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 | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 38 | 35 | 32 | 28 | 31 | 37 | 28 | 31 |
N.S. | 1 | 1.46 | 1.35 | 1.23 | 1.08 | 1.19 | 1.42 | 1.08 | 1.19 |
time (sec) |
N/A | 0.023 | 0.014 | 5.692 | 0.265 | 0.394 | 0.136 | 0.422 | 5.547 |
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 | 31 | 278 | 36 | 250 | 210 | 166 | 204 | 227 | 32 |
N.S. | 1 | 8.97 | 1.16 | 8.06 | 6.77 | 5.35 | 6.58 | 7.32 | 1.03 |
time (sec) |
N/A | 0.143 | 0.055 | 0.870 | 0.299 | 0.367 | 0.164 | 0.414 | 5.677 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | B | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 41 | 18 | 17 | 16 | 16 | 15 | 16 | 16 |
N.S. | 1 | 2.05 | 0.90 | 0.85 | 0.80 | 0.80 | 0.75 | 0.80 | 0.80 |
time (sec) |
N/A | 0.106 | 0.095 | 0.171 | 0.353 | 0.381 | 0.144 | 0.418 | 5.812 |
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 | 25 | 313 | 41 | 30 | 32 | 39 | 32 |
N.S. | 1 | 0.00 | 1.04 | 13.04 | 1.71 | 1.25 | 1.33 | 1.62 | 1.33 |
time (sec) |
N/A | 7.934 | 0.109 | 9.447 | 0.542 | 0.396 | 0.240 | 0.564 | 5.783 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | A | C | B | A | A | A | B |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 25 | 282 | 51 | 24 | 22 | 43 | 24 |
N.S. | 1 | 0.00 | 0.96 | 10.85 | 1.96 | 0.92 | 0.85 | 1.65 | 0.92 |
time (sec) |
N/A | 5.699 | 0.061 | 1.663 | 0.604 | 0.467 | 0.112 | 0.492 | 8.317 |
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 | 33 | 27 | 34 | 29 | 29 | 34 | 30 |
N.S. | 1 | 0.00 | 1.38 | 1.12 | 1.42 | 1.21 | 1.21 | 1.42 | 1.25 |
time (sec) |
N/A | 5.325 | 0.129 | 0.934 | 0.368 | 0.381 | 0.375 | 0.466 | 5.836 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | B | B | A | B | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 367 | 128 | 39 | 546 | 40 | 36 | 40 | 40 |
N.S. | 1 | 14.12 | 4.92 | 1.50 | 21.00 | 1.54 | 1.38 | 1.54 | 1.54 |
time (sec) |
N/A | 0.406 | 0.137 | 1.646 | 0.540 | 0.422 | 0.135 | 0.414 | 0.118 |
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 | 13 | 13 | 13 | 12 | 12 | 12 | 13 | 12 |
N.S. | 1 | 1.00 | 1.00 | 1.00 | 0.92 | 0.92 | 0.92 | 1.00 | 0.92 |
time (sec) |
N/A | 0.206 | 0.105 | 0.165 | 0.301 | 0.390 | 0.089 | 0.415 | 5.448 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | A | A | F(-2) | A | A | B | B |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 0 | 38 | 29 | 0 | 31 | 39 | 79 | 39 |
N.S. |
1 | 0.00 | 1.06 | 0.81 | 0.00 | 0.86 | 1.08 | 2.19 | 1.08 |
time (sec) |
N/A | 4.587 | 0.346 | 0.030 | 0.000 | 0.394 | 0.122 | 0.513 | 5.722 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | A | B | B | A | F(-2) | B | B |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 34 | 77 | 58 | 52 | 0 | 58 | 51 |
N.S. |
1 | 0.00 | 1.21 | 2.75 | 2.07 | 1.86 | 0.00 | 2.07 | 1.82 |
time (sec) |
N/A | 0.479 | 0.210 | 1.716 | 0.485 | 0.439 | 0.000 | 0.424 | 5.793 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | B | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 70 | 23 | 31 | 32 | 24 | 29 | 24 | 34 |
N.S. | 1 | 2.69 | 0.88 | 1.19 | 1.23 | 0.92 | 1.12 | 0.92 | 1.31 |
time (sec) |
N/A | 0.437 | 2.077 | 0.963 | 0.339 | 0.382 | 0.098 | 0.418 | 5.655 |
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 | 19 | 19 | 16 | 15 | 15 | 17 | 15 | 15 |
N.S. | 1 | 0.95 | 0.95 | 0.80 | 0.75 | 0.75 | 0.85 | 0.75 | 0.75 |
time (sec) |
N/A | 0.006 | 0.019 | 0.149 | 0.268 | 0.389 | 0.029 | 0.410 | 5.261 |
