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 | F | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 24 | 21 | 30 | 20 | 19 | 0 | 20 |
N.S. | 1 | 1.00 | 1.00 | 0.88 | 1.25 | 0.83 | 0.79 | 0.00 | 0.83 |
time (sec) |
N/A | 0.223 | 23.841 | 0.070 | 2.519 | 0.649 | 0.285 | 0.000 | 0.310 |
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 | 27 | 27 | 52 | 24 | 31 | 29 | 8 | 51 | 23 |
N.S. | 1 | 1.00 | 1.93 | 0.89 | 1.15 | 1.07 | 0.30 | 1.89 | 0.85 |
time (sec) |
N/A | 0.006 | 0.018 | 0.057 | 1.932 | 0.577 | 0.062 | 0.688 | 0.687 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | C | F | A | C | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 82 | 82 | 82 | 25 | 0 | 216 | 51 | 0 | -1 |
N.S. | 1 | 1.00 | 1.00 | 0.30 | 0.00 | 2.63 | 0.62 | 0.00 | -0.01 |
time (sec) |
N/A | 0.066 | 0.073 | 0.026 | 0.000 | 0.954 | 1.712 | 0.000 | 0.000 |
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 | 12 | 12 | 12 | 39 | 40 | 29 | 48 | 10 | 169 |
N.S. | 1 | 1.00 | 1.00 | 3.25 | 3.33 | 2.42 | 4.00 | 0.83 | 14.08 |
time (sec) |
N/A | 0.036 | 0.014 | 0.113 | 1.725 | 0.675 | 47.964 | 0.586 | 0.061 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | C | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 40 | 40 | 40 | 33 | 36 | 85 | 66 | 55 | 32 |
N.S. | 1 | 1.00 | 1.00 | 0.82 | 0.90 | 2.12 | 1.65 | 1.38 | 0.80 |
time (sec) |
N/A | 0.008 | 0.007 | 0.036 | 1.312 | 0.918 | 0.492 | 0.571 | 0.479 |
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 | 46 | 46 | 46 | 66 | 59 | 41 | 42 | 40 | 40 |
N.S. | 1 | 1.00 | 1.00 | 1.43 | 1.28 | 0.89 | 0.91 | 0.87 | 0.87 |
time (sec) |
N/A | 0.024 | 0.028 | 0.041 | 2.053 | 0.720 | 0.539 | 0.587 | 0.665 |
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 | 37 | 37 | 45 | 52 | 46 | 52 | 0 | 40 | 51 |
N.S. | 1 | 1.00 | 1.22 | 1.41 | 1.24 | 1.41 | 0.00 | 1.08 | 1.38 |
time (sec) |
N/A | 0.012 | 0.083 | 0.116 | 2.135 | 0.747 | 0.000 | 0.559 | 0.105 |
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 | 61 | 61 | 66 | 74 | 84 | 97 | 0 | 57 | 72 |
N.S. | 1 | 1.00 | 1.08 | 1.21 | 1.38 | 1.59 | 0.00 | 0.93 | 1.18 |
time (sec) |
N/A | 0.017 | 0.106 | 0.129 | 2.240 | 0.594 | 0.000 | 0.529 | 0.246 |
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 | 23 | 23 | 20 | 19 | 19 | 29 | 19 | 19 |
N.S. | 1 | 1.00 | 1.00 | 0.87 | 0.83 | 0.83 | 1.26 | 0.83 | 0.83 |
time (sec) |
N/A | 0.003 | 0.003 | 0.040 | 2.355 | 0.733 | 0.210 | 0.572 | 0.289 |
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 | 28 | 25 | 24 | 24 | 36 | 24 | 24 |
N.S. | 1 | 1.00 | 1.00 | 0.89 | 0.86 | 0.86 | 1.29 | 0.86 | 0.86 |
time (sec) |
