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 | F | A | A | A | A | A | F(-2) | B |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 27 | 36 | 24 | 35 | 32 | 0 | 69 |
N.S. |
1 | 0.00 | 0.84 | 1.12 | 0.75 | 1.09 | 1.00 | 0.00 | 2.16 |
time (sec) |
N/A | 5.520 | 0.118 | 0.111 | 0.299 | 0.347 | 0.197 | 0.000 | 1.786 |
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 | 22 | 22 | 22 | 20 | 21 | 43 | 19 | 21 | 21 |
N.S. | 1 | 1.00 | 1.00 | 0.91 | 0.95 | 1.95 | 0.86 | 0.95 | 0.95 |
time (sec) |
N/A | 1.579 | 0.224 | 0.322 | 0.355 | 0.338 | 0.094 | 0.393 | 0.274 |
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 | 29 | 25 | 32 | 35 | 39 | 39 | -1 |
N.S. | 1 | 0.00 | 1.00 | 0.86 | 1.10 | 1.21 | 1.34 | 1.34 | -0.03 |
time (sec) |
N/A | 3.648 | 0.091 | 2.719 | 0.530 | 0.364 | 0.156 | 0.450 | 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 | 16 | 17 | 17 | 16 | 15 | 17 | 14 | 17 | 15 |
N.S. | 1 | 1.06 | 1.06 | 1.00 | 0.94 | 1.06 | 0.88 | 1.06 | 0.94 |
time (sec) |
N/A | 0.023 | 0.004 | 0.314 | 0.257 | 0.335 | 0.028 | 0.387 | 1.448 |
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 | 25 | 20 | 20 | 19 | 18 | 18 | 19 | 19 | 18 |
N.S. | 1 | 0.80 | 0.80 | 0.76 | 0.72 | 0.72 | 0.76 | 0.76 | 0.72 |
time (sec) |
N/A | 0.006 | 0.002 | 0.046 | 0.256 | 0.360 | 0.020 | 0.382 | 0.029 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | B | A | C | A | B | F(-1) | B |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 0 | 71 | 59 | 111 | 64 | 100 | 0 | 67 |
N.S. |
1 | 0.00 | 2.03 | 1.69 | 3.17 | 1.83 | 2.86 | 0.00 | 1.91 |
time (sec) |
N/A | 0.865 | 0.118 | 0.274 | 0.402 | 0.362 | 0.173 | 0.000 | 0.157 |
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 | 22 | 20 | 17 | 16 | 16 | 17 | 16 | 17 |
N.S. | 1 | 1.10 | 1.00 | 0.85 | 0.80 | 0.80 | 0.85 | 0.80 | 0.85 |
time (sec) |
N/A | 0.011 | 0.018 | 0.086 | 0.260 | 0.342 | 0.031 | 0.402 | 1.567 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | A | C | B | B | B | B | B |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 47 | 2156 | 61 | 58 | 70 | 259 | 59 |
N.S. | 1 | 0.00 | 1.62 | 74.34 | 2.10 | 2.00 | 2.41 | 8.93 | 2.03 |
time (sec) |
N/A | 1.559 | 1.169 | 0.630 | 0.291 | 0.351 | 0.225 | 0.680 | 1.629 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | A | C | A | A | A | A | B |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 26 | 203 | 30 | 30 | 22 | 26 | 26 |
N.S. | 1 | 0.00 | 1.08 | 8.46 | 1.25 | 1.25 | 0.92 | 1.08 | 1.08 |
time (sec) |
N/A | 1.524 | 0.041 | 0.202 | 0.569 | 0.355 | 0.254 | 0.424 | 1.818 |
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 | 29 | 0 | 48 | 43 | 44 | 44 | 42 | 44 | 44 |
N.S. | 1 | 0.00 | 1.66 | 1.48 | 1.52 | 1.52 | 1.45 | 1.52 | 1.52 |
time (sec) |
N/A | 7.411 | 1.747 | 0.083 | 0.316 | 0.381 | 0.432 | 1.023 | 2.237 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 88 | 111 | 100 | 92 | 97 | 105 | 107 | 90 |
N.S. | 1 | 2.75 | 3.47 | 3.12 | 2.88 | 3.03 | 3.28 | 3.34 | 2.81 |
time (sec) |
N/A | 0.046 | 0.025 | 0.179 | 0.262 | 0.337 | 2.493 | 0.393 | 1.693 |
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 | 25 | 34 | 25 | 229 | 24 | 30 | 26 | 22 | 26 |
N.S. | 1 | 1.36 | 1.00 | 9.16 | 0.96 | 1.20 | 1.04 | 0.88 | 1.04 |
time (sec) |
N/A | 0.582 | 0.122 | 0.470 | 0.358 | 0.332 | 0.465 | 0.478 | 1.684 |
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 | 19 | 0 | 15 | 15 | 33 | 30 | 27 | 14 | 14 |