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 | 11 | 11 | 9 | 8 | 8 | 7 | 8 | 8 |
N.S. | 1 | 1.00 | 1.00 | 0.82 | 0.73 | 0.73 | 0.64 | 0.73 | 0.73 |
time (sec) |
N/A | 0.006 | 0.047 | 0.278 | 0.265 | 0.379 | 0.024 | 0.407 | 0.024 |
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 | 16 | 17 | 18 | 17 | 17 | 14 | 17 | 17 |
N.S. | 1 | 0.94 | 1.00 | 1.06 | 1.00 | 1.00 | 0.82 | 1.00 | 1.00 |
time (sec) |
N/A | 0.193 | 0.045 | 1.263 | 0.293 | 0.399 | 0.033 | 0.419 | 5.609 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | F | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 45 | 21 | 24 | 0 | 37 | 20 | 18 | 18 |
N.S. | 1 | 1.73 | 0.81 | 0.92 | 0.00 | 1.42 | 0.77 | 0.69 | 0.69 |
time (sec) |
N/A | 0.521 | 1.208 | 0.168 | 0.000 | 0.554 | 0.059 | 0.422 | 5.425 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | B | B | B | A | A | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 21 | 59 | 68 | 56 | 23 | 19 | 56 | 23 |
N.S. | 1 | 0.95 | 2.68 | 3.09 | 2.55 | 1.05 | 0.86 | 2.55 | 1.05 |
time (sec) |
N/A | 0.020 | 0.057 | 0.291 | 0.271 | 0.387 | 0.058 | 0.406 | 0.158 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | B | A | A | F(-2) | A | F(-2) | B | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 133 | 40 | 43 | 0 | 45 | 0 | 80 | -1 |
N.S. |
1 | 4.16 | 1.25 | 1.34 | 0.00 | 1.41 | 0.00 | 2.50 | -0.03 |
time (sec) |
N/A | 7.275 | 0.079 | 0.815 | 0.000 | 0.381 | 0.000 | 0.805 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | B | A | B | B | A | A | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 67 | 51 | 45 | 65 | 18 | 27 | 41 | 18 |
N.S. | 1 | 2.58 | 1.96 | 1.73 | 2.50 | 0.69 | 1.04 | 1.58 | 0.69 |
time (sec) |
N/A | 0.294 | 0.078 | 0.331 | 0.544 | 0.374 | 0.135 | 0.412 | 5.588 |
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 | 26 | 613 | 23 | 374 | 29 | 26 | 19 | 80 | 26 |
N.S. | 1 | 23.58 | 0.88 | 14.38 | 1.12 | 1.00 | 0.73 | 3.08 | 1.00 |
time (sec) |
N/A | 1.214 | 0.155 | 1.043 | 0.560 | 0.385 | 0.086 | 0.432 | 5.450 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | F(-2) | A | F(-2) | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 21 | 21 | 21 | 0 | 20 | 0 | 20 | 20 |
N.S. |
1 | 0.95 | 0.95 | 0.95 | 0.00 | 0.91 | 0.00 | 0.91 | 0.91 |
time (sec) |
N/A | 0.635 | 0.631 | 0.800 | 0.000 | 0.458 | 0.000 | 0.513 | 5.460 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | B | B | A | A | B | A | B |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 59 | 53 | 44 | 35 | 39 | 36 | 36 |
N.S. | 1 | 0.00 | 2.46 | 2.21 | 1.83 | 1.46 | 1.62 | 1.50 | 1.50 |
time (sec) |
N/A | 0.694 | 0.108 | 2.969 | 0.329 | 0.380 | 0.248 | 0.411 | 5.695 |
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 | 30 | 0 | 33 | 37 | 54 | 52 | 36 | 54 | -1 |
N.S. | 1 | 0.00 | 1.10 | 1.23 | 1.80 | 1.73 | 1.20 | 1.80 | -0.03 |
time (sec) |
N/A | 2.495 | 0.117 | 9.224 | 0.314 | 0.393 | 0.123 | 0.427 | 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 | 22 | 21 | 21 | 15 | 23 | 19 |
N.S. | 1 | 1.00 | 1.00 | 1.05 | 1.00 | 1.00 | 0.71 | 1.10 | 0.90 |
time (sec) |
N/A | 0.035 | 0.009 | 1.375 | 0.290 | 0.384 | 0.030 | 0.405 | 0.060 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | A | F | A | A | A | C | F |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 26 | 0 | 32 | 27 | 20 | 699 | -1 |
N.S. | 1 | 0.00 | 0.96 | 0.00 | 1.19 | 1.00 | 0.74 | 25.89 | -0.04 |
time (sec) |
N/A | 2.666 | 0.118 | 2.282 | 0.657 | 0.420 | 0.138 | 2.198 | 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 | 22 | 0 | 22 | 20 | 19 | 19 | 15 | 19 | 85 |
