Detailed conclusion table per each integral is given by 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 just an F.
In this table,the column N.S. in the table below, which stands for normalized size is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To help make the table fit, Mathematica was abbreviated to MMA.
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | B | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 37 | 26 | 34 | 69 | 24 | 26 | 24 | 23 |
N.S. | 1 | 1.68 | 1.18 | 1.55 | 3.14 | 1.09 | 1.18 | 1.09 | 1.05 |
time (sec) |
N/A | 0.074 | 0.111 | 0.429 | 0.275 | 0.341 | 0.060 | 0.387 | 0.084 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 0 | 15 | 15 | 14 | 14 | 14 | 14 | 14 |
N.S. | 1 | 0.00 | 0.88 | 0.88 | 0.82 | 0.82 | 0.82 | 0.82 | 0.82 |
time (sec) |
N/A | 0.941 | 0.082 | 0.542 | 0.532 | 0.403 | 0.049 | 0.394 | 4.511 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | A | C | F(-2) | A | A | A | B |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 23 | 129 | 0 | 21 | 20 | 24 | 24 |
N.S. |
1 | 0.00 | 0.96 | 5.38 | 0.00 | 0.88 | 0.83 | 1.00 | 1.00 |
time (sec) |
N/A | 5.935 | 0.388 | 6.660 | 0.000 | 0.375 | 7.023 | 0.893 | 4.679 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 25 | 21 | 22 | 21 | 21 | 20 | 28 | -1 |
N.S. | 1 | 0.89 | 0.75 | 0.79 | 0.75 | 0.75 | 0.71 | 1.00 | -0.04 |
time (sec) |
N/A | 0.232 | 0.042 | 9.386 | 0.545 | 0.393 | 0.058 | 0.427 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | B | A | A | B | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 64 | 17 | 18 | 44 | 16 | 15 | 22 | 46 |
N.S. | 1 | 3.37 | 0.89 | 0.95 | 2.32 | 0.84 | 0.79 | 1.16 | 2.42 |
time (sec) |
N/A | 0.114 | 0.101 | 0.218 | 0.710 | 0.370 | 0.138 | 0.460 | 4.375 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | B | A | A | A | A | A | B | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 164 | 33 | 31 | 50 | 52 | 31 | 78 | -1 |
N.S. | 1 | 4.56 | 0.92 | 0.86 | 1.39 | 1.44 | 0.86 | 2.17 | -0.03 |
time (sec) |
N/A | 1.315 | 0.073 | 58.697 | 0.540 | 0.371 | 0.077 | 0.412 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 25 | 25 | 25 | 24 | 24 | 20 | 24 | 24 |
N.S. | 1 | 1.04 | 1.04 | 1.04 | 1.00 | 1.00 | 0.83 | 1.00 | 1.00 |
time (sec) |
N/A | 0.532 | 0.062 | 0.272 | 0.574 | 0.399 | 0.103 | 0.410 | 4.294 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 31 | 27 | 21 | 15 | 15 | 27 | 15 | 22 |
N.S. | 1 | 1.35 | 1.17 | 0.91 | 0.65 | 0.65 | 1.17 | 0.65 | 0.96 |
time (sec) |
N/A | 0.006 | 0.002 | 0.255 | 0.282 | 0.354 | 0.078 | 0.391 | 0.048 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 17 | 17 | 17 | 16 | 16 | 15 | 16 | 16 |
N.S. | 1 | 1.06 | 1.06 | 1.06 | 1.00 | 1.00 | 0.94 | 1.00 | 1.00 |
time (sec) |
N/A | 0.003 | 0.003 | 0.020 | 0.290 | 0.356 | 0.025 | 0.391 | 4.175 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | B | A | B | C | A | A | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 51 | 18 | 38 | 372 | 21 | 20 | 35 | 16 |
N.S. | 1 | 2.83 | 1.00 | 2.11 | 20.67 | 1.17 | 1.11 | 1.94 | 0.89 |
time (sec) |
N/A | 0.283 | 0.435 | 0.450 | 0.358 | 0.357 | 0.092 | 0.389 | 4.039 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | C | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 29 | 29 | 28 | 31 | 20 | 19 | 20 | 20 |
N.S. | 1 | 1.45 | 1.45 | 1.40 | 1.55 | 1.00 | 0.95 | 1.00 | 1.00 |
time (sec) |
N/A | 0.057 | 0.055 | 0.574 | 0.304 | 0.402 | 0.066 | 0.382 | 0.083 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 29 | 29 | 40 | 27 | 36 | 34 | 0 | 29 |
N.S. | 1 | 0.97 | 0.97 | 1.33 | 0.90 | 1.20 | 1.13 | 0.00 | 0.97 |
time (sec) |
N/A | 1.274 | 0.385 | 0.984 | 0.364 | 0.378 | 0.312 | 0.000 | 4.248 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 0 | 14 | 19 | 15 | 18 | 15 | 18 | 18 |
