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 | B | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 49 | 53 | 117 | 0 | 0 | 0 | 0 | 0 | 15 | 0 |
N.S. |
1 | 1.08 | 2.39 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.31 | 0.00 |
time (sec) |
N/A | 0.207 | 0.208 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.193 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F(-2) | A | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 116 | 123 | 68 | 319 | 0 | 377 | 0 | 0 | 80 | 144 |
N.S. |
1 | 1.06 | 0.59 | 2.75 | 0.00 | 3.25 | 0.00 | 0.00 | 0.69 | 1.24 |
time (sec) |
N/A | 0.629 | 0.144 | 0.316 | 0.000 | 0.090 | 0.000 | 0.000 | 0.169 | 10.973 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F(-2) | B | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 94 | 101 | 67 | 303 | 0 | 334 | 0 | 0 | 59 | 98 |
N.S. |
1 | 1.07 | 0.71 | 3.22 | 0.00 | 3.55 | 0.00 | 0.00 | 0.63 | 1.04 |
time (sec) |
N/A | 0.446 | 0.067 | 0.259 | 0.000 | 0.115 | 0.000 | 0.000 | 0.169 | 10.089 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F(-2) | A | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 71 | 74 | 154 | 287 | 0 | 236 | 0 | 0 | 49 | 128 |
N.S. |
1 | 1.04 | 2.17 | 4.04 | 0.00 | 3.32 | 0.00 | 0.00 | 0.69 | 1.80 |
time (sec) |
N/A | 0.344 | 0.176 | 0.256 | 0.000 | 0.092 | 0.000 | 0.000 | 0.165 | 9.451 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F(-2) | B | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 49 | 53 | 165 | 273 | 0 | 172 | 0 | 0 | 35 | 65 |
N.S. |
1 | 1.08 | 3.37 | 5.57 | 0.00 | 3.51 | 0.00 | 0.00 | 0.71 | 1.33 |
time (sec) |
N/A | 0.240 | 0.241 | 0.334 | 0.000 | 0.084 | 0.000 | 0.000 | 0.166 | 9.374 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F(-2) | B | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 75 | 78 | 191 | 294 | 0 | 321 | 0 | 0 | 44 | 84 |
N.S. |
1 | 1.04 | 2.55 | 3.92 | 0.00 | 4.28 | 0.00 | 0.00 | 0.59 | 1.12 |
time (sec) |
N/A | 0.350 | 0.173 | 0.246 | 0.000 | 0.092 | 0.000 | 0.000 | 0.180 | 9.660 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F(-2) | B | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 99 | 108 | 203 | 309 | 0 | 358 | 0 | 0 | 44 | 103 |
N.S. |
1 | 1.09 | 2.05 | 3.12 | 0.00 | 3.62 | 0.00 | 0.00 | 0.44 | 1.04 |
time (sec) |
N/A | 0.527 | 0.292 | 0.270 | 0.000 | 0.090 | 0.000 | 0.000 | 0.170 | 10.415 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | F | F | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 216 | 261 | 187 | 187 | 0 | 559 | 0 | 0 | 78 | 125 |
N.S. |
1 | 1.21 | 0.87 | 0.87 | 0.00 | 2.59 | 0.00 | 0.00 | 0.36 | 0.58 |
time (sec) |
N/A | 0.762 | 0.827 | 0.372 | 0.000 | 0.094 | 0.000 | 0.000 | 0.178 | 11.031 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | F | F | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 193 | 231 | 112 | 172 | 0 | 451 | 0 | 0 | 50 | 104 |
N.S. |
1 | 1.20 | 0.58 | 0.89 | 0.00 | 2.34 | 0.00 | 0.00 | 0.26 | 0.54 |
time (sec) |
N/A | 0.663 | 0.629 | 0.263 | 0.000 | 0.101 | 0.000 | 0.000 | 0.190 | 10.005 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | F | F | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 190 | 235 | 175 | 170 | 0 | 406 | 0 | 0 | 56 | 104 |
N.S. |
1 | 1.24 | 0.92 | 0.89 | 0.00 | 2.14 | 0.00 | 0.00 | 0.29 | 0.55 |
time (sec) |
N/A | 0.645 | 0.366 | 0.268 | 0.000 | 0.098 | 0.000 | 0.000 | 0.208 | 9.418 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | F | F | B |
verified |
N/A | No | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 168 | 200 | 237 | 155 | 0 | 315 | 0 | 0 | 34 | 86 |
N.S. |
1 | 1.19 | 1.41 | 0.92 | 0.00 | 1.88 | 0.00 | 0.00 | 0.20 | 0.51 |
time (sec) |
N/A | 0.543 | 5.402 | 0.299 | 0.000 | 0.086 | 0.000 | 0.000 | 0.169 | 9.093 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | F | F | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 169 | 206 | 184 | 159 | 0 | 408 | 0 | 0 | 57 | 86 |
N.S. |
1 | 1.22 | 1.09 | 0.94 | 0.00 | 2.41 | 0.00 | 0.00 | 0.34 | 0.51 |
time (sec) |
N/A | 0.537 | 0.314 | 0.261 | 0.000 | 0.086 | 0.000 | 0.000 | 0.193 | 9.750 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | F(-2) | B | F | F | F | B |
verified |
N/A | No | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 194 | 231 | 400 | 174 | 0 | 430 | 0 | 0 | 66 | 99 |
