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 | B | A | A | A | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 51 | 51 | 52 | 93 | 58 | 54 | 102 | 272 | 7 | 0 |
N.S. |
1 | 1.00 | 1.02 | 1.82 | 1.14 | 1.06 | 2.00 | 5.33 | 0.14 | 0.00 |
time (sec) |
N/A | 0.181 | 0.018 | 0.146 | 0.277 | 0.263 | 3.722 | 0.281 | 0.001 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 17 | 17 | 16 | 15 | 15 | 12 | 15 | 14 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.94 | 0.88 | 0.88 | 0.71 | 0.88 | 0.82 | 0.00 |
time (sec) |
N/A | 0.165 | 0.006 | 0.213 | 0.307 | 0.241 | 0.084 | 0.296 | 0.001 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | C | A | A | F | F | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 69 | 0 | 106 | 252 | 4 | 49 | 0 | 0 | 12 | 0 |
N.S. |
1 | 0.00 | 1.54 | 3.65 | 0.06 | 0.71 | 0.00 | 0.00 | 0.17 | 0.00 |
time (sec) |
N/A | 0.000 | 0.700 | 1.098 | 0.907 | 23.673 | 0.000 | 0.000 | 0.008 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | B | F | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 97 | 332 | 188 | 413 | 0 | 451 | 0 | 235 | 199 | 666 |
N.S. |
1 | 3.42 | 1.94 | 4.26 | 0.00 | 4.65 | 0.00 | 2.42 | 2.05 | 6.87 |
time (sec) |
N/A | 0.847 | 0.273 | 0.179 | 0.000 | 0.255 | 0.000 | 0.399 | 0.006 | 1.504 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | C | C | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 45 | 306 | 159 | 312 | 0 | 33 | 0 | 0 | 30 | 0 |
N.S. |
1 | 6.80 | 3.53 | 6.93 | 0.00 | 0.73 | 0.00 | 0.00 | 0.67 | 0.00 |
time (sec) |
N/A | 0.655 | 0.806 | 2.597 | 0.000 | 0.302 | 0.000 | 0.000 | 0.003 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 56 | 54 | 74 | 64 | 0 | 88 | 0 | 79 | 12 | 0 |
N.S. |
1 | 0.96 | 1.32 | 1.14 | 0.00 | 1.57 | 0.00 | 1.41 | 0.21 | 0.00 |
time (sec) |
N/A | 0.228 | 0.084 | 0.259 | 0.000 | 0.308 | 0.000 | 0.301 | 0.003 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 15 | 12 | 27 | 30 | 0 | 28 | 20 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.80 | 1.80 | 2.00 | 0.00 | 1.87 | 1.33 | 0.00 |
time (sec) |
N/A | 0.194 | 0.012 | 0.576 | 0.205 | 0.306 | 0.000 | 0.299 | 0.002 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | C | C | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 137 | 149 | 99 | 1604 | 4065 | 226 | 0 | 495 | 13 | 0 |
N.S. |
1 | 1.09 | 0.72 | 11.71 | 29.67 | 1.65 | 0.00 | 3.61 | 0.09 | 0.00 |
time (sec) |
N/A | 0.406 | 0.201 | 1.602 | 0.781 | 0.300 | 0.000 | 0.336 | 0.002 | 0.000 |
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 | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 41 | 39 | 70 | 36 | 60 | 32 | 0 | 0 | 11 | 60 |
N.S. |
1 | 0.95 | 1.71 | 0.88 | 1.46 | 0.78 | 0.00 | 0.00 | 0.27 | 1.46 |
time (sec) |
N/A | 0.211 | 0.249 | 0.297 | 0.289 | 0.258 | 0.000 | 0.000 | 0.002 | 0.420 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | A | A | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 44 | 67 | 38 | 0 | 0 | 28 | 56 | 46 | 20 | 0 |
N.S. |