N.S. | 1 | 0.00 | 1.00 | 1.36 | 1.07 | 1.29 | 1.07 | 1.29 | 1.29 |
time (sec) |
N/A | 0.259 | 0.041 | 13.003 | 0.528 | 0.370 | 0.047 | 0.387 | 4.399 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | A | A | A | A | B | A | B |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 0 | 43 | 48 | 44 | 42 | 60 | 54 | 179 |
N.S. | 1 | 0.00 | 1.23 | 1.37 | 1.26 | 1.20 | 1.71 | 1.54 | 5.11 |
time (sec) |
N/A | 3.587 | 0.072 | 0.309 | 0.327 | 0.362 | 0.116 | 0.393 | 4.448 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 19 | 19 | 20 | 19 | 21 | 17 | 19 | 19 |
N.S. | 1 | 0.86 | 0.86 | 0.91 | 0.86 | 0.95 | 0.77 | 0.86 | 0.86 |
time (sec) |
N/A | 0.005 | 0.002 | 0.313 | 0.273 | 0.370 | 0.015 | 0.373 | 0.037 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | A | A | B | A | A | A | F |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 28 | 25 | 585 | 42 | 24 | 44 | -1 |
N.S. | 1 | 0.00 | 1.08 | 0.96 | 22.50 | 1.62 | 0.92 | 1.69 | -0.04 |
time (sec) |
N/A | 1.822 | 1.556 | 1.735 | 0.567 | 0.416 | 0.094 | 0.462 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | B | A | C | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 55 | 24 | 314 | 42 | 21 | 27 | 21 | 22 |
N.S. | 1 | 2.39 | 1.04 | 13.65 | 1.83 | 0.91 | 1.17 | 0.91 | 0.96 |
time (sec) |
N/A | 0.869 | 0.824 | 0.665 | 0.310 | 0.352 | 0.331 | 0.405 | 4.269 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 21 | 21 | 21 | 20 | 20 | 19 | 22 | 20 |
N.S. | 1 | 0.95 | 0.95 | 0.95 | 0.91 | 0.91 | 0.86 | 1.00 | 0.91 |
time (sec) |
N/A | 0.039 | 0.011 | 0.331 | 0.302 | 0.351 | 0.477 | 0.391 | 4.373 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | B | B | C | B | B | B | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 74 | 68 | 879 | 189 | 152 | 104 | 205 | 170 |
N.S. | 1 | 3.36 | 3.09 | 39.95 | 8.59 | 6.91 | 4.73 | 9.32 | 7.73 |
time (sec) |
N/A | 0.730 | 0.088 | 3.327 | 0.324 | 0.418 | 0.102 | 0.398 | 4.911 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | A | B | B | A | B | A | B |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 0 | 20 | 58 | 107 | 26 | 39 | 38 | 41 |
N.S. | 1 | 0.00 | 1.00 | 2.90 | 5.35 | 1.30 | 1.95 | 1.90 | 2.05 |
time (sec) |
N/A | 0.921 | 0.188 | 0.896 | 0.365 | 0.348 | 0.190 | 0.415 | 4.475 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | B | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 13 | 12 | 12 | 266 | 14 | 25 | 10 | 14 | 28 |
N.S. | 1 | 0.92 | 0.92 | 20.46 | 1.08 | 1.92 | 0.77 | 1.08 | 2.15 |
time (sec) |
N/A | 0.043 | 0.132 | 2.479 | 0.282 | 0.361 | 0.038 | 0.379 | 4.163 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | B | A | A | F | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 54 | 21 | 20 | 0 | 23 | 19 | 27 | 18 |
N.S. | 1 | 2.45 | 0.95 | 0.91 | 0.00 | 1.05 | 0.86 | 1.23 | 0.82 |
time (sec) |
N/A | 0.168 | 0.046 | 0.312 | 0.000 | 0.356 | 0.086 | 0.380 | 4.456 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | A | A | F | A | A | F | B |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 42 | 28 | 0 | 40 | 34 | 0 | 73 |
N.S. | 1 | 0.00 | 1.50 | 1.00 | 0.00 | 1.43 | 1.21 | 0.00 | 2.61 |
time (sec) |
N/A | 18.028 | 0.155 | 2.691 | 0.000 | 0.412 | 8.283 | 0.000 | 4.513 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | A | A | A | A | A | F | F |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 25 | 24 | 26 | 22 | 20 | 0 | -1 |
N.S. | 1 | 0.00 | 1.00 | 0.96 | 1.04 | 0.88 | 0.80 | 0.00 | -0.04 |
time (sec) |
N/A | 6.782 | 0.077 | 0.080 | 0.347 | 0.388 | 0.121 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | A | A | B | A | B | A | B |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 42 | 42 | 63 | 42 | 41 | 42 | 121 |