N.S. |
1 | 1.19 | 2.06 | 0.90 | 0.00 | 2.22 | 0.00 | 0.00 | 0.34 | 0.51 |
time (sec) |
N/A | 0.636 | 1.957 | 0.290 | 0.000 | 0.091 | 0.000 | 0.000 | 0.167 | 9.099 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F(-1) | A | F(-2) | B | F | F(-1) | F | B |
verified |
N/A | No | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 195 | 239 | 0 | 174 | 0 | 534 | 0 | 0 | 66 | 99 |
N.S. |
1 | 1.23 | 0.00 | 0.89 | 0.00 | 2.74 | 0.00 | 0.00 | 0.34 | 0.51 |
time (sec) |
N/A | 0.651 | 0.000 | 0.280 | 0.000 | 0.091 | 0.000 | 0.000 | 0.191 | 10.092 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | F(-2) | A | F | F | F | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 186 | 203 | 401 | 354 | 0 | 535 | 0 | 0 | 120 | 177 |
N.S. |
1 | 1.09 | 2.16 | 1.90 | 0.00 | 2.88 | 0.00 | 0.00 | 0.65 | 0.95 |
time (sec) |
N/A | 1.140 | 4.913 | 0.638 | 0.000 | 0.092 | 0.000 | 0.000 | 0.177 | 11.930 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | F(-2) | A | F | F | F | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 160 | 179 | 380 | 339 | 0 | 487 | 0 | 0 | 101 | 143 |
N.S. |
1 | 1.12 | 2.38 | 2.12 | 0.00 | 3.04 | 0.00 | 0.00 | 0.63 | 0.89 |
time (sec) |
N/A | 0.874 | 2.933 | 0.298 | 0.000 | 0.103 | 0.000 | 0.000 | 0.175 | 10.398 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | F(-2) | A | F | F | F | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 138 | 153 | 360 | 323 | 0 | 366 | 0 | 0 | 91 | 136 |
N.S. |
1 | 1.11 | 2.61 | 2.34 | 0.00 | 2.65 | 0.00 | 0.00 | 0.66 | 0.99 |
time (sec) |
N/A | 0.707 | 1.879 | 0.306 | 0.000 | 0.095 | 0.000 | 0.000 | 0.168 | 10.448 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | F(-2) | A | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 117 | 127 | 342 | 309 | 0 | 349 | 0 | 0 | 75 | 100 |
N.S. |
1 | 1.09 | 2.92 | 2.64 | 0.00 | 2.98 | 0.00 | 0.00 | 0.64 | 0.85 |
time (sec) |
N/A | 0.554 | 0.890 | 0.329 | 0.000 | 0.102 | 0.000 | 0.000 | 0.198 | 9.739 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | F(-2) | A | F | F | F | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 114 | 128 | 357 | 305 | 0 | 372 | 0 | 0 | 75 | 119 |
N.S. |
1 | 1.12 | 3.13 | 2.68 | 0.00 | 3.26 | 0.00 | 0.00 | 0.66 | 1.04 |
time (sec) |
N/A | 0.560 | 1.712 | 0.299 | 0.000 | 0.090 | 0.000 | 0.000 | 0.169 | 9.229 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | F(-2) | A | F | F(-1) | F | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 117 | 132 | 403 | 303 | 0 | 378 | 0 | 0 | 77 | 101 |
N.S. |
1 | 1.13 | 3.44 | 2.59 | 0.00 | 3.23 | 0.00 | 0.00 | 0.66 | 0.86 |
time (sec) |
N/A | 0.623 | 3.834 | 0.322 | 0.000 | 0.126 | 0.000 | 0.000 | 0.167 | 9.650 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | F(-2) | A | F | F(-1) | F | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 141 | 162 | 415 | 323 | 0 | 485 | 0 | 0 | 86 | 126 |
N.S. |
1 | 1.15 | 2.94 | 2.29 | 0.00 | 3.44 | 0.00 | 0.00 | 0.61 | 0.89 |
time (sec) |
N/A | 0.796 | 3.454 | 0.309 | 0.000 | 0.118 | 0.000 | 0.000 | 0.165 | 10.418 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | F(-2) | A | F | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 165 | 194 | 625 | 338 | 0 | 514 | 0 | 0 | 86 | 129 |
N.S. |
1 | 1.18 | 3.79 | 2.05 | 0.00 | 3.12 | 0.00 | 0.00 | 0.52 | 0.78 |
time (sec) |
N/A | 0.925 | 6.160 | 0.317 | 0.000 | 0.097 | 0.000 | 0.000 | 0.182 | 10.284 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | F(-2) | A | F | F | F | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 111 | 115 | 296 | 312 | 0 | 408 | 0 | 0 | 37 | 123 |
N.S. |
1 | 1.04 | 2.67 | 2.81 | 0.00 | 3.68 | 0.00 | 0.00 | 0.33 | 1.11 |
time (sec) |
N/A | 0.954 | 0.534 | 0.307 | 0.000 | 0.095 | 0.000 | 0.000 | 0.173 | 8.888 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | F(-2) | B | F | F | F | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 87 | 87 | 280 | 298 | 0 | 342 | 0 | 0 | 33 | 79 |
N.S. |
1 | 1.00 | 3.22 | 3.43 | 0.00 | 3.93 | 0.00 | 0.00 | 0.38 | 0.91 |
time (sec) |
N/A | 0.657 | 0.292 | 0.256 | 0.000 | 0.092 | 0.000 | 0.000 | 0.161 | 9.457 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | F(-2) | B | F | F | F | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 87 | 85 | 283 | 304 | 0 | 338 | 0 | 0 | 26 | 102 |
