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 | A | B | B | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 26 | 25 | 17 | 49 | 66 | 17 | 17 |
N.S. | 1 | 1.00 | 1.00 | 0.96 | 0.65 | 1.88 | 2.54 | 0.65 | 0.65 |
time (sec) |
N/A | 0.012 | 0.032 | 4.793 | 0.264 | 0.375 | 0.411 | 0.432 | 0.101 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | B | B | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 26 | 25 | 17 | 71 | 90 | 17 | 17 |
N.S. | 1 | 1.00 | 1.00 | 0.96 | 0.65 | 2.73 | 3.46 | 0.65 | 0.65 |
time (sec) |
N/A | 0.012 | 0.033 | 5.053 | 0.265 | 0.372 | 0.680 | 0.408 | 1.470 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 24 | 25 | 17 | 24 | 0 | 17 | 15 |
N.S. | 1 | 1.00 | 0.92 | 0.96 | 0.65 | 0.92 | 0.00 | 0.65 | 0.58 |
time (sec) |
N/A | 0.012 | 0.018 | 2.605 | 0.262 | 0.364 | 0.000 | 0.409 | 1.585 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 24 | 25 | 17 | 42 | 0 | 17 | 15 |
N.S. | 1 | 1.00 | 0.92 | 0.96 | 0.65 | 1.62 | 0.00 | 0.65 | 0.58 |
time (sec) |
N/A | 0.013 | 0.027 | 2.764 | 0.273 | 0.407 | 0.000 | 0.422 | 1.566 |
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 | 24 | 24 | 47 | 25 | 24 | 22 | 29 | 56 | 15 |
N.S. | 1 | 1.00 | 1.96 | 1.04 | 1.00 | 0.92 | 1.21 | 2.33 | 0.62 |
time (sec) |
N/A | 0.012 | 0.017 | 2.010 | 0.256 | 0.372 | 0.062 | 0.409 | 0.048 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | B | B | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 27 | 71 | 89 | 43 | 44 | 17 | 17 |
N.S. | 1 | 1.00 | 1.00 | 2.63 | 3.30 | 1.59 | 1.63 | 0.63 | 0.63 |
time (sec) |
N/A | 0.012 | 0.024 | 3.355 | 0.261 | 0.391 | 0.080 | 0.406 | 0.060 |
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 | 27 | 27 | 27 | 36 | 147 | 62 | 83 | 17 | 17 |
N.S. | 1 | 1.00 | 1.00 | 1.33 | 5.44 | 2.30 | 3.07 | 0.63 | 0.63 |
time (sec) |
N/A | 0.012 | 0.021 | 3.678 | 0.270 | 0.375 | 0.128 | 0.413 | 1.849 |
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 | 28 | 27 | 29 | 20 | 39 | 39 | 23 | 21 |
N.S. | 1 | 1.00 | 0.96 | 1.04 | 0.71 | 1.39 | 1.39 | 0.82 | 0.75 |
time (sec) |
N/A | 0.012 | 0.033 | 3.572 | 0.259 | 0.385 | 0.083 | 0.428 | 1.659 |
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 | 24 | 22 | 22 | 13 | 20 | 32 | 13 | 13 |
N.S. | 1 | 1.00 | 0.92 | 0.92 | 0.54 | 0.83 | 1.33 | 0.54 | 0.54 |
time (sec) |
N/A | 0.013 | 0.006 | 6.758 | 0.267 | 0.364 | 0.189 | 0.407 | 1.533 |
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 | 27 | 27 | 27 | 36 | 17 | 41 | 65 | 17 | 17 |
N.S. | 1 | 1.00 | 1.00 | 1.33 | 0.63 | 1.52 | 2.41 | 0.63 | 0.63 |
time (sec) |
N/A | 0.013 | 0.033 | 5.218 | 0.273 | 0.375 | 0.290 | 0.413 | 0.096 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | B | A | B | B | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 27 | 55 | 17 | 59 | 88 | 17 | 17 |
N.S. | 1 | 1.00 | 1.00 | 2.04 | 0.63 | 2.19 | 3.26 | 0.63 | 0.63 |
time (sec) |
N/A | 0.013 | 0.050 | 4.930 | 0.277 | 0.415 | 0.476 | 0.395 | 0.056 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 26 | 26 | 17 | 24 | 0 | 17 | 18 |
N.S. | 1 | 1.00 | 0.96 | 0.96 | 0.63 | 0.89 | 0.00 | 0.63 | 0.67 |
time (sec) |
N/A | 0.017 | 0.019 | 3.335 | 0.272 | 0.394 | 0.000 | 0.414 | 1.551 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 26 | 26 | 17 | 40 | 0 | 17 | 27 |
N.S. | 1 | 1.00 | 0.96 | 0.96 | 0.63 | 1.48 | 0.00 | 0.63 | 1.00 |
time (sec) |
N/A | 0.014 | 0.022 | 2.640 | 0.286 | 0.373 | 0.000 | 0.389 | 0.173 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | B | C | B | B | F | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 124 | 124 | 355 | 290 | 279 | 2040 | 0 | 240 | 495 |
N.S. | 1 | 1.00 | 2.86 | 2.34 | 2.25 | 16.45 | 0.00 | 1.94 | 3.99 |