1 | 1.52 | 0.86 | 0.00 | 0.00 | 0.64 | 1.27 | 1.05 | 0.45 | 0.00 |
time (sec) |
N/A | 0.792 | 0.169 | 0.000 | 0.000 | 0.246 | 0.383 | 0.276 | 0.005 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 68 | 74 | 64 | 0 | 0 | 43 | 0 | 0 | 27 | 0 |
N.S. |
1 | 1.09 | 0.94 | 0.00 | 0.00 | 0.63 | 0.00 | 0.00 | 0.40 | 0.00 |
time (sec) |
N/A | 0.374 | 0.038 | 0.000 | 0.000 | 0.262 | 0.000 | 0.000 | 0.005 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | C | C | F | A | F(-1) | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 141 | 274 | 226 | 471 | 0 | 191 | 0 | 364 | 107 | 661 |
N.S. |
1 | 1.94 | 1.60 | 3.34 | 0.00 | 1.35 | 0.00 | 2.58 | 0.76 | 4.69 |
time (sec) |
N/A | 0.880 | 0.132 | 0.096 | 0.000 | 0.268 | 0.000 | 0.291 | 0.012 | 1.375 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | C | F | F | A | F(-1) | B | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 152 | 283 | 2175 | 0 | 0 | 200 | 0 | 373 | 115 | 0 |
N.S. |
1 | 1.86 | 14.31 | 0.00 | 0.00 | 1.32 | 0.00 | 2.45 | 0.76 | 0.00 |
time (sec) |
N/A | 0.686 | 3.092 | 0.000 | 0.000 | 0.266 | 0.000 | 0.341 | 0.010 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 45 | 51 | 44 | 0 | 0 | 63 | 0 | 57 | 31 | 0 |
N.S. |
1 | 1.13 | 0.98 | 0.00 | 0.00 | 1.40 | 0.00 | 1.27 | 0.69 | 0.00 |
time (sec) |
N/A | 0.280 | 0.034 | 0.000 | 0.000 | 0.259 | 0.000 | 0.290 | 0.004 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | B | F(-1) | A | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 34 | 76 | 0 | 0 | 62 | 0 | 36 | 32 | 0 |
N.S. |
1 | 1.00 | 2.24 | 0.00 | 0.00 | 1.82 | 0.00 | 1.06 | 0.94 | 0.00 |
time (sec) |
N/A | 0.182 | 0.073 | 0.000 | 0.000 | 0.282 | 0.000 | 0.285 | 0.007 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | A | B | C | A | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 22 | 0 | 18 | 56 | 78 | 18 | 24 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.82 | 2.55 | 3.55 | 0.82 | 1.09 | 0.00 |
time (sec) |
N/A | 0.172 | 0.020 | 0.000 | 0.262 | 0.275 | 20.249 | 0.280 | 0.006 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | B | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 32 | 89 | 0 | 0 | 58 | 0 | 36 | 30 | 0 |
N.S. |
1 | 1.00 | 2.78 | 0.00 | 0.00 | 1.81 | 0.00 | 1.12 | 0.94 | 0.00 |
time (sec) |
N/A | 0.182 | 0.054 | 0.000 | 0.000 | 0.257 | 0.000 | 0.269 | 0.007 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 43 | 43 | 43 | 89 | 41 | 32 | 42 | 62 | 44 | 0 |
N.S. |
1 | 1.00 | 1.00 | 2.07 | 0.95 | 0.74 | 0.98 | 1.44 | 1.02 | 0.00 |
time (sec) |
N/A | 0.184 | 0.017 | 0.080 | 0.272 | 0.261 | 2.687 | 0.282 | 0.003 | 0.000 |
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 | 28 | 28 | 28 | 21 | 34 | 34 | 48 | 35 | 31 | 174 |
N.S. |
1 | 1.00 | 1.00 | 0.75 | 1.21 | 1.21 | 1.71 | 1.25 | 1.11 | 6.21 |
time (sec) |
N/A | 0.138 | 0.015 | 0.336 | 0.181 | 0.228 | 0.901 | 0.270 | 0.000 | 0.144 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 26 | 0 | 22 | 22 | 20 | 22 | 20 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.85 | 0.85 | 0.77 | 0.85 | 0.77 | 0.00 |