N.S. |
1 | 0.98 | 3.25 | 3.49 | 0.00 | 3.89 | 0.00 | 0.00 | 0.30 | 1.17 |
time (sec) |
N/A | 0.639 | 0.231 | 0.244 | 0.000 | 0.092 | 0.000 | 0.000 | 0.163 | 8.931 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | F(-2) | B | F | F | F | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 83 | 81 | 283 | 304 | 0 | 345 | 0 | 0 | 36 | 79 |
N.S. |
1 | 0.98 | 3.41 | 3.66 | 0.00 | 4.16 | 0.00 | 0.00 | 0.43 | 0.95 |
time (sec) |
N/A | 0.611 | 0.258 | 0.256 | 0.000 | 0.090 | 0.000 | 0.000 | 0.164 | 8.890 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F(-2) | B | F | F | F | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 111 | 118 | 229 | 319 | 0 | 496 | 0 | 0 | 38 | 123 |
N.S. |
1 | 1.06 | 2.06 | 2.87 | 0.00 | 4.47 | 0.00 | 0.00 | 0.34 | 1.11 |
time (sec) |
N/A | 0.994 | 0.432 | 0.247 | 0.000 | 0.091 | 0.000 | 0.000 | 0.162 | 9.611 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F(-2) | B | F | F | F | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 135 | 146 | 86 | 333 | 0 | 524 | 0 | 0 | 38 | 132 |
N.S. |
1 | 1.08 | 0.64 | 2.47 | 0.00 | 3.88 | 0.00 | 0.00 | 0.28 | 0.98 |
time (sec) |
N/A | 1.354 | 0.326 | 0.246 | 0.000 | 0.104 | 0.000 | 0.000 | 0.159 | 10.443 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | B | F | F | F | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 225 | 254 | 288 | 191 | 0 | 571 | 0 | 0 | 47 | 375 |
N.S. |
1 | 1.13 | 1.28 | 0.85 | 0.00 | 2.54 | 0.00 | 0.00 | 0.21 | 1.67 |
time (sec) |
N/A | 1.315 | 1.382 | 0.573 | 0.000 | 0.100 | 0.000 | 0.000 | 0.161 | 9.757 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | B | F | F | F | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 223 | 244 | 155 | 197 | 0 | 539 | 0 | 0 | 43 | 376 |
N.S. |
1 | 1.09 | 0.70 | 0.88 | 0.00 | 2.42 | 0.00 | 0.00 | 0.19 | 1.69 |
time (sec) |
N/A | 1.245 | 0.631 | 0.261 | 0.000 | 0.109 | 0.000 | 0.000 | 0.164 | 9.557 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | F | F | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 222 | 249 | 221 | 200 | 0 | 518 | 0 | 0 | 36 | 366 |
N.S. |
1 | 1.12 | 1.00 | 0.90 | 0.00 | 2.33 | 0.00 | 0.00 | 0.16 | 1.65 |
time (sec) |
N/A | 1.207 | 1.193 | 0.254 | 0.000 | 0.130 | 0.000 | 0.000 | 0.161 | 9.529 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | F | F | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 225 | 249 | 131 | 197 | 0 | 519 | 0 | 0 | 46 | 366 |
N.S. |
1 | 1.11 | 0.58 | 0.88 | 0.00 | 2.31 | 0.00 | 0.00 | 0.20 | 1.63 |
time (sec) |
N/A | 1.300 | 0.882 | 0.253 | 0.000 | 0.105 | 0.000 | 0.000 | 0.164 | 9.472 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | B | F | F | F | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 250 | 288 | 227 | 212 | 0 | 540 | 0 | 0 | 48 | 414 |
N.S. |
1 | 1.15 | 0.91 | 0.85 | 0.00 | 2.16 | 0.00 | 0.00 | 0.19 | 1.66 |
time (sec) |
N/A | 1.648 | 0.556 | 0.259 | 0.000 | 0.101 | 0.000 | 0.000 | 0.164 | 9.805 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | B | F | F | F | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 275 | 316 | 84 | 227 | 0 | 724 | 0 | 0 | 48 | 425 |
N.S. |
1 | 1.15 | 0.31 | 0.83 | 0.00 | 2.63 | 0.00 | 0.00 | 0.17 | 1.55 |
time (sec) |
N/A | 2.061 | 0.529 | 0.256 | 0.000 | 0.124 | 0.000 | 0.000 | 0.169 | 9.713 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F(-2) | A | F | F | F | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 164 | 179 | 390 | 349 | 0 | 566 | 0 | 0 | 57 | 154 |
N.S. |
1 | 1.09 | 2.38 | 2.13 | 0.00 | 3.45 | 0.00 | 0.00 | 0.35 | 0.94 |
time (sec) |
N/A | 1.261 | 2.107 | 1.489 | 0.000 | 0.100 | 0.000 | 0.000 | 0.173 | 9.811 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F(-2) | A | F | F | F | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 164 | 178 | 365 | 349 | 0 | 534 | 0 | 0 | 53 | 178 |
N.S. |
1 | 1.09 | 2.23 | 2.13 | 0.00 | 3.26 | 0.00 | 0.00 | 0.32 | 1.09 |
time (sec) |
N/A | 1.332 | 2.255 | 0.303 | 0.000 | 0.097 | 0.000 | 0.000 | 0.166 | 9.718 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F(-2) | A | F | F | F | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 161 | 175 | 315 | 349 | 0 | 522 | 0 | 0 | 46 | 151 |
N.S. |
