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 | B | B | F | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 106 | 108 | 112 | 122 | 255 | 289 | 0 | 0 | 64 | 0 |
N.S. |
1 | 1.02 | 1.06 | 1.15 | 2.41 | 2.73 | 0.00 | 0.00 | 0.60 | 0.00 |
time (sec) |
N/A | 0.308 | 0.700 | 0.345 | 0.231 | 0.101 | 0.000 | 0.000 | 0.204 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | B | F | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 106 | 108 | 112 | 269 | 127 | 339 | 0 | 0 | 187 | 0 |
N.S. |
1 | 1.02 | 1.06 | 2.54 | 1.20 | 3.20 | 0.00 | 0.00 | 1.76 | 0.00 |
time (sec) |
N/A | 0.314 | 0.771 | 0.342 | 0.181 | 0.095 | 0.000 | 0.000 | 0.200 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | F | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 43 | 43 | 43 | 35 | 35 | 67 | 0 | 0 | 212 | 62 |
N.S. |
1 | 1.00 | 1.00 | 0.81 | 0.81 | 1.56 | 0.00 | 0.00 | 4.93 | 1.44 |
time (sec) |
N/A | 0.284 | 0.733 | 1.085 | 0.187 | 0.068 | 0.000 | 0.000 | 0.238 | 2.592 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 90 | 99 | 79 | 75 | 86 | 79 | 0 | 0 | 164 | 159 |
N.S. |
1 | 1.10 | 0.88 | 0.83 | 0.96 | 0.88 | 0.00 | 0.00 | 1.82 | 1.77 |
time (sec) |
N/A | 0.299 | 1.132 | 0.359 | 0.200 | 0.069 | 0.000 | 0.000 | 0.202 | 3.098 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 136 | 153 | 91 | 85 | 136 | 91 | 0 | 0 | 265 | 182 |
N.S. |
1 | 1.12 | 0.67 | 0.62 | 1.00 | 0.67 | 0.00 | 0.00 | 1.95 | 1.34 |
time (sec) |
N/A | 0.327 | 1.469 | 0.343 | 0.239 | 0.076 | 0.000 | 0.000 | 0.377 | 3.621 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | F | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 182 | 207 | 103 | 97 | 186 | 103 | 0 | 0 | 267 | 205 |
N.S. |
1 | 1.14 | 0.57 | 0.53 | 1.02 | 0.57 | 0.00 | 0.00 | 1.47 | 1.13 |
time (sec) |
N/A | 0.353 | 2.106 | 0.350 | 0.195 | 0.077 | 0.000 | 0.000 | 0.457 | 4.380 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 168 | 162 | 151 | 164 | 1173 | 507 | 0 | 0 | 108 | 0 |
N.S. |
1 | 0.96 | 0.90 | 0.98 | 6.98 | 3.02 | 0.00 | 0.00 | 0.64 | 0.00 |
time (sec) |
N/A | 0.326 | 1.788 | 0.309 | 0.372 | 0.115 | 0.000 | 0.000 | 0.228 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 159 | 157 | 133 | 186 | 887 | 432 | 0 | 0 | 140 | 0 |
N.S. |
1 | 0.99 | 0.84 | 1.17 | 5.58 | 2.72 | 0.00 | 0.00 | 0.88 | 0.00 |
time (sec) |
N/A | 0.320 | 1.202 | 0.324 | 0.278 | 0.113 | 0.000 | 0.000 | 0.225 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 154 | 157 | 126 | 153 | 445 | 361 | 0 | 0 | 103 | 0 |
N.S. |
1 | 1.02 | 0.82 | 0.99 | 2.89 | 2.34 | 0.00 | 0.00 | 0.67 | 0.00 |
time (sec) |
N/A | 0.319 | 0.858 | 0.330 | 0.261 | 0.123 | 0.000 | 0.000 | 0.219 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | A | B | F | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 153 | 156 | 86 | 300 | 185 | 360 | 0 | 0 | 222 | 0 |
N.S. |
1 | 1.02 | 0.56 | 1.96 | 1.21 | 2.35 | 0.00 | 0.00 | 1.45 | 0.00 |
time (sec) |
N/A | 0.331 | 0.827 | 0.346 | 0.203 | 0.098 | 0.000 | 0.000 | 0.229 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | B | B | F | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 155 | 158 | 88 | 350 | 410 | 386 | 0 | 0 | 484 | 0 |
N.S. |
1 | 1.02 | 0.57 | 2.26 | 2.65 | 2.49 | 0.00 | 0.00 | 3.12 | 0.00 |
time (sec) |
N/A | 0.333 | 1.096 | 0.313 | 0.219 | 0.102 | 0.000 | 0.000 | 0.290 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | F | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 43 | 43 | 43 | 35 | 39 | 71 | 0 | 0 | 246 | 65 |
N.S. |
1 | 1.00 | 1.00 | 0.81 | 0.91 | 1.65 | 0.00 | 0.00 | 5.72 | 1.51 |
time (sec) |
N/A | 0.272 | 1.505 | 1.020 | 0.206 | 0.074 | 0.000 | 0.000 | 0.222 | 4.613 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 90 | 99 | 83 | 87 | 94 | 85 | 0 | 0 | 439 | 161 |
N.S. |
1 | 1.10 | 0.92 | 0.97 | 1.04 | 0.94 | 0.00 | 0.00 | 4.88 | 1.79 |
time (sec) |
