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 | F | B | F(-1) | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 151 | 169 | 261 | 162 | 0 | 363 | 0 | 223 | 83 | 0 |
N.S. |
1 | 1.12 | 1.73 | 1.07 | 0.00 | 2.40 | 0.00 | 1.48 | 0.55 | 0.00 |
time (sec) |
N/A | 1.000 | 6.676 | 0.972 | 0.000 | 0.105 | 0.000 | 0.172 | 0.235 | 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 | 227 | 275 | 360 | 222 | 0 | 485 | 0 | 290 | 83 | 0 |
N.S. |
1 | 1.21 | 1.59 | 0.98 | 0.00 | 2.14 | 0.00 | 1.28 | 0.37 | 0.00 |
time (sec) |
N/A | 1.910 | 7.801 | 6.654 | 0.000 | 0.111 | 0.000 | 0.182 | 0.240 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 150 | 241 | 118 | 241 | 0 | 229 | 0 | 211 | 36 | 0 |
N.S. |
1 | 1.61 | 0.79 | 1.61 | 0.00 | 1.53 | 0.00 | 1.41 | 0.24 | 0.00 |
time (sec) |
N/A | 1.321 | 1.340 | 0.312 | 0.000 | 0.101 | 0.000 | 0.198 | 0.175 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | B | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 107 | 109 | 118 | 134 | 0 | 200 | 0 | 156 | 36 | 0 |
N.S. |
1 | 1.02 | 1.10 | 1.25 | 0.00 | 1.87 | 0.00 | 1.46 | 0.34 | 0.00 |
time (sec) |
N/A | 0.521 | 0.800 | 0.301 | 0.000 | 0.101 | 0.000 | 0.189 | 0.192 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | F | B | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 62 | 62 | 138 | 103 | 0 | 263 | 0 | 132 | 36 | 0 |
N.S. |
1 | 1.00 | 2.23 | 1.66 | 0.00 | 4.24 | 0.00 | 2.13 | 0.58 | 0.00 |
time (sec) |
N/A | 0.352 | 0.881 | 0.271 | 0.000 | 0.095 | 0.000 | 0.159 | 0.169 | 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 | 135 | 253 | 292 | 144 | 0 | 369 | 0 | 185 | 36 | 0 |
N.S. |
1 | 1.87 | 2.16 | 1.07 | 0.00 | 2.73 | 0.00 | 1.37 | 0.27 | 0.00 |
time (sec) |
N/A | 1.567 | 1.317 | 0.289 | 0.000 | 0.104 | 0.000 | 0.170 | 0.173 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F(-1) | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 177 | 195 | 334 | 311 | 0 | 270 | 0 | 220 | 46 | 0 |
N.S. |
1 | 1.10 | 1.89 | 1.76 | 0.00 | 1.53 | 0.00 | 1.24 | 0.26 | 0.00 |
time (sec) |
N/A | 1.747 | 1.121 | 0.321 | 0.000 | 0.129 | 0.000 | 0.237 | 0.185 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | B | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 134 | 146 | 128 | 212 | 0 | 237 | 0 | 121 | 46 | 0 |
N.S. |
1 | 1.09 | 0.96 | 1.58 | 0.00 | 1.77 | 0.00 | 0.90 | 0.34 | 0.00 |
time (sec) |
N/A | 0.639 | 1.111 | 0.298 | 0.000 | 0.124 | 0.000 | 0.227 | 0.188 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | B | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 113 | 121 | 206 | 134 | 0 | 421 | 0 | 205 | 46 | 0 |
N.S. |
1 | 1.07 | 1.82 | 1.19 | 0.00 | 3.73 | 0.00 | 1.81 | 0.41 | 0.00 |
time (sec) |
N/A | 0.636 | 3.032 | 0.294 | 0.000 | 0.108 | 0.000 | 0.166 | 0.175 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | F(-1) | B | F | A | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 144 | 262 | 294 | 144 | 0 | 383 | 0 | 168 | 46 | 0 |
N.S. |
1 | 1.82 | 2.04 | 1.00 | 0.00 | 2.66 | 0.00 | 1.17 | 0.32 | 0.00 |
time (sec) |
N/A | 1.726 | 1.538 | 0.293 | 0.000 | 0.096 | 0.000 | 0.161 | 0.168 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F(-1) | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 207 | 344 | 394 | 381 | 0 | 307 | 0 | 184 | 56 | 0 |
N.S. |
1 | 1.66 | 1.90 | 1.84 | 0.00 | 1.48 | 0.00 | 0.89 | 0.27 | 0.00 |
time (sec) |
N/A | 2.173 | 1.319 | 0.355 | 0.000 | 0.112 | 0.000 | 0.267 | 0.193 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 167 | 175 | 284 | 288 | 0 | 279 | 0 | 140 | 56 | 0 |
N.S. |
1 | 1.05 | 1.70 | 1.72 | 0.00 | 1.67 | 0.00 | 0.84 | 0.34 | 0.00 |
time (sec) |