N.S. | 1 | 0.00 | 1.40 | 1.40 | 2.10 | 1.40 | 1.37 | 1.40 | 4.03 |
time (sec) |
N/A | 7.927 | 0.075 | 1.084 | 0.544 | 0.362 | 4.884 | 1.003 | 5.187 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | B | A | B | B | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 99 | 34 | 71 | 147 | 44 | 32 | 42 | 40 |
N.S. | 1 | 3.54 | 1.21 | 2.54 | 5.25 | 1.57 | 1.14 | 1.50 | 1.43 |
time (sec) |
N/A | 0.261 | 0.112 | 0.579 | 0.339 | 0.366 | 0.114 | 0.392 | 4.349 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | F | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 45 | 71 | 27 | 30 | 28 | 26 | 29 | 33 |
N.S. | 1 | 1.29 | 2.03 | 0.77 | 0.86 | 0.80 | 0.74 | 0.83 | 0.94 |
time (sec) |
N/A | 0.788 | 1.025 | 0.076 | 0.810 | 0.404 | 0.219 | 0.435 | 4.365 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | B | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 54 | 13 | 13 | 12 | 12 | 12 | 0 | 12 |
N.S. | 1 | 3.60 | 0.87 | 0.87 | 0.80 | 0.80 | 0.80 | 0.00 | 0.80 |
time (sec) |
N/A | 0.146 | 0.108 | 0.298 | 0.318 | 0.356 | 7.099 | 0.000 | 4.332 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | F | A | F | A | A | A | F |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 84 | 44 | 0 | 32 | 27 | 53 | -1 |
N.S. | 1 | 0.00 | 2.62 | 1.38 | 0.00 | 1.00 | 0.84 | 1.66 | -0.03 |
time (sec) |
N/A | 9.041 | 1.285 | 0.300 | 0.000 | 0.367 | 0.401 | 0.414 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | A | B | A | A | A | A | B |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 31 | 936 | 26 | 28 | 22 | 26 | 46 |
N.S. | 1 | 0.00 | 1.29 | 39.00 | 1.08 | 1.17 | 0.92 | 1.08 | 1.92 |
time (sec) |
N/A | 1.624 | 0.095 | 21.366 | 0.300 | 0.378 | 0.072 | 0.415 | 4.600 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | B | B | B | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 34 | 43 | 51 | 78 | 62 | 60 | 48 | 32 |
N.S. | 1 | 1.31 | 1.65 | 1.96 | 3.00 | 2.38 | 2.31 | 1.85 | 1.23 |
time (sec) |
N/A | 1.243 | 0.069 | 1.179 | 0.528 | 0.348 | 0.217 | 0.391 | 4.237 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | F | A | F | A | F(-1) | A | B |
verified |
N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 0 | 19 | 0 | 18 | 0 | 18 | 19 |
N.S. |
1 | 0.00 | 0.00 | 0.73 | 0.00 | 0.69 | 0.00 | 0.69 | 0.73 |
time (sec) |
N/A | 1.808 | 0.146 | 0.853 | 0.000 | 0.388 | 0.000 | 0.388 | 4.216 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 25 | 25 | 22 | 21 | 22 | 22 | 21 | 20 |
N.S. | 1 | 0.89 | 0.89 | 0.79 | 0.75 | 0.79 | 0.79 | 0.75 | 0.71 |
time (sec) |
N/A | 0.009 | 0.005 | 0.328 | 0.285 | 0.345 | 0.042 | 0.397 | 0.052 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 11 | 5 | 5 | 6 | 5 | 5 | 3 | 5 | 5 |
N.S. | 1 | 0.45 | 0.45 | 0.55 | 0.45 | 0.45 | 0.27 | 0.45 | 0.45 |
time (sec) |
N/A | 0.001 | 0.000 | 0.008 | 0.288 | 0.341 | 0.008 | 0.388 | 0.031 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 30 | 31 | 27 | 26 | 26 | 34 | 26 | 24 |
N.S. | 1 | 0.83 | 0.86 | 0.75 | 0.72 | 0.72 | 0.94 | 0.72 | 0.67 |
time (sec) |
N/A | 0.011 | 0.011 | 0.432 | 0.278 | 0.393 | 0.069 | 0.396 | 0.049 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 18 | 18 | 18 | 17 | 17 | 14 | 17 | 17 |
N.S. | 1 | 0.90 | 0.90 | 0.90 | 0.85 | 0.85 | 0.70 | 0.85 | 0.85 |
time (sec) |
N/A | 0.009 | 0.008 | 0.335 | 0.287 | 0.404 | 0.041 | 0.393 | 4.111 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 28 | 24 | 33 | 29 | 31 | 56 | 35 | 31 |
N.S. | 1 | 1.27 | 1.09 | 1.50 | 1.32 | 1.41 | 2.55 | 1.59 | 1.41 |
time (sec) |
N/A | 1.059 | 0.040 | 0.632 | 0.315 | 0.368 | 0.362 | 0.441 | 4.577 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | C | A | A | A | C | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 52 | 45 | 587 | 38 | 51 | 36 | 60 | 36 |