N/A | 0.299 | 2.055 | 0.384 | 0.243 | 0.078 | 0.000 | 0.000 | 0.461 | 3.532 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | F | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 136 | 153 | 95 | 99 | 148 | 99 | 0 | 0 | 359 | 184 |
N.S. |
1 | 1.12 | 0.70 | 0.73 | 1.09 | 0.73 | 0.00 | 0.00 | 2.64 | 1.35 |
time (sec) |
N/A | 0.322 | 2.766 | 0.334 | 0.214 | 0.081 | 0.000 | 0.000 | 0.548 | 4.207 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | F | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 182 | 207 | 105 | 110 | 202 | 113 | 0 | 0 | 445 | 207 |
N.S. |
1 | 1.14 | 0.58 | 0.60 | 1.11 | 0.62 | 0.00 | 0.00 | 2.45 | 1.14 |
time (sec) |
N/A | 0.343 | 4.074 | 0.337 | 0.193 | 0.073 | 0.000 | 0.000 | 0.725 | 5.150 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 204 | 205 | 206 | 328 | 787 | 396 | 0 | 0 | 327 | 0 |
N.S. |
1 | 1.00 | 1.01 | 1.61 | 3.86 | 1.94 | 0.00 | 0.00 | 1.60 | 0.00 |
time (sec) |
N/A | 0.351 | 3.361 | 0.358 | 0.225 | 0.135 | 0.000 | 0.000 | 0.208 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 153 | 156 | 191 | 299 | 540 | 342 | 0 | 0 | 223 | 0 |
N.S. |
1 | 1.02 | 1.25 | 1.95 | 3.53 | 2.24 | 0.00 | 0.00 | 1.46 | 0.00 |
time (sec) |
N/A | 0.323 | 1.936 | 0.333 | 0.263 | 0.094 | 0.000 | 0.000 | 0.201 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 106 | 108 | 106 | 267 | 319 | 321 | 0 | 0 | 187 | 0 |
N.S. |
1 | 1.02 | 1.00 | 2.52 | 3.01 | 3.03 | 0.00 | 0.00 | 1.76 | 0.00 |
time (sec) |
N/A | 0.303 | 0.753 | 0.333 | 0.242 | 0.107 | 0.000 | 0.000 | 0.246 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | F | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 41 | 41 | 41 | 35 | 25 | 64 | 0 | 0 | 56 | 49 |
N.S. |
1 | 1.00 | 1.00 | 0.85 | 0.61 | 1.56 | 0.00 | 0.00 | 1.37 | 1.20 |
time (sec) |
N/A | 0.274 | 0.455 | 1.032 | 0.175 | 0.100 | 0.000 | 0.000 | 0.177 | 2.358 |
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 | 44 | 44 | 44 | 74 | 16 | 67 | 0 | 0 | 55 | 112 |
N.S. |
1 | 1.00 | 1.00 | 1.68 | 0.36 | 1.52 | 0.00 | 0.00 | 1.25 | 2.55 |
time (sec) |
N/A | 0.275 | 0.517 | 0.365 | 0.176 | 0.080 | 0.000 | 0.000 | 0.186 | 2.465 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | F | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 94 | 103 | 78 | 109 | 0 | 111 | 0 | 0 | 67 | 135 |
N.S. |
1 | 1.10 | 0.83 | 1.16 | 0.00 | 1.18 | 0.00 | 0.00 | 0.71 | 1.44 |
time (sec) |
N/A | 0.302 | 0.734 | 0.360 | 0.000 | 0.088 | 0.000 | 0.000 | 0.184 | 2.547 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | F | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 140 | 157 | 90 | 118 | 0 | 122 | 0 | 0 | 107 | 158 |
N.S. |
1 | 1.12 | 0.64 | 0.84 | 0.00 | 0.87 | 0.00 | 0.00 | 0.76 | 1.13 |
time (sec) |
N/A | 0.325 | 1.097 | 0.364 | 0.000 | 0.089 | 0.000 | 0.000 | 0.186 | 2.948 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | F | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 186 | 211 | 100 | 130 | 0 | 133 | 0 | 0 | 92 | 183 |
N.S. |
1 | 1.13 | 0.54 | 0.70 | 0.00 | 0.72 | 0.00 | 0.00 | 0.49 | 0.98 |
time (sec) |
N/A | 0.337 | 1.538 | 0.357 | 0.000 | 0.097 | 0.000 | 0.000 | 0.289 | 3.519 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | B | B | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 255 | 257 | 524 | 409 | 915 | 430 | 0 | 0 | 782 | 0 |
N.S. |
1 | 1.01 | 2.05 | 1.60 | 3.59 | 1.69 | 0.00 | 0.00 | 3.07 | 0.00 |
time (sec) |
N/A | 0.370 | 8.259 | 0.365 | 0.232 | 0.123 | 0.000 | 0.000 | 0.422 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | B | B | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 204 | 208 | 258 | 379 | 660 | 368 | 0 | 0 | 634 | 0 |
N.S. |
1 | 1.02 | 1.26 | 1.86 | 3.24 | 1.80 | 0.00 | 0.00 | 3.11 | 0.00 |
time (sec) |
N/A | 0.344 | 4.000 | 0.347 | 0.211 | 0.118 | 0.000 | 0.000 | 0.311 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 155 | 158 | 199 | 348 | 386 | 368 | 0 | 0 | 486 | 0 |
N.S. |
1 | 1.02 | 1.28 | 2.25 | 2.49 | 2.37 | 0.00 | 0.00 | 3.14 | 0.00 |
time (sec) |