N/A | 0.812 | 1.702 | 0.324 | 0.000 | 0.156 | 0.000 | 0.259 | 0.177 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | B | F | B | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 141 | 152 | 451 | 219 | 0 | 539 | 0 | 262 | 56 | 0 |
N.S. |
1 | 1.08 | 3.20 | 1.55 | 0.00 | 3.82 | 0.00 | 1.86 | 0.40 | 0.00 |
time (sec) |
N/A | 0.880 | 1.445 | 0.315 | 0.000 | 0.125 | 0.000 | 0.169 | 0.178 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-1) | B | F | A | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 191 | 376 | 332 | 182 | 0 | 564 | 0 | 240 | 56 | 0 |
N.S. |
1 | 1.97 | 1.74 | 0.95 | 0.00 | 2.95 | 0.00 | 1.26 | 0.29 | 0.00 |
time (sec) |
N/A | 2.985 | 3.319 | 0.316 | 0.000 | 0.112 | 0.000 | 0.174 | 0.179 | 0.000 |
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 | No | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 964 | 988 | 232 | 0 | 0 | 0 | 0 | 0 | 25 | 0 |
N.S. |
1 | 1.02 | 0.24 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.03 | 0.00 |
time (sec) |
N/A | 0.883 | 5.516 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.194 | 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 | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 123 | 131 | 209 | 0 | 0 | 0 | 0 | 0 | 25 | 0 |
N.S. |
1 | 1.07 | 1.70 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.20 | 0.00 |
time (sec) |
N/A | 0.608 | 3.866 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.196 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | No | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 80 | 136 | 2692 | 0 | 0 | 0 | 0 | 0 | 25 | 0 |
N.S. |
1 | 1.70 | 33.65 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.31 | 0.00 |
time (sec) |
N/A | 0.375 | 43.363 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.182 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | No | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 80 | 136 | 2796 | 0 | 0 | 0 | 0 | 0 | 25 | 0 |
N.S. |
1 | 1.70 | 34.95 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.31 | 0.00 |
time (sec) |
N/A | 0.378 | 49.282 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.186 | 0.000 |
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 | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 538 | 578 | 128 | 0 | 0 | 0 | 0 | 0 | 25 | 0 |
N.S. |
1 | 1.07 | 0.24 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 0.489 | 1.524 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.194 | 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 | 126 | 133 | 100 | 0 | 0 | 0 | 0 | 0 | 25 | 0 |
N.S. |
1 | 1.06 | 0.79 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.20 | 0.00 |
time (sec) |
N/A | 0.612 | 1.057 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.168 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | No | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 80 | 136 | 0 | 0 | 0 | 0 | 0 | 0 | 25 | 0 |
N.S. |
1 | 1.70 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.31 | 0.00 |
time (sec) |
N/A | 0.359 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.196 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | No | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 80 | 136 | 0 | 0 | 0 | 0 | 0 | 0 | 25 | 0 |
N.S. |
1 | 1.70 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.31 | 0.00 |
time (sec) |
N/A | 0.352 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.199 | 0.000 |
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 | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 269 | 269 | 4726 | 0 | 0 | 0 | 0 | 0 | 77 | 0 |
N.S. |
1 | 1.00 | 17.57 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 0.645 | 35.514 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.221 | 0.000 |
