | 0.086 | 0.000 | 0.131 | 0.185 | 18.275 |
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 | 50 | 36 | 37 | 46 | 59 | 0 | 51 | 80 | 87 |
N.S. |
1 | 0.96 | 0.69 | 0.71 | 0.88 | 1.13 | 0.00 | 0.98 | 1.54 | 1.67 |
time (sec) |
N/A | 0.246 | 0.064 | 0.704 | 0.032 | 0.091 | 0.000 | 0.125 | 0.167 | 17.646 |
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 | 65 | 61 | 49 | 49 | 55 | 76 | 0 | 61 | 76 | 103 |
N.S. |
1 | 0.94 | 0.75 | 0.75 | 0.85 | 1.17 | 0.00 | 0.94 | 1.17 | 1.58 |
time (sec) |
N/A | 0.255 | 0.080 | 2.028 | 0.035 | 0.155 | 0.000 | 0.126 | 0.183 | 17.688 |
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 | 50 | 38 | 39 | 36 | 57 | 0 | 36 | 46 | 36 |
N.S. |
1 | 0.91 | 0.69 | 0.71 | 0.65 | 1.04 | 0.00 | 0.65 | 0.84 | 0.65 |
time (sec) |
N/A | 0.240 | 0.089 | 4.292 | 0.028 | 0.110 | 0.000 | 0.133 | 0.193 | 17.870 |
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 | 73 | 65 | 48 | 49 | 46 | 94 | 0 | 46 | 56 | 46 |
N.S. |
1 | 0.89 | 0.66 | 0.67 | 0.63 | 1.29 | 0.00 | 0.63 | 0.77 | 0.63 |
time (sec) |
N/A | 0.252 | 0.116 | 8.789 | 0.031 | 0.079 | 0.000 | 0.145 | 0.203 | 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 | 127 | 110 | 78 | 79 | 76 | 127 | 0 | 76 | 86 | 76 |
N.S. |
1 | 0.87 | 0.61 | 0.62 | 0.60 | 1.00 | 0.00 | 0.60 | 0.68 | 0.60 |
time (sec) |
N/A | 0.279 | 0.162 | 16.946 | 0.042 | 0.086 | 0.000 | 0.151 | 0.186 | 17.848 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 145 | 125 | 88 | 89 | 86 | 162 | 0 | 86 | 96 | 85 |
N.S. |
1 | 0.86 | 0.61 | 0.61 | 0.59 | 1.12 | 0.00 | 0.59 | 0.66 | 0.59 |
time (sec) |
N/A | 0.287 | 0.232 | 31.311 | 0.026 | 0.137 | 0.000 | 0.152 | 0.197 | 17.927 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 199 | 170 | 118 | 119 | 116 | 195 | 0 | 116 | 126 | 116 |
N.S. |
1 | 0.85 | 0.59 | 0.60 | 0.58 | 0.98 | 0.00 | 0.58 | 0.63 | 0.58 |
time (sec) |
N/A | 0.313 | 0.364 | 54.459 | 0.043 | 0.174 | 0.000 | 0.150 | 0.181 | 17.871 |
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 | 171 | 149 | 102 | 115 | 188 | 248 | 0 | 125 | 468 | 418 |
N.S. |
1 | 0.87 | 0.60 | 0.67 | 1.10 | 1.45 | 0.00 | 0.73 | 2.74 | 2.44 |
time (sec) |
N/A | 0.338 | 0.832 | 3.814 | 0.034 | 0.103 | 0.000 | 0.160 | 0.181 | 20.359 |
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 | 126 | 110 | 82 | 91 | 146 | 226 | 0 | 105 | 344 | 302 |
N.S. |
1 | 0.87 | 0.65 | 0.72 | 1.16 | 1.79 | 0.00 | 0.83 | 2.73 | 2.40 |
time (sec) |
N/A | 0.303 | 0.387 | 1.818 | 0.043 | 0.096 | 0.000 | 0.147 | 0.184 | 20.431 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 82 | 73 | 52 | 67 | 98 | 154 | 0 | 75 | 216 | 186 |