N/A | 0.330 | 1.936 | 0.340 | 0.259 | 0.096 | 0.000 | 0.000 | 0.264 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | F | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 43 | 43 | 69 | 35 | 35 | 67 | 0 | 0 | 205 | 108 |
N.S. |
1 | 1.00 | 1.60 | 0.81 | 0.81 | 1.56 | 0.00 | 0.00 | 4.77 | 2.51 |
time (sec) |
N/A | 0.285 | 0.794 | 0.961 | 0.232 | 0.082 | 0.000 | 0.000 | 0.239 | 0.769 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | F | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 90 | 99 | 66 | 64 | 0 | 76 | 0 | 0 | 179 | 114 |
N.S. |
1 | 1.10 | 0.73 | 0.71 | 0.00 | 0.84 | 0.00 | 0.00 | 1.99 | 1.27 |
time (sec) |
N/A | 0.296 | 0.751 | 0.358 | 0.000 | 0.085 | 0.000 | 0.000 | 0.216 | 2.195 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | F | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 137 | 149 | 78 | 88 | 0 | 111 | 0 | 0 | 70 | 117 |
N.S. |
1 | 1.09 | 0.57 | 0.64 | 0.00 | 0.81 | 0.00 | 0.00 | 0.51 | 0.85 |
time (sec) |
N/A | 0.318 | 0.984 | 0.373 | 0.000 | 0.101 | 0.000 | 0.000 | 0.206 | 0.395 |
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 | 101 | 107 | 63 | 95 | 45 | 89 | 0 | 0 | 78 | 138 |
N.S. |
1 | 1.06 | 0.62 | 0.94 | 0.45 | 0.88 | 0.00 | 0.00 | 0.77 | 1.37 |
time (sec) |
N/A | 0.294 | 1.296 | 0.339 | 0.247 | 0.088 | 0.000 | 0.000 | 0.204 | 2.594 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | F | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 147 | 161 | 115 | 130 | 0 | 133 | 0 | 0 | 88 | 163 |
N.S. |
1 | 1.10 | 0.78 | 0.88 | 0.00 | 0.90 | 0.00 | 0.00 | 0.60 | 1.11 |
time (sec) |
N/A | 0.319 | 1.908 | 0.341 | 0.000 | 0.085 | 0.000 | 0.000 | 0.213 | 2.965 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | F | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 193 | 215 | 127 | 141 | 0 | 144 | 0 | 0 | 144 | 186 |
N.S. |
1 | 1.11 | 0.66 | 0.73 | 0.00 | 0.75 | 0.00 | 0.00 | 0.75 | 0.96 |
time (sec) |
N/A | 0.348 | 2.511 | 0.370 | 0.000 | 0.099 | 0.000 | 0.000 | 0.182 | 3.426 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | B | A | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 304 | 309 | 366 | 490 | 1083 | 444 | 0 | 0 | 505 | 0 |
N.S. |
1 | 1.02 | 1.20 | 1.61 | 3.56 | 1.46 | 0.00 | 0.00 | 1.66 | 0.00 |
time (sec) |
N/A | 0.393 | 8.619 | 0.359 | 0.249 | 0.119 | 0.000 | 0.000 | 0.190 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | B | B | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 253 | 260 | 277 | 460 | 772 | 382 | 0 | 0 | 421 | 0 |
N.S. |
1 | 1.03 | 1.09 | 1.82 | 3.05 | 1.51 | 0.00 | 0.00 | 1.66 | 0.00 |
time (sec) |
N/A | 0.369 | 5.358 | 0.373 | 0.223 | 0.106 | 0.000 | 0.000 | 0.194 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 204 | 208 | 220 | 429 | 440 | 382 | 0 | 0 | 337 | 0 |
N.S. |
1 | 1.02 | 1.08 | 2.10 | 2.16 | 1.87 | 0.00 | 0.00 | 1.65 | 0.00 |
time (sec) |
N/A | 0.349 | 3.874 | 0.346 | 0.273 | 0.110 | 0.000 | 0.000 | 0.209 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | F | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 43 | 43 | 73 | 35 | 39 | 71 | 0 | 0 | 252 | 114 |
N.S. |
1 | 1.00 | 1.70 | 0.81 | 0.91 | 1.65 | 0.00 | 0.00 | 5.86 | 2.65 |
time (sec) |
N/A | 0.276 | 1.776 | 0.886 | 0.212 | 0.103 | 0.000 | 0.000 | 0.198 | 2.438 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 90 | 99 | 79 | 71 | 112 | 79 | 0 | 0 | 167 | 136 |
N.S. |
1 | 1.10 | 0.88 | 0.79 | 1.24 | 0.88 | 0.00 | 0.00 | 1.86 | 1.51 |
time (sec) |
N/A | 0.301 | 1.370 | 0.347 | 0.202 | 0.080 | 0.000 | 0.000 | 0.207 | 2.554 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | F | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 136 | 153 | 89 | 77 | 0 | 87 | 0 | 0 | 84 | 137 |
N.S. |
1 | 1.12 | 0.65 | 0.57 | 0.00 | 0.64 | 0.00 | 0.00 | 0.62 | 1.01 |
time (sec) |
N/A | 0.311 | 1.214 | 0.326 | 0.000 | 0.105 | 0.000 | 0.000 | 0.226 | 2.603 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | F | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 186 | 203 | 90 | 99 | 0 | 122 | 0 | 0 | 107 | 128 |
N.S. |