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 | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 187 | 187 | 2054 | 0 | 0 | 0 | 0 | 0 | 56 | 0 |
N.S. |
1 | 1.00 | 10.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.30 | 0.00 |
time (sec) |
N/A | 0.486 | 16.832 | 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 | F | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 129 | 129 | 0 | 0 | 0 | 0 | 0 | 0 | 33 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 0.372 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.199 | 0.000 |
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 | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 108 | 108 | 232 | 0 | 0 | 0 | 0 | 0 | 28 | 0 |
N.S. |
1 | 1.00 | 2.15 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 0.421 | 2.571 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.208 | 0.000 |
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 | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 138 | 142 | 626 | 0 | 0 | 0 | 0 | 0 | 38 | 0 |
N.S. |
1 | 1.03 | 4.54 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.28 | 0.00 |
time (sec) |
N/A | 0.492 | 7.282 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.195 | 0.000 |
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 | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 248 | 252 | 1276 | 0 | 0 | 0 | 0 | 0 | 25 | 0 |
N.S. |
1 | 1.02 | 5.15 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.10 | 0.00 |
time (sec) |
N/A | 0.650 | 17.797 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 200.024 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 111 | 156 | 0 | 0 | 0 | 0 | 0 | 0 | 27 | 0 |
N.S. |
1 | 1.41 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.24 | 0.00 |
time (sec) |
N/A | 0.389 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.194 | 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 | 163 | 167 | 105 | 0 | 0 | 0 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.02 | 0.64 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.14 | 0.00 |
time (sec) |
N/A | 0.300 | 0.183 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.174 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 72 | 75 | 63 | 0 | 0 | 0 | 0 | 0 | 21 | 0 |
N.S. |
1 | 1.04 | 0.88 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 0.226 | 0.061 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.184 | 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 | 43 | 43 | 43 | 0 | 0 | 0 | 0 | 0 | 21 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.49 | 0.00 |
time (sec) |
N/A | 0.220 | 0.043 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.171 | 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 | 83 | 81 | 68 | 0 | 0 | 0 | 0 | 0 | 23 | 0 |
N.S. |
1 | 0.98 | 0.82 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.28 | 0.00 |
time (sec) |
N/A | 0.245 | 0.134 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.181 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F(-1) | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 123 | 123 | 83 | 0 | 0 | 0 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.00 | 0.67 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.19 | 0.00 |
time (sec) |
N/A | 0.278 | 0.202 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.189 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 319 | 352 | 0 | 0 | 0 | 0 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.10 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.07 | 0.00 |
time (sec) |