N/A | 0.003 | 0.004 | 0.043 | 1.798 | 0.662 | 0.284 | 0.548 | 0.272 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | B | A | F(-2) | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 56 | 56 | 150 | 47 | 0 | 155 | 0 | 60 | 50 |
N.S. |
1 | 1.00 | 2.68 | 0.84 | 0.00 | 2.77 | 0.00 | 1.07 | 0.89 |
time (sec) |
N/A | 0.030 | 0.177 | 0.026 | 0.000 | 0.692 | 0.000 | 0.454 | 0.979 |
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 | 81 | 81 | 86 | 70 | 68 | 94 | 0 | 72 | 67 |
N.S. | 1 | 1.00 | 1.06 | 0.86 | 0.84 | 1.16 | 0.00 | 0.89 | 0.83 |
time (sec) |
N/A | 0.022 | 0.197 | 0.117 | 1.110 | 0.557 | 0.000 | 0.498 | 0.237 |
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 | 44 | 44 | 53 | 56 | 0 | 58 | 0 | 45 | 54 |
N.S. |
1 | 1.00 | 1.20 | 1.27 | 0.00 | 1.32 | 0.00 | 1.02 | 1.23 |
time (sec) |
N/A | 0.028 | 0.081 | 0.028 | 0.000 | 0.584 | 0.000 | 0.467 | 0.400 |
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 | 68 | 68 | 72 | 78 | 0 | 106 | 0 | 62 | 72 |
N.S. |
1 | 1.00 | 1.06 | 1.15 | 0.00 | 1.56 | 0.00 | 0.91 | 1.06 |
time (sec) |
N/A | 0.035 | 0.110 | 0.028 | 0.000 | 0.574 | 0.000 | 0.454 | 0.442 |
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 | 12 | 11 | 22 | 10 | 11 | 11 |
N.S. | 1 | 1.00 | 1.00 | 0.92 | 0.85 | 1.69 | 0.77 | 0.85 | 0.85 |
time (sec) |
N/A | 0.013 | 0.005 | 0.039 | 3.117 | 0.618 | 0.082 | 0.448 | 0.089 |
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 | 16 | 15 | 11 | 17 | 15 | 11 |
N.S. | 1 | 1.00 | 1.00 | 0.84 | 0.79 | 0.58 | 0.89 | 0.79 | 0.58 |
time (sec) |
N/A | 0.005 | 0.002 | 0.008 | 1.560 | 0.554 | 0.031 | 0.418 | 0.165 |
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 | 12 | 12 | 21 | 20 | 12 | 10 | 12 | 12 |
N.S. | 1 | 1.00 | 1.00 | 1.75 | 1.67 | 1.00 | 0.83 | 1.00 | 1.00 |
time (sec) |
N/A | 0.008 | 0.021 | 0.025 | 2.204 | 0.888 | 0.054 | 0.486 | 0.083 |
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 | 11 | 10 | 10 | 7 | 10 | 10 |
N.S. | 1 | 1.00 | 1.00 | 1.00 | 0.91 | 0.91 | 0.64 | 0.91 | 0.91 |
time (sec) |
N/A | 0.017 | 0.007 | 0.013 | 3.580 | 0.803 | 0.050 | 0.448 | 0.216 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 27 | 24 | 23 | 22 | 20 | 24 | 22 |
N.S. | 1 | 1.00 | 1.00 | 0.89 | 0.85 | 0.81 | 0.74 | 0.89 | 0.81 |
time (sec) |
N/A | 0.012 | 0.004 | 0.026 | 5.543 | 0.850 | 0.048 | 0.438 | 0.154 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | B | C | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 33 | 21 | 32 | 20 | 50 | 167 | 66 | 15 |
N.S. | 1 | 1.00 | 0.64 | 0.97 | 0.61 | 1.52 | 5.06 | 2.00 | 0.45 |
time (sec) |
N/A | 0.002 | 0.051 | 0.033 | 1.704 | 0.786 | 2.880 | 0.497 | 0.299 |
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 | 9 | 9 | 10 | 9 | 9 | 7 | 11 | 8 |
N.S. | 1 | 1.00 | 1.00 | 1.11 | 1.00 | 1.00 | 0.78 | 1.22 | 0.89 |
time (sec) |