N.S. | 1 | 0.00 | 1.00 | 0.91 | 0.86 | 0.86 | 0.68 | 0.86 | 3.86 |
time (sec) |
N/A | 2.634 | 0.244 | 0.046 | 0.405 | 0.486 | 0.083 | 0.447 | 5.418 |
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 | 22 | 20 | 19 | 19 | 19 | 19 | 19 |
N.S. | 1 | 0.00 | 1.16 | 1.05 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.332 | 1.115 | 0.369 | 0.310 | 0.388 | 0.078 | 0.408 | 0.098 |
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 | 16 | 0 | 16 | 15 | 14 | 20 | 14 | 20 | 14 |
N.S. | 1 | 0.00 | 1.00 | 0.94 | 0.88 | 1.25 | 0.88 | 1.25 | 0.88 |
time (sec) |
N/A | 0.323 | 0.059 | 0.019 | 0.335 | 0.378 | 0.057 | 0.399 | 5.224 |
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 | 13 | 13 | 11 | 10 | 10 | 7 | 15 | 10 |
N.S. | 1 | 0.62 | 0.62 | 0.52 | 0.48 | 0.48 | 0.33 | 0.71 | 0.48 |
time (sec) |
N/A | 0.013 | 0.008 | 0.763 | 0.299 | 0.372 | 0.031 | 0.409 | 5.189 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | F | A | B | B | A | A | B |
verified |
N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 21 | 0 | 29 | 47 | 47 | 32 | 28 | 28 |
N.S. | 1 | 0.88 | 0.00 | 1.21 | 1.96 | 1.96 | 1.33 | 1.17 | 1.17 |
time (sec) |
N/A | 0.035 | 6.164 | 1.475 | 0.306 | 0.380 | 0.400 | 0.426 | 5.295 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | B | A | A | A | A | F(-1) | B | B |
verified |
N/A | NO | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 1004 | 24 | 43 | 42 | 42 | 0 | 47 | 42 |
N.S. |
1 | 43.65 | 1.04 | 1.87 | 1.83 | 1.83 | 0.00 | 2.04 | 1.83 |
time (sec) |
N/A | 2.402 | 0.141 | 1.086 | 0.513 | 0.486 | 0.000 | 0.476 | 5.494 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | B | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 56 | 21 | 21 | 20 | 20 | 17 | 20 | 22 |
N.S. | 1 | 3.11 | 1.17 | 1.17 | 1.11 | 1.11 | 0.94 | 1.11 | 1.22 |
time (sec) |
N/A | 0.063 | 0.733 | 0.151 | 0.328 | 0.426 | 0.085 | 0.413 | 5.252 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F(-1) | A | A | B | B | A | F | B |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 0 | 57 | 53 | 264 | 203 | 48 | 0 | 130 |
N.S. |
1 | 0.00 | 1.63 | 1.51 | 7.54 | 5.80 | 1.37 | 0.00 | 3.71 |
time (sec) |
N/A | 180.002 | 1.145 | 27.018 | 0.696 | 0.431 | 3.934 | 0.000 | 7.529 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | F | A | B | A | A | F | B |
verified |
N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 0 | 18 | 42 | 22 | 20 | 0 | 19 |
N.S. | 1 | 0.00 | 0.00 | 0.58 | 1.35 | 0.71 | 0.65 | 0.00 | 0.61 |
time (sec) |
N/A | 10.752 | 1.926 | 0.432 | 0.568 | 0.398 | 13.416 | 0.000 | 5.464 |
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 | 16 | 13 | 14 | 17 | 17 | 14 | 18 | 28 |
N.S. | 1 | 1.33 | 1.08 | 1.17 | 1.42 | 1.42 | 1.17 | 1.50 | 2.33 |
time (sec) |
N/A | 0.005 | 0.011 | 1.283 | 0.259 | 0.420 | 0.164 | 0.416 | 5.295 |
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 | 23 | 0 | 17 | 18 | 18 | 18 | 14 | 19 | 34 |
N.S. | 1 | 0.00 | 0.74 | 0.78 | 0.78 | 0.78 | 0.61 | 0.83 | 1.48 |
time (sec) |
N/A | 0.698 | 0.074 | 1.554 | 0.304 | 0.472 | 0.068 | 0.415 | 5.498 |
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 | 8 | 8 | 8 | 7 | 6 | 6 | 5 | 7 | 6 |
N.S. | 1 | 1.00 | 1.00 | 0.88 | 0.75 | 0.75 | 0.62 | 0.88 | 0.75 |
time (sec) |
N/A | 0.001 | 0.002 | 0.966 | 0.257 | 0.433 | 0.011 | 0.406 | 0.027 |
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 | 9 | 8 | 8 | 9 | 8 | 8 | 7 | 9 | 8 |