time (sec) |
N/A | 0.166 | 0.016 | 0.000 | 0.227 | 0.241 | 3.249 | 0.284 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | B | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 43 | 85 | 0 | 0 | 138 | 0 | 38 | 25 | 0 |
N.S. |
1 | 1.13 | 2.24 | 0.00 | 0.00 | 3.63 | 0.00 | 1.00 | 0.66 | 0.00 |
time (sec) |
N/A | 0.217 | 0.053 | 0.000 | 0.000 | 0.259 | 0.000 | 0.285 | 0.015 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | B | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 70 | 82 | 88 | 0 | 0 | 110 | 0 | 52 | 21 | 0 |
N.S. |
1 | 1.17 | 1.26 | 0.00 | 0.00 | 1.57 | 0.00 | 0.74 | 0.30 | 0.00 |
time (sec) |
N/A | 0.283 | 0.063 | 0.000 | 0.000 | 0.255 | 0.000 | 0.296 | 0.015 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | F(-1) | F | B | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 58 | 58 | 0 | 0 | 48 | 0 | 0 | 65 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.83 | 0.00 | 0.00 | 1.12 | 0.00 |
time (sec) |
N/A | 0.407 | 0.026 | 0.000 | 0.000 | 0.256 | 0.000 | 0.000 | 0.004 | 0.000 |
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 | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 55 | 49 | 41 | 37 | 36 | 35 | 31 | 36 | 43 | 27 |
N.S. |
1 | 0.89 | 0.75 | 0.67 | 0.65 | 0.64 | 0.56 | 0.65 | 0.78 | 0.49 |
time (sec) |
N/A | 0.233 | 0.016 | 0.052 | 0.190 | 0.234 | 2.143 | 0.263 | 0.001 | 0.398 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 26 | 0 | 22 | 22 | 20 | 22 | 20 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.85 | 0.85 | 0.77 | 0.85 | 0.77 | 0.00 |
time (sec) |
N/A | 0.171 | 0.015 | 0.000 | 0.321 | 0.244 | 3.568 | 0.279 | 0.001 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 78 | 78 | 119 | 0 | 0 | 115 | 0 | 122 | 148 | 0 |
N.S. |
1 | 1.00 | 1.53 | 0.00 | 0.00 | 1.47 | 0.00 | 1.56 | 1.90 | 0.00 |
time (sec) |
N/A | 0.457 | 0.041 | 0.000 | 0.000 | 0.246 | 0.000 | 0.347 | 0.005 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 39 | 39 | 25 | 35 | 35 | 39 | 0 | 73 | 49 | 0 |
N.S. |
1 | 1.00 | 0.64 | 0.90 | 0.90 | 1.00 | 0.00 | 1.87 | 1.26 | 0.00 |
time (sec) |
N/A | 0.196 | 0.023 | 0.073 | 0.274 | 0.241 | 0.000 | 0.280 | 0.003 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | B | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 17 | 17 | 54 | 15 | 23 | 29 | 23 | 21 | 0 |
N.S. |
1 | 1.00 | 1.00 | 3.18 | 0.88 | 1.35 | 1.71 | 1.35 | 1.24 | 0.00 |
time (sec) |
N/A | 0.170 | 0.012 | 0.645 | 0.268 | 0.252 | 0.435 | 0.284 | 0.002 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 57 | 63 | 77 | 0 | 0 | 81 | 0 | 104 | 99 | 0 |
N.S. |
1 | 1.11 | 1.35 | 0.00 | 0.00 | 1.42 | 0.00 | 1.82 | 1.74 | 0.00 |
time (sec) |
N/A | 0.236 | 0.045 | 0.000 | 0.000 | 0.250 | 0.000 | 0.298 | 0.010 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | C | A | F | B | B | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 45 | 45 | 45 | 0 | 387 | 69 | 0 | 108 | 152 | 37 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 8.60 | 1.53 | 0.00 | 2.40 | 3.38 | 0.82 |