1 | 1.09 | 1.96 | 2.17 | 0.00 | 3.24 | 0.00 | 0.00 | 0.29 | 0.94 |
time (sec) |
N/A | 1.237 | 4.392 | 0.305 | 0.000 | 0.120 | 0.000 | 0.000 | 0.163 | 9.405 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F(-2) | A | F | F | F | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 165 | 180 | 339 | 349 | 0 | 528 | 0 | 0 | 56 | 173 |
N.S. |
1 | 1.09 | 2.05 | 2.12 | 0.00 | 3.20 | 0.00 | 0.00 | 0.34 | 1.05 |
time (sec) |
N/A | 1.332 | 1.716 | 0.304 | 0.000 | 0.100 | 0.000 | 0.000 | 0.166 | 9.551 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F(-2) | B | F | F | F | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 189 | 209 | 325 | 364 | 0 | 721 | 0 | 0 | 58 | 175 |
N.S. |
1 | 1.11 | 1.72 | 1.93 | 0.00 | 3.81 | 0.00 | 0.00 | 0.31 | 0.93 |
time (sec) |
N/A | 1.727 | 0.557 | 0.296 | 0.000 | 0.105 | 0.000 | 0.000 | 0.174 | 9.839 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F(-2) | A | F | F(-1) | F | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 215 | 244 | 124 | 379 | 0 | 742 | 0 | 0 | 58 | 193 |
N.S. |
1 | 1.13 | 0.58 | 1.76 | 0.00 | 3.45 | 0.00 | 0.00 | 0.27 | 0.90 |
time (sec) |
N/A | 2.133 | 0.582 | 0.299 | 0.000 | 0.107 | 0.000 | 0.000 | 0.168 | 10.532 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 173 | 233 | 69 | 356 | 0 | 344 | 0 | 0 | 12 | 119 |
N.S. |
1 | 1.35 | 0.40 | 2.06 | 0.00 | 1.99 | 0.00 | 0.00 | 0.07 | 0.69 |
time (sec) |
N/A | 0.566 | 0.303 | 0.297 | 0.000 | 0.084 | 0.000 | 0.000 | 0.175 | 9.217 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | B | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 135 | 153 | 61 | 174 | 0 | 304 | 0 | 0 | 10 | 210 |
N.S. |
1 | 1.13 | 0.45 | 1.29 | 0.00 | 2.25 | 0.00 | 0.00 | 0.07 | 1.56 |
time (sec) |
N/A | 0.552 | 0.179 | 0.139 | 0.000 | 0.097 | 0.000 | 0.000 | 0.158 | 9.647 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-1) | B | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 139 | 168 | 75 | 197 | 0 | 325 | 0 | 0 | 25 | 254 |
N.S. |
1 | 1.21 | 0.54 | 1.42 | 0.00 | 2.34 | 0.00 | 0.00 | 0.18 | 1.83 |
time (sec) |
N/A | 0.637 | 0.332 | 0.151 | 0.000 | 0.084 | 0.000 | 0.000 | 0.163 | 10.080 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 172 | 255 | 67 | 452 | 0 | 313 | 0 | 0 | 23 | 254 |
N.S. |
1 | 1.48 | 0.39 | 2.63 | 0.00 | 1.82 | 0.00 | 0.00 | 0.13 | 1.48 |
time (sec) |
N/A | 0.613 | 0.245 | 0.131 | 0.000 | 0.091 | 0.000 | 0.000 | 0.163 | 9.458 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 168 | 243 | 67 | 442 | 0 | 277 | 0 | 0 | 18 | 238 |
N.S. |
1 | 1.45 | 0.40 | 2.63 | 0.00 | 1.65 | 0.00 | 0.00 | 0.11 | 1.42 |
time (sec) |
N/A | 0.513 | 0.263 | 0.156 | 0.000 | 0.106 | 0.000 | 0.000 | 0.160 | 8.838 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 121 | 143 | 51 | 181 | 0 | 256 | 0 | 0 | 16 | 230 |
N.S. |
1 | 1.18 | 0.42 | 1.50 | 0.00 | 2.12 | 0.00 | 0.00 | 0.13 | 1.90 |
time (sec) |
N/A | 0.404 | 0.146 | 0.240 | 0.000 | 0.082 | 0.000 | 0.000 | 0.160 | 8.824 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | B | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 139 | 156 | 62 | 173 | 0 | 363 | 0 | 0 | 24 | 208 |
N.S. |
1 | 1.12 | 0.45 | 1.24 | 0.00 | 2.61 | 0.00 | 0.00 | 0.17 | 1.50 |
time (sec) |
N/A | 0.513 | 0.262 | 0.143 | 0.000 | 0.089 | 0.000 | 0.000 | 0.160 | 8.951 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 178 | 230 | 71 | 356 | 0 | 367 | 0 | 0 | 22 | 121 |
N.S. |
1 | 1.29 | 0.40 | 2.00 | 0.00 | 2.06 | 0.00 | 0.00 | 0.12 | 0.68 |
time (sec) |
N/A | 0.514 | 0.452 | 0.138 | 0.000 | 0.091 | 0.000 | 0.000 | 0.158 | 9.110 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | B | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 143 | 170 | 62 | 197 | 0 | 325 | 0 | 0 | 30 | 242 |
N.S. |
1 | 1.19 | 0.43 | 1.38 | 0.00 | 2.27 | 0.00 | 0.00 | 0.21 | 1.69 |
time (sec) |
N/A | 0.602 | 0.309 | 0.140 | 0.000 | 0.089 | 0.000 | 0.000 | 0.158 | 9.834 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 170 | 242 | 69 | 444 | 0 | 317 | 0 | 0 | 28 | 238 |
N.S. |
1 | 1.42 | 0.41 | 2.61 | 0.00 | 1.86 | 0.00 | 0.00 | 0.16 | 1.40 |
time (sec) |
N/A | 0.510 | 0.250 | 0.131 | 0.000 | 0.081 | 0.000 | 0.000 | 0.155 | 9.560 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F(-2) | B | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 186 | 240 | 68 | 303 | 0 | 843 | 0 | 0 | 61 | 153 |