N.S. | 1 | 1.58 | 1.36 | 17.79 | 1.15 | 1.55 | 1.09 | 1.82 | 1.09 |
time (sec) |
N/A | 4.060 | 0.119 | 1.061 | 0.524 | 0.368 | 0.616 | 0.429 | 4.516 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 32 | 35 | 44 | 44 | 29 | 78 | 32 |
N.S. | 1 | 0.00 | 1.39 | 1.52 | 1.91 | 1.91 | 1.26 | 3.39 | 1.39 |
time (sec) |
N/A | 0.373 | 0.026 | 5.217 | 0.559 | 0.374 | 0.053 | 0.784 | 0.297 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | B | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 36 | 32 | 26 | 31 | 43 | 29 | 24 | 24 |
N.S. | 1 | 1.71 | 1.52 | 1.24 | 1.48 | 2.05 | 1.38 | 1.14 | 1.14 |
time (sec) |
N/A | 0.033 | 0.017 | 0.492 | 0.278 | 0.331 | 0.079 | 0.403 | 0.079 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 28 | 28 | 28 | 25 | 42 | 24 | 59 | 27 |
N.S. | 1 | 0.97 | 0.97 | 0.97 | 0.86 | 1.45 | 0.83 | 2.03 | 0.93 |
time (sec) |
N/A | 0.150 | 0.051 | 7.066 | 0.310 | 0.352 | 0.042 | 0.398 | 4.336 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | C | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 27 | 27 | 399 | 26 | 25 | 24 | 26 | 23 |
N.S. | 1 | 0.93 | 0.93 | 13.76 | 0.90 | 0.86 | 0.83 | 0.90 | 0.79 |
time (sec) |
N/A | 0.131 | 0.040 | 0.678 | 0.315 | 0.357 | 0.123 | 0.398 | 4.383 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | A | A | A | A | A | A | F |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 25 | 29 | 25 | 31 | 27 | 25 | -1 |
N.S. | 1 | 0.00 | 0.96 | 1.12 | 0.96 | 1.19 | 1.04 | 0.96 | -0.04 |
time (sec) |
N/A | 2.332 | 0.153 | 0.360 | 0.333 | 0.370 | 0.095 | 0.398 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | B | A | C | B | A | B | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 86 | 35 | 1157 | 71 | 43 | 76 | 88 | 46 |
N.S. | 1 | 2.77 | 1.13 | 37.32 | 2.29 | 1.39 | 2.45 | 2.84 | 1.48 |
time (sec) |
N/A | 3.025 | 0.064 | 1.791 | 0.513 | 0.397 | 0.282 | 0.423 | 4.217 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | A | A | B | B | F(-1) | B | F |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 29 | 22 | 90 | 76 | 0 | 103 | -1 |
N.S. |
1 | 0.00 | 1.12 | 0.85 | 3.46 | 2.92 | 0.00 | 3.96 | -0.04 |
time (sec) |
N/A | 0.993 | 2.080 | 1.461 | 0.351 | 0.355 | 0.000 | 0.401 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | A | B | A | A | A | A | B |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 29 | 61 | 35 | 30 | 34 | 30 | 23 |
N.S. | 1 | 0.00 | 1.12 | 2.35 | 1.35 | 1.15 | 1.31 | 1.15 | 0.88 |
time (sec) |
N/A | 1.198 | 0.238 | 1.095 | 0.334 | 0.364 | 0.067 | 0.405 | 4.569 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 13 | 25 | 13 | 12 | 22 | 11 | 0 | 19 | 78 |
N.S. |
1 | 1.92 | 1.00 | 0.92 | 1.69 | 0.85 | 0.00 | 1.46 | 6.00 |
time (sec) |
N/A | 0.268 | 0.057 | 0.147 | 0.307 | 0.361 | 0.000 | 0.405 | 4.248 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | B | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 14 | 16 | 17 | 57 | 16 | 12 | 14 | 14 |
N.S. | 1 | 0.67 | 0.76 | 0.81 | 2.71 | 0.76 | 0.57 | 0.67 | 0.67 |
time (sec) |
N/A | 0.015 | 0.029 | 0.836 | 0.484 | 0.351 | 0.044 | 0.384 | 4.219 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 27 | 30 | 25 | 22 | 22 | 19 | 22 | 24 |
N.S. | 1 | 1.17 | 1.30 | 1.09 | 0.96 | 0.96 | 0.83 | 0.96 | 1.04 |
time (sec) |
N/A | 0.008 | 0.008 | 0.042 | 0.267 | 0.359 | 0.030 | 0.383 | 4.017 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | B | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 60 | 30 | 28 | 25 | 32 | 31 | 25 | 21 |
N.S. | 1 | 2.50 | 1.25 | 1.17 | 1.04 | 1.33 | 1.29 | 1.04 | 0.88 |
time (sec) |