N/A | 0.480 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.187 | 0.000 |
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 | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 157 | 161 | 1756 | 0 | 0 | 0 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.03 | 11.18 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.15 | 0.00 |
time (sec) |
N/A | 0.598 | 23.635 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.194 | 0.000 |
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 | 74 | 74 | 70 | 0 | 0 | 0 | 0 | 0 | 14 | 0 |
N.S. |
1 | 1.00 | 0.95 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.19 | 0.00 |
time (sec) |
N/A | 0.267 | 0.112 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.184 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F | F | F | F(-1) |
verified |
N/A | No | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 105 | 116 | 0 | 0 | 0 | 0 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.10 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.22 | 0.00 |
time (sec) |
N/A | 0.303 | 0.000 | 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 | F | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 105 | 116 | 0 | 0 | 0 | 0 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.10 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.22 | 0.00 |
time (sec) |
N/A | 0.305 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.213 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 85 | 96 | 82 | 81 | 73 | 90 | 0 | 91 | 100 | 176 |
N.S. |
1 | 1.13 | 0.96 | 0.95 | 0.86 | 1.06 | 0.00 | 1.07 | 1.18 | 2.07 |
time (sec) |
N/A | 0.317 | 0.093 | 0.655 | 0.033 | 0.144 | 0.000 | 0.166 | 0.205 | 17.766 |
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 | 46 | 38 | 41 | 43 | 45 | 0 | 51 | 58 | 74 |
N.S. |
1 | 0.84 | 0.69 | 0.75 | 0.78 | 0.82 | 0.00 | 0.93 | 1.05 | 1.35 |
time (sec) |
N/A | 0.221 | 0.013 | 0.384 | 0.027 | 0.093 | 0.000 | 0.135 | 0.190 | 17.684 |
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 | 42 | 47 |
N.S. |
1 | 1.00 | 1.46 | 0.96 | 0.92 | 1.00 | 0.00 | 0.96 | 1.75 | 1.96 |
time (sec) |
N/A | 0.202 | 0.026 | 0.232 | 0.033 | 0.087 | 0.000 | 0.123 | 0.189 | 17.690 |
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 | 94 | 146 |
N.S. |
1 | 0.89 | 1.00 | 1.24 | 0.83 | 1.28 | 0.00 | 0.85 | 1.74 | 2.70 |
time (sec) |
N/A | 0.231 | 0.014 | 0.635 | 0.031 | 0.092 | 0.000 | 0.132 | 0.190 | 17.471 |
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 | 116 | 207 |
N.S. |
1 | 0.85 | 1.00 | 1.25 | 0.85 | 1.36 | 0.00 | 0.86 | 1.43 | 2.56 |
time (sec) |
N/A | 0.251 | 0.025 | 1.064 | 0.032 | 0.097 | 0.000 | 0.134 | 0.179 | 17.499 |
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 | 73 | 0 | 0 | 277 | 110 |
N.S. |
1 | 1.00 | 1.12 | 1.36 | 0.90 | 1.01 | 0.00 | 0.00 | 3.85 | 1.53 |
time (sec) |
N/A | 0.284 | 0.124 | 1.030 | 0.110 | 0.140 | 0.000 | 0.000 | 0.197 | 19.849 |
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 | 38 | 38 | 47 | 59 | 39 | 47 | 0 | 1008 | 82 | 55 |
N.S. |
1 | 1.00 | 1.24 | 1.55 | 1.03 | 1.24 | 0.00 | 26.53 | 2.16 | 1.45 |
time (sec) |
N/A | 0.243 | 0.081 | 0.599 | 0.114 | 0.081 | 0.000 | 0.662 | 0.191 | 17.514 |
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 | 74 | 158 |
N.S. |
1 | 1.00 | 1.83 | 1.20 | 1.32 | 2.05 | 0.00 | 2.63 | 1.80 | 3.85 |
time (sec) |
N/A | 0.240 | 0.071 | 0.325 | 0.108 | 0.139 | 0.000 | 0.136 | 0.198 | 17.794 |
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 | 105 | 225 |
N.S. |
1 | 1.05 | 1.60 | 1.10 | 1.18 | 2.05 | 0.00 | 1.81 | 1.35 | 2.88 |
time (sec) |
N/A | 0.296 | 0.096 | 0.618 | 0.111 | 0.094 | 0.000 | 0.159 | 0.213 | 17.465 |