time (sec) |
N/A | 0.203 | 0.026 | 0.000 | 0.442 | 0.258 | 0.000 | 0.284 | 0.006 | 0.031 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | A | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 33 | 56 | 22 | 47 | 19 | 54 | 40 | 0 |
N.S. |
1 | 1.00 | 1.14 | 1.93 | 0.76 | 1.62 | 0.66 | 1.86 | 1.38 | 0.00 |
time (sec) |
N/A | 0.196 | 0.019 | 0.677 | 0.272 | 0.249 | 3.830 | 0.278 | 0.006 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 21 | 20 | 19 | 22 | 0 | 40 | 18 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.95 | 0.90 | 1.05 | 0.00 | 1.90 | 0.86 | 0.00 |
time (sec) |
N/A | 0.182 | 0.011 | 0.229 | 0.272 | 0.252 | 0.000 | 0.291 | 0.002 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 41 | 27 | 119 | 27 | 27 | 29 | 28 | 29 | 0 |
N.S. |
1 | 1.21 | 0.79 | 3.50 | 0.79 | 0.79 | 0.85 | 0.82 | 0.85 | 0.00 |
time (sec) |
N/A | 0.175 | 0.014 | 0.083 | 0.281 | 0.248 | 1.369 | 0.293 | 0.002 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 33 | 21 | 29 | 29 | 33 | 26 | 58 | 55 | 0 |
N.S. |
1 | 1.00 | 0.64 | 0.88 | 0.88 | 1.00 | 0.79 | 1.76 | 1.67 | 0.00 |
time (sec) |
N/A | 0.174 | 0.019 | 0.069 | 0.275 | 0.244 | 2.951 | 0.266 | 0.003 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | A | A | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 35 | 34 | 15 | 15 | 22 | 22 | 14 | 0 |
N.S. |
1 | 1.00 | 1.40 | 1.36 | 0.60 | 0.60 | 0.88 | 0.88 | 0.56 | 0.00 |
time (sec) |
N/A | 0.173 | 0.031 | 0.388 | 0.202 | 0.245 | 16.148 | 0.303 | 0.003 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 41 | 40 | 39 | 25 | 41 | 41 | 44 | 40 | 0 |
N.S. |
1 | 1.21 | 1.18 | 1.15 | 0.74 | 1.21 | 1.21 | 1.29 | 1.18 | 0.00 |
time (sec) |
N/A | 0.172 | 0.013 | 0.064 | 0.295 | 0.268 | 2.595 | 0.272 | 0.002 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 46 | 14 | 24 | 29 | 46 | 27 | 45 | 13 |
N.S. |
1 | 1.00 | 2.88 | 0.88 | 1.50 | 1.81 | 2.88 | 1.69 | 2.81 | 0.81 |
time (sec) |
N/A | 0.163 | 0.074 | 0.154 | 0.274 | 0.255 | 9.243 | 0.275 | 0.002 | 0.220 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 23 | 22 | 0 | 42 | 0 | 0 | 28 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.96 | 0.00 | 1.83 | 0.00 | 0.00 | 1.22 | 0.00 |
time (sec) |
N/A | 0.168 | 0.300 | 1.543 | 0.000 | 0.269 | 0.000 | 0.000 | 0.001 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 23 | 19 | 0 | 18 | 0 | 0 | 50 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 0.00 | 0.78 | 0.00 | 0.00 | 2.17 | 0.00 |
time (sec) |
N/A | 0.169 | 0.262 | 1.048 | 0.000 | 0.271 | 0.000 | 0.000 | 0.007 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 39 | 24 | 82 | 93 | 105 | 36 | 66 | 55 |
N.S. |
1 | 1.00 | 1.77 | 1.09 | 3.73 | 4.23 | 4.77 | 1.64 | 3.00 | 2.50 |
time (sec) |
N/A | 0.279 | 0.033 | 0.606 | 0.284 | 0.264 | 0.659 | 0.304 | 0.002 | 0.386 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | B | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 42 | 45 | 87 | 0 | 0 | 146 | 0 | 90 | 11 | 0 |