N/A | 0.001 | 0.002 | 0.031 | 1.721 | 0.813 | 0.025 | 0.454 | 0.197 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 19 | 14 | 28 | 28 | 39 | 32 | 13 |
N.S. | 1 | 1.00 | 1.00 | 0.74 | 1.47 | 1.47 | 2.05 | 1.68 | 0.68 |
time (sec) |
N/A | 0.004 | 0.023 | 0.072 | 1.597 | 0.617 | 0.099 | 0.480 | 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 | 19 | 19 | 16 | 12 | 11 | 14 | 15 | 11 | 12 |
N.S. | 1 | 1.00 | 0.84 | 0.63 | 0.58 | 0.74 | 0.79 | 0.58 | 0.63 |
time (sec) |
N/A | 0.002 | 0.009 | 0.012 | 3.376 | 0.707 | 0.506 | 0.453 | 0.024 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | C | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 88 | 88 | 112 | 89 | 86 | 104 | 153 | 103 | 119 |
N.S. | 1 | 1.00 | 1.27 | 1.01 | 0.98 | 1.18 | 1.74 | 1.17 | 1.35 |
time (sec) |
N/A | 0.028 | 0.063 | 0.039 | 3.132 | 0.702 | 0.945 | 0.676 | 0.181 |
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 | 9 | 9 | 9 | 10 | 34 | 9 | 7 | 17 | 9 |
N.S. | 1 | 1.00 | 1.00 | 1.11 | 3.78 | 1.00 | 0.78 | 1.89 | 1.00 |
time (sec) |
N/A | 0.008 | 0.003 | 0.016 | 2.108 | 0.620 | 0.060 | 0.472 | 0.021 |
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 | 9 | 9 | 9 | 10 | 34 | 9 | 7 | 17 | 9 |
N.S. | 1 | 1.00 | 1.00 | 1.11 | 3.78 | 1.00 | 0.78 | 1.89 | 1.00 |
time (sec) |
N/A | 0.008 | 0.004 | 0.015 | 1.310 | 0.632 | 0.058 | 0.544 | 0.026 |
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 | 9 | 9 | 9 | 8 | 7 | 26 | 7 | 13 | 7 |
N.S. | 1 | 1.00 | 1.00 | 0.89 | 0.78 | 2.89 | 0.78 | 1.44 | 0.78 |
time (sec) |
N/A | 0.003 | 0.005 | 0.014 | 5.812 | 0.568 | 0.039 | 0.515 | 0.186 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 12 | 16 | 13 | 26 | 22 | 23 | 13 |
N.S. | 1 | 1.00 | 1.00 | 1.33 | 1.08 | 2.17 | 1.83 | 1.92 | 1.08 |
time (sec) |
N/A | 0.023 | 0.042 | 0.032 | 1.702 | 0.829 | 0.146 | 0.492 | 0.321 |
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 | 28 | 28 | 28 | 23 | 22 | 32 | 76 | 22 | 22 |
N.S. | 1 | 1.00 | 1.00 | 0.82 | 0.79 | 1.14 | 2.71 | 0.79 | 0.79 |
time (sec) |
N/A | 0.016 | 0.016 | 0.051 | 1.252 | 1.095 | 0.334 | 0.489 | 0.332 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 21 | 16 | 15 | 13 | 15 | 15 | 14 |
N.S. | 1 | 1.00 | 1.00 | 0.76 | 0.71 | 0.62 | 0.71 | 0.71 | 0.67 |
time (sec) |
N/A | 0.006 | 0.004 | 0.000 | 2.303 | 1.007 | 0.077 | 0.482 | 0.019 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 21 | 16 | 15 | 13 | 15 | 19 | 15 |
N.S. | 1 | 1.00 | 1.00 | 0.76 | 0.71 | 0.62 | 0.71 | 0.90 | 0.71 |
time (sec) |
N/A | 0.006 | 0.003 | 0.034 | 1.679 | 1.026 | 0.082 | 0.474 | 0.048 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 22 | 23 | 22 | 19 | 26 | 22 | 41 |
N.S. | 1 | 1.00 | 0.96 | 1.00 | 0.96 | 0.83 | 1.13 | 0.96 | 1.78 |
time (sec) |