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 | 150 | 288 |
N.S. |
1 | 1.04 | 1.40 | 1.10 | 1.07 | 1.90 | 0.00 | 1.70 | 1.28 | 2.46 |
time (sec) |
N/A | 0.332 | 0.128 | 1.255 | 0.112 | 0.124 | 0.000 | 0.167 | 0.206 | 17.735 |
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 | 111 | 123 | 108 | 135 | 105 | 140 | 0 | 129 | 347 | 232 |
N.S. |
1 | 1.11 | 0.97 | 1.22 | 0.95 | 1.26 | 0.00 | 1.16 | 3.13 | 2.09 |
time (sec) |
N/A | 0.368 | 0.322 | 1.884 | 0.032 | 0.105 | 0.000 | 0.195 | 0.224 | 17.759 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 78 | 70 | 145 | 69 | 70 | 74 | 0 | 83 | 129 | 150 |
N.S. |
1 | 0.90 | 1.86 | 0.88 | 0.90 | 0.95 | 0.00 | 1.06 | 1.65 | 1.92 |
time (sec) |
N/A | 0.275 | 0.059 | 0.934 | 0.027 | 0.158 | 0.000 | 0.123 | 0.173 | 17.285 |
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 | 46 | 43 | 46 | 40 | 40 | 42 | 0 | 41 | 62 | 117 |
N.S. |
1 | 0.93 | 1.00 | 0.87 | 0.87 | 0.91 | 0.00 | 0.89 | 1.35 | 2.54 |
time (sec) |
N/A | 0.229 | 0.020 | 0.367 | 0.032 | 0.094 | 0.000 | 0.117 | 0.171 | 17.106 |
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 | 75 | 92 | 93 | 69 | 115 | 0 | 70 | 166 | 221 |
N.S. |
1 | 0.89 | 1.10 | 1.11 | 0.82 | 1.37 | 0.00 | 0.83 | 1.98 | 2.63 |
time (sec) |
N/A | 0.273 | 0.035 | 1.022 | 0.031 | 0.101 | 0.000 | 0.128 | 0.163 | 17.246 |
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 | 111 | 142 | 157 | 105 | 177 | 0 | 106 | 218 | 310 |
N.S. |
1 | 0.88 | 1.13 | 1.25 | 0.83 | 1.40 | 0.00 | 0.84 | 1.73 | 2.46 |
time (sec) |
N/A | 0.311 | 0.056 | 2.106 | 0.032 | 0.132 | 0.000 | 0.135 | 0.166 | 17.641 |
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 | 143 | 149 | 176 | 185 | 119 | 118 | 0 | 0 | 307 | 235 |
N.S. |
1 | 1.04 | 1.23 | 1.29 | 0.83 | 0.83 | 0.00 | 0.00 | 2.15 | 1.64 |
time (sec) |
N/A | 0.402 | 0.895 | 2.823 | 0.108 | 0.097 | 0.000 | 0.000 | 0.170 | 19.580 |
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 | 89 | 94 | 77 | 116 | 83 | 81 | 0 | 7670 | 119 | 147 |
N.S. |
1 | 1.06 | 0.87 | 1.30 | 0.93 | 0.91 | 0.00 | 86.18 | 1.34 | 1.65 |
time (sec) |
N/A | 0.342 | 0.622 | 1.542 | 0.112 | 0.104 | 0.000 | 4.676 | 0.163 | 19.287 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 78 | 78 | 116 | 79 | 79 | 118 | 0 | 148 | 114 | 277 |
N.S. |
1 | 1.00 | 1.49 | 1.01 | 1.01 | 1.51 | 0.00 | 1.90 | 1.46 | 3.55 |
time (sec) |
N/A | 0.298 | 0.672 | 0.571 | 0.108 | 0.096 | 0.000 | 0.149 | 0.177 | 17.430 |
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 | 127 | 133 | 293 | 145 | 138 | 218 | 0 | 241 | 180 | 584 |
N.S. |
1 | 1.05 | 2.31 | 1.14 | 1.09 | 1.72 | 0.00 | 1.90 | 1.42 | 4.60 |
time (sec) |
N/A | 0.387 | 6.569 | 1.445 | 0.113 | 0.161 | 0.000 | 0.174 | 0.170 | 18.870 |
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 | 192 | 202 | 351 | 216 | 183 | 306 | 0 | 337 | 236 | 888 |
N.S. |
1 | 1.05 | 1.83 | 1.12 | 0.95 | 1.59 | 0.00 | 1.76 | 1.23 | 4.62 |
time (sec) |
N/A | 0.435 | 1.283 | 2.983 | 0.120 | 0.111 | 0.000 | 0.200 | 0.178 | 20.988 |
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 | 150 | 157 | 141 | 206 | 162 | 194 | 0 | 197 | 491 | 366 |
N.S. |
1 | 1.05 | 0.94 | 1.37 | 1.08 | 1.29 | 0.00 | 1.31 | 3.27 | 2.44 |
time (sec) |
N/A | 0.435 | 0.196 | 6.173 | 0.037 | 0.140 | 0.000 | 0.239 | 0.197 | 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 | 105 | 104 | 90 | 110 | 113 | 116 | 0 | 139 | 198 | 226 |
N.S. |
1 | 0.99 | 0.86 | 1.05 | 1.08 | 1.10 | 0.00 | 1.32 | 1.89 | 2.15 |
time (sec) |
N/A | 0.351 | 0.147 | 3.455 | 0.028 | 0.100 | 0.000 | 0.143 | 0.190 | 17.498 |
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 | 67 | 61 | 67 | 56 | 57 | 66 | 0 | 58 | 79 | 118 |