time (sec) |
N/A | 0.144 | 1.291 | 1.030 | 0.466 | 0.456 | 0.000 | 0.418 | 1.918 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | B | B | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 100 | 100 | 79 | 111 | 210 | 207 | 0 | 110 | 145 |
N.S. | 1 | 1.00 | 0.79 | 1.11 | 2.10 | 2.07 | 0.00 | 1.10 | 1.45 |
time (sec) |
N/A | 0.148 | 0.125 | 0.911 | 0.283 | 0.377 | 0.000 | 0.410 | 1.520 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | B | C | B | B | F | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 58 | 194 | 134 | 120 | 502 | 0 | 117 | 233 |
N.S. | 1 | 1.00 | 3.34 | 2.31 | 2.07 | 8.66 | 0.00 | 2.02 | 4.02 |
time (sec) |
N/A | 0.074 | 1.353 | 0.971 | 0.482 | 0.394 | 0.000 | 0.414 | 1.613 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 26 | 32 | 43 | 42 | 0 | 31 | 33 |
N.S. | 1 | 1.00 | 0.90 | 1.10 | 1.48 | 1.45 | 0.00 | 1.07 | 1.14 |
time (sec) |
N/A | 0.040 | 0.034 | 0.625 | 0.262 | 0.417 | 0.000 | 0.401 | 1.566 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | B | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 11 | 11 | 16 | 12 | 11 | 30 | 0 | 21 | 40 |
N.S. | 1 | 1.00 | 1.45 | 1.09 | 1.00 | 2.73 | 0.00 | 1.91 | 3.64 |
time (sec) |
N/A | 0.007 | 0.007 | 0.466 | 0.262 | 0.381 | 0.000 | 0.412 | 0.071 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | B | B | B | B | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 11 | 11 | 11 | 50 | 28 | 27 | 32 | 22 | 25 |
N.S. | 1 | 1.00 | 1.00 | 4.55 | 2.55 | 2.45 | 2.91 | 2.00 | 2.27 |
time (sec) |
N/A | 0.031 | 0.006 | 0.987 | 0.259 | 0.356 | 0.235 | 0.403 | 0.080 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | C | A | A | B | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 62 | 62 | 502 | 101 | 100 | 362 | 0 | 97 | 132 |
N.S. | 1 | 1.00 | 8.10 | 1.63 | 1.61 | 5.84 | 0.00 | 1.56 | 2.13 |
time (sec) |
N/A | 0.095 | 1.440 | 1.131 | 0.481 | 0.395 | 0.000 | 0.409 | 1.741 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | B | B | B | B | A | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 48 | 48 | 80 | 141 | 117 | 543 | 651 | 75 | -1 |
N.S. | 1 | 1.00 | 1.67 | 2.94 | 2.44 | 11.31 | 13.56 | 1.56 | -0.02 |
time (sec) |
N/A | 0.058 | 0.087 | 1.216 | 0.290 | 0.431 | 1.300 | 0.430 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | C | B | B | B | F | A | F |
verified |
N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
size | 146 | 146 | 3430 | 357 | 375 | 2978 | 0 | 267 | -1 |
N.S. | 1 | 1.00 | 23.49 | 2.45 | 2.57 | 20.40 | 0.00 | 1.83 | -0.01 |
time (sec) |
N/A | 0.259 | 6.302 | 1.319 | 0.504 | 0.415 | 0.000 | 0.436 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | B | B | B | B | A | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 95 | 95 | 140 | 285 | 297 | 2640 | 2162 | 152 | -1 |
N.S. | 1 | 1.00 | 1.47 | 3.00 | 3.13 | 27.79 | 22.76 | 1.60 | -0.01 |
time (sec) |
N/A | 0.079 | 0.226 | 1.261 | 0.301 | 0.399 | 7.261 | 0.425 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | B | B | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 40 | 40 | 62 | 40 | 235 | 94 | 0 | 34 | 90 |
N.S. | 1 | 1.00 | 1.55 | 1.00 | 5.88 | 2.35 | 0.00 | 0.85 | 2.25 |
time (sec) |
N/A | 0.047 | 0.084 | 2.107 | 0.493 | 0.393 | 0.000 | 0.421 | 0.285 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | B | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 38 | 74 | 26 | 181 | 52 | 0 | 22 | 65 |
N.S. | 1 | 1.00 | 1.95 | 0.68 | 4.76 | 1.37 | 0.00 | 0.58 | 1.71 |
time (sec) |
N/A | 0.072 | 0.095 | 1.422 | 0.262 | 0.397 | 0.000 | 0.423 | 1.632 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | B | B | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 39 | 26 | 73 | 50 | 0 | 21 | 39 |