N/A | 0.021 | 0.040 | 0.457 | 0.273 | 0.351 | 0.050 | 0.403 | 0.059 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 11 | 8 | 8 | 9 | 8 | 8 | 7 | 9 | 8 |
N.S. | 1 | 0.73 | 0.73 | 0.82 | 0.73 | 0.73 | 0.64 | 0.82 | 0.73 |
time (sec) |
N/A | 0.002 | 0.001 | 0.090 | 0.294 | 0.379 | 0.017 | 0.395 | 0.016 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 10 | 10 | 10 | 9 | 9 | 10 | 9 | 9 |
N.S. | 1 | 0.53 | 0.53 | 0.53 | 0.47 | 0.47 | 0.53 | 0.47 | 0.47 |
time (sec) |
N/A | 0.001 | 0.000 | 0.332 | 0.296 | 0.345 | 0.004 | 0.384 | 0.002 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 25 | 23 | 19 | 18 | 24 | 15 | 18 | 21 |
N.S. | 1 | 1.09 | 1.00 | 0.83 | 0.78 | 1.04 | 0.65 | 0.78 | 0.91 |
time (sec) |
N/A | 0.097 | 0.072 | 0.563 | 0.278 | 0.339 | 0.122 | 0.397 | 4.142 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 13 | 6 | 6 | 7 | 6 | 6 | 5 | 7 | 6 |
N.S. | 1 | 0.46 | 0.46 | 0.54 | 0.46 | 0.46 | 0.38 | 0.54 | 0.46 |
time (sec) |
N/A | 0.001 | 0.002 | 0.180 | 0.269 | 0.374 | 0.016 | 0.395 | 0.015 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | A | A | B | A | A | F | B |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 0 | 34 | 32 | 357 | 30 | 27 | 0 | 46 |
N.S. | 1 | 0.00 | 1.03 | 0.97 | 10.82 | 0.91 | 0.82 | 0.00 | 1.39 |
time (sec) |
N/A | 79.843 | 0.277 | 2.783 | 0.619 | 0.363 | 13.070 | 0.000 | 4.755 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 17 | 16 | 14 | 14 | 14 | 14 | 14 | 14 |
N.S. | 1 | 0.77 | 0.73 | 0.64 | 0.64 | 0.64 | 0.64 | 0.64 | 0.64 |
time (sec) |
N/A | 0.094 | 0.028 | 0.075 | 0.274 | 0.359 | 0.031 | 0.389 | 4.150 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | B | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 22 | 22 | 22 | 79 | 21 | 15 | 25 | 21 |
N.S. | 1 | 1.38 | 1.38 | 1.38 | 4.94 | 1.31 | 0.94 | 1.56 | 1.31 |
time (sec) |
N/A | 0.196 | 0.029 | 0.026 | 0.272 | 0.379 | 0.119 | 0.383 | 4.254 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | B | A | B | B | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 98 | 51 | 66 | 81 | 40 | 48 | 41 | 42 |
N.S. | 1 | 2.97 | 1.55 | 2.00 | 2.45 | 1.21 | 1.45 | 1.24 | 1.27 |
time (sec) |
N/A | 0.088 | 0.023 | 0.356 | 0.281 | 0.374 | 0.125 | 0.381 | 4.271 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | B | A | B | A | A | A | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 52 | 24 | 212 | 15 | 30 | 15 | 34 | 19 |
N.S. | 1 | 2.74 | 1.26 | 11.16 | 0.79 | 1.58 | 0.79 | 1.79 | 1.00 |
time (sec) |
N/A | 0.117 | 0.410 | 1.217 | 0.536 | 0.360 | 0.064 | 0.396 | 4.296 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | A | B | A | A | A | F(-1) | B |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 21 | 42 | 30 | 34 | 19 | 0 | 20 |
N.S. |
1 | 0.00 | 0.84 | 1.68 | 1.20 | 1.36 | 0.76 | 0.00 | 0.80 |
time (sec) |
N/A | 0.238 | 0.073 | 5.085 | 0.309 | 0.367 | 0.058 | 0.000 | 5.271 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | B | B | B | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 29 | 40 | 41 | 40 | 23 | 27 | 28 | 16 |
N.S. | 1 | 1.81 | 2.50 | 2.56 | 2.50 | 1.44 | 1.69 | 1.75 | 1.00 |
time (sec) |
N/A | 0.034 | 0.022 | 0.452 | 0.269 | 0.382 | 0.059 | 0.382 | 4.259 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | F | C | F | A | A | F | B |
verified |
N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 0 | 1475 | 0 | 42 | 34 | 0 | 38 |
N.S. | 1 | 0.00 | 0.00 | 56.73 | 0.00 | 1.62 | 1.31 | 0.00 | 1.46 |
time (sec) |
N/A | 5.869 | 0.532 | 1.839 | 0.000 | 0.428 | 0.475 | 0.000 | 4.537 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | B | A | B | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 22 | 22 | 28 | 51 | 28 | 54 | 25 | 29 |
N.S. | 1 | 1.22 | 1.22 | 1.56 | 2.83 | 1.56 | 3.00 | 1.39 | 1.61 |
time (sec) |