N.S. |
1 | 0.89 | 0.63 | 0.82 | 1.20 | 1.88 | 0.00 | 0.91 | 2.63 | 2.27 |
time (sec) |
N/A | 0.272 | 0.172 | 1.831 | 0.034 | 0.122 | 0.000 | 0.122 | 0.172 | 19.517 |
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 | 74 | 69 | 52 | 49 | 72 | 104 | 0 | 62 | 146 | 148 |
N.S. |
1 | 0.93 | 0.70 | 0.66 | 0.97 | 1.41 | 0.00 | 0.84 | 1.97 | 2.00 |
time (sec) |
N/A | 0.257 | 0.200 | 1.896 | 0.031 | 0.120 | 0.000 | 0.124 | 0.179 | 17.893 |
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 | 86 | 78 | 61 | 61 | 80 | 147 | 0 | 81 | 140 | 169 |
N.S. |
1 | 0.91 | 0.71 | 0.71 | 0.93 | 1.71 | 0.00 | 0.94 | 1.63 | 1.97 |
time (sec) |
N/A | 0.273 | 0.219 | 6.091 | 0.031 | 0.087 | 0.000 | 0.129 | 0.176 | 18.030 |
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 | 96 | 86 | 69 | 67 | 75 | 131 | 0 | 81 | 98 | 171 |
N.S. |
1 | 0.90 | 0.72 | 0.70 | 0.78 | 1.36 | 0.00 | 0.84 | 1.02 | 1.78 |
time (sec) |
N/A | 0.272 | 0.343 | 12.318 | 0.035 | 0.130 | 0.000 | 0.141 | 0.173 | 18.345 |
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 | 73 | 65 | 48 | 49 | 46 | 84 | 0 | 46 | 56 | 46 |
N.S. |
1 | 0.89 | 0.66 | 0.67 | 0.63 | 1.15 | 0.00 | 0.63 | 0.77 | 0.63 |
time (sec) |
N/A | 0.255 | 0.110 | 23.195 | 0.029 | 0.082 | 0.000 | 0.145 | 0.185 | 18.045 |
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 | 109 | 95 | 68 | 69 | 66 | 117 | 0 | 66 | 76 | 66 |
N.S. |
1 | 0.87 | 0.62 | 0.63 | 0.61 | 1.07 | 0.00 | 0.61 | 0.70 | 0.61 |
time (sec) |
N/A | 0.269 | 0.086 | 41.343 | 0.032 | 0.084 | 0.000 | 0.152 | 0.196 | 17.912 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 145 | 125 | 88 | 89 | 86 | 152 | 0 | 86 | 96 | 86 |
N.S. |
1 | 0.86 | 0.61 | 0.61 | 0.59 | 1.05 | 0.00 | 0.59 | 0.66 | 0.59 |
time (sec) |
N/A | 0.288 | 0.137 | 70.988 | 0.039 | 0.113 | 0.000 | 0.167 | 0.231 | 18.070 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 145 | 125 | 88 | 89 | 86 | 185 | 0 | 86 | 96 | 85 |
N.S. |
1 | 0.86 | 0.61 | 0.61 | 0.59 | 1.28 | 0.00 | 0.59 | 0.66 | 0.59 |
time (sec) |
N/A | 0.280 | 0.134 | 113.197 | 0.035 | 0.105 | 0.000 | 0.151 | 0.360 | 18.127 |
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 | 195 | 168 | 112 | 127 | 213 | 290 | 0 | 135 | 536 | 476 |
N.S. |
1 | 0.86 | 0.57 | 0.65 | 1.09 | 1.49 | 0.00 | 0.69 | 2.75 | 2.44 |
time (sec) |
N/A | 0.351 | 1.587 | 7.726 | 0.037 | 0.108 | 0.000 | 0.160 | 0.235 | 20.489 |
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 | 132 | 115 | 50 | 81 | 95 | 102 | 0 | 77 | 86 | 172 |
N.S. |
1 | 0.87 | 0.38 | 0.61 | 0.72 | 0.77 | 0.00 | 0.58 | 0.65 | 1.30 |