N.S. |
1 | 1.29 | 0.37 | 1.63 | 0.00 | 4.53 | 0.00 | 0.00 | 0.33 | 0.82 |
time (sec) |
N/A | 0.648 | 0.119 | 0.248 | 0.000 | 0.098 | 0.000 | 0.000 | 0.174 | 9.963 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F(-2) | B | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 167 | 217 | 155 | 287 | 0 | 730 | 0 | 0 | 51 | 128 |
N.S. |
1 | 1.30 | 0.93 | 1.72 | 0.00 | 4.37 | 0.00 | 0.00 | 0.31 | 0.77 |
time (sec) |
N/A | 0.501 | 0.192 | 0.248 | 0.000 | 0.095 | 0.000 | 0.000 | 0.165 | 9.224 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F(-2) | B | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 148 | 197 | 166 | 273 | 0 | 721 | 0 | 0 | 38 | 118 |
N.S. |
1 | 1.33 | 1.12 | 1.84 | 0.00 | 4.87 | 0.00 | 0.00 | 0.26 | 0.80 |
time (sec) |
N/A | 0.410 | 0.132 | 0.306 | 0.000 | 0.108 | 0.000 | 0.000 | 0.163 | 9.139 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F(-2) | B | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 171 | 222 | 194 | 295 | 0 | 890 | 0 | 0 | 47 | 137 |
N.S. |
1 | 1.30 | 1.13 | 1.73 | 0.00 | 5.20 | 0.00 | 0.00 | 0.27 | 0.80 |
time (sec) |
N/A | 0.528 | 0.221 | 0.263 | 0.000 | 0.100 | 0.000 | 0.000 | 0.165 | 9.186 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | B | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 191 | 244 | 196 | 311 | 0 | 905 | 0 | 0 | 47 | 158 |
N.S. |
1 | 1.28 | 1.03 | 1.63 | 0.00 | 4.74 | 0.00 | 0.00 | 0.25 | 0.83 |
time (sec) |
N/A | 0.671 | 0.471 | 0.250 | 0.000 | 0.100 | 0.000 | 0.000 | 0.163 | 9.823 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | B | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 248 | 292 | 224 | 360 | 0 | 1313 | 0 | 0 | 124 | 1274 |
N.S. |
1 | 1.18 | 0.90 | 1.45 | 0.00 | 5.29 | 0.00 | 0.00 | 0.50 | 5.14 |
time (sec) |
N/A | 0.909 | 1.286 | 0.278 | 0.000 | 0.117 | 0.000 | 0.000 | 0.184 | 11.454 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | B | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 219 | 261 | 220 | 321 | 0 | 1230 | 0 | 0 | 78 | 1157 |
N.S. |
1 | 1.19 | 1.00 | 1.47 | 0.00 | 5.62 | 0.00 | 0.00 | 0.36 | 5.28 |
time (sec) |
N/A | 0.703 | 0.360 | 0.282 | 0.000 | 0.107 | 0.000 | 0.000 | 0.166 | 10.089 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | B | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 199 | 239 | 192 | 306 | 0 | 1183 | 0 | 0 | 83 | 1234 |
N.S. |
1 | 1.20 | 0.96 | 1.54 | 0.00 | 5.94 | 0.00 | 0.00 | 0.42 | 6.20 |
time (sec) |
N/A | 0.588 | 0.559 | 0.304 | 0.000 | 0.103 | 0.000 | 0.000 | 0.166 | 10.196 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | B | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 199 | 242 | 188 | 301 | 0 | 1298 | 0 | 0 | 64 | 1196 |
N.S. |
1 | 1.22 | 0.94 | 1.51 | 0.00 | 6.52 | 0.00 | 0.00 | 0.32 | 6.01 |
time (sec) |
N/A | 0.605 | 0.490 | 0.289 | 0.000 | 0.132 | 0.000 | 0.000 | 0.162 | 10.086 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | B | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 222 | 265 | 82 | 326 | 0 | 1318 | 0 | 0 | 73 | 1214 |
N.S. |
1 | 1.19 | 0.37 | 1.47 | 0.00 | 5.94 | 0.00 | 0.00 | 0.33 | 5.47 |
time (sec) |
N/A | 0.759 | 0.194 | 0.294 | 0.000 | 0.123 | 0.000 | 0.000 | 0.166 | 10.396 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | B | F | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 253 | 301 | 85 | 347 | 0 | 1436 | 0 | 0 | 73 | 1227 |
N.S. |
1 | 1.19 | 0.34 | 1.37 | 0.00 | 5.68 | 0.00 | 0.00 | 0.29 | 4.85 |
time (sec) |
N/A | 0.995 | 0.225 | 0.283 | 0.000 | 0.150 | 0.000 | 0.000 | 0.172 | 10.981 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | B | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 302 | 351 | 251 | 410 | 0 | 1795 | 0 | 0 | 153 | 2317 |
N.S. |
1 | 1.16 | 0.83 | 1.36 | 0.00 | 5.94 | 0.00 | 0.00 | 0.51 | 7.67 |
time (sec) |
N/A | 1.302 | 1.766 | 0.306 | 0.000 | 0.161 | 0.000 | 0.000 | 0.173 | 14.301 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | B | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 270 | 317 | 247 | 371 | 0 | 1643 | 0 | 0 | 142 | 2071 |
N.S. |
1 | 1.17 | 0.91 | 1.37 | 0.00 | 6.09 | 0.00 | 0.00 | 0.53 | 7.67 |
time (sec) |