N/A | 0.014 | 0.004 | 0.012 | 1.228 | 0.558 | 0.061 | 0.515 | 0.144 |
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 | 18 | 18 | 18 | 15 | 14 | 28 | 32 | 14 | 14 |
N.S. | 1 | 1.00 | 1.00 | 0.83 | 0.78 | 1.56 | 1.78 | 0.78 | 0.78 |
time (sec) |
N/A | 0.012 | 0.015 | 0.066 | 1.557 | 0.938 | 0.127 | 0.464 | 0.026 |
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 | 18 | 18 | 18 | 15 | 14 | 28 | 32 | 14 | 14 |
N.S. | 1 | 1.00 | 1.00 | 0.83 | 0.78 | 1.56 | 1.78 | 0.78 | 0.78 |
time (sec) |
N/A | 0.009 | 0.011 | 0.047 | 2.222 | 0.991 | 0.126 | 0.463 | 0.024 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | B | A | F | B | F | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 40 | 17 | 0 | 24 | 0 | 22 | 16 |
N.S. | 1 | 1.00 | 3.33 | 1.42 | 0.00 | 2.00 | 0.00 | 1.83 | 1.33 |
time (sec) |
N/A | 0.005 | 0.009 | 0.062 | 0.000 | 1.114 | 0.000 | 0.452 | 0.139 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | B | A | F | B | F | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 42 | 23 | 0 | 26 | 0 | 35 | 18 |
N.S. | 1 | 1.00 | 3.00 | 1.64 | 0.00 | 1.86 | 0.00 | 2.50 | 1.29 |
time (sec) |
N/A | 0.007 | 0.009 | 0.087 | 0.000 | 1.271 | 0.000 | 0.455 | 0.136 |
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 | 12 | 12 | 16 | 22 | 9 | 10 | 36 | 14 | 10 |
N.S. | 1 | 1.00 | 1.33 | 1.83 | 0.75 | 0.83 | 3.00 | 1.17 | 0.83 |
time (sec) |
N/A | 0.005 | 0.007 | 0.043 | 2.631 | 0.824 | 0.358 | 0.452 | 0.145 |
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 | 14 | 14 | 18 | 22 | 20 | 18 | 0 | 23 | 12 |
N.S. | 1 | 1.00 | 1.29 | 1.57 | 1.43 | 1.29 | 0.00 | 1.64 | 0.86 |
time (sec) |
N/A | 0.007 | 0.008 | 0.052 | 1.929 | 0.821 | 0.000 | 0.480 | 0.033 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | F | A | B | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 17 | 14 | 0 | 13 | 63 | 13 | 21 |
N.S. | 1 | 1.00 | 0.81 | 0.67 | 0.00 | 0.62 | 3.00 | 0.62 | 1.00 |
time (sec) |
N/A | 0.006 | 0.068 | 0.025 | 0.000 | 0.769 | 0.168 | 0.405 | 0.193 |
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 | 31 | 18 | 18 | 20 | 19 | 18 |
N.S. | 1 | 1.00 | 0.92 | 1.29 | 0.75 | 0.75 | 0.83 | 0.79 | 0.75 |
time (sec) |
N/A | 0.007 | 0.011 | 0.039 | 2.463 | 0.589 | 0.044 | 0.431 | 0.106 |
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 | 12 | 18 | 9 | 33 | 16 | 7 | 16 | 8 |
N.S. | 1 | 1.00 | 1.50 | 0.75 | 2.75 | 1.33 | 0.58 | 1.33 | 0.67 |
time (sec) |
N/A | 0.003 | 0.070 | 0.079 | 1.769 | 0.701 | 0.398 | 0.421 | 0.037 |
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 | 32 | 32 | 33 | 92 | 24 | 24 | 0 | 24 | 24 |
N.S. | 1 | 1.00 | 1.03 | 2.88 | 0.75 | 0.75 | 0.00 | 0.75 | 0.75 |
time (sec) |