time (sec) |
N/A | 0.293 | 0.126 | 5.438 | 0.032 | 0.084 | 0.000 | 0.144 | 0.184 | 18.030 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 105 | 92 | 62 | 79 | 121 | 198 | 0 | 85 | 280 | 240 |
N.S. |
1 | 0.88 | 0.59 | 0.75 | 1.15 | 1.89 | 0.00 | 0.81 | 2.67 | 2.29 |
time (sec) |
N/A | 0.266 | 0.311 | 5.352 | 0.029 | 0.143 | 0.000 | 0.127 | 0.192 | 19.829 |
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 | 94 | 73 | 71 | 103 | 196 | 0 | 90 | 202 | 228 |
N.S. |
1 | 0.89 | 0.69 | 0.67 | 0.97 | 1.85 | 0.00 | 0.85 | 1.91 | 2.15 |
time (sec) |
N/A | 0.282 | 0.836 | 16.509 | 0.027 | 0.131 | 0.000 | 0.137 | 0.198 | 17.791 |
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 | 135 | 119 | 89 | 89 | 95 | 186 | 0 | 101 | 118 | 235 |
N.S. |
1 | 0.88 | 0.66 | 0.66 | 0.70 | 1.38 | 0.00 | 0.75 | 0.87 | 1.74 |
time (sec) |
N/A | 0.290 | 0.197 | 53.191 | 0.027 | 0.093 | 0.000 | 0.153 | 0.194 | 17.733 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | B | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 127 | 131 | 124 | 109 | 356 | 129 | 0 | 146 | 176 | 231 |
N.S. |
1 | 1.03 | 0.98 | 0.86 | 2.80 | 1.02 | 0.00 | 1.15 | 1.39 | 1.82 |
time (sec) |
N/A | 0.525 | 1.416 | 5.329 | 0.046 | 0.081 | 0.000 | 0.290 | 0.226 | 18.355 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | B | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 108 | 112 | 315 | 119 | 288 | 369 | 0 | 135 | 298 | 203 |
N.S. |
1 | 1.04 | 2.92 | 1.10 | 2.67 | 3.42 | 0.00 | 1.25 | 2.76 | 1.88 |
time (sec) |
N/A | 0.519 | 1.305 | 11.590 | 0.040 | 0.092 | 0.000 | 0.160 | 0.177 | 21.072 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | B | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 120 | 106 | 589 | 143 | 285 | 445 | 0 | 179 | 252 | 171 |
N.S. |
1 | 0.88 | 4.91 | 1.19 | 2.38 | 3.71 | 0.00 | 1.49 | 2.10 | 1.42 |
time (sec) |
N/A | 0.450 | 6.852 | 22.679 | 0.040 | 0.122 | 0.000 | 0.181 | 0.196 | 18.472 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | B | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 133 | 137 | 733 | 165 | 279 | 439 | 0 | 204 | 206 | 209 |
N.S. |
1 | 1.03 | 5.51 | 1.24 | 2.10 | 3.30 | 0.00 | 1.53 | 1.55 | 1.57 |
time (sec) |
N/A | 0.467 | 7.112 | 40.283 | 0.040 | 0.139 | 0.000 | 0.190 | 0.193 | 18.376 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 162 | 195 | 394 | 176 | 0 | 194 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.20 | 2.43 | 1.09 | 0.00 | 1.20 | 0.00 | 0.00 | 0.14 | 0.00 |
time (sec) |