N/A | 1.062 | 1.529 | 0.297 | 0.000 | 0.135 | 0.000 | 0.000 | 0.181 | 11.291 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | B | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 244 | 285 | 215 | 337 | 0 | 1633 | 0 | 0 | 110 | 1896 |
N.S. |
1 | 1.17 | 0.88 | 1.38 | 0.00 | 6.69 | 0.00 | 0.00 | 0.45 | 7.77 |
time (sec) |
N/A | 0.834 | 0.605 | 0.343 | 0.000 | 0.176 | 0.000 | 0.000 | 0.171 | 9.884 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | B | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 242 | 287 | 193 | 332 | 0 | 1679 | 0 | 0 | 110 | 1951 |
N.S. |
1 | 1.19 | 0.80 | 1.37 | 0.00 | 6.94 | 0.00 | 0.00 | 0.45 | 8.06 |
time (sec) |
N/A | 0.867 | 2.059 | 0.303 | 0.000 | 0.181 | 0.000 | 0.000 | 0.168 | 9.645 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | B | F | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 243 | 286 | 104 | 331 | 0 | 1692 | 0 | 0 | 90 | 1946 |
N.S. |
1 | 1.18 | 0.43 | 1.36 | 0.00 | 6.96 | 0.00 | 0.00 | 0.37 | 8.01 |
time (sec) |
N/A | 0.883 | 0.248 | 0.318 | 0.000 | 0.184 | 0.000 | 0.000 | 0.165 | 10.061 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | B | F | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 271 | 324 | 108 | 359 | 0 | 1804 | 0 | 0 | 99 | 1969 |
N.S. |
1 | 1.20 | 0.40 | 1.32 | 0.00 | 6.66 | 0.00 | 0.00 | 0.37 | 7.27 |
time (sec) |
N/A | 1.105 | 0.401 | 0.301 | 0.000 | 0.177 | 0.000 | 0.000 | 0.170 | 11.488 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | B | F | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 308 | 365 | 116 | 388 | 0 | 1839 | 0 | 0 | 99 | 1992 |
N.S. |
1 | 1.19 | 0.38 | 1.26 | 0.00 | 5.97 | 0.00 | 0.00 | 0.32 | 6.47 |
time (sec) |
N/A | 1.361 | 0.450 | 0.301 | 0.000 | 0.219 | 0.000 | 0.000 | 0.172 | 13.858 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | B | F | F | F | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 256 | 292 | 286 | 347 | 0 | 3267 | 0 | 0 | 36 | 5579 |
N.S. |
1 | 1.14 | 1.12 | 1.36 | 0.00 | 12.76 | 0.00 | 0.00 | 0.14 | 21.79 |
time (sec) |
N/A | 1.294 | 0.565 | 0.299 | 0.000 | 0.177 | 0.000 | 0.000 | 0.163 | 10.323 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | B | F | F | F | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 234 | 262 | 249 | 326 | 0 | 3137 | 0 | 0 | 32 | 5129 |
N.S. |
1 | 1.12 | 1.06 | 1.39 | 0.00 | 13.41 | 0.00 | 0.00 | 0.14 | 21.92 |
time (sec) |
N/A | 0.953 | 0.300 | 0.251 | 0.000 | 0.154 | 0.000 | 0.000 | 0.161 | 10.352 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | B | F | F | F | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 232 | 260 | 226 | 332 | 0 | 3088 | 0 | 0 | 25 | 4808 |
N.S. |
1 | 1.12 | 0.97 | 1.43 | 0.00 | 13.31 | 0.00 | 0.00 | 0.11 | 20.72 |
time (sec) |
N/A | 0.931 | 0.154 | 0.241 | 0.000 | 0.165 | 0.000 | 0.000 | 0.160 | 10.139 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | B | F | F | F | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 235 | 259 | 245 | 332 | 0 | 3135 | 0 | 0 | 37 | 4871 |
N.S. |
1 | 1.10 | 1.04 | 1.41 | 0.00 | 13.34 | 0.00 | 0.00 | 0.16 | 20.73 |
time (sec) |
N/A | 0.915 | 0.174 | 0.244 | 0.000 | 0.159 | 0.000 | 0.000 | 0.168 | 10.585 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | B | F | F | F | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 256 | 295 | 198 | 354 | 0 | 3612 | 0 | 0 | 39 | 4899 |
N.S. |
1 | 1.15 | 0.77 | 1.38 | 0.00 | 14.11 | 0.00 | 0.00 | 0.15 | 19.14 |
time (sec) |
N/A | 1.259 | 0.259 | 0.238 | 0.000 | 0.188 | 0.000 | 0.000 | 0.164 | 10.676 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | B | F | F | F | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 283 | 329 | 109 | 371 | 0 | 3717 | 0 | 0 | 39 | 6042 |
N.S. |
1 | 1.16 | 0.39 | 1.31 | 0.00 | 13.13 | 0.00 | 0.00 | 0.14 | 21.35 |
time (sec) |
N/A | 1.657 | 0.172 | 0.246 | 0.000 | 0.244 | 0.000 | 0.000 | 0.167 | 11.664 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | B | F(-1) | F | F | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 360 | 397 | 461 | 409 | 0 | 6403 | 0 | 0 | 52 | 13244 |
N.S. |
1 | 1.10 | 1.28 | 1.14 | 0.00 | 17.79 | 0.00 | 0.00 | 0.14 | 36.79 |
time (sec) |