N/A | 0.009 | 0.023 | 0.033 | 2.443 | 0.610 | 0.000 | 0.444 | 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 | 33 | 33 | 33 | 27 | 26 | 32 | 31 | 26 | 26 |
N.S. | 1 | 1.00 | 1.00 | 0.82 | 0.79 | 0.97 | 0.94 | 0.79 | 0.79 |
time (sec) |
N/A | 0.008 | 0.010 | 0.017 | 2.170 | 0.665 | 0.046 | 0.441 | 0.060 |
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 | 3 | 3 | 3 | 4 | 3 | 11 | 3 | 4 | 3 |
N.S. | 1 | 1.00 | 1.00 | 1.33 | 1.00 | 3.67 | 1.00 | 1.33 | 1.00 |
time (sec) |
N/A | 0.002 | 0.003 | 0.004 | 1.376 | 0.561 | 0.026 | 0.450 | 0.025 |
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 | 12 | 12 | 18 | 16 | 16 | 48 | 19 | 34 | 10 |
N.S. | 1 | 1.00 | 1.50 | 1.33 | 1.33 | 4.00 | 1.58 | 2.83 | 0.83 |
time (sec) |
N/A | 0.009 | 0.004 | 0.001 | 1.661 | 0.613 | 0.015 | 0.437 | 0.028 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 3 | 3 | 3 | 4 | 3 | 18 | 7 | 11 | 3 |
N.S. | 1 | 1.00 | 1.00 | 1.33 | 1.00 | 6.00 | 2.33 | 3.67 | 1.00 |
time (sec) |
N/A | 0.003 | 0.002 | 0.009 | 1.328 | 0.629 | 0.038 | 0.444 | 0.011 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 3 | 3 | 3 | 4 | 3 | 18 | 12 | 12 | 3 |
N.S. | 1 | 1.00 | 1.00 | 1.33 | 1.00 | 6.00 | 4.00 | 4.00 | 1.00 |
time (sec) |
N/A | 0.003 | 0.004 | 0.008 | 2.455 | 0.619 | 0.134 | 0.451 | 0.137 |
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 | 9 | 8 | 8 | 8 | 8 | 8 |
N.S. | 1 | 1.00 | 1.00 | 1.12 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.002 | 0.000 | 0.012 | 3.451 | 1.001 | 0.024 | 0.470 | 0.165 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 49 | 49 | 29 | 32 | 10 | 10 | 0 | 11 | -1 |
N.S. | 1 | 1.00 | 0.59 | 0.65 | 0.20 | 0.20 | 0.00 | 0.22 | -0.02 |
time (sec) |
N/A | 0.011 | 0.007 | 0.013 | 3.629 | 0.747 | 0.000 | 0.476 | 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 | 16 | 17 | 13 | 12 | 12 | 12 | 13 | 10 |
N.S. | 1 | 1.00 | 1.06 | 0.81 | 0.75 | 0.75 | 0.75 | 0.81 | 0.62 |
time (sec) |
N/A | 0.005 | 0.003 | 0.028 | 2.949 | 0.777 | 0.017 | 0.439 | 0.145 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | F | F | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 40 | 40 | 36 | 0 | 0 | 30 | 0 | 40 | 32 |
N.S. | 1 | 1.00 | 0.90 | 0.00 | 0.00 | 0.75 | 0.00 | 1.00 | 0.80 |
time (sec) |
N/A | 0.014 | 0.008 | 0.003 | 0.000 | 0.728 | 0.000 | 0.469 | 0.042 |
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 | 128 | 128 | 67 | 63 | 58 | 55 | 109 | 57 | 69 |
N.S. | 1 | 1.00 | 0.52 | 0.49 | 0.45 | 0.43 | 0.85 | 0.45 | 0.54 |
time (sec) |
N/A | 0.133 | 0.107 | 0.041 | 2.082 | 0.881 | 0.699 | 0.459 | 0.278 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 30 | 18 | 20 | 17 | 17 | 27 | 15 | 17 |
N.S. | 1 | 1.00 | 0.60 | 0.67 | 0.57 | 0.57 | 0.90 | 0.50 | 0.57 |
time (sec) |
N/A | 0.027 | 0.019 | 0.026 | 2.459 | 1.118 | 0.165 | 0.457 | 0.171 |