N.S. | 1 | 0.89 | 0.89 | 1.00 | 0.89 | 0.89 | 0.78 | 1.00 | 0.89 |
time (sec) |
N/A | 0.002 | 0.001 | 0.118 | 0.268 | 0.391 | 0.015 | 0.412 | 0.016 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | B | A | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 44 | 33 | 37 | 47 | 47 | 36 | 47 | 30 |
N.S. | 1 | 2.20 | 1.65 | 1.85 | 2.35 | 2.35 | 1.80 | 2.35 | 1.50 |
time (sec) |
N/A | 0.011 | 0.009 | 0.383 | 0.261 | 0.400 | 0.021 | 0.418 | 0.091 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | C | C | A | A | F | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 17 | 17 | 54 | 30 | 18 | 19 | 0 | 16 |
N.S. | 1 | 0.81 | 0.81 | 2.57 | 1.43 | 0.86 | 0.90 | 0.00 | 0.76 |
time (sec) |
N/A | 0.028 | 0.027 | 1.960 | 0.479 | 0.393 | 0.087 | 0.000 | 5.447 |
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 | 20 | 36 | 29 | 35 | 17 | 20 | 23 |
N.S. | 1 | 0.00 | 0.69 | 1.24 | 1.00 | 1.21 | 0.59 | 0.69 | 0.79 |
time (sec) |
N/A | 0.464 | 0.102 | 1.581 | 0.286 | 0.371 | 0.073 | 0.419 | 5.364 |
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 | 50 | 26 | 26 | 27 | 28 | 22 | 28 | 29 |
N.S. | 1 | 2.00 | 1.04 | 1.04 | 1.08 | 1.12 | 0.88 | 1.12 | 1.16 |
time (sec) |
N/A | 0.067 | 1.134 | 0.441 | 0.314 | 0.367 | 0.080 | 0.410 | 5.312 |
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 | 21 | 0 | 24 | 22 | 31 | 21 | 17 | 21 | 21 |
N.S. | 1 | 0.00 | 1.14 | 1.05 | 1.48 | 1.00 | 0.81 | 1.00 | 1.00 |
time (sec) |
N/A | 0.616 | 0.170 | 0.563 | 0.530 | 0.447 | 0.125 | 0.406 | 5.395 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | C | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 35 | 48 | 34 | 30 | 33 | 29 | 35 | 33 |
N.S. | 1 | 1.09 | 1.50 | 1.06 | 0.94 | 1.03 | 0.91 | 1.09 | 1.03 |
time (sec) |
N/A | 0.327 | 0.114 | 0.540 | 0.279 | 0.387 | 0.756 | 0.412 | 5.409 |
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 | 21 | 21 | 40 | 23 | 23 | 22 | 23 | 21 |
N.S. | 1 | 0.91 | 0.91 | 1.74 | 1.00 | 1.00 | 0.96 | 1.00 | 0.91 |
time (sec) |
N/A | 0.032 | 0.011 | 0.278 | 0.253 | 0.391 | 0.238 | 0.416 | 5.316 |
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 | 19 | 0 | 19 | 120 | 28 | 25 | 20 | 28 | -1 |
N.S. | 1 | 0.00 | 1.00 | 6.32 | 1.47 | 1.32 | 1.05 | 1.47 | -0.05 |
time (sec) |
N/A | 2.014 | 0.154 | 5.348 | 0.511 | 0.460 | 0.167 | 0.552 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | A | B | B | B | A | B | B |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 42 | 70 | 54 | 52 | 37 | 76 | 57 |
N.S. | 1 | 0.00 | 1.62 | 2.69 | 2.08 | 2.00 | 1.42 | 2.92 | 2.19 |
time (sec) |
N/A | 1.868 | 0.115 | 0.210 | 0.292 | 0.397 | 0.112 | 0.434 | 5.504 |
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 | 19 | 19 | 19 | 17 | 17 | 19 | 17 | 18 |
N.S. | 1 | 1.00 | 1.00 | 1.00 | 0.89 | 0.89 | 1.00 | 0.89 | 0.95 |
time (sec) |
N/A | 0.003 | 0.003 | 2.192 | 0.255 | 0.360 | 0.031 | 0.418 | 0.075 |
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 | 11 | 12 | 12 | 11 | 10 | 10 | 11 | 11 |
N.S. | 1 | 0.44 | 0.48 | 0.48 | 0.44 | 0.40 | 0.40 | 0.44 | 0.44 |
time (sec) |
N/A | 0.002 | 0.000 | 0.241 | 0.250 | 0.378 | 0.004 | 0.414 | 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 | 21 | 26 | 20 | 25 | 18 | 26 | 22 | 18 | 22 |
N.S. | 1 | 1.24 | 0.95 | 1.19 | 0.86 | 1.24 | 1.05 | 0.86 | 1.05 |
time (sec) |
N/A | 0.173 | 0.073 | 1.054 | 0.533 | 0.394 | 0.049 | 0.431 | 5.301 |
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 | 30 | 29 | 27 | 32 | 30 | 22 | 26 | 26 |