N.S. |
1 | 0.91 | 1.00 | 0.84 | 0.85 | 0.99 | 0.00 | 0.87 | 1.18 | 1.76 |
time (sec) |
N/A | 0.240 | 0.022 | 0.787 | 0.028 | 0.196 | 0.000 | 0.119 | 0.180 | 17.872 |
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 | 104 | 130 | 118 | 98 | 153 | 0 | 102 | 200 | 312 |
N.S. |
1 | 0.90 | 1.12 | 1.02 | 0.84 | 1.32 | 0.00 | 0.88 | 1.72 | 2.69 |
time (sec) |
N/A | 0.307 | 0.066 | 2.005 | 0.027 | 0.160 | 0.000 | 0.135 | 0.164 | 17.844 |
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 | 165 | 147 | 195 | 212 | 142 | 225 | 0 | 146 | 268 | 424 |
N.S. |
1 | 0.89 | 1.18 | 1.28 | 0.86 | 1.36 | 0.00 | 0.88 | 1.62 | 2.57 |
time (sec) |
N/A | 0.359 | 0.096 | 4.264 | 0.033 | 0.115 | 0.000 | 0.157 | 0.165 | 17.801 |
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 | 211 | 220 | 226 | 268 | 167 | 157 | 0 | 0 | 398 | 297 |
N.S. |
1 | 1.04 | 1.07 | 1.27 | 0.79 | 0.74 | 0.00 | 0.00 | 1.89 | 1.41 |
time (sec) |
N/A | 0.511 | 1.054 | 8.574 | 0.115 | 0.091 | 0.000 | 0.000 | 0.159 | 19.279 |
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 | 142 | 146 | 113 | 169 | 119 | 116 | 0 | 0 | 171 | 249 |
N.S. |
1 | 1.03 | 0.80 | 1.19 | 0.84 | 0.82 | 0.00 | 0.00 | 1.20 | 1.75 |
time (sec) |
N/A | 0.410 | 0.976 | 4.910 | 0.112 | 0.090 | 0.000 | 0.000 | 0.172 | 19.158 |
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 | 102 | 102 | 143 | 96 | 95 | 143 | 0 | 199 | 171 | 289 |
N.S. |
1 | 1.00 | 1.40 | 0.94 | 0.93 | 1.40 | 0.00 | 1.95 | 1.68 | 2.83 |
time (sec) |
N/A | 0.330 | 1.394 | 1.720 | 0.107 | 0.101 | 0.000 | 0.159 | 0.201 | 18.012 |
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 | 186 | 194 | 355 | 186 | 187 | 293 | 0 | 421 | 265 | 405 |
N.S. |
1 | 1.04 | 1.91 | 1.00 | 1.01 | 1.58 | 0.00 | 2.26 | 1.42 | 2.18 |
time (sec) |
N/A | 0.451 | 6.672 | 2.920 | 0.110 | 0.104 | 0.000 | 0.201 | 0.184 | 18.100 |
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 | 273 | 291 | 346 | 289 | 252 | 412 | 0 | 471 | 343 | 507 |
N.S. |
1 | 1.07 | 1.27 | 1.06 | 0.92 | 1.51 | 0.00 | 1.73 | 1.26 | 1.86 |
time (sec) |
N/A | 0.540 | 2.495 | 6.036 | 0.113 | 0.122 | 0.000 | 0.240 | 0.165 | 18.062 |
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 | 244 | 264 | 184 | 189 | 288 | 261 | 0 | 307 | 988 | 498 |
N.S. |
1 | 1.08 | 0.75 | 0.77 | 1.18 | 1.07 | 0.00 | 1.26 | 4.05 | 2.04 |
time (sec) |
N/A | 0.696 | 0.998 | 1.020 | 0.038 | 0.179 | 0.000 | 0.150 | 0.184 | 18.333 |
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 | 138 | 159 | 117 | 121 | 142 | 157 | 0 | 184 | 454 | 217 |
N.S. |
1 | 1.15 | 0.85 | 0.88 | 1.03 | 1.14 | 0.00 | 1.33 | 3.29 | 1.57 |
time (sec) |
N/A | 0.414 | 0.391 | 0.550 | 0.033 | 0.121 | 0.000 | 0.146 | 0.175 | 18.069 |
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 | 75 | 65 | 71 | 65 | 63 | 0 | 74 | 105 | 91 |
N.S. |
1 | 1.01 | 0.88 | 0.96 | 0.88 | 0.85 | 0.00 | 1.00 | 1.42 | 1.23 |
time (sec) |
N/A | 0.275 | 0.053 | 0.311 | 0.031 | 0.096 | 0.000 | 0.122 | 0.166 | 17.899 |
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 | 34 | 34 | 34 | 33 | 33 | 31 | 0 | 36 | 48 | 48 |
N.S. |
1 | 1.00 | 1.00 | 0.97 | 0.97 | 0.91 | 0.00 | 1.06 | 1.41 | 1.41 |
time (sec) |
N/A | 0.233 | 0.018 | 0.319 | 0.029 | 0.090 | 0.000 | 0.121 | 0.169 | 17.864 |
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 | 78 | 65 | 76 | 77 | 118 | 0 | 91 | 172 | 144 |
N.S. |
1 | 0.93 | 0.77 | 0.90 | 0.92 | 1.40 | 0.00 | 1.08 | 2.05 | 1.71 |
time (sec) |
N/A | 0.299 | 0.128 | 0.687 | 0.034 | 0.095 | 0.000 | 0.125 | 0.162 | 17.805 |
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 | 148 | 136 | 115 | 137 | 139 | 271 | 0 | 152 | 318 | 281 |