1 | 1.09 | 0.48 | 0.53 | 0.00 | 0.66 | 0.00 | 0.00 | 0.58 | 0.69 |
time (sec) |
N/A | 0.336 | 1.445 | 0.381 | 0.000 | 0.097 | 0.000 | 0.000 | 0.209 | 2.552 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | F | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 234 | 257 | 115 | 130 | 0 | 133 | 0 | 0 | 91 | 140 |
N.S. |
1 | 1.10 | 0.49 | 0.56 | 0.00 | 0.57 | 0.00 | 0.00 | 0.39 | 0.60 |
time (sec) |
N/A | 0.378 | 2.093 | 0.346 | 0.000 | 0.089 | 0.000 | 0.000 | 0.237 | 2.615 |
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 | 154 | 168 | 75 | 105 | 71 | 111 | 0 | 0 | 98 | 163 |
N.S. |
1 | 1.09 | 0.49 | 0.68 | 0.46 | 0.72 | 0.00 | 0.00 | 0.64 | 1.06 |
time (sec) |
N/A | 0.324 | 2.768 | 0.334 | 0.192 | 0.098 | 0.000 | 0.000 | 0.207 | 2.911 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | F | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 200 | 222 | 137 | 151 | 0 | 155 | 0 | 0 | 109 | 186 |
N.S. |
1 | 1.11 | 0.68 | 0.76 | 0.00 | 0.78 | 0.00 | 0.00 | 0.54 | 0.93 |
time (sec) |
N/A | 0.343 | 4.167 | 0.369 | 0.000 | 0.095 | 0.000 | 0.000 | 0.235 | 3.366 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | B | F | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 134 | 113 | 113 | 204 | 862 | 240 | 2225 | 0 | 165 | 229 |
N.S. |
1 | 0.84 | 0.84 | 1.52 | 6.43 | 1.79 | 16.60 | 0.00 | 1.23 | 1.71 |
time (sec) |
N/A | 0.394 | 0.767 | 0.941 | 0.307 | 0.094 | 1.560 | 0.000 | 0.245 | 6.297 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | F | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 99 | 85 | 75 | 129 | 547 | 150 | 979 | 0 | 93 | 230 |
N.S. |
1 | 0.86 | 0.76 | 1.30 | 5.53 | 1.52 | 9.89 | 0.00 | 0.94 | 2.32 |
time (sec) |
N/A | 0.387 | 0.471 | 0.814 | 0.285 | 0.110 | 0.823 | 0.000 | 0.205 | 1.554 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | F | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 64 | 59 | 47 | 78 | 272 | 78 | 311 | 0 | 45 | 112 |
N.S. |
1 | 0.92 | 0.73 | 1.22 | 4.25 | 1.22 | 4.86 | 0.00 | 0.70 | 1.75 |
time (sec) |
N/A | 0.366 | 0.603 | 0.725 | 0.198 | 0.105 | 0.492 | 0.000 | 0.209 | 0.398 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | F | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 26 | 25 | 24 | 27 | 70 | 0 | 23 | 40 |
N.S. |
1 | 1.00 | 1.00 | 0.96 | 0.92 | 1.04 | 2.69 | 0.00 | 0.88 | 1.54 |
time (sec) |
N/A | 0.307 | 0.288 | 0.571 | 0.162 | 0.097 | 0.231 | 0.000 | 0.208 | 1.988 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F(-2) | F | F | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 52 | 56 | 52 | 0 | 0 | 0 | 0 | 0 | 107 | 0 |
N.S. |
1 | 1.08 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 2.06 | 0.00 |
time (sec) |
N/A | 0.353 | 0.180 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.217 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F(-2) | F | F | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 52 | 56 | 52 | 0 | 0 | 0 | 0 | 0 | 43 | 0 |
N.S. |
1 | 1.08 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.83 | 0.00 |
time (sec) |
N/A | 0.354 | 0.208 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.226 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F(-2) | F | F | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 52 | 56 | 52 | 0 | 0 | 0 | 0 | 0 | 274 | 0 |
N.S. |
1 | 1.08 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 5.27 | 0.00 |
time (sec) |
N/A | 0.357 | 0.205 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.261 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 66 | 87 | 87 | 0 | 0 | 0 | 0 | 0 | 120 | 0 |
N.S. |
1 | 1.32 | 1.32 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.82 | 0.00 |
time (sec) |
N/A | 0.286 | 0.252 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.214 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | B | F | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 134 | 113 | 104 | 204 | 0 | 247 | 2225 | 0 | 165 | 332 |
N.S. |
1 | 0.84 | 0.78 | 1.52 | 0.00 | 1.84 | 16.60 | 0.00 | 1.23 | 2.48 |