N.S. | 1 | 1.11 | 1.07 | 1.00 | 1.19 | 1.11 | 0.81 | 0.96 | 0.96 |
time (sec) |
N/A | 0.091 | 0.430 | 0.173 | 0.270 | 0.363 | 0.051 | 0.405 | 0.074 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | B | B | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 59 | 52 | 49 | 67 | 56 | 44 | 90 | 56 |
N.S. | 1 | 2.36 | 2.08 | 1.96 | 2.68 | 2.24 | 1.76 | 3.60 | 2.24 |
time (sec) |
N/A | 0.350 | 11.080 | 0.192 | 0.303 | 0.385 | 0.106 | 0.411 | 5.353 |
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 | 33 | 0 | 42 | 21 | 41 | 41 | 17 | 41 | 23 |
N.S. | 1 | 0.00 | 1.27 | 0.64 | 1.24 | 1.24 | 0.52 | 1.24 | 0.70 |
time (sec) |
N/A | 1.576 | 5.202 | 1.112 | 0.304 | 0.449 | 0.061 | 0.423 | 5.321 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | F | B | B | B | B | B | B |
verified |
N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 0 | 49 | 53 | 53 | 51 | 50 | 229 |
N.S. | 1 | 0.00 | 0.00 | 2.23 | 2.41 | 2.41 | 2.32 | 2.27 | 10.41 |
time (sec) |
N/A | 0.591 | 0.624 | 2.928 | 0.506 | 0.464 | 0.065 | 0.429 | 5.790 |
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 | 31 | 39 | 25 | 39 | 68 | 36 | 39 | 38 | 22 |
N.S. | 1 | 1.26 | 0.81 | 1.26 | 2.19 | 1.16 | 1.26 | 1.23 | 0.71 |
time (sec) |
N/A | 0.152 | 0.090 | 0.533 | 0.272 | 0.367 | 3.703 | 0.422 | 5.517 |
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 | 43 | 44 | 43 | 35 | 32 | 43 | 49 |
N.S. | 1 | 0.00 | 1.43 | 1.47 | 1.43 | 1.17 | 1.07 | 1.43 | 1.63 |
time (sec) |
N/A | 6.391 | 0.187 | 0.224 | 0.669 | 0.411 | 0.563 | 0.597 | 5.481 |
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 | 6 | 6 | 7 | 6 | 6 | 5 | 7 | 6 |
N.S. | 1 | 0.60 | 0.60 | 0.70 | 0.60 | 0.60 | 0.50 | 0.70 | 0.60 |
time (sec) |
N/A | 0.000 | 0.002 | 0.708 | 0.273 | 0.372 | 0.008 | 0.396 | 0.021 |
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 | 14 | 14 | 15 | 14 | 14 | 10 | 14 | 13 |
N.S. | 1 | 0.88 | 0.88 | 0.94 | 0.88 | 0.88 | 0.62 | 0.88 | 0.81 |
time (sec) |
N/A | 0.002 | 0.000 | 0.127 | 0.262 | 0.365 | 0.006 | 0.400 | 0.025 |
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 | 26 | 23 | 25 | 25 | 17 | 17 | 25 | 23 |
N.S. | 1 | 1.37 | 1.21 | 1.32 | 1.32 | 0.89 | 0.89 | 1.32 | 1.21 |
time (sec) |
N/A | 0.248 | 0.075 | 0.855 | 0.300 | 0.378 | 1.361 | 0.408 | 5.285 |
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 | 22 | 22 | 20 | 18 | 24 | 17 | 17 | 74 | 17 |
N.S. | 1 | 1.00 | 0.91 | 0.82 | 1.09 | 0.77 | 0.77 | 3.36 | 0.77 |
time (sec) |
N/A | 0.092 | 0.043 | 0.035 | 0.533 | 0.376 | 0.835 | 0.466 | 5.673 |
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 | 12 | 12 | 13 | 12 | 12 | 12 | 14 | 12 |
N.S. | 1 | 0.86 | 0.86 | 0.93 | 0.86 | 0.86 | 0.86 | 1.00 | 0.86 |
time (sec) |
N/A | 0.013 | 0.005 | 0.831 | 0.257 | 0.360 | 0.035 | 0.409 | 0.047 |
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 | 33 | 25 | 25 | 29 | 20 | 31 | 25 |
N.S. | 1 | 0.00 | 1.32 | 1.00 | 1.00 | 1.16 | 0.80 | 1.24 | 1.00 |
time (sec) |
N/A | 2.264 | 5.280 | 0.324 | 0.298 | 0.408 | 0.160 | 0.420 | 0.203 |
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 | 18 | 17 | 17 | 17 | 18 | 17 |
N.S. | 1 | 0.85 | 0.85 | 0.90 | 0.85 | 0.85 | 0.85 | 0.90 | 0.85 |
time (sec) |
N/A | 0.004 | 0.002 | 0.253 | 0.260 | 0.408 | 0.021 | 0.420 | 0.035 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | B | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 96 | 40 | 36 | 35 | 35 | 37 | 35 | 40 |