N.S. | 1 | 1.00 | 1.50 | 1.00 | 2.81 | 1.92 | 0.00 | 0.81 | 1.50 |
time (sec) |
N/A | 0.037 | 0.021 | 1.497 | 0.473 | 0.350 | 0.000 | 0.406 | 1.647 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 14 | 15 | 25 | 17 | 0 | 12 | 14 |
N.S. | 1 | 1.00 | 0.70 | 0.75 | 1.25 | 0.85 | 0.00 | 0.60 | 0.70 |
time (sec) |
N/A | 0.052 | 0.008 | 0.952 | 0.277 | 0.369 | 0.000 | 0.408 | 1.640 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 11 | 11 | 17 | 11 | 9 | 11 | 0 | 18 | 14 |
N.S. | 1 | 1.00 | 1.55 | 1.00 | 0.82 | 1.00 | 0.00 | 1.64 | 1.27 |
time (sec) |
N/A | 0.006 | 0.005 | 0.465 | 0.262 | 0.371 | 0.000 | 0.409 | 1.595 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | B | A | A | B | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 13 | 13 | 17 | 33 | 15 | 11 | 22 | 13 | 14 |
N.S. | 1 | 1.00 | 1.31 | 2.54 | 1.15 | 0.85 | 1.69 | 1.00 | 1.08 |
time (sec) |
N/A | 0.023 | 0.014 | 1.466 | 0.261 | 0.397 | 0.102 | 0.420 | 1.565 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 31 | 29 | 14 | 17 | 0 | 12 | 14 |
N.S. | 1 | 1.00 | 1.55 | 1.45 | 0.70 | 0.85 | 0.00 | 0.60 | 0.70 |
time (sec) |
N/A | 0.031 | 0.021 | 1.770 | 0.260 | 0.405 | 0.000 | 0.397 | 1.504 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | B | A | B | B | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 40 | 56 | 33 | 50 | 432 | 27 | 41 |
N.S. | 1 | 1.00 | 1.43 | 2.00 | 1.18 | 1.79 | 15.43 | 0.96 | 1.46 |
time (sec) |
N/A | 0.036 | 0.031 | 2.067 | 0.266 | 0.362 | 0.836 | 0.399 | 0.187 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 38 | 75 | 41 | 40 | 52 | 0 | 22 | 67 |
N.S. | 1 | 1.00 | 1.97 | 1.08 | 1.05 | 1.37 | 0.00 | 0.58 | 1.76 |
time (sec) |
N/A | 0.055 | 0.056 | 1.951 | 0.283 | 0.490 | 0.000 | 0.403 | 0.172 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | B | B | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 42 | 42 | 45 | 68 | 58 | 94 | 1445 | 38 | 94 |
N.S. | 1 | 1.00 | 1.07 | 1.62 | 1.38 | 2.24 | 34.40 | 0.90 | 2.24 |
time (sec) |
N/A | 0.040 | 0.080 | 2.285 | 0.266 | 0.404 | 2.831 | 0.407 | 1.679 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | B | B | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 42 | 42 | 62 | 40 | 235 | 94 | 0 | 34 | 94 |
N.S. | 1 | 1.00 | 1.48 | 0.95 | 5.60 | 2.24 | 0.00 | 0.81 | 2.24 |
time (sec) |
N/A | 0.039 | 0.039 | 1.721 | 0.483 | 0.371 | 0.000 | 0.409 | 1.604 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | B | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 38 | 75 | 26 | 181 | 52 | 0 | 22 | 67 |
N.S. | 1 | 1.00 | 1.97 | 0.68 | 4.76 | 1.37 | 0.00 | 0.58 | 1.76 |
time (sec) |
N/A | 0.074 | 0.037 | 1.448 | 0.264 | 0.406 | 0.000 | 0.424 | 0.128 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | B | B | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 39 | 26 | 73 | 50 | 0 | 21 | 41 |
N.S. | 1 | 1.00 | 1.39 | 0.93 | 2.61 | 1.79 | 0.00 | 0.75 | 1.46 |
time (sec) |
N/A | 0.035 | 0.021 | 1.551 | 0.464 | 0.391 | 0.000 | 0.405 | 0.155 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 14 | 15 | 25 | 17 | 0 | 12 | 14 |
N.S. | 1 | 1.00 | 0.70 | 0.75 | 1.25 | 0.85 | 0.00 | 0.60 | 0.70 |
time (sec) |
N/A | 0.055 | 0.008 | 1.000 | 0.260 | 0.355 | 0.000 | 0.416 | 1.560 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 11 | 11 | 17 | 11 | 9 | 11 | 0 | 18 | 14 |
N.S. | 1 | 1.00 | 1.55 | 1.00 | 0.82 | 1.00 | 0.00 | 1.64 | 1.27 |
time (sec) |
N/A | 0.006 | 0.006 | 0.517 | 0.256 | 0.391 | 0.000 | 0.423 | 1.471 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | B | B | A | B | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 11 | 11 | 17 | 33 | 15 | 11 | 22 | 13 | 14 |