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 | 11 | 11 | 9 | 8 | 7 | 17 | 17 | 7 | 7 |
N.S. | 1 | 1.00 | 0.82 | 0.73 | 0.64 | 1.55 | 1.55 | 0.64 | 0.64 |
time (sec) |
N/A | 0.001 | 0.002 | 0.038 | 5.060 | 1.421 | 0.031 | 0.453 | 0.066 |
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 | 40 | 40 | 40 | 33 | 32 | 32 | 41 | 33 | 46 |
N.S. | 1 | 1.00 | 1.00 | 0.82 | 0.80 | 0.80 | 1.02 | 0.82 | 1.15 |
time (sec) |
N/A | 0.014 | 0.007 | 0.036 | 2.406 | 1.060 | 0.046 | 0.482 | 0.115 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 8 | 8 | 23 | 22 | 17 | 17 | 15 | 18 | 6 |
N.S. | 1 | 1.00 | 2.88 | 2.75 | 2.12 | 2.12 | 1.88 | 2.25 | 0.75 |
time (sec) |
N/A | 0.002 | 0.003 | 0.034 | 4.490 | 0.936 | 0.029 | 0.459 | 0.067 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | B | F | F | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 227 | 227 | 194 | 394 | 0 | 0 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 0.85 | 1.74 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A | 0.139 | 0.193 | 0.043 | 0.000 | 0.000 | 0.000 | 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 | 24 | 24 | 30 | 26 | 25 | 24 | 37 | 25 | 51 |
N.S. | 1 | 1.00 | 1.25 | 1.08 | 1.04 | 1.00 | 1.54 | 1.04 | 2.12 |
time (sec) |
N/A | 0.007 | 0.006 | 0.011 | 2.423 | 0.774 | 0.687 | 0.457 | 0.443 |
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 | 78 | 78 | 71 | 54 | 57 | 69 | 73 | 58 | 70 |
N.S. | 1 | 1.00 | 0.91 | 0.69 | 0.73 | 0.88 | 0.94 | 0.74 | 0.90 |
time (sec) |
N/A | 0.032 | 0.018 | 0.027 | 3.608 | 0.807 | 0.131 | 0.454 | 0.272 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | B | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 2 | 2 | 12 | 3 | 2 | 14 | 2 | 25 | 2 |
N.S. | 1 | 1.00 | 6.00 | 1.50 | 1.00 | 7.00 | 1.00 | 12.50 | 1.00 |
time (sec) |
N/A | 0.001 | 0.001 | 0.028 | 4.330 | 0.663 | 0.043 | 0.451 | 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 | 27 | 27 | 31 | 21 | 20 | 25 | 24 | 25 | 20 |
N.S. | 1 | 1.00 | 1.15 | 0.78 | 0.74 | 0.93 | 0.89 | 0.93 | 0.74 |
time (sec) |
N/A | 0.002 | 0.021 | 0.049 | 3.816 | 0.615 | 0.065 | 0.454 | 0.048 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 10 | 10 | 10 | 11 | 10 | 16 | 8 | 11 | 10 |
N.S. | 1 | 1.00 | 1.00 | 1.10 | 1.00 | 1.60 | 0.80 | 1.10 | 1.00 |
time (sec) |
N/A | 0.003 | 0.003 | 0.028 | 1.824 | 0.584 | 0.020 | 0.454 | 0.031 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 16 | 15 | 14 | 14 | 12 | 14 | 14 |
N.S. | 1 | 1.00 | 1.00 | 0.94 | 0.88 | 0.88 | 0.75 | 0.88 | 0.88 |
time (sec) |
N/A | 0.003 | 0.002 | 0.003 | 2.429 | 0.917 | 0.042 | 0.446 | 0.220 |
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 | 40 | 40 | 29 | 34 | 33 | 24 | 32 | 38 | 24 |