N.S. | 1 | 0.00 | 0.79 | 0.79 | 1.74 | 1.58 | 1.42 | 0.74 | 0.74 |
time (sec) |
N/A | 0.771 | 0.064 | 0.021 | 0.295 | 0.348 | 0.164 | 0.402 | 1.664 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | C | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 32 | 223 | 42 | 62 | 41 | 39 | 79 | 39 |
N.S. | 1 | 1.19 | 8.26 | 1.56 | 2.30 | 1.52 | 1.44 | 2.93 | 1.44 |
time (sec) |
N/A | 17.287 | 1.689 | 0.406 | 0.469 | 0.343 | 0.098 | 0.722 | 1.731 |
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 | 22 | 24 | 18 | 17 | 17 | 15 | 17 | 18 |
N.S. | 1 | 0.79 | 0.86 | 0.64 | 0.61 | 0.61 | 0.54 | 0.61 | 0.64 |
time (sec) |
N/A | 0.007 | 0.004 | 0.098 | 0.268 | 0.363 | 0.035 | 0.387 | 1.425 |
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 | 14 | 7 | 7 | 7 | 6 | 6 | 5 | 6 | 7 |
N.S. | 1 | 0.50 | 0.50 | 0.50 | 0.43 | 0.43 | 0.36 | 0.43 | 0.50 |
time (sec) |
N/A | 0.003 | 0.013 | 0.088 | 0.273 | 0.332 | 0.020 | 0.388 | 0.030 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | A | A | C | A | A | A | B |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 0 | 16 | 22 | 30 | 20 | 12 | 16 | 16 |
N.S. | 1 | 0.00 | 1.00 | 1.38 | 1.88 | 1.25 | 0.75 | 1.00 | 1.00 |
time (sec) |
N/A | 0.151 | 0.034 | 0.049 | 0.289 | 0.340 | 0.029 | 0.390 | 1.485 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | A | B | B | B | B | B | F |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 31 | 61 | 76 | 101 | 94 | 107 | -1 |
N.S. | 1 | 0.00 | 1.35 | 2.65 | 3.30 | 4.39 | 4.09 | 4.65 | -0.04 |
time (sec) |
N/A | 103.022 | 0.713 | 0.517 | 0.599 | 0.365 | 0.377 | 1.692 | 0.000 |
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 | 22 | 22 | 22 | 134 | 37 | 19 | 17 | 28 | 19 |
N.S. | 1 | 1.00 | 1.00 | 6.09 | 1.68 | 0.86 | 0.77 | 1.27 | 0.86 |
time (sec) |
N/A | 0.900 | 0.136 | 0.804 | 0.522 | 0.352 | 5.634 | 0.424 | 1.801 |
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 | 18 | 18 | 18 | 161 | 28 | 28 | 26 | 28 | 33 |
N.S. | 1 | 1.00 | 1.00 | 8.94 | 1.56 | 1.56 | 1.44 | 1.56 | 1.83 |
time (sec) |
N/A | 0.056 | 0.026 | 0.109 | 0.262 | 0.344 | 0.045 | 0.395 | 0.139 |
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 | 12 | 12 | 13 | 12 | 10 | 10 | 12 | 12 |
N.S. | 1 | 1.09 | 1.09 | 1.18 | 1.09 | 0.91 | 0.91 | 1.09 | 1.09 |
time (sec) |
N/A | 0.003 | 0.002 | 0.027 | 0.265 | 0.343 | 0.035 | 0.393 | 1.411 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | B | B | A | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 28 | 29 | 29 | 80 | 52 | 27 | 60 | 69 |
N.S. | 1 | 1.17 | 1.21 | 1.21 | 3.33 | 2.17 | 1.12 | 2.50 | 2.88 |
time (sec) |
N/A | 0.496 | 0.074 | 0.136 | 0.512 | 0.349 | 0.112 | 0.378 | 2.011 |
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 | 23 | 0 | 26 | 25 | 24 | 24 | 24 | 0 | 24 |
N.S. | 1 | 0.00 | 1.13 | 1.09 | 1.04 | 1.04 | 1.04 | 0.00 | 1.04 |
time (sec) |
N/A | 10.959 | 1.624 | 1.540 | 0.304 | 0.358 | 0.523 | 0.000 | 1.711 |
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 | 22 | 0 | 19 | 23 | 22 | 22 | 29 | 22 | 22 |
N.S. | 1 | 0.00 | 0.86 | 1.05 | 1.00 | 1.00 | 1.32 | 1.00 | 1.00 |
time (sec) |
N/A | 0.330 | 0.043 | 1.341 | 0.506 | 0.356 | 0.072 | 0.410 | 2.441 |
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 | 30 | 39 | 28 | 118 | 34 | 34 | 29 | 49 | 31 |
N.S. | 1 | 1.30 | 0.93 | 3.93 | 1.13 | 1.13 | 0.97 | 1.63 | 1.03 |
time (sec) |