N/A | 0.057 | 0.023 | 1.906 | 0.548 | 0.379 | 0.442 | 0.405 | 4.394 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | B | B | B | B | A | A | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 61 | 51 | 46 | 183 | 16 | 31 | 58 | 16 |
N.S. | 1 | 2.77 | 2.32 | 2.09 | 8.32 | 0.73 | 1.41 | 2.64 | 0.73 |
time (sec) |
N/A | 0.110 | 0.039 | 1.524 | 0.515 | 0.376 | 0.131 | 0.402 | 4.656 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | B | A | B | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 36 | 36 | 29 | 64 | 36 | 42 | 35 | 192 |
N.S. | 1 | 1.29 | 1.29 | 1.04 | 2.29 | 1.29 | 1.50 | 1.25 | 6.86 |
time (sec) |
N/A | 0.956 | 0.719 | 0.415 | 0.540 | 0.407 | 0.158 | 0.388 | 4.466 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | B | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 21 | 21 | 45 | 20 | 23 | 14 | 23 | 20 |
N.S. | 1 | 0.95 | 0.95 | 2.05 | 0.91 | 1.05 | 0.64 | 1.05 | 0.91 |
time (sec) |
N/A | 0.011 | 0.013 | 1.167 | 0.353 | 0.380 | 0.035 | 0.390 | 4.120 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 12 | 18 | 11 | 15 | 16 | 10 | 14 | 10 | 14 |
N.S. | 1 | 1.50 | 0.92 | 1.25 | 1.33 | 0.83 | 1.17 | 0.83 | 1.17 |
time (sec) |
N/A | 0.008 | 0.009 | 0.352 | 0.271 | 0.378 | 0.033 | 0.406 | 0.064 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | A | A | A | A | A | A | F |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 33 | 38 | 28 | 28 | 42 | 43 | -1 |
N.S. | 1 | 0.00 | 1.03 | 1.19 | 0.88 | 0.88 | 1.31 | 1.34 | -0.03 |
time (sec) |
N/A | 5.716 | 4.014 | 0.098 | 0.340 | 0.371 | 0.130 | 0.859 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 23 | 28 | 23 | 23 | 24 | 23 | 26 |
N.S. | 1 | 0.00 | 0.77 | 0.93 | 0.77 | 0.77 | 0.80 | 0.77 | 0.87 |
time (sec) |
N/A | 2.503 | 0.137 | 0.325 | 0.375 | 0.395 | 0.281 | 0.408 | 4.394 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | A | A | A | A | A | A | F |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 20 | 20 | 18 | 18 | 17 | 18 | -1 |
N.S. | 1 | 0.00 | 0.91 | 0.91 | 0.82 | 0.82 | 0.77 | 0.82 | -0.05 |
time (sec) |
N/A | 1.401 | 0.109 | 0.069 | 0.319 | 0.371 | 0.116 | 0.422 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 14 | 12 | 14 | 13 | 13 | 10 | 13 | 12 |
N.S. | 1 | 0.82 | 0.71 | 0.82 | 0.76 | 0.76 | 0.59 | 0.76 | 0.71 |
time (sec) |
N/A | 0.003 | 0.000 | 0.325 | 0.270 | 0.343 | 0.009 | 0.384 | 4.101 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | A | A | A | A | A | A | F |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 30 | 24 | 23 | 36 | 22 | 45 | -1 |
N.S. | 1 | 0.00 | 1.03 | 0.83 | 0.79 | 1.24 | 0.76 | 1.55 | -0.03 |
time (sec) |
N/A | 0.786 | 3.675 | 0.618 | 0.332 | 0.387 | 0.064 | 0.400 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | F | C | A | A | A | A | F |
verified |
N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 0 | 1010 | 43 | 28 | 31 | 40 | -1 |
N.S. | 1 | 0.00 | 0.00 | 37.41 | 1.59 | 1.04 | 1.15 | 1.48 | -0.04 |
time (sec) |
N/A | 3.165 | 6.922 | 1.406 | 0.331 | 0.412 | 0.092 | 0.406 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 11 | 9 | 9 | 8 | 7 | 7 | 5 | 7 | 8 |
N.S. | 1 | 0.82 | 0.82 | 0.73 | 0.64 | 0.64 | 0.45 | 0.64 | 0.73 |
time (sec) |
N/A | 0.008 | 0.007 | 0.036 | 0.263 | 0.367 | 0.035 | 0.385 | 0.039 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | C | A | A | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 35 | 20 | 37 | 40 | 26 | 34 | 32 | 33 |
N.S. | 1 | 1.35 | 0.77 | 1.42 | 1.54 | 1.00 | 1.31 | 1.23 | 1.27 |
time (sec) |
N/A | 0.046 | 0.029 | 3.126 | 0.293 | 0.366 | 0.069 | 0.381 | 4.162 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | A | A | F(-2) | A | A | F(-1) | B |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 0 | 29 | 30 | 0 | 29 | 26 | 0 | 31 |