N.S. | 1 | 1.00 | 0.72 | 0.85 | 0.82 | 0.60 | 0.80 | 0.95 | 0.60 |
time (sec) |
N/A | 0.016 | 0.010 | 0.004 | 4.266 | 0.930 | 0.092 | 0.503 | 0.029 |
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 | 21 | 21 | 29 | 14 | 13 | 29 | 0 | 15 | 9 |
N.S. | 1 | 1.00 | 1.38 | 0.67 | 0.62 | 1.38 | 0.00 | 0.71 | 0.43 |
time (sec) |
N/A | 0.083 | 0.026 | 0.105 | 3.120 | 0.858 | 0.000 | 0.443 | 0.810 |
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 | 14 | 14 | 11 | 10 | 10 | 10 | 16 | 10 |
N.S. | 1 | 1.00 | 1.00 | 0.79 | 0.71 | 0.71 | 0.71 | 1.14 | 0.71 |
time (sec) |
N/A | 0.005 | 0.003 | 0.018 | 1.495 | 0.984 | 0.011 | 0.450 | 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 | 18 | 18 | 18 | 17 | 16 | 18 | 14 | 18 | 16 |
N.S. | 1 | 1.00 | 1.00 | 0.94 | 0.89 | 1.00 | 0.78 | 1.00 | 0.89 |
time (sec) |
N/A | 0.010 | 0.004 | 0.043 | 2.539 | 1.461 | 0.039 | 0.454 | 0.152 |
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 | 10 | 10 | 20 | 7 | 6 | 16 | 7 | 29 | 6 |
N.S. | 1 | 1.00 | 2.00 | 0.70 | 0.60 | 1.60 | 0.70 | 2.90 | 0.60 |
time (sec) |
N/A | 0.001 | 0.013 | 0.047 | 2.988 | 1.113 | 0.051 | 0.464 | 0.038 |
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 | 6 | 6 | 12 | 5 | 4 | 14 | 3 | 25 | 4 |
N.S. | 1 | 1.00 | 2.00 | 0.83 | 0.67 | 2.33 | 0.50 | 4.17 | 0.67 |
time (sec) |
N/A | 0.001 | 0.012 | 0.047 | 3.493 | 1.027 | 0.049 | 0.441 | 0.029 |
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 | 17 | 16 | 16 | 22 | 16 | 16 |
N.S. | 1 | 1.00 | 1.00 | 0.81 | 0.76 | 0.76 | 1.05 | 0.76 | 0.76 |
time (sec) |
N/A | 0.012 | 0.007 | 0.159 | 2.652 | 0.927 | 0.036 | 0.444 | 0.142 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 53 | 53 | 51 | 42 | 47 | 73 | 46 | 46 | 45 |
N.S. | 1 | 1.00 | 0.96 | 0.79 | 0.89 | 1.38 | 0.87 | 0.87 | 0.85 |
time (sec) |
N/A | 0.021 | 0.015 | 0.020 | 2.895 | 1.140 | 0.068 | 0.463 | 0.061 |
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 | 49 | 49 | 49 | 46 | 41 | 41 | 762 | 44 | 46 |
N.S. | 1 | 1.00 | 1.00 | 0.94 | 0.84 | 0.84 | 15.55 | 0.90 | 0.94 |
time (sec) |
N/A | 0.053 | 0.019 | 0.044 | 2.248 | 1.277 | 56.795 | 0.466 | 0.210 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | A |
verified |
N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.07 |
time (sec) |
N/A | 0.003 | 2.591 | 0.055 | 0.000 | 0.000 | 0.000 | 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 | 28 | 28 | 28 | 28 | 27 | 44 | 26 | 27 | 27 |
N.S. | 1 | 1.00 | 1.00 | 1.00 | 0.96 | 1.57 | 0.93 | 0.96 | 0.96 |
time (sec) |
N/A | 0.148 | 40.005 | 0.190 | 3.925 | 0.846 | 0.159 | 0.435 | 0.338 |
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 | 199 | 199 | 136 | 128 | 160 | 145 | 1277 | 114 | 140 |