N.S. | 1 | 1.00 | 1.55 | 3.00 | 1.36 | 1.00 | 2.00 | 1.18 | 1.27 |
time (sec) |
N/A | 0.022 | 0.014 | 1.846 | 0.274 | 0.362 | 0.108 | 0.413 | 0.128 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 31 | 29 | 14 | 17 | 0 | 12 | 14 |
N.S. | 1 | 1.00 | 1.55 | 1.45 | 0.70 | 0.85 | 0.00 | 0.60 | 0.70 |
time (sec) |
N/A | 0.033 | 0.020 | 1.720 | 0.256 | 0.373 | 0.000 | 0.406 | 1.506 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | B | A | B | B | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 27 | 56 | 33 | 50 | 432 | 27 | 39 |
N.S. | 1 | 1.00 | 1.04 | 2.15 | 1.27 | 1.92 | 16.62 | 1.04 | 1.50 |
time (sec) |
N/A | 0.036 | 0.028 | 2.247 | 0.271 | 0.412 | 0.818 | 0.416 | 0.172 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 38 | 74 | 41 | 40 | 52 | 0 | 22 | 65 |
N.S. | 1 | 1.00 | 1.95 | 1.08 | 1.05 | 1.37 | 0.00 | 0.58 | 1.71 |
time (sec) |
N/A | 0.055 | 0.014 | 1.905 | 0.261 | 0.352 | 0.000 | 0.406 | 1.611 |
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 | 40 | 40 | 45 | 68 | 58 | 94 | 1445 | 38 | 90 |
N.S. | 1 | 1.00 | 1.12 | 1.70 | 1.45 | 2.35 | 36.12 | 0.95 | 2.25 |
time (sec) |
N/A | 0.043 | 0.075 | 2.229 | 0.291 | 0.367 | 2.789 | 0.399 | 1.687 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | B | B | B | F | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 124 | 124 | 244 | 276 | 330 | 2716 | 0 | 234 | 392 |
N.S. | 1 | 1.00 | 1.97 | 2.23 | 2.66 | 21.90 | 0.00 | 1.89 | 3.16 |
time (sec) |
N/A | 0.173 | 0.328 | 0.865 | 0.269 | 0.429 | 0.000 | 0.404 | 0.202 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | B | B | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 101 | 101 | 95 | 113 | 214 | 209 | 0 | 112 | 146 |
N.S. | 1 | 1.00 | 0.94 | 1.12 | 2.12 | 2.07 | 0.00 | 1.11 | 1.45 |
time (sec) |
N/A | 0.160 | 0.190 | 0.793 | 0.263 | 0.357 | 0.000 | 0.408 | 1.550 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | B | B | B | F | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 59 | 59 | 99 | 123 | 152 | 674 | 0 | 115 | 169 |
N.S. | 1 | 1.00 | 1.68 | 2.08 | 2.58 | 11.42 | 0.00 | 1.95 | 2.86 |
time (sec) |
N/A | 0.087 | 0.180 | 0.796 | 0.276 | 0.379 | 0.000 | 0.407 | 1.540 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 23 | 30 | 45 | 37 | 0 | 29 | 33 |
N.S. | 1 | 1.00 | 0.85 | 1.11 | 1.67 | 1.37 | 0.00 | 1.07 | 1.22 |
time (sec) |
N/A | 0.045 | 0.089 | 0.609 | 0.251 | 0.354 | 0.000 | 0.396 | 1.605 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | B | F | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 15 | 14 | 13 | 29 | 0 | 33 | 35 |
N.S. | 1 | 1.00 | 1.25 | 1.17 | 1.08 | 2.42 | 0.00 | 2.75 | 2.92 |
time (sec) |
N/A | 0.008 | 0.006 | 0.453 | 0.259 | 0.393 | 0.000 | 0.398 | 0.064 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | B | B | B | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 11 | 11 | 11 | 51 | 26 | 27 | 0 | 19 | 23 |
N.S. | 1 | 1.00 | 1.00 | 4.64 | 2.36 | 2.45 | 0.00 | 1.73 | 2.09 |
time (sec) |
N/A | 0.030 | 0.015 | 1.131 | 0.264 | 0.371 | 0.000 | 0.427 | 0.086 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | F(-2) | B | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 67 | 67 | 61 | 96 | 0 | 682 | 0 | 68 | 139 |
N.S. |
1 | 1.00 | 0.91 | 1.43 | 0.00 | 10.18 | 0.00 | 1.01 | 2.07 |
time (sec) |
N/A | 0.097 | 0.241 | 1.036 | 0.000 | 0.420 | 0.000 | 0.414 | 1.789 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | B | B | B | F | A | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 50 | 50 | 77 | 114 | 111 | 521 | 0 | 66 | -1 |
N.S. | 1 | 1.00 | 1.54 | 2.28 | 2.22 | 10.42 | 0.00 | 1.32 | -0.02 |
time (sec) |