N/A | 0.923 | 0.118 | 0.113 | 0.330 | 0.343 | 0.161 | 0.497 | 1.847 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | A | F | A | A | A | A | B |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 23 | 0 | 22 | 39 | 19 | 22 | 78 |
N.S. | 1 | 0.00 | 1.00 | 0.00 | 0.96 | 1.70 | 0.83 | 0.96 | 3.39 |
time (sec) |
N/A | 0.326 | 0.072 | 0.040 | 0.491 | 0.352 | 0.093 | 0.496 | 1.827 |
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 | 25 | 0 | 49 | 24 | 42 | 26 | 29 | 501 | 40 |
N.S. | 1 | 0.00 | 1.96 | 0.96 | 1.68 | 1.04 | 1.16 | 20.04 | 1.60 |
time (sec) |
N/A | 2.515 | 7.063 | 0.334 | 0.316 | 0.342 | 0.067 | 0.403 | 2.771 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | B | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 49 | 30 | 39 | 35 | 46 | 51 | 55 | 54 |
N.S. | 1 | 2.13 | 1.30 | 1.70 | 1.52 | 2.00 | 2.22 | 2.39 | 2.35 |
time (sec) |
N/A | 0.296 | 0.088 | 0.105 | 0.541 | 0.366 | 0.144 | 0.424 | 1.657 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 47 | 31 | 35 | 30 | 50 | 27 | 54 | 56 |
N.S. | 1 | 1.88 | 1.24 | 1.40 | 1.20 | 2.00 | 1.08 | 2.16 | 2.24 |
time (sec) |
N/A | 1.351 | 2.108 | 0.250 | 0.296 | 0.341 | 0.063 | 0.396 | 1.527 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 182 | 163 | 476 | 149 | 240 | 168 | 93 | 640 |
N.S. | 1 | 6.28 | 5.62 | 16.41 | 5.14 | 8.28 | 5.79 | 3.21 | 22.07 |
time (sec) |
N/A | 0.331 | 0.137 | 2.440 | 0.307 | 0.361 | 18.386 | 0.422 | 20.396 |
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 | 33 | 64 | 96 | 51 | 317 | 31 | 27 | 45 | 32 |
N.S. | 1 | 1.94 | 2.91 | 1.55 | 9.61 | 0.94 | 0.82 | 1.36 | 0.97 |
time (sec) |
N/A | 0.721 | 0.120 | 0.159 | 0.533 | 0.344 | 0.109 | 0.438 | 2.060 |
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 | 23 | 21 | 16 | 15 | 15 | 15 | 15 | 14 |
N.S. | 1 | 0.92 | 0.84 | 0.64 | 0.60 | 0.60 | 0.60 | 0.60 | 0.56 |
time (sec) |
N/A | 0.007 | 0.007 | 0.104 | 0.265 | 0.336 | 0.036 | 0.389 | 0.057 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | B | B | B | A | B | B | F(-2) | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 64 | 97 | 104 | 52 | 82 | 58 | 0 | 48 |
N.S. |
1 | 2.13 | 3.23 | 3.47 | 1.73 | 2.73 | 1.93 | 0.00 | 1.60 |
time (sec) |
N/A | 0.148 | 0.103 | 0.306 | 0.266 | 0.350 | 0.895 | 0.000 | 1.815 |
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 | 26 | 0 | 23 | 27 | 37 | 21 | 27 | 0 | 34 |
N.S. | 1 | 0.00 | 0.88 | 1.04 | 1.42 | 0.81 | 1.04 | 0.00 | 1.31 |
time (sec) |
N/A | 0.406 | 0.064 | 0.075 | 0.513 | 0.362 | 0.087 | 0.000 | 0.170 |
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 | 13 | 31 | 14 | 20 | 25 | 11 | 10 | 11 | 9 |
N.S. | 1 | 2.38 | 1.08 | 1.54 | 1.92 | 0.85 | 0.77 | 0.85 | 0.69 |
time (sec) |
N/A | 0.013 | 0.045 | 0.159 | 0.269 | 0.333 | 0.031 | 0.386 | 0.045 |
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 | 20 | 20 | 32 | 17 | 17 | 24 | 18 | 35 |
N.S. | 1 | 1.18 | 1.18 | 1.88 | 1.00 | 1.00 | 1.41 | 1.06 | 2.06 |
time (sec) |
N/A | 0.017 | 0.009 | 0.316 | 0.259 | 0.352 | 0.025 | 0.387 | 0.267 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | F | A | B | B | B | B | B |
verified |
N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 0 | 33 | 174 | 85 | 87 | 174 | 155 |
N.S. | 1 | 0.00 | 0.00 | 1.06 | 5.61 | 2.74 | 2.81 | 5.61 | 5.00 |
time (sec) |
N/A | 87.410 | 5.386 | 0.138 | 0.944 | 0.344 | 1.336 | 0.799 | 2.329 |
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 | 20 | 20 | 20 | 15 | 14 | 22 | 14 | 59 | 14 |