time (sec) |
N/A | 0.402 | 1.285 | 1.001 | 0.000 | 0.106 | 1.549 | 0.000 | 0.207 | 6.734 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | B | F | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 99 | 85 | 75 | 129 | 0 | 157 | 979 | 0 | 91 | 229 |
N.S. |
1 | 0.86 | 0.76 | 1.30 | 0.00 | 1.59 | 9.89 | 0.00 | 0.92 | 2.31 |
time (sec) |
N/A | 0.388 | 1.046 | 0.760 | 0.000 | 0.119 | 0.899 | 0.000 | 0.282 | 1.427 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | B | F | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 64 | 59 | 47 | 78 | 0 | 85 | 313 | 0 | 45 | 112 |
N.S. |
1 | 0.92 | 0.73 | 1.22 | 0.00 | 1.33 | 4.89 | 0.00 | 0.70 | 1.75 |
time (sec) |
N/A | 0.373 | 0.810 | 0.691 | 0.000 | 0.084 | 0.484 | 0.000 | 0.267 | 0.385 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | F | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 26 | 25 | 24 | 36 | 71 | 0 | 23 | 46 |
N.S. |
1 | 1.00 | 1.00 | 0.96 | 0.92 | 1.38 | 2.73 | 0.00 | 0.88 | 1.77 |
time (sec) |
N/A | 0.307 | 0.309 | 0.531 | 0.160 | 0.114 | 0.221 | 0.000 | 0.206 | 0.184 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F(-2) | F | F | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 52 | 56 | 52 | 0 | 0 | 0 | 0 | 0 | 106 | 0 |
N.S. |
1 | 1.08 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 2.04 | 0.00 |
time (sec) |
N/A | 0.355 | 0.725 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.263 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F(-2) | F | F | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 52 | 56 | 52 | 0 | 0 | 0 | 0 | 0 | 42 | 0 |
N.S. |
1 | 1.08 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.81 | 0.00 |
time (sec) |
N/A | 0.349 | 0.758 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.197 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F(-2) | F | F | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 52 | 56 | 52 | 0 | 0 | 0 | 0 | 0 | 271 | 0 |
N.S. |
1 | 1.08 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 5.21 | 0.00 |
time (sec) |
N/A | 0.344 | 0.853 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.224 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F(-2) | F | F | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 52 | 56 | 52 | 0 | 0 | 0 | 0 | 0 | 382 | 0 |
N.S. |
1 | 1.08 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 7.35 | 0.00 |
time (sec) |
N/A | 0.365 | 0.212 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.218 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F | F(-1) | F(-2) | F | F(-1) |
verified | N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 67 | 88 | 141 | 0 | 0 | 0 | 0 | 0 | 274 | 0 |
N.S. |
1 | 1.31 | 2.10 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 4.09 | 0.00 |
time (sec) |
N/A | 0.295 | 12.935 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.289 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F | F | F(-2) | F | F(-1) |
verified | N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 67 | 88 | 141 | 0 | 0 | 0 | 0 | 0 | 80 | 0 |
N.S. |
1 | 1.31 | 2.10 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.19 | 0.00 |
time (sec) |
N/A | 0.280 | 7.527 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.288 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F | F | F(-2) | F | F(-1) |
verified | N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 65 | 86 | 141 | 0 | 0 | 0 | 0 | 0 | 116 | 0 |
N.S. |
1 | 1.32 | 2.17 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.78 | 0.00 |
time (sec) |
N/A | 0.282 | 2.151 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.281 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F | F | F(-2) | F | F(-1) |
verified | N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 65 | 86 | 141 | 0 | 0 | 0 | 0 | 0 | 886 | 0 |
N.S. |
1 | 1.32 | 2.17 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 13.63 | 0.00 |
time (sec) |