N/A | 1.283 | 5.915 | 0.458 | 0.000 | 0.142 | 0.000 | 0.000 | 0.212 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 101 | 107 | 114 | 89 | 0 | 169 | 0 | 428 | 23 | 0 |
N.S. |
1 | 1.06 | 1.13 | 0.88 | 0.00 | 1.67 | 0.00 | 4.24 | 0.23 | 0.00 |
time (sec) |
N/A | 0.517 | 0.892 | 0.318 | 0.000 | 0.093 | 0.000 | 0.324 | 0.200 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | F | B | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 89 | 99 | 206 | 129 | 0 | 279 | 0 | 149 | 23 | 0 |
N.S. |
1 | 1.11 | 2.31 | 1.45 | 0.00 | 3.13 | 0.00 | 1.67 | 0.26 | 0.00 |
time (sec) |
N/A | 0.541 | 1.475 | 0.321 | 0.000 | 0.121 | 0.000 | 0.164 | 0.195 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 163 | 175 | 309 | 170 | 0 | 380 | 0 | 211 | 23 | 0 |
N.S. |
1 | 1.07 | 1.90 | 1.04 | 0.00 | 2.33 | 0.00 | 1.29 | 0.14 | 0.00 |
time (sec) |
N/A | 1.028 | 2.192 | 0.343 | 0.000 | 0.136 | 0.000 | 0.169 | 0.193 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-1) | A | F(-1) | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 167 | 195 | 141 | 139 | 0 | 230 | 0 | 917 | 51 | 0 |
N.S. |
1 | 1.17 | 0.84 | 0.83 | 0.00 | 1.38 | 0.00 | 5.49 | 0.31 | 0.00 |
time (sec) |
N/A | 1.470 | 6.200 | 0.370 | 0.000 | 0.103 | 0.000 | 0.968 | 0.226 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 88 | 93 | 46 | 55 | 145 | 48 | 0 | 209 | 51 | 0 |
N.S. |
1 | 1.06 | 0.52 | 0.62 | 1.65 | 0.55 | 0.00 | 2.38 | 0.58 | 0.00 |
time (sec) |
N/A | 0.507 | 5.706 | 0.303 | 0.142 | 0.077 | 0.000 | 0.390 | 0.219 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 121 | 134 | 233 | 154 | 0 | 315 | 0 | 183 | 51 | 0 |
N.S. |
1 | 1.11 | 1.93 | 1.27 | 0.00 | 2.60 | 0.00 | 1.51 | 0.42 | 0.00 |
time (sec) |
N/A | 0.765 | 6.366 | 0.312 | 0.000 | 0.096 | 0.000 | 0.163 | 0.221 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F(-1) | A | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 197 | 208 | 334 | 196 | 0 | 424 | 0 | 246 | 51 | 0 |
N.S. |
1 | 1.06 | 1.70 | 0.99 | 0.00 | 2.15 | 0.00 | 1.25 | 0.26 | 0.00 |
time (sec) |
N/A | 1.356 | 2.173 | 0.338 | 0.000 | 0.100 | 0.000 | 0.168 | 0.227 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 151 | 212 | 112 | 87 | 277 | 98 | 0 | 1485 | 83 | 0 |
N.S. |
1 | 1.40 | 0.74 | 0.58 | 1.83 | 0.65 | 0.00 | 9.83 | 0.55 | 0.00 |
time (sec) |
N/A | 1.657 | 6.169 | 13.281 | 0.136 | 0.092 | 0.000 | 4.547 | 0.240 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 118 | 131 | 60 | 67 | 191 | 70 | 0 | 1411 | 83 | 0 |
N.S. |
1 | 1.11 | 0.51 | 0.57 | 1.62 | 0.59 | 0.00 | 11.96 | 0.70 | 0.00 |
time (sec) |
N/A | 0.612 | 6.038 | 1.939 | 0.131 | 0.085 | 0.000 | 1.451 | 0.237 | 0.000 |