N.S. | 1 | 1.00 | 1.00 | 0.75 | 0.70 | 1.10 | 0.70 | 2.95 | 0.70 |
time (sec) |
N/A | 0.023 | 0.027 | 0.317 | 0.254 | 0.343 | 0.048 | 0.401 | 1.510 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | B | A | A | B | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 28 | 26 | 48 | 47 | 46 | 27 | 47 | -1 |
N.S. | 1 | 1.17 | 1.08 | 2.00 | 1.96 | 1.92 | 1.12 | 1.96 | -0.04 |
time (sec) |
N/A | 0.488 | 0.119 | 1.232 | 0.509 | 0.346 | 0.053 | 0.395 | 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 | 22 | 14 | 12 | 10 | 9 | 9 | 10 | 9 | 11 |
N.S. | 1 | 0.64 | 0.55 | 0.45 | 0.41 | 0.41 | 0.45 | 0.41 | 0.50 |
time (sec) |
N/A | 0.003 | 0.002 | 0.522 | 0.271 | 0.329 | 0.023 | 0.382 | 0.038 |
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 | 25 | 0 | 37 | 28 | 47 | 28 | 22 | 26 | 26 |
N.S. | 1 | 0.00 | 1.48 | 1.12 | 1.88 | 1.12 | 0.88 | 1.04 | 1.04 |
time (sec) |
N/A | 0.681 | 8.962 | 0.210 | 0.301 | 0.365 | 0.104 | 0.385 | 0.250 |
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 | 7 | 7 | 7 | 6 | 5 | 5 | 7 | 5 | 5 |
N.S. | 1 | 1.00 | 1.00 | 0.86 | 0.71 | 0.71 | 1.00 | 0.71 | 0.71 |
time (sec) |
N/A | 0.001 | 0.000 | 0.003 | 0.257 | 0.313 | 0.004 | 0.404 | 0.002 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | B | A | A | B | A | A | F | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 57 | 30 | 35 | 57 | 30 | 29 | 0 | 34 |
N.S. | 1 | 2.19 | 1.15 | 1.35 | 2.19 | 1.15 | 1.12 | 0.00 | 1.31 |
time (sec) |
N/A | 0.340 | 0.111 | 0.715 | 0.513 | 0.356 | 0.126 | 0.000 | 1.707 |
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 | 24 | 0 | 23 | 37 | 86 | 26 | 20 | 36 | -1 |
N.S. | 1 | 0.00 | 0.96 | 1.54 | 3.58 | 1.08 | 0.83 | 1.50 | -0.04 |
time (sec) |
N/A | 23.189 | 0.065 | 0.973 | 0.549 | 0.365 | 0.121 | 0.513 | 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 | 20 | 22 | 22 | 20 | 25 | 19 | 19 | 19 | 19 |
N.S. | 1 | 1.10 | 1.10 | 1.00 | 1.25 | 0.95 | 0.95 | 0.95 | 0.95 |
time (sec) |
N/A | 0.523 | 0.095 | 0.186 | 0.501 | 0.373 | 0.135 | 0.394 | 1.644 |
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 | 28 | 0 | 25 | 23 | 26 | 23 | 36 | 62 | 22 |
N.S. | 1 | 0.00 | 0.89 | 0.82 | 0.93 | 0.82 | 1.29 | 2.21 | 0.79 |
time (sec) |
N/A | 2.864 | 0.175 | 71.226 | 0.523 | 0.360 | 0.120 | 0.411 | 1.890 |
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 | 28 | 158 | 26 | 159 | 120 | 120 | 153 | 120 | 96 |
N.S. | 1 | 5.64 | 0.93 | 5.68 | 4.29 | 4.29 | 5.46 | 4.29 | 3.43 |
time (sec) |
N/A | 0.052 | 0.021 | 0.405 | 0.254 | 0.357 | 0.025 | 0.395 | 1.502 |
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 | 18 | 16 | 25 | 19 | 18 | 26 | 17 | 18 | 17 |
N.S. | 1 | 0.89 | 1.39 | 1.06 | 1.00 | 1.44 | 0.94 | 1.00 | 0.94 |
time (sec) |
N/A | 0.126 | 0.031 | 0.278 | 0.529 | 0.356 | 1.441 | 0.392 | 1.542 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 103 | 198 | 695 | 1477 | 193 | 291 | 415 | 586 |
N.S. | 1 | 3.22 | 6.19 | 21.72 | 46.16 | 6.03 | 9.09 | 12.97 | 18.31 |
time (sec) |
N/A | 1.235 | 0.121 | 0.244 | 0.501 | 0.358 | 1.351 | 0.408 | 1.661 |
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 | 31 | 0 | 27 | 25 | 24 | 28 | 22 | 28 | 22 |
N.S. | 1 | 0.00 | 0.87 | 0.81 | 0.77 | 0.90 | 0.71 | 0.90 | 0.71 |
time (sec) |
N/A | 0.051 | 0.133 | 0.037 | 0.261 | 0.365 | 0.074 | 0.384 | 1.544 |
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 | 25 | 31 | 31 | 26 | 32 | 29 | 26 | 30 | 26 |