N.S. | 1 | 2.91 | 1.21 | 1.09 | 1.06 | 1.06 | 1.12 | 1.06 | 1.21 |
time (sec) |
N/A | 0.209 | 7.671 | 0.454 | 0.413 | 0.359 | 0.066 | 0.464 | 5.357 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F(-1) | F | C | B | A | A | A | B |
verified |
N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 0 | 102 | 36 | 13 | 19 | 25 | 24 |
N.S. |
1 | 0.00 | 0.00 | 4.25 | 1.50 | 0.54 | 0.79 | 1.04 | 1.00 |
time (sec) |
N/A | 180.014 | 1.504 | 0.960 | 0.500 | 0.409 | 108.566 | 0.434 | 5.524 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F(-1) | A | B | B | B | F(-1) | B | B |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 43 | 80 | 166 | 191 | 0 | 89 | 2500 |
N.S. |
1 | 0.00 | 1.65 | 3.08 | 6.38 | 7.35 | 0.00 | 3.42 | 96.15 |
time (sec) |
N/A | 180.002 | 0.098 | 0.768 | 0.293 | 0.388 | 0.000 | 0.499 | 15.276 |
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 | 20 | 0 | 22 | 22 | 38 | 38 | 17 | 38 | 65 |
N.S. | 1 | 0.00 | 1.10 | 1.10 | 1.90 | 1.90 | 0.85 | 1.90 | 3.25 |
time (sec) |
N/A | 1.049 | 0.190 | 7.859 | 0.305 | 0.380 | 0.107 | 0.427 | 5.891 |
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 | 26 | 27 | 24 | 22 | 21 | 20 | 14 | 25 | 21 |
N.S. | 1 | 1.04 | 0.92 | 0.85 | 0.81 | 0.77 | 0.54 | 0.96 | 0.81 |
time (sec) |
N/A | 0.131 | 0.027 | 0.793 | 0.284 | 0.395 | 0.035 | 0.411 | 5.501 |
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 | 26 | 26 | 32 | 21 | 20 | 49 | 20 | 76 | 20 |
N.S. | 1 | 1.00 | 1.23 | 0.81 | 0.77 | 1.88 | 0.77 | 2.92 | 0.77 |
time (sec) |
N/A | 0.513 | 0.143 | 0.511 | 0.330 | 0.399 | 0.152 | 0.406 | 5.548 |
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 | 34 | 19 | 21 | 15 | 27 | 26 | 20 | 15 |
N.S. | 1 | 1.55 | 0.86 | 0.95 | 0.68 | 1.23 | 1.18 | 0.91 | 0.68 |
time (sec) |
N/A | 0.074 | 0.040 | 0.176 | 0.302 | 0.360 | 0.057 | 0.403 | 5.250 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | A | C | B | B | A | A | F |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 0 | 38 | 233 | 51 | 49 | 32 | 37 | -1 |
N.S. | 1 | 0.00 | 1.90 | 11.65 | 2.55 | 2.45 | 1.60 | 1.85 | -0.05 |
time (sec) |
N/A | 24.862 | 0.433 | 33.813 | 0.295 | 0.376 | 0.543 | 0.507 | 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 | 14 | 14 | 15 | 14 | 14 | 12 | 14 | 11 |
N.S. | 1 | 0.58 | 0.58 | 0.62 | 0.58 | 0.58 | 0.50 | 0.58 | 0.46 |
time (sec) |
N/A | 0.003 | 0.000 | 0.132 | 0.268 | 0.348 | 0.009 | 0.414 | 0.024 |
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 | 31 | 31 | 40 | 28 | 23 | 32 | 35 | 35 |
N.S. | 1 | 1.41 | 1.41 | 1.82 | 1.27 | 1.05 | 1.45 | 1.59 | 1.59 |
time (sec) |
N/A | 0.821 | 0.267 | 0.900 | 0.465 | 0.362 | 0.137 | 0.435 | 5.795 |
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 | 26 | 21 | 19 | 44 | 20 | 15 | 18 | 16 |
N.S. | 1 | 1.18 | 0.95 | 0.86 | 2.00 | 0.91 | 0.68 | 0.82 | 0.73 |
time (sec) |
N/A | 0.041 | 0.020 | 0.219 | 0.264 | 0.479 | 0.065 | 0.417 | 5.582 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | A | B | B | B | A | B | F |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 23 | 75 | 87 | 87 | 34 | 68 | -1 |
N.S. | 1 | 0.00 | 0.72 | 2.34 | 2.72 | 2.72 | 1.06 | 2.12 | -0.03 |
time (sec) |
N/A | 0.913 | 0.049 | 1.709 | 0.293 | 0.371 | 0.081 | 0.402 | 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 | 25 | 30 | 23 | 25 | 24 | 24 | 26 | 24 | 28 |
N.S. | 1 | 1.20 | 0.92 | 1.00 | 0.96 | 0.96 | 1.04 | 0.96 | 1.12 |
time (sec) |
N/A | 0.131 | 0.890 | 0.252 | 0.265 | 0.385 | 0.047 | 0.414 | 0.159 |