N/A | 0.283 | 5.932 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.265 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F(-2) | F | F | F(-2) | F | F(-1) |
verified | N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 67 | 88 | 141 | 0 | 0 | 0 | 0 | 0 | 31 | 0 |
N.S. |
1 | 1.31 | 2.10 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.46 | 0.00 |
time (sec) |
N/A | 0.282 | 9.012 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 200.028 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F(-2) | F | F | F(-2) | F | F(-1) |
verified | N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 67 | 88 | 158 | 0 | 0 | 0 | 0 | 0 | 84 | 0 |
N.S. |
1 | 1.31 | 2.36 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.25 | 0.00 |
time (sec) |
N/A | 0.285 | 12.429 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.222 | 0.000 |
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 | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 110 | 99 | 73 | 100 | 109 | 196 | 184 | 115 | 103 | 125 |
N.S. |
1 | 0.90 | 0.66 | 0.91 | 0.99 | 1.78 | 1.67 | 1.05 | 0.94 | 1.14 |
time (sec) |
N/A | 0.483 | 0.708 | 0.211 | 0.173 | 0.092 | 0.387 | 0.513 | 0.234 | 2.028 |
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 | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 80 | 70 | 58 | 76 | 83 | 135 | 122 | 74 | 79 | 76 |
N.S. |
1 | 0.88 | 0.72 | 0.95 | 1.04 | 1.69 | 1.52 | 0.92 | 0.99 | 0.95 |
time (sec) |
N/A | 0.370 | 0.344 | 0.188 | 0.115 | 0.101 | 0.328 | 0.476 | 0.188 | 1.993 |
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 | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 46 | 46 | 66 | 50 | 52 | 64 | 53 | 35 | 55 | 38 |
N.S. |
1 | 1.00 | 1.43 | 1.09 | 1.13 | 1.39 | 1.15 | 0.76 | 1.20 | 0.83 |
time (sec) |
N/A | 0.260 | 0.028 | 0.137 | 0.117 | 0.079 | 0.260 | 0.417 | 0.190 | 1.911 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 47 | 47 | 56 | 54 | 0 | 42 | 87 | 70 | 44 | 45 |
N.S. |
1 | 1.00 | 1.19 | 1.15 | 0.00 | 0.89 | 1.85 | 1.49 | 0.94 | 0.96 |
time (sec) |
N/A | 0.228 | 0.204 | 0.165 | 0.000 | 0.096 | 0.151 | 0.477 | 0.195 | 2.073 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 80 | 79 | 89 | 73 | 0 | 54 | 162 | 83 | 64 | 70 |
N.S. |
1 | 0.99 | 1.11 | 0.91 | 0.00 | 0.68 | 2.02 | 1.04 | 0.80 | 0.88 |
time (sec) |
N/A | 0.319 | 0.551 | 0.291 | 0.000 | 0.083 | 0.196 | 0.477 | 0.226 | 2.052 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 112 | 111 | 109 | 128 | 0 | 76 | 258 | 100 | 88 | 111 |
N.S. |
1 | 0.99 | 0.97 | 1.14 | 0.00 | 0.68 | 2.30 | 0.89 | 0.79 | 0.99 |
time (sec) |
N/A | 0.416 | 0.692 | 0.217 | 0.000 | 0.079 | 0.265 | 0.489 | 0.285 | 2.135 |
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 | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 153 | 132 | 99 | 176 | 181 | 359 | 313 | 207 | 192 | 217 |
N.S. |
1 | 0.86 | 0.65 | 1.15 | 1.18 | 2.35 | 2.05 | 1.35 | 1.25 | 1.42 |
time (sec) |
N/A | 0.667 | 1.034 | 0.217 | 0.119 | 0.116 | 0.541 | 0.573 | 0.200 | 1.964 |
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 | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 116 | 100 | 100 | 135 | 144 | 277 | 236 | 150 | 151 | 139 |
N.S. |
1 | 0.86 | 0.86 | 1.16 | 1.24 | 2.39 | 2.03 | 1.29 | 1.30 | 1.20 |
time (sec) |
N/A | 0.553 | 0.744 | 0.193 | 0.112 | 0.086 | 0.450 | 0.467 | 0.197 | 1.930 |
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 | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 78 | 78 | 66 | 94 | 94 | 152 | 119 | 78 | 111 | 75 |
N.S. |
1 | 1.00 | 0.85 | 1.21 | 1.21 | 1.95 | 1.53 | 1.00 | 1.42 | 0.96 |
time (sec) |
N/A | 0.409 | 0.321 | 0.157 | 0.118 | 0.093 | 0.345 | 0.469 | 0.189 | 1.911 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 75 | 76 | 143 | 126 | 0 | 84 | 170 | 96 | 75 | 112 |
N.S. |
1 | 1.01 | 1.91 | 1.68 | 0.00 | 1.12 | 2.27 | 1.28 | 1.00 | 1.49 |
time (sec) |
N/A | 0.303 | 1.011 | 0.225 | 0.000 | 0.095 | 0.286 | 0.546 | 0.194 | 2.274 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 91 | 93 | 119 | 132 | 0 | 80 | 258 | 117 | 104 | 93 |