N.S. | 1 | 1.24 | 1.24 | 1.04 | 1.28 | 1.16 | 1.04 | 1.20 | 1.04 |
time (sec) |
N/A | 0.066 | 0.049 | 0.318 | 0.288 | 0.329 | 0.049 | 0.371 | 0.070 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | F | B | A | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 23 | 23 | 24 | 0 | 51 | 22 | 77 | 22 |
N.S. | 1 | 1.10 | 1.10 | 1.14 | 0.00 | 2.43 | 1.05 | 3.67 | 1.05 |
time (sec) |
N/A | 0.102 | 0.020 | 0.275 | 0.000 | 0.342 | 0.079 | 0.389 | 0.099 |
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 | 31 | 104 | 23 | 102 | 51 | 39 | 20 | 47 | 22 |
N.S. | 1 | 3.35 | 0.74 | 3.29 | 1.65 | 1.26 | 0.65 | 1.52 | 0.71 |
time (sec) |
N/A | 0.404 | 1.098 | 0.110 | 0.501 | 0.359 | 0.092 | 0.391 | 1.596 |
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 | 32 | 21 | 22 | 16 | 21 | 27 | 16 | 18 |
N.S. | 1 | 1.52 | 1.00 | 1.05 | 0.76 | 1.00 | 1.29 | 0.76 | 0.86 |
time (sec) |
N/A | 0.125 | 0.055 | 0.250 | 0.350 | 0.353 | 0.085 | 0.419 | 0.069 |
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 | 26 | 0 | 38 | 48 | 43 | 43 | 41 | 38 | 60 |
N.S. | 1 | 0.00 | 1.46 | 1.85 | 1.65 | 1.65 | 1.58 | 1.46 | 2.31 |
time (sec) |
N/A | 0.642 | 0.500 | 2.414 | 0.292 | 0.346 | 0.196 | 0.411 | 1.647 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | A | A | F | A | A | B | B |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 26 | 31 | 0 | 50 | 31 | 70 | 27 |
N.S. | 1 | 0.00 | 0.96 | 1.15 | 0.00 | 1.85 | 1.15 | 2.59 | 1.00 |
time (sec) |
N/A | 0.281 | 0.071 | 0.595 | 0.000 | 0.381 | 0.240 | 0.382 | 1.651 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | A | A | A | A | A | F(-1) | B |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 0 | 28 | 26 | 37 | 55 | 20 | 0 | 31 |
N.S. |
1 | 0.00 | 0.85 | 0.79 | 1.12 | 1.67 | 0.61 | 0.00 | 0.94 |
time (sec) |
N/A | 0.952 | 3.654 | 0.362 | 0.288 | 0.351 | 0.060 | 0.000 | 1.627 |
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 | 24 | 0 | 46 | 20 | 26 | 22 | 48 | 26 | 19 |
N.S. | 1 | 0.00 | 1.92 | 0.83 | 1.08 | 0.92 | 2.00 | 1.08 | 0.79 |
time (sec) |
N/A | 0.995 | 0.264 | 0.304 | 0.518 | 0.364 | 0.101 | 0.395 | 1.690 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F(-1) | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 0 | 13 | 15 | 12 | 12 | 14 | 12 | 12 |
N.S. |
1 | 0.00 | 0.93 | 1.07 | 0.86 | 0.86 | 1.00 | 0.86 | 0.86 |
time (sec) |
N/A | 180.010 | 0.062 | 0.219 | 0.290 | 0.371 | 0.157 | 0.415 | 0.269 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F(-1) | B | C | F | A | B | F | F |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 0 | 77 | 242 | 0 | 66 | 100 | 0 | -1 |
N.S. |
1 | 0.00 | 2.20 | 6.91 | 0.00 | 1.89 | 2.86 | 0.00 | -0.03 |
time (sec) |
N/A | 180.000 | 0.251 | 0.800 | 0.000 | 0.368 | 0.673 | 0.000 | 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 | 29 | 23 | 23 | 22 | 21 | 21 | 22 | 21 | 21 |
N.S. | 1 | 0.79 | 0.79 | 0.76 | 0.72 | 0.72 | 0.76 | 0.72 | 0.72 |
time (sec) |
N/A | 0.008 | 0.004 | 0.064 | 0.256 | 0.339 | 0.034 | 0.399 | 1.481 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | A | C | B | A | A | B | B |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 24 | 105 | 98 | 43 | 22 | 1320 | 118 |
N.S. | 1 | 0.00 | 0.96 | 4.20 | 3.92 | 1.72 | 0.88 | 52.80 | 4.72 |
time (sec) |
N/A | 1.636 | 0.099 | 29.266 | 0.518 | 0.349 | 0.278 | 3.018 | 2.475 |