N/A | 1.979 | 6.101 | 0.536 | 0.000 | 0.497 | 0.000 | 0.000 | 0.184 | 12.942 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | B | F | F | F | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 316 | 353 | 390 | 387 | 0 | 6258 | 0 | 0 | 52 | 12617 |
N.S. |
1 | 1.12 | 1.23 | 1.22 | 0.00 | 19.80 | 0.00 | 0.00 | 0.16 | 39.93 |
time (sec) |
N/A | 1.500 | 1.814 | 0.514 | 0.000 | 0.364 | 0.000 | 0.000 | 0.170 | 11.645 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | B | F | F | F | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 309 | 343 | 321 | 391 | 0 | 6150 | 0 | 0 | 48 | 11953 |
N.S. |
1 | 1.11 | 1.04 | 1.27 | 0.00 | 19.90 | 0.00 | 0.00 | 0.16 | 38.68 |
time (sec) |
N/A | 1.435 | 1.954 | 0.269 | 0.000 | 0.284 | 0.000 | 0.000 | 0.167 | 11.865 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | B | F | F | F | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 308 | 341 | 346 | 391 | 0 | 6104 | 0 | 0 | 41 | 11731 |
N.S. |
1 | 1.11 | 1.12 | 1.27 | 0.00 | 19.82 | 0.00 | 0.00 | 0.13 | 38.09 |
time (sec) |
N/A | 1.380 | 4.237 | 0.252 | 0.000 | 0.335 | 0.000 | 0.000 | 0.164 | 11.599 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | B | F | F | F | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 317 | 355 | 295 | 396 | 0 | 6223 | 0 | 0 | 53 | 9400 |
N.S. |
1 | 1.12 | 0.93 | 1.25 | 0.00 | 19.63 | 0.00 | 0.00 | 0.17 | 29.65 |
time (sec) |
N/A | 1.464 | 1.704 | 0.261 | 0.000 | 0.392 | 0.000 | 0.000 | 0.162 | 16.722 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | B | F | F(-1) | F | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 360 | 401 | 244 | 414 | 0 | 6494 | 0 | 0 | 55 | 15251 |
N.S. |
1 | 1.11 | 0.68 | 1.15 | 0.00 | 18.04 | 0.00 | 0.00 | 0.15 | 42.36 |
time (sec) |
N/A | 2.061 | 0.363 | 0.252 | 0.000 | 0.547 | 0.000 | 0.000 | 0.180 | 12.819 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | B | F(-1) | F | F | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 450 | 494 | 626 | 471 | 0 | 9101 | 0 | 0 | 68 | 20651 |
N.S. |
1 | 1.10 | 1.39 | 1.05 | 0.00 | 20.22 | 0.00 | 0.00 | 0.15 | 45.89 |
time (sec) |
N/A | 2.762 | 6.178 | 1.449 | 0.000 | 1.769 | 0.000 | 0.000 | 0.175 | 19.192 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | B | F(-1) | F | F | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 396 | 446 | 574 | 460 | 0 | 9029 | 0 | 0 | 68 | 20089 |
N.S. |
1 | 1.13 | 1.45 | 1.16 | 0.00 | 22.80 | 0.00 | 0.00 | 0.17 | 50.73 |
time (sec) |
N/A | 2.092 | 6.132 | 1.455 | 0.000 | 58.770 | 0.000 | 0.000 | 0.168 | 16.322 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | B | F(-1) | F | F | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 392 | 440 | 448 | 457 | 0 | 8955 | 0 | 0 | 68 | 19256 |
N.S. |
1 | 1.12 | 1.14 | 1.17 | 0.00 | 22.84 | 0.00 | 0.00 | 0.17 | 49.12 |
time (sec) |
N/A | 2.148 | 5.456 | 1.448 | 0.000 | 37.794 | 0.000 | 0.000 | 0.166 | 15.575 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | B | F | F | F | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 380 | 429 | 535 | 456 | 0 | 8891 | 0 | 0 | 64 | 19000 |
N.S. |
1 | 1.13 | 1.41 | 1.20 | 0.00 | 23.40 | 0.00 | 0.00 | 0.17 | 50.00 |
time (sec) |
N/A | 2.055 | 6.114 | 0.270 | 0.000 | 0.547 | 0.000 | 0.000 | 0.185 | 15.047 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | B | F | F | F | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 384 | 431 | 422 | 460 | 0 | 8853 | 0 | 0 | 57 | 19534 |
N.S. |
1 | 1.12 | 1.10 | 1.20 | 0.00 | 23.05 | 0.00 | 0.00 | 0.15 | 50.87 |
time (sec) |
N/A | 2.018 | 4.374 | 0.269 | 0.000 | 0.751 | 0.000 | 0.000 | 0.168 | 15.192 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | B | F | F | F | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 396 | 450 | 358 | 465 | 0 | 8967 | 0 | 0 | 69 | 20155 |
N.S. |
1 | 1.14 | 0.90 | 1.17 | 0.00 | 22.64 | 0.00 | 0.00 | 0.17 | 50.90 |
time (sec) |
N/A | 2.130 | 3.964 | 0.280 | 0.000 | 1.216 | 0.000 | 0.000 | 0.168 | 15.378 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | B | F | F(-1) | F | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 451 | 499 | 303 | 480 | 0 | 10284 | 0 | 0 | 71 | 21158 |
N.S. |
1 | 1.11 | 0.67 | 1.06 | 0.00 | 22.80 | 0.00 | 0.00 | 0.16 | 46.91 |
time (sec) |
N/A | 2.810 | 0.959 | 0.269 | 0.000 | 2.020 | 0.000 | 0.000 | 0.166 | 18.494 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 167 | 165 | 118 | 0 | 0 | 0 | 0 | 0 | 14 | 0 |