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 | 21 | 0 | 17 | 16 | 40 | 34 | 15 | 0 | 19 |
N.S. | 1 | 0.00 | 0.81 | 0.76 | 1.90 | 1.62 | 0.71 | 0.00 | 0.90 |
time (sec) |
N/A | 1.864 | 0.464 | 0.179 | 0.371 | 0.459 | 0.159 | 0.000 | 5.871 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | A | A | B | B | B | B | B |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 26 | 54 | 68 | 66 | 71 | 140 | 70 |
N.S. | 1 | 0.00 | 0.87 | 1.80 | 2.27 | 2.20 | 2.37 | 4.67 | 2.33 |
time (sec) |
N/A | 2.960 | 0.108 | 24.602 | 0.305 | 0.370 | 0.352 | 0.464 | 6.575 |
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 | 12 | 22 | 12 | 12 | 27 | 14 | 10 | 14 | 11 |
N.S. | 1 | 1.83 | 1.00 | 1.00 | 2.25 | 1.17 | 0.83 | 1.17 | 0.92 |
time (sec) |
N/A | 0.751 | 0.204 | 0.618 | 0.285 | 0.340 | 0.033 | 0.409 | 5.511 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | A | A | A | A | A | F(-1) | F |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 42 | 49 | 26 | 40 | 20 | 0 | -1 |
N.S. |
1 | 0.00 | 1.40 | 1.63 | 0.87 | 1.33 | 0.67 | 0.00 | -0.03 |
time (sec) |
N/A | 36.188 | 0.151 | 0.493 | 0.323 | 0.391 | 0.319 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | F | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 24 | 24 | 0 | 29 | 24 | 22 | 24 | 24 |
N.S. | 1 | 0.89 | 0.89 | 0.00 | 1.07 | 0.89 | 0.81 | 0.89 | 0.89 |
time (sec) |
N/A | 0.098 | 0.064 | 0.004 | 0.495 | 0.376 | 0.149 | 0.409 | 5.732 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | A | B | A | A | B | B | F |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 48 | 103 | 39 | 43 | 146 | 55 | -1 |
N.S. | 1 | 0.00 | 1.71 | 3.68 | 1.39 | 1.54 | 5.21 | 1.96 | -0.04 |
time (sec) |
N/A | 8.350 | 0.421 | 0.221 | 0.302 | 0.424 | 0.578 | 0.402 | 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 | 17 | 17 | 14 | 13 | 17 | 14 | 14 | 13 |
N.S. | 1 | 0.59 | 0.59 | 0.48 | 0.45 | 0.59 | 0.48 | 0.48 | 0.45 |
time (sec) |
N/A | 0.008 | 0.004 | 0.244 | 0.261 | 0.374 | 0.029 | 0.408 | 5.892 |
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 | 18 | 0 | 20 | 17 | 16 | 16 | 17 | 16 | 63 |
N.S. | 1 | 0.00 | 1.11 | 0.94 | 0.89 | 0.89 | 0.94 | 0.89 | 3.50 |
time (sec) |
N/A | 1.639 | 0.210 | 1.235 | 0.291 | 0.359 | 0.080 | 0.418 | 6.116 |
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 | 16 | 16 | 16 | 39 | 17 | 14 | 15 | 15 |
N.S. | 1 | 0.64 | 0.64 | 0.64 | 1.56 | 0.68 | 0.56 | 0.60 | 0.60 |
time (sec) |
N/A | 0.131 | 0.144 | 0.247 | 0.264 | 0.388 | 0.042 | 0.393 | 5.333 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | B | A | C | A | A | B | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 79 | 28 | 516 | 34 | 40 | 39 | 51 | 44 |
N.S. | 1 | 3.16 | 1.12 | 20.64 | 1.36 | 1.60 | 1.56 | 2.04 | 1.76 |
time (sec) |
N/A | 1.567 | 1.203 | 0.984 | 0.315 | 0.367 | 0.305 | 0.417 | 5.647 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | C | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 140 | 34 | 36 | 28 | 31 | 30 | 21 |
N.S. | 1 | 1.00 | 5.00 | 1.21 | 1.29 | 1.00 | 1.11 | 1.07 | 0.75 |
time (sec) |
N/A | 0.079 | 0.660 | 0.499 | 0.263 | 0.374 | 0.137 | 0.427 | 0.157 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | A | A | B | A | B | B | B |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 39 | 29 | 54 | 51 | 73 | 71 | 562 |
N.S. | 1 | 0.00 | 1.50 | 1.12 | 2.08 | 1.96 | 2.81 | 2.73 | 21.62 |
time (sec) |
N/A | 0.838 | 0.195 | 4.034 | 0.507 | 0.349 | 0.166 | 0.442 | 7.423 |