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 | 22 | 0 | 28 | 30 | 33 | 33 | 27 | 34 | 402 |
N.S. | 1 | 0.00 | 1.27 | 1.36 | 1.50 | 1.50 | 1.23 | 1.55 | 18.27 |
time (sec) |
N/A | 3.311 | 0.079 | 0.981 | 0.311 | 0.339 | 0.103 | 0.401 | 2.371 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | A | A | A | B | A | F | B |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 32 | 30 | 29 | 77 | 31 | 0 | 32 |
N.S. | 1 | 0.00 | 1.10 | 1.03 | 1.00 | 2.66 | 1.07 | 0.00 | 1.10 |
time (sec) |
N/A | 2.647 | 0.442 | 0.281 | 0.568 | 0.383 | 0.154 | 0.000 | 1.771 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | A | C | A | A | A | A | B |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 40 | 309 | 41 | 40 | 37 | 38 | 39 |
N.S. | 1 | 0.00 | 1.33 | 10.30 | 1.37 | 1.33 | 1.23 | 1.27 | 1.30 |
time (sec) |
N/A | 0.433 | 0.031 | 1.034 | 0.551 | 0.352 | 0.160 | 0.484 | 1.613 |
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 | 32 | 31 | 26 | 28 | 308 | 34 | 27 | 38 | 27 |
N.S. | 1 | 0.97 | 0.81 | 0.88 | 9.62 | 1.06 | 0.84 | 1.19 | 0.84 |
time (sec) |
N/A | 0.297 | 0.063 | 0.299 | 0.533 | 0.337 | 0.115 | 0.395 | 1.755 |
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 | 25 | 26 | 25 | 17 | 18 | 19 | 14 | 18 | 18 |
N.S. | 1 | 1.04 | 1.00 | 0.68 | 0.72 | 0.76 | 0.56 | 0.72 | 0.72 |
time (sec) |
N/A | 0.177 | 0.056 | 0.183 | 0.289 | 0.337 | 0.086 | 0.391 | 1.505 |
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 | 18 | 0 | 15 | 23 | 25 | 20 | 20 | 0 | 20 |
N.S. | 1 | 0.00 | 0.83 | 1.28 | 1.39 | 1.11 | 1.11 | 0.00 | 1.11 |
time (sec) |
N/A | 0.466 | 0.031 | 0.083 | 0.327 | 0.333 | 0.125 | 0.000 | 1.584 |
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 | 45 | 25 | 34 | 39 | 33 | 32 | 33 | 37 |
N.S. | 1 | 1.80 | 1.00 | 1.36 | 1.56 | 1.32 | 1.28 | 1.32 | 1.48 |
time (sec) |
N/A | 0.023 | 0.104 | 0.109 | 0.266 | 0.351 | 0.078 | 0.387 | 1.540 |
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 | 17 | 17 | 16 | 15 | 15 | 19 | 15 | 15 |
N.S. | 1 | 0.85 | 0.85 | 0.80 | 0.75 | 0.75 | 0.95 | 0.75 | 0.75 |
time (sec) |
N/A | 0.021 | 0.019 | 0.020 | 0.258 | 0.360 | 0.033 | 0.387 | 1.507 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | C | A | A | F(-1) | A | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 40 | 35 | 429 | 39 | 48 | 0 | 39 | -1 |
N.S. |
1 | 1.05 | 0.92 | 11.29 | 1.03 | 1.26 | 0.00 | 1.03 | -0.03 |
time (sec) |
N/A | 2.947 | 0.167 | 0.293 | 0.321 | 0.350 | 0.000 | 0.429 | 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 | 24 | 0 | 24 | 19 | 19 | 20 | 19 | 19 | 18 |
N.S. | 1 | 0.00 | 1.00 | 0.79 | 0.79 | 0.83 | 0.79 | 0.79 | 0.75 |
time (sec) |
N/A | 2.180 | 0.060 | 0.075 | 0.335 | 0.410 | 0.226 | 0.415 | 1.721 |
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 | 14 | 22 | 22 | 21 | 20 | 22 | 16 |
N.S. | 1 | 0.90 | 0.70 | 1.10 | 1.10 | 1.05 | 1.00 | 1.10 | 0.80 |
time (sec) |
N/A | 0.010 | 0.006 | 0.146 | 0.275 | 0.352 | 0.042 | 0.388 | 0.040 |
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 | 18 | 19 | 24 | 19 | 18 | 18 | 15 | 18 | 18 |
N.S. | 1 | 1.06 | 1.33 | 1.06 | 1.00 | 1.00 | 0.83 | 1.00 | 1.00 |
time (sec) |
N/A | 0.374 | 0.410 | 0.102 | 0.317 | 0.371 | 0.064 | 0.385 | 0.144 |
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 | 18 | 21 | 19 | 23 | 21 | 21 | 14 | 21 | 16 |
N.S. | 1 | 1.17 | 1.06 | 1.28 | 1.17 | 1.17 | 0.78 | 1.17 | 0.89 |
time (sec) |
N/A | 0.005 | 0.005 | 0.101 | 0.264 | 0.332 | 0.010 | 0.385 | 0.060 |