N.S. |
1 | 0.00 | 0.88 | 0.91 | 0.00 | 0.88 | 0.79 | 0.00 | 0.94 |
time (sec) |
N/A | 3.444 | 0.172 | 1.152 | 0.000 | 0.370 | 0.129 | 0.000 | 4.523 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | C | C | A | B | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 45 | 85 | 11 | 39 | 13 | 10 | 13 | 13 |
N.S. | 1 | 2.25 | 4.25 | 0.55 | 1.95 | 0.65 | 0.50 | 0.65 | 0.65 |
time (sec) |
N/A | 0.126 | 0.029 | 1.752 | 0.280 | 0.407 | 0.040 | 0.385 | 4.169 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | B | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 24 | 21 | 22 | 148 | 21 | 24 | 21 | 21 |
N.S. | 1 | 1.71 | 1.50 | 1.57 | 10.57 | 1.50 | 1.71 | 1.50 | 1.50 |
time (sec) |
N/A | 0.126 | 0.058 | 2.828 | 0.542 | 0.362 | 0.057 | 0.409 | 0.617 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 27 | 24 | 26 | 25 | 26 | 19 | 25 | 27 |
N.S. | 1 | 0.84 | 0.75 | 0.81 | 0.78 | 0.81 | 0.59 | 0.78 | 0.84 |
time (sec) |
N/A | 0.013 | 0.006 | 0.637 | 0.298 | 0.367 | 0.043 | 0.395 | 0.058 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | F | C | A | A | A | A | B |
verified |
N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 37 | 0 | 0 | 46 | 53 | 45 | 36 | 51 | 48 |
N.S. | 1 | 0.00 | 0.00 | 1.24 | 1.43 | 1.22 | 0.97 | 1.38 | 1.30 |
time (sec) |
N/A | 13.684 | 6.676 | 5.798 | 0.528 | 0.377 | 0.579 | 0.495 | 4.745 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 10 | 15 | 15 | 15 | 14 | 14 | 17 | 14 | 8 |
N.S. | 1 | 1.50 | 1.50 | 1.50 | 1.40 | 1.40 | 1.70 | 1.40 | 0.80 |
time (sec) |
N/A | 0.002 | 0.001 | 0.452 | 0.281 | 0.362 | 0.009 | 0.379 | 0.046 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | A | A | B | A | A | B | B |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 25 | 23 | 102 | 21 | 24 | 80 | 149 |
N.S. | 1 | 0.00 | 0.96 | 0.88 | 3.92 | 0.81 | 0.92 | 3.08 | 5.73 |
time (sec) |
N/A | 0.492 | 0.093 | 3.819 | 0.551 | 0.371 | 0.114 | 0.484 | 4.554 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | C | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 31 | 27 | 78 | 23 | 26 | 24 | 23 | 30 |
N.S. | 1 | 1.11 | 0.96 | 2.79 | 0.82 | 0.93 | 0.86 | 0.82 | 1.07 |
time (sec) |
N/A | 0.166 | 0.031 | 165.301 | 0.528 | 0.352 | 0.375 | 0.405 | 4.796 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | A | A | B | A | A | A | B |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 21 | 24 | 63 | 21 | 22 | 24 | 21 |
N.S. | 1 | 0.00 | 0.81 | 0.92 | 2.42 | 0.81 | 0.85 | 0.92 | 0.81 |
time (sec) |
N/A | 0.607 | 0.056 | 0.762 | 0.595 | 0.364 | 0.212 | 0.473 | 4.543 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | A | A | B | A | A | A | B |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 35 | 30 | 65 | 31 | 24 | 31 | 29 |
N.S. | 1 | 0.00 | 1.17 | 1.00 | 2.17 | 1.03 | 0.80 | 1.03 | 0.97 |
time (sec) |
N/A | 73.712 | 0.107 | 0.236 | 0.527 | 0.398 | 0.098 | 0.403 | 4.389 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 30 | 28 | 33 | 31 | 31 | 24 | 31 | 26 |
N.S. | 1 | 1.20 | 1.12 | 1.32 | 1.24 | 1.24 | 0.96 | 1.24 | 1.04 |
time (sec) |
N/A | 0.014 | 0.033 | 0.519 | 0.282 | 0.388 | 0.075 | 0.384 | 4.238 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 13 | 10 | 19 | 7 | 8 | 8 | 7 | 13 | 6 |
N.S. | 1 | 0.77 | 1.46 | 0.54 | 0.62 | 0.62 | 0.54 | 1.00 | 0.46 |
time (sec) |
N/A | 0.002 | 0.002 | 1.159 | 0.287 | 0.335 | 0.023 | 0.392 | 0.057 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | A | C | A | A | A | A | F |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 49 | 321 | 44 | 44 | 42 | 46 | -1 |
N.S. | 1 | 0.00 | 1.53 | 10.03 | 1.38 | 1.38 | 1.31 | 1.44 | -0.03 |
time (sec) |