N/A | 0.075 | 0.082 | 1.063 | 0.279 | 0.403 | 0.000 | 0.403 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | F(-2) | B | F | A | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 159 | 159 | 150 | 206 | 0 | 5830 | 0 | 242 | -1 |
N.S. |
1 | 1.00 | 0.94 | 1.30 | 0.00 | 36.67 | 0.00 | 1.52 | -0.01 |
time (sec) |
N/A | 0.276 | 0.322 | 1.132 | 0.000 | 0.427 | 0.000 | 0.424 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | B | B | B | F | A | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 98 | 98 | 138 | 198 | 285 | 2564 | 0 | 135 | -1 |
N.S. | 1 | 1.00 | 1.41 | 2.02 | 2.91 | 26.16 | 0.00 | 1.38 | -0.01 |
time (sec) |
N/A | 0.111 | 0.223 | 1.529 | 0.300 | 0.408 | 0.000 | 0.428 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | B | B | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 53 | 32 | 236 | 270 | 0 | 33 | 81 |
N.S. | 1 | 1.00 | 1.89 | 1.14 | 8.43 | 9.64 | 0.00 | 1.18 | 2.89 |
time (sec) |
N/A | 0.048 | 0.064 | 1.043 | 0.270 | 0.460 | 0.000 | 0.407 | 1.522 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | B | B | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 30 | 30 | 23 | 183 | 68 | 0 | 22 | 59 |
N.S. | 1 | 1.00 | 1.00 | 0.77 | 6.10 | 2.27 | 0.00 | 0.73 | 1.97 |
time (sec) |
N/A | 0.081 | 0.040 | 0.846 | 0.269 | 0.361 | 0.000 | 0.413 | 0.049 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | B | A | B | B | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 41 | 22 | 66 | 91 | 0 | 22 | 33 |
N.S. | 1 | 1.00 | 2.28 | 1.22 | 3.67 | 5.06 | 0.00 | 1.22 | 1.83 |
time (sec) |
N/A | 0.047 | 0.039 | 0.808 | 0.264 | 0.350 | 0.000 | 0.407 | 0.046 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | B | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 10 | 11 | 25 | 22 | 0 | 10 | 10 |
N.S. | 1 | 1.00 | 0.71 | 0.79 | 1.79 | 1.57 | 0.00 | 0.71 | 0.71 |
time (sec) |
N/A | 0.055 | 0.020 | 0.652 | 0.269 | 0.348 | 0.000 | 0.404 | 1.665 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 9 | 9 | 11 | 10 | 9 | 13 | 0 | 25 | 11 |
N.S. | 1 | 1.00 | 1.22 | 1.11 | 1.00 | 1.44 | 0.00 | 2.78 | 1.22 |
time (sec) |
N/A | 0.006 | 0.005 | 0.454 | 0.258 | 0.410 | 0.000 | 0.405 | 0.036 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | B | B | B | F | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 5 | 5 | 9 | 20 | 11 | 13 | 0 | 11 | 11 |
N.S. | 1 | 1.00 | 1.80 | 4.00 | 2.20 | 2.60 | 0.00 | 2.20 | 2.20 |
time (sec) |
N/A | 0.023 | 0.015 | 0.989 | 0.255 | 0.383 | 0.000 | 0.395 | 0.044 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 10 | 24 | 12 | 20 | 0 | 10 | 10 |
N.S. | 1 | 1.00 | 0.83 | 2.00 | 1.00 | 1.67 | 0.00 | 0.83 | 0.83 |
time (sec) |
N/A | 0.039 | 0.016 | 0.986 | 0.264 | 0.364 | 0.000 | 0.401 | 0.177 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | B | B | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 18 | 28 | 31 | 89 | 0 | 21 | 33 |
N.S. | 1 | 1.00 | 1.29 | 2.00 | 2.21 | 6.36 | 0.00 | 1.50 | 2.36 |
time (sec) |
N/A | 0.046 | 0.016 | 1.056 | 0.260 | 0.379 | 0.000 | 0.414 | 1.550 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | B | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 30 | 32 | 38 | 68 | 0 | 22 | 57 |
N.S. | 1 | 1.00 | 1.15 | 1.23 | 1.46 | 2.62 | 0.00 | 0.85 | 2.19 |
time (sec) |
N/A | 0.064 | 0.017 | 1.015 | 0.272 | 0.360 | 0.000 | 0.394 | 1.553 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | B | B | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 32 | 36 | 52 | 266 | 0 | 30 | 79 |
N.S. | 1 | 1.00 | 1.45 | 1.64 | 2.36 | 12.09 | 0.00 | 1.36 | 3.59 |
time (sec) |
N/A | 0.046 | 0.017 | 1.054 | 0.280 | 0.431 | 0.000 | 0.417 | 1.613 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | B | A | B | B | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 55 | 28 | 238 | 265 | 0 | 28 | 77 |