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 | 13 | 11 | 11 | 11 | 71 | 9 | 10 | 9 | 9 |
N.S. | 1 | 0.85 | 0.85 | 0.85 | 5.46 | 0.69 | 0.77 | 0.69 | 0.69 |
time (sec) |
N/A | 0.068 | 0.031 | 0.252 | 0.516 | 0.350 | 0.046 | 0.391 | 0.184 |
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 | 12 | 21 | 21 | 20 | 19 | 19 | 17 | 21 | 19 |
N.S. | 1 | 1.75 | 1.75 | 1.67 | 1.58 | 1.58 | 1.42 | 1.75 | 1.58 |
time (sec) |
N/A | 0.037 | 0.006 | 0.056 | 0.276 | 0.358 | 0.039 | 0.387 | 0.085 |
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 | 20 | 87 | 20 | 88 | 87 | 70 | 85 | 107 | 21 |
N.S. | 1 | 4.35 | 1.00 | 4.40 | 4.35 | 3.50 | 4.25 | 5.35 | 1.05 |
time (sec) |
N/A | 0.745 | 0.104 | 0.273 | 0.497 | 0.370 | 0.212 | 0.395 | 1.555 |
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 | 23 | 23 | 24 | 23 | 34 | 19 | 24 | 23 |
N.S. | 1 | 0.82 | 0.82 | 0.86 | 0.82 | 1.21 | 0.68 | 0.86 | 0.82 |
time (sec) |
N/A | 0.038 | 0.009 | 0.078 | 0.258 | 0.342 | 0.027 | 0.385 | 0.043 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | F | B | B | A | A | F(-1) | B |
verified |
N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 0 | 0 | 72 | 64 | 47 | 48 | 0 | 2500 |
N.S. |
1 | 0.00 | 0.00 | 2.12 | 1.88 | 1.38 | 1.41 | 0.00 | 73.53 |
time (sec) |
N/A | 3.851 | 1.587 | 4.483 | 0.534 | 0.361 | 0.135 | 0.000 | 5.245 |
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 | 29 | 0 | 29 | 38 | 96 | 41 | 24 | 40 | 54 |
N.S. | 1 | 0.00 | 1.00 | 1.31 | 3.31 | 1.41 | 0.83 | 1.38 | 1.86 |
time (sec) |
N/A | 1.376 | 0.055 | 1.959 | 0.517 | 0.395 | 0.153 | 0.406 | 1.953 |
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 | 29 | 31 | 30 | 27 | 26 | 26 | 27 | 26 | 28 |
N.S. | 1 | 1.07 | 1.03 | 0.93 | 0.90 | 0.90 | 0.93 | 0.90 | 0.97 |
time (sec) |
N/A | 0.108 | 0.133 | 0.108 | 0.342 | 0.346 | 0.122 | 0.421 | 1.595 |
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 | 10 | 12 | 11 | 10 | 10 | 8 | 11 | 10 |
N.S. | 1 | 1.00 | 1.20 | 1.10 | 1.00 | 1.00 | 0.80 | 1.10 | 1.00 |
time (sec) |
N/A | 0.006 | 0.003 | 0.251 | 0.263 | 0.368 | 0.021 | 0.386 | 0.034 |
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 | 33 | 24 | 26 | 19 | 20 | 26 | 17 | 20 | 20 |
N.S. | 1 | 0.73 | 0.79 | 0.58 | 0.61 | 0.79 | 0.52 | 0.61 | 0.61 |
time (sec) |
N/A | 0.040 | 0.008 | 0.088 | 0.260 | 0.333 | 0.029 | 0.384 | 1.465 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | B | A | A | A | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 42 | 24 | 115 | 37 | 26 | 24 | 54 | 29 |
N.S. | 1 | 1.62 | 0.92 | 4.42 | 1.42 | 1.00 | 0.92 | 2.08 | 1.12 |
time (sec) |
N/A | 0.024 | 0.085 | 0.280 | 0.259 | 0.383 | 0.051 | 0.381 | 0.069 |
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 | 25 | 129 | 101 | 139 | 78 | 80 | 117 | 81 | 73 |
N.S. | 1 | 5.16 | 4.04 | 5.56 | 3.12 | 3.20 | 4.68 | 3.24 | 2.92 |
time (sec) |
N/A | 0.074 | 0.279 | 0.123 | 0.270 | 0.371 | 0.125 | 0.386 | 1.578 |
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 | 28 | 31 | 31 | 27 | 89 | 37 | 24 | 41 | 26 |
N.S. | 1 | 1.11 | 1.11 | 0.96 | 3.18 | 1.32 | 0.86 | 1.46 | 0.93 |
time (sec) |
N/A | 0.124 | 0.026 | 0.049 | 0.297 | 0.372 | 0.078 | 0.375 | 1.591 |
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 | 27 | 31 | 27 | 25 | 27 | 26 | 27 | 35 | 25 |
N.S. | 1 | 1.15 | 1.00 | 0.93 | 1.00 | 0.96 | 1.00 | 1.30 | 0.93 |
time (sec) |