N.S. |
1 | 1.02 | 1.31 | 1.45 | 0.00 | 0.88 | 2.84 | 1.29 | 1.14 | 1.02 |
time (sec) |
N/A | 0.409 | 0.892 | 0.197 | 0.000 | 0.096 | 0.263 | 0.543 | 0.192 | 2.169 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 129 | 127 | 178 | 212 | 0 | 110 | 401 | 144 | 140 | 148 |
N.S. |
1 | 0.98 | 1.38 | 1.64 | 0.00 | 0.85 | 3.11 | 1.12 | 1.09 | 1.15 |
time (sec) |
N/A | 0.497 | 1.447 | 0.208 | 0.000 | 0.109 | 0.344 | 0.560 | 0.205 | 2.335 |
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 | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 190 | 205 | 191 | 269 | 262 | 562 | 476 | 320 | 298 | 356 |
N.S. |
1 | 1.08 | 1.01 | 1.42 | 1.38 | 2.96 | 2.51 | 1.68 | 1.57 | 1.87 |
time (sec) |
N/A | 1.092 | 1.948 | 0.291 | 0.140 | 0.086 | 0.727 | 0.663 | 0.237 | 2.045 |
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 | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 141 | 141 | 111 | 210 | 218 | 457 | 381 | 242 | 240 | 223 |
N.S. |
1 | 1.00 | 0.79 | 1.49 | 1.55 | 3.24 | 2.70 | 1.72 | 1.70 | 1.58 |
time (sec) |
N/A | 0.745 | 2.947 | 0.240 | 0.120 | 0.090 | 0.630 | 0.601 | 0.272 | 2.018 |
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 | 107 | 107 | 107 | 149 | 145 | 279 | 223 | 146 | 186 | 122 |
N.S. |
1 | 1.00 | 1.00 | 1.39 | 1.36 | 2.61 | 2.08 | 1.36 | 1.74 | 1.14 |
time (sec) |
N/A | 0.550 | 0.702 | 0.188 | 0.137 | 0.097 | 0.467 | 0.502 | 0.204 | 1.964 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 129 | 127 | 234 | 224 | 0 | 197 | 260 | 137 | 163 | 175 |
N.S. |
1 | 0.98 | 1.81 | 1.74 | 0.00 | 1.53 | 2.02 | 1.06 | 1.26 | 1.36 |
time (sec) |
N/A | 0.530 | 1.545 | 0.258 | 0.000 | 0.128 | 0.399 | 0.561 | 0.194 | 2.504 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 136 | 149 | 208 | 224 | 0 | 126 | 393 | 143 | 144 | 184 |
N.S. |
1 | 1.10 | 1.53 | 1.65 | 0.00 | 0.93 | 2.89 | 1.05 | 1.06 | 1.35 |
time (sec) |
N/A | 0.823 | 3.626 | 0.269 | 0.000 | 0.085 | 0.422 | 0.600 | 0.197 | 2.581 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | A | A | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 140 | 144 | 270 | 294 | 0 | 139 | 552 | 182 | 192 | 183 |
N.S. |
1 | 1.03 | 1.93 | 2.10 | 0.00 | 0.99 | 3.94 | 1.30 | 1.37 | 1.31 |
time (sec) |
N/A | 0.573 | 1.237 | 0.218 | 0.000 | 0.081 | 0.401 | 0.560 | 0.214 | 2.468 |
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 | 115 | 126 | 109 | 107 | 140 | 211 | 257 | 95 | 161 | 99 |
N.S. |
1 | 1.10 | 0.95 | 0.93 | 1.22 | 1.83 | 2.23 | 0.83 | 1.40 | 0.86 |
time (sec) |
N/A | 0.893 | 0.931 | 0.252 | 0.175 | 0.116 | 9.108 | 0.475 | 0.213 | 4.014 |
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 | 106 | 96 | 59 | 84 | 114 | 84 | 92 | 64 | 112 | 64 |
N.S. |
1 | 0.91 | 0.56 | 0.79 | 1.08 | 0.79 | 0.87 | 0.60 | 1.06 | 0.60 |
time (sec) |
N/A | 0.518 | 0.714 | 0.218 | 0.127 | 0.093 | 3.972 | 0.467 | 0.199 | 2.427 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 45 | 45 | 39 | 65 | 90 | 43 | 44 | 52 | 84 | 43 |
N.S. |
1 | 1.00 | 0.87 | 1.44 | 2.00 | 0.96 | 0.98 | 1.16 | 1.87 | 0.96 |
time (sec) |
N/A | 0.317 | 0.194 | 0.151 | 0.121 | 0.082 | 0.763 | 0.436 | 0.287 | 2.012 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 128 | 106 | 122 | 178 | 0 | 127 | 248 | 143 | 38 | 2639 |
N.S. |
1 | 0.83 | 0.95 | 1.39 | 0.00 | 0.99 | 1.94 | 1.12 | 0.30 | 20.62 |
time (sec) |
N/A | 0.521 | 0.496 | 0.261 | 0.000 | 0.084 | 2.464 | 0.466 | 0.257 | 6.156 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 174 | 186 | 160 | 235 | 0 | 183 | 610 | 217 | 64 | 1384 |
N.S. |
1 | 1.07 | 0.92 | 1.35 | 0.00 | 1.05 | 3.51 | 1.25 | 0.37 | 7.95 |
time (sec) |
N/A | 0.899 | 0.795 | 0.432 | 0.000 | 0.089 | 5.499 | 0.504 | 0.231 | 6.221 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 234 | 270 | 210 | 370 | 0 | 269 | 1192 | 307 | 88 | 1952 |
N.S. |
1 | 1.15 | 0.90 | 1.58 | 0.00 | 1.15 | 5.09 | 1.31 | 0.38 | 8.34 |
time (sec) |