N.S. | 1 | 1.00 | 2.29 | 1.17 | 9.92 | 11.04 | 0.00 | 1.17 | 3.21 |
time (sec) |
N/A | 0.047 | 0.063 | 0.871 | 0.273 | 0.382 | 0.000 | 0.425 | 1.501 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | B | B | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 30 | 23 | 183 | 68 | 0 | 22 | 57 |
N.S. | 1 | 1.00 | 1.15 | 0.88 | 7.04 | 2.62 | 0.00 | 0.85 | 2.19 |
time (sec) |
N/A | 0.084 | 0.007 | 0.833 | 0.265 | 0.379 | 0.000 | 0.402 | 1.514 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | B | A | B | B | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 43 | 20 | 68 | 88 | 0 | 19 | 31 |
N.S. | 1 | 1.00 | 2.69 | 1.25 | 4.25 | 5.50 | 0.00 | 1.19 | 1.94 |
time (sec) |
N/A | 0.039 | 0.040 | 0.852 | 0.265 | 0.406 | 0.000 | 0.418 | 1.536 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | B | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 18 | 11 | 25 | 20 | 0 | 10 | 10 |
N.S. | 1 | 1.00 | 1.50 | 0.92 | 2.08 | 1.67 | 0.00 | 0.83 | 0.83 |
time (sec) |
N/A | 0.055 | 0.005 | 0.656 | 0.280 | 0.376 | 0.000 | 0.390 | 0.057 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 11 | 11 | 13 | 12 | 11 | 11 | 0 | 25 | 9 |
N.S. | 1 | 1.00 | 1.18 | 1.09 | 1.00 | 1.00 | 0.00 | 2.27 | 0.82 |
time (sec) |
N/A | 0.006 | 0.007 | 0.605 | 0.265 | 0.367 | 0.000 | 0.404 | 1.536 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | B | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 9 | 9 | 9 | 23 | 13 | 11 | 0 | 10 | 9 |
N.S. | 1 | 1.00 | 1.00 | 2.56 | 1.44 | 1.22 | 0.00 | 1.11 | 1.00 |
time (sec) |
N/A | 0.023 | 0.016 | 1.389 | 0.268 | 0.417 | 0.000 | 0.409 | 0.040 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | C | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 24 | 26 | 12 | 22 | 0 | 10 | 10 |
N.S. | 1 | 1.00 | 1.71 | 1.86 | 0.86 | 1.57 | 0.00 | 0.71 | 0.71 |
time (sec) |
N/A | 0.037 | 0.008 | 1.037 | 0.267 | 0.352 | 0.000 | 0.401 | 1.672 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | B | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 18 | 29 | 35 | 90 | 0 | 20 | 31 |
N.S. | 1 | 1.00 | 0.90 | 1.45 | 1.75 | 4.50 | 0.00 | 1.00 | 1.55 |
time (sec) |
N/A | 0.040 | 0.018 | 1.026 | 0.261 | 0.389 | 0.000 | 0.408 | 1.511 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | C | A | A | B | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 30 | 28 | 34 | 38 | 68 | 0 | 22 | 59 |
N.S. | 1 | 1.00 | 0.93 | 1.13 | 1.27 | 2.27 | 0.00 | 0.73 | 1.97 |
time (sec) |
N/A | 0.064 | 0.007 | 1.072 | 0.267 | 0.366 | 0.000 | 0.410 | 1.532 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | B | B | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 30 | 32 | 37 | 58 | 269 | 0 | 31 | 79 |
N.S. | 1 | 1.00 | 1.07 | 1.23 | 1.93 | 8.97 | 0.00 | 1.03 | 2.63 |
time (sec) |
N/A | 0.046 | 0.019 | 1.047 | 0.274 | 0.384 | 0.000 | 0.413 | 1.523 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | B | F | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 8 | 8 | 10 | 9 | 8 | 53 | 0 | 24 | 27 |
N.S. | 1 | 1.00 | 1.25 | 1.12 | 1.00 | 6.62 | 0.00 | 3.00 | 3.38 |
time (sec) |
N/A | 0.006 | 0.004 | 0.384 | 0.254 | 0.496 | 0.000 | 0.397 | 0.045 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 18 | 27 | 26 | 32 | 0 | 39 | 26 |
N.S. | 1 | 1.00 | 0.82 | 1.23 | 1.18 | 1.45 | 0.00 | 1.77 | 1.18 |
time (sec) |
N/A | 0.017 | 0.005 | 0.753 | 0.271 | 0.401 | 0.000 | 0.421 | 1.576 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | B | B | B | F | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 34 | 45 | 56 | 67 | 616 | 0 | 62 | 71 |
N.S. | 1 | 1.00 | 1.32 | 1.65 | 1.97 | 18.12 | 0.00 | 1.82 | 2.09 |
time (sec) |