N.S. |
1 | 1.07 | 2.07 | 0.00 | 0.00 | 3.48 | 0.00 | 2.14 | 0.26 | 0.00 |
time (sec) |
N/A | 0.422 | 0.067 | 0.000 | 0.000 | 0.268 | 0.000 | 0.321 | 0.002 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | B | F | B | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 77 | 45 | 78 | 0 | 54 | 0 | 92 | 20 | 0 |
N.S. |
1 | 2.75 | 1.61 | 2.79 | 0.00 | 1.93 | 0.00 | 3.29 | 0.71 | 0.00 |
time (sec) |
N/A | 0.385 | 0.028 | 0.773 | 0.000 | 0.279 | 0.000 | 0.509 | 0.002 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 34 | 55 | 37 | 565 | 186 | 0 | 50 | 20 | 0 |
N.S. |
1 | 1.00 | 1.62 | 1.09 | 16.62 | 5.47 | 0.00 | 1.47 | 0.59 | 0.00 |
time (sec) |
N/A | 0.210 | 0.044 | 0.220 | 0.370 | 0.262 | 0.000 | 0.293 | 0.001 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F(-1) | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 39 | 50 | 65 | 67 | 0 | 63 | 0 | 67 | 24 | 0 |
N.S. |
1 | 1.28 | 1.67 | 1.72 | 0.00 | 1.62 | 0.00 | 1.72 | 0.62 | 0.00 |
time (sec) |
N/A | 0.234 | 0.058 | 0.888 | 0.000 | 0.298 | 0.000 | 0.328 | 0.004 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | F | F | C | F | F | F | F(-1) |
verified |
N/A | N/A | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 337 | 0 | 552 | 0 | 0 | 337 | 0 | 0 | 16 | 0 |
N.S. |
1 | 0.00 | 1.64 | 0.00 | 0.00 | 1.00 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 0.000 | 2.848 | 0.000 | 0.000 | 0.272 | 0.000 | 0.000 | 0.002 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 101 | 58 | 78 | 67 | 52 | 87 | 0 | 77 | 78 |
N.S. |
1 | 1.31 | 0.75 | 1.01 | 0.87 | 0.68 | 1.13 | 0.00 | 1.00 | 1.01 |
time (sec) |
N/A | 0.978 | 0.088 | 4.497 | 0.277 | 0.247 | 0.501 | 0.000 | 0.000 | 0.256 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F | A | F | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 120 | 130 | 95 | 508 | 0 | 298 | 0 | 92 | 11 | 413 |
N.S. |
1 | 1.08 | 0.79 | 4.23 | 0.00 | 2.48 | 0.00 | 0.77 | 0.09 | 3.44 |
time (sec) |
N/A | 0.390 | 0.165 | 0.171 | 0.000 | 0.261 | 0.000 | 0.284 | 0.010 | 1.102 |
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 | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 41 | 31 | 28 | 26 | 22 | 29 | 27 | 27 | 40 |
N.S. |
1 | 1.32 | 1.00 | 0.90 | 0.84 | 0.71 | 0.94 | 0.87 | 0.87 | 1.29 |
time (sec) |
N/A | 0.195 | 0.092 | 0.041 | 0.317 | 0.253 | 9.144 | 0.286 | 0.011 | 0.802 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 29 | 138 | 0 | 60 | 0 | 34 | 15 | 0 |
N.S. |
1 | 1.00 | 1.00 | 4.76 | 0.00 | 2.07 | 0.00 | 1.17 | 0.52 | 0.00 |
time (sec) |
N/A | 0.180 | 0.025 | 0.194 | 0.000 | 0.261 | 0.000 | 0.326 | 0.007 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 106 | 106 | 106 | 210 | 0 | 205 | 0 | 111 | 279 | 455 |
N.S. |
1 | 1.00 | 1.00 | 1.98 | 0.00 | 1.93 | 0.00 | 1.05 | 2.63 | 4.29 |
time (sec) |
N/A | 0.323 | 0.177 | 0.096 | 0.000 | 0.275 | 0.000 | 0.345 | 0.032 | 1.153 |