N/A | 1.374 | 1.047 | 0.456 | 0.000 | 0.093 | 13.018 | 0.554 | 0.222 | 7.375 |
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 | 142 | 163 | 189 | 175 | 245 | 298 | 374 | 156 | 533 | 133 |
N.S. |
1 | 1.15 | 1.33 | 1.23 | 1.73 | 2.10 | 2.63 | 1.10 | 3.75 | 0.94 |
time (sec) |
N/A | 0.977 | 1.239 | 0.257 | 0.121 | 0.139 | 15.445 | 0.538 | 0.193 | 4.084 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 93 | 118 | 169 | 153 | 214 | 140 | 156 | 117 | 435 | 139 |
N.S. |
1 | 1.27 | 1.82 | 1.65 | 2.30 | 1.51 | 1.68 | 1.26 | 4.68 | 1.49 |
time (sec) |
N/A | 0.588 | 0.834 | 0.229 | 0.134 | 0.089 | 1.678 | 0.486 | 0.200 | 2.331 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 75 | 100 | 74 | 139 | 180 | 125 | 143 | 98 | 438 | 135 |
N.S. |
1 | 1.33 | 0.99 | 1.85 | 2.40 | 1.67 | 1.91 | 1.31 | 5.84 | 1.80 |
time (sec) |
N/A | 0.514 | 0.562 | 0.219 | 0.246 | 0.085 | 1.537 | 0.448 | 0.195 | 2.255 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 202 | 198 | 223 | 358 | 0 | 329 | 510 | 249 | 71 | 1334 |
N.S. |
1 | 0.98 | 1.10 | 1.77 | 0.00 | 1.63 | 2.52 | 1.23 | 0.35 | 6.60 |
time (sec) |
N/A | 0.863 | 3.460 | 0.376 | 0.000 | 0.091 | 13.779 | 0.540 | 0.206 | 6.087 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | A | A | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 271 | 278 | 276 | 572 | 0 | 505 | 966 | 383 | 113 | 1984 |
N.S. |
1 | 1.03 | 1.02 | 2.11 | 0.00 | 1.86 | 3.56 | 1.41 | 0.42 | 7.32 |
time (sec) |
N/A | 1.298 | 2.142 | 0.519 | 0.000 | 0.101 | 29.107 | 0.546 | 0.257 | 7.589 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | A | A | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 357 | 387 | 359 | 830 | 0 | 600 | 1792 | 507 | 154 | 2653 |
N.S. |
1 | 1.08 | 1.01 | 2.32 | 0.00 | 1.68 | 5.02 | 1.42 | 0.43 | 7.43 |
time (sec) |
N/A | 1.874 | 2.303 | 0.837 | 0.000 | 0.163 | 65.273 | 0.641 | 0.255 | 8.823 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | B | B | B | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 134 | 175 | 283 | 239 | 403 | 305 | 377 | 199 | 1041 | 314 |
N.S. |
1 | 1.31 | 2.11 | 1.78 | 3.01 | 2.28 | 2.81 | 1.49 | 7.77 | 2.34 |
time (sec) |
N/A | 0.800 | 1.708 | 0.311 | 0.225 | 0.082 | 3.759 | 0.599 | 0.203 | 2.708 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | B | B | B | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 125 | 170 | 262 | 216 | 380 | 310 | 391 | 179 | 1007 | 297 |
N.S. |
1 | 1.36 | 2.10 | 1.73 | 3.04 | 2.48 | 3.13 | 1.43 | 8.06 | 2.38 |
time (sec) |
N/A | 0.809 | 2.164 | 0.317 | 0.145 | 0.118 | 3.790 | 0.621 | 0.206 | 2.544 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | B | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 104 | 149 | 89 | 200 | 325 | 272 | 354 | 144 | 976 | 281 |
N.S. |
1 | 1.43 | 0.86 | 1.92 | 3.12 | 2.62 | 3.40 | 1.38 | 9.38 | 2.70 |
time (sec) |
N/A | 0.734 | 1.188 | 0.290 | 0.140 | 0.112 | 3.788 | 0.542 | 0.191 | 2.464 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | A | A | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 273 | 274 | 280 | 619 | 0 | 709 | 821 | 384 | 104 | 1910 |
N.S. |
1 | 1.00 | 1.03 | 2.27 | 0.00 | 2.60 | 3.01 | 1.41 | 0.38 | 7.00 |
time (sec) |
N/A | 1.235 | 3.331 | 0.549 | 0.000 | 0.114 | 49.552 | 0.613 | 0.224 | 7.184 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | A | A | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 354 | 365 | 336 | 834 | 0 | 907 | 1583 | 505 | 162 | 2640 |
N.S. |
1 | 1.03 | 0.95 | 2.36 | 0.00 | 2.56 | 4.47 | 1.43 | 0.46 | 7.46 |
time (sec) |
N/A | 1.692 | 4.616 | 0.858 | 0.000 | 0.113 | 91.616 | 0.606 | 0.217 | 8.839 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F(-1) | A | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 448 | 489 | 418 | 1092 | 0 | 1139 | 0 | 658 | 220 | 3368 |
N.S. |
1 | 1.09 | 0.93 | 2.44 | 0.00 | 2.54 | 0.00 | 1.47 | 0.49 | 7.52 |
time (sec) |
N/A | 2.434 | 4.837 | 1.215 | 0.000 | 0.143 | 0.000 | 0.887 | 0.254 | 10.400 |