N/A | 7.758 | 0.160 | 0.825 | 0.496 | 0.377 | 6.096 | 1.386 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 21 | 16 | 15 | 17 | 17 | 17 | 15 |
N.S. | 1 | 1.00 | 1.00 | 0.76 | 0.71 | 0.81 | 0.81 | 0.81 | 0.71 |
time (sec) |
N/A | 0.025 | 0.005 | 1.173 | 0.259 | 0.370 | 0.026 | 0.378 | 4.085 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | A | A | A | B | A | A | B |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 31 | 30 | 50 | 66 | 34 | 54 | 48 |
N.S. | 1 | 0.00 | 0.97 | 0.94 | 1.56 | 2.06 | 1.06 | 1.69 | 1.50 |
time (sec) |
N/A | 3.896 | 0.070 | 0.388 | 0.334 | 0.393 | 0.094 | 0.416 | 4.318 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | B | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 174 | 32 | 443 | 368 | 86 | 105 | 103 | 31 |
N.S. | 1 | 6.69 | 1.23 | 17.04 | 14.15 | 3.31 | 4.04 | 3.96 | 1.19 |
time (sec) |
N/A | 0.409 | 1.379 | 1.239 | 0.295 | 0.352 | 0.093 | 0.386 | 4.362 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | B | A | B | B | B | B | F |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 66 | 23 | 106 | 113 | 60 | 130 | -1 |
N.S. | 1 | 0.00 | 2.36 | 0.82 | 3.79 | 4.04 | 2.14 | 4.64 | -0.04 |
time (sec) |
N/A | 1.590 | 3.772 | 1.422 | 0.368 | 0.420 | 0.176 | 0.553 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 26 | 29 | 22 | 19 | 19 | 44 | 19 | 17 |
N.S. | 1 | 0.87 | 0.97 | 0.73 | 0.63 | 0.63 | 1.47 | 0.63 | 0.57 |
time (sec) |
N/A | 0.008 | 0.003 | 0.404 | 0.366 | 0.369 | 0.072 | 0.391 | 4.138 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | A | A | A | A | A | F | B |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 0 | 34 | 28 | 27 | 29 | 29 | 0 | 27 |
N.S. | 1 | 0.00 | 0.97 | 0.80 | 0.77 | 0.83 | 0.83 | 0.00 | 0.77 |
time (sec) |
N/A | 6.385 | 0.163 | 0.552 | 0.691 | 0.402 | 26.246 | 0.000 | 4.698 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | B | B | B | B | A | B | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 299 | 277 | 401 | 606 | 45 | 51 | 45 | 400 |
N.S. | 1 | 11.50 | 10.65 | 15.42 | 23.31 | 1.73 | 1.96 | 1.73 | 15.38 |
time (sec) |
N/A | 0.368 | 0.270 | 1.813 | 0.524 | 0.399 | 0.099 | 0.394 | 5.262 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | C | B | B | C | B | B | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 217 | 111 | 232 | 219 | 131 | 122 | 230 | 207 |
N.S. | 1 | 7.48 | 3.83 | 8.00 | 7.55 | 4.52 | 4.21 | 7.93 | 7.14 |
time (sec) |
N/A | 1.061 | 0.051 | 6.628 | 0.351 | 0.427 | 0.119 | 0.399 | 4.851 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | B | B | C | B | B | B | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 66 | 60 | 187 | 67 | 151 | 76 | 16 | 84 |
N.S. | 1 | 3.00 | 2.73 | 8.50 | 3.05 | 6.86 | 3.45 | 0.73 | 3.82 |
time (sec) |
N/A | 0.168 | 0.040 | 1.893 | 0.271 | 0.358 | 0.539 | 0.400 | 4.332 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | C | A | A | B | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 39 | 39 | 127 | 36 | 36 | 36 | 38 | 36 |
N.S. | 1 | 1.86 | 1.86 | 6.05 | 1.71 | 1.71 | 1.71 | 1.81 | 1.71 |
time (sec) |
N/A | 0.099 | 0.057 | 1.681 | 0.280 | 0.367 | 5.411 | 0.398 | 4.374 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 9 | 9 | 10 | 9 | 9 | 7 | 9 | 7 |
N.S. | 1 | 0.45 | 0.45 | 0.50 | 0.45 | 0.45 | 0.35 | 0.45 | 0.35 |
time (sec) |
N/A | 0.001 | 0.000 | 0.006 | 0.279 | 0.365 | 0.008 | 0.387 | 0.029 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | C | C | A | B | A | A | B | B |
verified |
N/A | NO | NO | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 3127 | 10260 | 29 | 60 | 28 | 24 | 60 | 25 |
N.S. | 1 | 130.29 | 427.50 | 1.21 | 2.50 | 1.17 | 1.00 | 2.50 | 1.04 |
time (sec) |
N/A | 5.461 | 9.195 | 2.270 | 0.959 | 0.369 | 0.083 | 0.527 | 4.390 |