N/A | 0.229 | 0.061 | 0.119 | 0.572 | 0.369 | 118.375 | 0.843 | 1.944 |
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 | 25 | 0 | 20 | 23 | 18 | 22 | 19 | 18 | 19 |
N.S. | 1 | 0.00 | 0.80 | 0.92 | 0.72 | 0.88 | 0.76 | 0.72 | 0.76 |
time (sec) |
N/A | 0.822 | 0.152 | 0.319 | 0.348 | 0.348 | 0.125 | 0.449 | 1.536 |
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 | 18 | 12 | 12 | 13 | 12 | 12 | 10 | 12 | 12 |
N.S. | 1 | 0.67 | 0.67 | 0.72 | 0.67 | 0.67 | 0.56 | 0.67 | 0.67 |
time (sec) |
N/A | 0.001 | 0.000 | 0.045 | 0.267 | 0.328 | 0.006 | 0.384 | 0.022 |
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 | 32 | 29 | 29 | 27 | 39 | 33 | 26 | 33 | 26 |
N.S. | 1 | 0.91 | 0.91 | 0.84 | 1.22 | 1.03 | 0.81 | 1.03 | 0.81 |
time (sec) |
N/A | 0.283 | 0.164 | 0.054 | 0.295 | 0.332 | 0.070 | 0.395 | 1.551 |
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 | 21 | 15 | 15 | 14 | 18 | 15 | 18 | 14 |
N.S. | 1 | 1.24 | 0.88 | 0.88 | 0.82 | 1.06 | 0.88 | 1.06 | 0.82 |
time (sec) |
N/A | 0.053 | 0.008 | 0.364 | 0.482 | 0.332 | 0.063 | 0.390 | 1.548 |
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 | 32 | 0 | 32 | 32 | 301 | 41 | 39 | 76 | 45 |
N.S. | 1 | 0.00 | 1.00 | 1.00 | 9.41 | 1.28 | 1.22 | 2.38 | 1.41 |
time (sec) |
N/A | 7.093 | 0.059 | 0.421 | 2.799 | 0.354 | 4.175 | 0.413 | 178.821 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | C | A | C | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 79 | 19 | 439 | 21 | 35 | 29 | 27 | 17 |
N.S. | 1 | 3.76 | 0.90 | 20.90 | 1.00 | 1.67 | 1.38 | 1.29 | 0.81 |
time (sec) |
N/A | 0.162 | 0.034 | 1.286 | 0.498 | 0.353 | 0.054 | 0.391 | 1.606 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | B | A | A | B | A | A | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 128 | 23 | 23 | 141 | 33 | 29 | 0 | -1 |
N.S. | 1 | 4.92 | 0.88 | 0.88 | 5.42 | 1.27 | 1.12 | 0.00 | -0.04 |
time (sec) |
N/A | 3.525 | 0.125 | 0.131 | 1.508 | 0.350 | 0.348 | 0.000 | 0.000 |
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 | 24 | 0 | 26 | 22 | 75 | 21 | 15 | 0 | 21 |
N.S. | 1 | 0.00 | 1.08 | 0.92 | 3.12 | 0.88 | 0.62 | 0.00 | 0.88 |
time (sec) |
N/A | 1.372 | 0.212 | 0.833 | 0.592 | 0.363 | 0.165 | 0.000 | 1.930 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | A | A | F(-2) | A | A | A | B |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 34 | 32 | 0 | 31 | 42 | 35 | 29 |
N.S. |
1 | 0.00 | 1.10 | 1.03 | 0.00 | 1.00 | 1.35 | 1.13 | 0.94 |
time (sec) |
N/A | 1.161 | 0.186 | 33.735 | 0.000 | 0.349 | 0.238 | 0.412 | 2.536 |
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 | 22 | 0 | 22 | 24 | 21 | 21 | 17 | 21 | 18 |
N.S. | 1 | 0.00 | 1.00 | 1.09 | 0.95 | 0.95 | 0.77 | 0.95 | 0.82 |
time (sec) |
N/A | 0.275 | 0.064 | 1.356 | 0.506 | 0.358 | 0.053 | 0.387 | 2.022 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | B | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 40 | 38 | 41 | 47 | 48 | 37 | 77 | -1 |
N.S. | 1 | 1.38 | 1.31 | 1.41 | 1.62 | 1.66 | 1.28 | 2.66 | -0.03 |
time (sec) |
N/A | 0.679 | 0.070 | 1.475 | 0.297 | 0.351 | 0.242 | 0.434 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | B | A | A | B | B | A | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 47 | 35 | 36 | 109 | 39 | 37 | 37 | 23 |
N.S. | 1 | 2.14 | 1.59 | 1.64 | 4.95 | 1.77 | 1.68 | 1.68 | 1.05 |
time (sec) |
N/A | 0.232 | 0.037 | 0.164 | 0.276 | 0.359 | 0.083 | 0.390 | 1.748 |