N/A | 0.040 | 0.050 | 0.777 | 0.267 | 0.413 | 0.000 | 0.402 | 0.064 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | B | B | B | B | F | F | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 13 | 13 | 35 | 42 | 54 | 55 | 0 | 0 | 13 |
N.S. | 1 | 1.00 | 2.69 | 3.23 | 4.15 | 4.23 | 0.00 | 0.00 | 1.00 |
time (sec) |
N/A | 0.051 | 0.051 | 3.434 | 0.482 | 0.464 | 0.000 | 0.000 | 1.539 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | F | B | B | F(-2) | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 31 | 21 | 0 | 109 | 97 | 0 | 0 | -1 |
N.S. |
1 | 1.00 | 0.68 | 0.00 | 3.52 | 3.13 | 0.00 | 0.00 | -0.03 |
time (sec) |
N/A | 0.091 | 0.036 | 2.346 | 0.489 | 0.392 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | F | B | B | F(-1) | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 50 | 50 | 44 | 0 | 163 | 259 | 0 | 0 | -1 |
N.S. |
1 | 1.00 | 0.88 | 0.00 | 3.26 | 5.18 | 0.00 | 0.00 | -0.02 |
time (sec) |
N/A | 0.111 | 0.224 | 2.283 | 0.486 | 0.397 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | B | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 8 | 8 | 14 | 9 | 8 | 42 | 0 | 16 | 16 |
N.S. | 1 | 1.00 | 1.75 | 1.12 | 1.00 | 5.25 | 0.00 | 2.00 | 2.00 |
time (sec) |
N/A | 0.005 | 0.004 | 0.395 | 0.257 | 0.393 | 0.000 | 0.414 | 1.491 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 16 | 27 | 26 | 30 | 0 | 37 | 26 |
N.S. | 1 | 1.00 | 0.73 | 1.23 | 1.18 | 1.36 | 0.00 | 1.68 | 1.18 |
time (sec) |
N/A | 0.016 | 0.019 | 0.743 | 0.254 | 0.341 | 0.000 | 0.396 | 1.543 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | C | B | B | F | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 34 | 37 | 59 | 56 | 486 | 0 | 66 | 57 |
N.S. | 1 | 1.00 | 1.09 | 1.74 | 1.65 | 14.29 | 0.00 | 1.94 | 1.68 |
time (sec) |
N/A | 0.034 | 0.021 | 0.895 | 0.460 | 0.357 | 0.000 | 0.404 | 0.062 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | B | B | B | F | F | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 14 | 43 | 39 | 57 | 0 | 0 | 15 |
N.S. | 1 | 1.00 | 1.00 | 3.07 | 2.79 | 4.07 | 0.00 | 0.00 | 1.07 |
time (sec) |
N/A | 0.042 | 0.040 | 4.063 | 0.474 | 0.353 | 0.000 | 0.000 | 1.604 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | F | B | B | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 33 | 24 | 0 | 77 | 99 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 0.73 | 0.00 | 2.33 | 3.00 | 0.00 | 0.00 | -0.03 |
time (sec) |
N/A | 0.065 | 0.058 | 2.321 | 0.479 | 0.372 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | F | B | B | F(-2) | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 53 | 53 | 30 | 0 | 115 | 257 | 0 | 0 | -1 |
N.S. |
1 | 1.00 | 0.57 | 0.00 | 2.17 | 4.85 | 0.00 | 0.00 | -0.02 |
time (sec) |
N/A | 0.096 | 0.092 | 2.282 | 0.474 | 0.403 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | B | B | F | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 24 | 35 | 17 | 39 | 96 | 0 | 43 | 39 |
N.S. | 1 | 1.33 | 1.94 | 0.94 | 2.17 | 5.33 | 0.00 | 2.39 | 2.17 |
time (sec) |
N/A | 0.060 | 0.019 | 1.132 | 0.276 | 0.366 | 0.000 | 0.409 | 0.045 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | B | A | B | B | F | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 24 | 50 | 17 | 40 | 96 | 0 | 43 | 41 |
N.S. | 1 | 1.20 | 2.50 | 0.85 | 2.00 | 4.80 | 0.00 | 2.15 | 2.05 |
time (sec) |
N/A | 0.053 | 0.040 | 1.103 | 0.264 | 0.385 | 0.000 | 0.409 | 0.042 |
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 | 39 | 39 | 29 | 70 | 40 | 43 | 143 | 43 | 30 |
N.S. | 1 | 1.00 | 0.74 | 1.79 | 1.03 | 1.10 | 3.67 | 1.10 | 0.77 |
time (sec) |
N/A | 0.048 | 0.054 | 1.068 | 0.270 | 0.418 | 0.291 | 0.400 | 0.087 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | F(-2) | B | B | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 74 | 74 | 89 | 93 | 0 | 435 | 685 | 61 | 157 |