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 | 34 | 0 | 27 | 25 | 24 | 24 | 26 | 24 | 27 |
N.S. | 1 | 0.00 | 0.79 | 0.74 | 0.71 | 0.71 | 0.76 | 0.71 | 0.79 |
time (sec) |
N/A | 3.202 | 0.373 | 1.924 | 0.363 | 0.363 | 0.333 | 0.414 | 5.641 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | B | B | B | B | B | B | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 23 | 66 | 59 | 51 | 52 | 65 | 57 | -1 |
N.S. | 1 | 1.05 | 3.00 | 2.68 | 2.32 | 2.36 | 2.95 | 2.59 | -0.05 |
time (sec) |
N/A | 0.618 | 0.276 | 2.943 | 0.293 | 0.403 | 0.231 | 0.404 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | F | B | B | B | B | B | F |
verified |
N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 0 | 153 | 136 | 138 | 173 | 150 | -1 |
N.S. | 1 | 0.00 | 0.00 | 6.38 | 5.67 | 5.75 | 7.21 | 6.25 | -0.04 |
time (sec) |
N/A | 57.894 | 0.774 | 2.435 | 0.541 | 0.397 | 1.920 | 1.187 | 0.000 |
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 | 22 | 0 | 20 | 20 | 17 | 17 | 22 | 0 | 17 |
N.S. | 1 | 0.00 | 0.91 | 0.91 | 0.77 | 0.77 | 1.00 | 0.00 | 0.77 |
time (sec) |
N/A | 1.687 | 0.463 | 2.698 | 0.306 | 0.493 | 0.752 | 0.000 | 5.814 |
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 | 26 | 0 | 22 | 28 | 27 | 28 | 19 | 28 | 25 |
N.S. | 1 | 0.00 | 0.85 | 1.08 | 1.04 | 1.08 | 0.73 | 1.08 | 0.96 |
time (sec) |
N/A | 3.577 | 1.467 | 0.063 | 0.383 | 0.375 | 2.686 | 0.418 | 5.721 |
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 | 18 | 16 | 18 | 74 | 16 | 15 | 24 | 16 |
N.S. | 1 | 0.72 | 0.64 | 0.72 | 2.96 | 0.64 | 0.60 | 0.96 | 0.64 |
time (sec) |
N/A | 0.048 | 0.067 | 0.265 | 0.292 | 0.387 | 0.122 | 0.420 | 0.097 |
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 | 27 | 20 | 27 | 18 | 26 | 15 | 18 | 18 |
N.S. | 1 | 1.35 | 1.00 | 1.35 | 0.90 | 1.30 | 0.75 | 0.90 | 0.90 |
time (sec) |
N/A | 0.017 | 0.036 | 0.259 | 0.261 | 0.384 | 0.050 | 0.394 | 5.408 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | B | A | C | C | A | B | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 84 | 20 | 180 | 101 | 28 | 42 | 38 | 47 |
N.S. | 1 | 3.82 | 0.91 | 8.18 | 4.59 | 1.27 | 1.91 | 1.73 | 2.14 |
time (sec) |
N/A | 0.655 | 0.070 | 0.833 | 0.301 | 0.505 | 0.058 | 0.429 | 5.426 |
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 | 28 | 0 | 39 | 26 | 31 | 25 | 24 | 25 | -1 |
N.S. | 1 | 0.00 | 1.39 | 0.93 | 1.11 | 0.89 | 0.86 | 0.89 | -0.04 |
time (sec) |
N/A | 6.567 | 0.321 | 0.565 | 0.301 | 0.396 | 0.233 | 0.453 | 0.000 |
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 | 20 | 40 | 27 | 16 | 40 | 40 | 37 | 40 | 39 |
N.S. | 1 | 2.00 | 1.35 | 0.80 | 2.00 | 2.00 | 1.85 | 2.00 | 1.95 |
time (sec) |
N/A | 0.013 | 0.010 | 0.683 | 0.266 | 0.433 | 0.012 | 0.394 | 0.052 |
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 | 35 | 0 | 51 | 45 | 43 | 43 | 42 | 47 | 47 |
N.S. | 1 | 0.00 | 1.46 | 1.29 | 1.23 | 1.23 | 1.20 | 1.34 | 1.34 |
time (sec) |
N/A | 2.425 | 5.475 | 0.278 | 0.303 | 0.383 | 0.107 | 0.420 | 5.789 |
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 | 11 | 13 | 10 | 9 | 9 | 10 | 9 | 8 |
N.S. | 1 | 0.61 | 0.72 | 0.56 | 0.50 | 0.50 | 0.56 | 0.50 | 0.44 |
time (sec) |
N/A | 0.001 | 0.002 | 0.115 | 0.259 | 0.335 | 0.006 | 0.441 | 0.030 |
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 | 20 | 15 | 20 | 19 | 19 | 17 | 19 | 17 |
N.S. | 1 | 1.11 | 0.83 | 1.11 | 1.06 | 1.06 | 0.94 | 1.06 | 0.94 |
time (sec) |
N/A | 0.102 | 0.133 | 0.146 | 0.277 | 0.381 | 0.030 | 0.399 | 5.436 |