N.S. |
1 | 0.99 | 0.71 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 0.429 | 0.230 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.173 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F(-2) | F | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 195 | 214 | 0 | 0 | 0 | 0 | 0 | 0 | 25 | 0 |
N.S. |
1 | 1.10 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.13 | 0.00 |
time (sec) |
N/A | 0.545 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 200.025 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | F | F | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 45 | 35 | 45 | 734 | 0 | 159 | 0 | 0 | 61 | 1410 |
N.S. |
1 | 0.78 | 1.00 | 16.31 | 0.00 | 3.53 | 0.00 | 0.00 | 1.36 | 31.33 |
time (sec) |
N/A | 0.258 | 0.049 | 0.868 | 0.000 | 0.071 | 0.000 | 0.000 | 0.220 | 11.579 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | F | F | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 45 | 35 | 45 | 739 | 0 | 159 | 0 | 0 | 62 | 1410 |
N.S. |
1 | 0.78 | 1.00 | 16.42 | 0.00 | 3.53 | 0.00 | 0.00 | 1.38 | 31.33 |
time (sec) |
N/A | 0.258 | 0.297 | 0.471 | 0.000 | 0.112 | 0.000 | 0.000 | 0.204 | 10.406 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 59 | 59 | 67 | 63 | 89 | 79 | 524 | 95 | 1 | 155 |
N.S. |
1 | 1.00 | 1.14 | 1.07 | 1.51 | 1.34 | 8.88 | 1.61 | 0.02 | 2.63 |
time (sec) |
N/A | 0.365 | 0.106 | 0.212 | 0.108 | 0.105 | 0.515 | 0.126 | 0.192 | 10.002 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | B | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 111 | 122 | 144 | 147 | 185 | 340 | 3964 | 241 | 67 | 268 |
N.S. |
1 | 1.10 | 1.30 | 1.32 | 1.67 | 3.06 | 35.71 | 2.17 | 0.60 | 2.41 |
time (sec) |
N/A | 0.571 | 1.268 | 0.309 | 0.112 | 0.134 | 1.531 | 0.150 | 0.196 | 10.534 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | B | F(-2) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 175 | 197 | 202 | 216 | 337 | 549 | 0 | 412 | 301 | 481 |
N.S. |
1 | 1.13 | 1.15 | 1.23 | 1.93 | 3.14 | 0.00 | 2.35 | 1.72 | 2.75 |
time (sec) |
N/A | 0.861 | 3.123 | 0.553 | 0.112 | 0.113 | 0.000 | 0.208 | 0.197 | 12.140 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | F | B | F | F | F | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 188 | 171 | 379 | 2378 | 0 | 5073 | 0 | 0 | 98 | 3864 |
N.S. |
1 | 0.91 | 2.02 | 12.65 | 0.00 | 26.98 | 0.00 | 0.00 | 0.52 | 20.55 |
time (sec) |
N/A | 1.100 | 1.158 | 0.527 | 0.000 | 0.964 | 0.000 | 0.000 | 0.211 | 42.352 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | F | F | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 150 | 133 | 294 | 1653 | 0 | 3252 | 0 | 0 | 68 | 2823 |
N.S. |
1 | 0.89 | 1.96 | 11.02 | 0.00 | 21.68 | 0.00 | 0.00 | 0.45 | 18.82 |
time (sec) |
N/A | 0.826 | 0.604 | 0.456 | 0.000 | 0.424 | 0.000 | 0.000 | 0.211 | 24.598 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | F | F | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 122 | 105 | 212 | 807 | 0 | 1329 | 0 | 0 | 38 | 843 |
N.S. |
1 | 0.86 | 1.74 | 6.61 | 0.00 | 10.89 | 0.00 | 0.00 | 0.31 | 6.91 |
time (sec) |
N/A | 0.604 | 0.379 | 0.479 | 0.000 | 0.145 | 0.000 | 0.000 | 0.210 | 12.766 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | F | F | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 151 | 123 | 222 | 1375 | 0 | 1684 | 0 | 0 | 98 | 3442 |
N.S. |
1 | 0.81 | 1.47 | 9.11 | 0.00 | 11.15 | 0.00 | 0.00 | 0.65 | 22.79 |
time (sec) |
N/A | 0.703 | 0.731 | 0.454 | 0.000 | 0.114 | 0.000 | 0.000 | 0.188 | 35.043 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F | F | F | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 311 | 432 | 178 | 972 | 0 | 1148 | 0 | 0 | 45 | 2529 |
N.S. |
1 | 1.39 | 0.57 | 3.13 | 0.00 | 3.69 | 0.00 | 0.00 | 0.14 | 8.13 |
time (sec) |
N/A | 0.766 | 3.861 | 0.404 | 0.000 | 0.110 | 0.000 | 0.000 | 0.177 | 20.356 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | F | F | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 320 | 453 | 153 | 807 | 0 | 849 | 0 | 0 | 39 | 583 |
N.S. |
1 | 1.42 | 0.48 | 2.52 | 0.00 | 2.65 | 0.00 | 0.00 | 0.12 | 1.82 |
time (sec) |
N/A | 0.801 | 0.416 | 0.422 | 0.000 | 0.099 | 0.000 | 0.000 | 0.174 | 10.910 |