N.S. |
1 | 1.00 | 1.20 | 1.26 | 0.00 | 5.88 | 9.26 | 0.82 | 2.12 |
time (sec) |
N/A | 0.067 | 0.144 | 1.109 | 0.000 | 0.357 | 126.235 | 0.429 | 1.723 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | B | F(-1) | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 101 | 101 | 75 | 155 | 87 | 337 | 0 | 114 | 86 |
N.S. |
1 | 1.00 | 0.74 | 1.53 | 0.86 | 3.34 | 0.00 | 1.13 | 0.85 |
time (sec) |
N/A | 0.107 | 0.110 | 1.149 | 0.271 | 0.364 | 0.000 | 0.409 | 1.958 |
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 | 39 | 39 | 29 | 71 | 41 | 42 | 150 | 43 | 29 |
N.S. | 1 | 1.00 | 0.74 | 1.82 | 1.05 | 1.08 | 3.85 | 1.10 | 0.74 |
time (sec) |
N/A | 0.047 | 0.039 | 1.023 | 0.257 | 0.408 | 0.314 | 0.405 | 1.515 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | F(-2) | B | B | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 74 | 74 | 80 | 93 | 0 | 435 | 774 | 61 | 157 |
N.S. |
1 | 1.00 | 1.08 | 1.26 | 0.00 | 5.88 | 10.46 | 0.82 | 2.12 |
time (sec) |
N/A | 0.057 | 0.112 | 1.076 | 0.000 | 0.375 | 124.519 | 0.413 | 1.719 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | B | F(-1) | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 101 | 101 | 75 | 153 | 86 | 331 | 0 | 111 | 84 |
N.S. |
1 | 1.00 | 0.74 | 1.51 | 0.85 | 3.28 | 0.00 | 1.10 | 0.83 |
time (sec) |
N/A | 0.093 | 0.086 | 1.186 | 0.263 | 0.378 | 0.000 | 0.415 | 1.669 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | F(-2) | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 50 | 50 | 60 | 54 | 0 | 200 | 0 | 48 | 164 |
N.S. |
1 | 1.00 | 1.20 | 1.08 | 0.00 | 4.00 | 0.00 | 0.96 | 3.28 |
time (sec) |
N/A | 0.070 | 0.094 | 1.697 | 0.000 | 0.421 | 0.000 | 0.416 | 3.533 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | F(-2) | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 51 | 51 | 59 | 53 | 0 | 239 | 0 | 60 | 177 |
N.S. |
1 | 1.00 | 1.16 | 1.04 | 0.00 | 4.69 | 0.00 | 1.18 | 3.47 |
time (sec) |
N/A | 0.073 | 0.061 | 1.715 | 0.000 | 0.392 | 0.000 | 0.417 | 1.784 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | F(-2) | B | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 66 | 66 | 125 | 99 | 0 | 594 | 0 | 72 | 183 |
N.S. |
1 | 1.00 | 1.89 | 1.50 | 0.00 | 9.00 | 0.00 | 1.09 | 2.77 |
time (sec) |
N/A | 0.045 | 0.126 | 1.774 | 0.000 | 0.353 | 0.000 | 0.405 | 1.647 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | B | B | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 68 | 68 | 61 | 101 | 104 | 348 | 983 | 113 | 108 |
N.S. | 1 | 1.00 | 0.90 | 1.49 | 1.53 | 5.12 | 14.46 | 1.66 | 1.59 |
time (sec) |
N/A | 0.094 | 0.191 | 1.648 | 0.264 | 0.423 | 0.684 | 0.398 | 0.471 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | F(-2) | B | F(-1) | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 195 | 301 | 205 | 121 | 0 | 1633 | 0 | 174 | 255 |
N.S. |
1 | 1.54 | 1.05 | 0.62 | 0.00 | 8.37 | 0.00 | 0.89 | 1.31 |
time (sec) |
N/A | 0.938 | 0.318 | 1.388 | 0.000 | 0.389 | 0.000 | 0.427 | 1.792 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | F(-2) | B | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 64 | 64 | 124 | 98 | 0 | 596 | 0 | 72 | 183 |
N.S. |
1 | 1.00 | 1.94 | 1.53 | 0.00 | 9.31 | 0.00 | 1.12 | 2.86 |
time (sec) |
N/A | 0.039 | 0.093 | 1.376 | 0.000 | 0.374 | 0.000 | 0.412 | 1.709 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | B | B | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 67 | 67 | 66 | 104 | 104 | 348 | 952 | 114 | 104 |
N.S. | 1 | 1.00 | 0.99 | 1.55 | 1.55 | 5.19 | 14.21 | 1.70 | 1.55 |
time (sec) |
N/A | 0.086 | 0.224 | 1.454 | 0.267 | 0.384 | 0.687 | 0.401 | 0.424 |