N.S. |
1 | 0.92 | 0.78 | 0.93 | 0.94 | 1.83 | 0.00 | 1.03 | 2.15 | 1.90 |
time (sec) |
N/A | 0.358 | 0.778 | 1.408 | 0.033 | 0.152 | 0.000 | 0.126 | 0.175 | 17.960 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 177 | 184 | 195 | 214 | 0 | 476 | 0 | 241 | 827 | 372 |
N.S. |
1 | 1.04 | 1.10 | 1.21 | 0.00 | 2.69 | 0.00 | 1.36 | 4.67 | 2.10 |
time (sec) |
N/A | 0.969 | 1.269 | 0.727 | 0.000 | 0.104 | 0.000 | 0.219 | 0.197 | 19.692 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 96 | 102 | 152 | 112 | 0 | 305 | 0 | 107 | 191 | 148 |
N.S. |
1 | 1.06 | 1.58 | 1.17 | 0.00 | 3.18 | 0.00 | 1.11 | 1.99 | 1.54 |
time (sec) |
N/A | 0.503 | 0.340 | 0.410 | 0.000 | 0.107 | 0.000 | 0.200 | 0.185 | 17.916 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 80 | 93 | 108 | 109 | 0 | 314 | 0 | 129 | 89 | 204 |
N.S. |
1 | 1.16 | 1.35 | 1.36 | 0.00 | 3.92 | 0.00 | 1.61 | 1.11 | 2.55 |
time (sec) |
N/A | 0.676 | 0.349 | 0.563 | 0.000 | 0.124 | 0.000 | 0.144 | 0.185 | 18.142 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | F(-2) | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 154 | 170 | 350 | 223 | 0 | 633 | 0 | 273 | 232 | 654 |
N.S. |
1 | 1.10 | 2.27 | 1.45 | 0.00 | 4.11 | 0.00 | 1.77 | 1.51 | 4.25 |
time (sec) |
N/A | 1.022 | 6.276 | 1.067 | 0.000 | 0.235 | 0.000 | 0.163 | 0.173 | 18.420 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 307 | 345 | 504 | 390 | 0 | 1079 | 0 | 490 | 416 | 1099 |
N.S. |
1 | 1.12 | 1.64 | 1.27 | 0.00 | 3.51 | 0.00 | 1.60 | 1.36 | 3.58 |
time (sec) |
N/A | 2.325 | 1.403 | 1.951 | 0.000 | 0.376 | 0.000 | 0.174 | 0.188 | 18.157 |
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 | 277 | 288 | 204 | 205 | 505 | 555 | 0 | 409 | 2643 | 755 |
N.S. |
1 | 1.04 | 0.74 | 0.74 | 1.82 | 2.00 | 0.00 | 1.48 | 9.54 | 2.73 |
time (sec) |
N/A | 1.064 | 4.658 | 2.031 | 0.044 | 0.336 | 0.000 | 0.166 | 0.202 | 18.834 |
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 | 161 | 184 | 145 | 143 | 274 | 388 | 0 | 265 | 1400 | 351 |
N.S. |
1 | 1.14 | 0.90 | 0.89 | 1.70 | 2.41 | 0.00 | 1.65 | 8.70 | 2.18 |
time (sec) |
N/A | 0.606 | 0.576 | 1.041 | 0.036 | 0.162 | 0.000 | 0.149 | 0.189 | 18.374 |
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 | 127 | 162 | 98 | 124 | 195 | 0 | 149 | 459 | 158 |
N.S. |
1 | 1.17 | 1.49 | 0.90 | 1.14 | 1.79 | 0.00 | 1.37 | 4.21 | 1.45 |
time (sec) |
N/A | 0.347 | 0.233 | 0.705 | 0.033 | 0.125 | 0.000 | 0.122 | 0.185 | 18.063 |
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 | 53 | 50 | 42 | 49 | 47 | 69 | 0 | 55 | 119 | 105 |
N.S. |
1 | 0.94 | 0.79 | 0.92 | 0.89 | 1.30 | 0.00 | 1.04 | 2.25 | 1.98 |
time (sec) |
N/A | 0.249 | 0.065 | 0.581 | 0.033 | 0.105 | 0.000 | 0.133 | 0.160 | 17.841 |
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 | 114 | 105 | 96 | 105 | 116 | 259 | 0 | 125 | 347 | 235 |
N.S. |
1 | 0.92 | 0.84 | 0.92 | 1.02 | 2.27 | 0.00 | 1.10 | 3.04 | 2.06 |
time (sec) |
N/A | 0.324 | 0.467 | 1.890 | 0.035 | 0.140 | 0.000 | 0.139 | 0.203 | 17.966 |
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 | 188 | 173 | 187 | 172 | 189 | 542 | 0 | 198 | 578 | 439 |
N.S. |
1 | 0.92 | 0.99 | 0.91 | 1.01 | 2.88 | 0.00 | 1.05 | 3.07 | 2.34 |
time (sec) |
N/A | 0.407 | 6.108 | 3.910 | 0.038 | 0.120 | 0.000 | 0.135 | 0.199 | 17.849 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 333 | 333 | 341 | 248 | 0 | 815 | 0 | 406 | 1255 | 722 |
N.S. |
1 | 1.00 | 1.02 | 0.74 | 0.00 | 2.45 | 0.00 | 1.22 | 3.77 | 2.17 |
time (sec) |
N/A | 0.889 | 1.607 | 1.484 | 0.000 | 0.156 | 0.000 | 0.255 | 0.207 | 19.758 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 200 | 200 | 169 | 162 | 0 | 569 | 0 | 251 | 494 | 313 |
N.S. |
1 | 1.00 | 0.84 | 0.81 | 0.00 | 2.84 | 0.00 | 1.26 | 2.47 | 1.56 |
time (sec) |
N/A | 0.567 | 0.969 | 0.773 | 0.000 | 0.164 | 0.000 | 0.222 | 0.170 | 19.078 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 115 | 161 | 139 | 156 | 0 | 768 | 0 | 218 | 401 | 1616 |
N.S. |
1 | 1.40 | 1.21 | 1.36 | 0.00 | 6.68 | 0.00 | 1.90 | 3.49 | 14.05 |
time (sec) |
N/A | 1.020 | 0.818 | 1.444 | 0.000 | 0.248 | 0.000 | 0.157 | 0.175 | 19.029 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 238 | 266 | 403 | 287 | 0 | 1149 | 0 | 356 | 438 | 973 |
N.S. |
1 | 1.12 | 1.69 | 1.21 | 0.00 | 4.83 | 0.00 | 1.50 | 1.84 | 4.09 |
time (sec) |
N/A | 1.524 | 6.371 | 2.849 | 0.000 | 0.263 | 0.000 | 0.175 | 0.176 | 17.925 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 424 | 506 | 361 | 465 | 0 | 2011 | 0 | 596 | 723 | 1424 |
N.S. |
1 | 1.19 | 0.85 | 1.10 | 0.00 | 4.74 | 0.00 | 1.41 | 1.71 | 3.36 |
time (sec) |
N/A | 3.433 | 1.471 | 5.559 | 0.000 | 0.428 | 0.000 | 0.185 | 0.196 | 17.708 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 373 | 365 | 304 | 263 | 730 | 981 | 0 | 607 | 4732 | 1229 |
N.S. |
1 | 0.98 | 0.82 | 0.71 | 1.96 | 2.63 | 0.00 | 1.63 | 12.69 | 3.29 |
time (sec) |
N/A | 1.502 | 6.285 | 4.006 | 0.047 | 0.562 | 0.000 | 0.177 | 0.276 | 20.629 |
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 | 232 | 256 | 196 | 197 | 441 | 788 | 0 | 363 | 2813 | 690 |
N.S. |
1 | 1.10 | 0.84 | 0.85 | 1.90 | 3.40 | 0.00 | 1.56 | 12.12 | 2.97 |
time (sec) |
N/A | 0.836 | 1.706 | 1.976 | 0.046 | 0.419 | 0.000 | 0.162 | 0.197 | 18.633 |
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 | 149 | 163 | 213 | 134 | 228 | 462 | 0 | 210 | 1005 | 304 |
N.S. |
1 | 1.09 | 1.43 | 0.90 | 1.53 | 3.10 | 0.00 | 1.41 | 6.74 | 2.04 |
time (sec) |
N/A | 0.393 | 1.638 | 1.832 | 0.037 | 0.198 | 0.000 | 0.130 | 0.194 | 18.175 |
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 | 75 | 69 | 60 | 66 | 81 | 154 | 0 | 72 | 225 | 369 |
N.S. |
1 | 0.92 | 0.80 | 0.88 | 1.08 | 2.05 | 0.00 | 0.96 | 3.00 | 4.92 |
time (sec) |
N/A | 0.267 | 0.217 | 1.253 | 0.030 | 0.151 | 0.000 | 0.127 | 0.191 | 17.507 |
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 | 145 | 133 | 121 | 131 | 156 | 404 | 0 | 158 | 534 | 334 |
N.S. |
1 | 0.92 | 0.83 | 0.90 | 1.08 | 2.79 | 0.00 | 1.09 | 3.68 | 2.30 |
time (sec) |
N/A | 0.358 | 0.715 | 5.352 | 0.035 | 0.115 | 0.000 | 0.130 | 0.291 | 17.593 |
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 | 221 | 203 | 195 | 207 | 236 | 754 | 0 | 229 | 851 | 563 |
N.S. |
1 | 0.92 | 0.88 | 0.94 | 1.07 | 3.41 | 0.00 | 1.04 | 3.85 | 2.55 |
time (sec) |
N/A | 0.474 | 4.902 | 10.671 | 0.036 | 0.132 | 0.000 | 0.142 | 0.308 | 17.924 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 474 | 474 | 351 | 354 | 0 | 1249 | 0 | 632 | 2221 | 1099 |
N.S. |
1 | 1.00 | 0.74 | 0.75 | 0.00 | 2.64 | 0.00 | 1.33 | 4.69 | 2.32 |
time (sec) |
N/A | 1.219 | 1.082 | 2.809 | 0.000 | 0.180 | 0.000 | 0.320 | 0.312 | 21.015 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 350 | 350 | 212 | 258 | 0 | 934 | 0 | 384 | 1084 | 627 |
N.S. |
1 | 1.00 | 0.61 | 0.74 | 0.00 | 2.67 | 0.00 | 1.10 | 3.10 | 1.79 |
time (sec) |
N/A | 0.860 | 2.781 | 1.863 | 0.000 | 0.130 | 0.000 | 0.278 | 0.185 | 20.398 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 202 | 249 | 195 | 299 | 0 | 1394 | 0 | 339 | 1147 | 1762 |
N.S. |
1 | 1.23 | 0.97 | 1.48 | 0.00 | 6.90 | 0.00 | 1.68 | 5.68 | 8.72 |
time (sec) |
N/A | 1.611 | 4.276 | 3.793 | 0.000 | 0.389 | 0.000 | 0.171 | 0.194 | 18.710 |