N.S. | 1 | 1.00 | 0.68 | 0.64 | 0.80 | 0.73 | 6.42 | 0.57 | 0.70 |
time (sec) |
N/A | 0.074 | 0.155 | 0.177 | 5.234 | 0.759 | 147.269 | 0.451 | 1.111 |
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 | 18 | 18 | 16 | 15 | 20 | 15 | 15 | 15 |
N.S. | 1 | 1.00 | 1.00 | 0.89 | 0.83 | 1.11 | 0.83 | 0.83 | 0.83 |
time (sec) |
N/A | 0.004 | 0.006 | 0.013 | 3.164 | 0.954 | 0.133 | 0.444 | 0.155 |
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 | 24 | 22 | 21 | 37 | 36 | 37 | 21 |
N.S. | 1 | 1.00 | 1.00 | 0.92 | 0.88 | 1.54 | 1.50 | 1.54 | 0.88 |
time (sec) |
N/A | 0.006 | 0.021 | 0.016 | 2.985 | 0.821 | 0.219 | 0.491 | 0.066 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | C | B | F | B | F | F | F |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 94 | 0 | 5137 | 1197351 | 0 | 179 | 0 | 0 | -1 |
N.S. | 1 | 0.00 | 54.65 | 12737.78 | 0.00 | 1.90 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A | 1.282 | 16.125 | 1.343 | 0.000 | 1.473 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | C | C | F | A | F | F | F |
verified |
N/A | N/A | NO | TBD | TBD | TBD | TBD | TBD | TBD |
size | 142 | 0 | 630 | 354 | 0 | 223 | 0 | 0 | -1 |
N.S. | 1 | 0.00 | 4.44 | 2.49 | 0.00 | 1.57 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A | 2.180 | 3.627 | 0.339 | 0.000 | 1.358 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | B | B | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 31 | 1088 | 171 | 162 | 0 | 76 | 172 |
N.S. |
1 | 1.00 | 1.48 | 51.81 | 8.14 | 7.71 | 0.00 | 3.62 | 8.19 |
time (sec) |
N/A | 0.193 | 0.619 | 0.199 | 2.533 | 0.835 | 0.000 | 0.444 | 2.373 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | C | A | F | F | F | F | F |
verified |
N/A | N/A | NO | TBD | TBD | TBD | TBD | TBD | TBD |
size | 4030 | 0 | 3168 | 4640 | 0 | 0 | 0 | 0 | -1 |
N.S. | 1 | 0.00 | 0.79 | 1.15 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A | 0.019 | 16.687 | 0.868 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | C | F | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 330 | 330 | 181 | 1356 | 0 | 269 | 330 | 472 | 265 |
N.S. | 1 | 1.00 | 0.55 | 4.11 | 0.00 | 0.82 | 1.00 | 1.43 | 0.80 |
time (sec) |
N/A | 0.634 | 0.103 | 0.135 | 0.000 | 0.648 | 9.754 | 0.606 | 0.767 |
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 | 4 | 4 | 4 | 5 | 4 | 4 | 5 | 4 | 4 |
N.S. | 1 | 1.00 | 1.00 | 1.25 | 1.00 | 1.00 | 1.25 | 1.00 | 1.00 |
time (sec) |
N/A | 0.008 | 0.002 | 0.031 | 2.657 | 0.639 | 0.382 | 0.495 | 0.020 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | A | A | F | B | A | A | B |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 71 | 0 | 71 | 61 | 0 | 137 | 76 | 94 | 103 |
N.S. | 1 | 0.00 | 1.00 | 0.86 | 0.00 | 1.93 | 1.07 | 1.32 | 1.45 |
time (sec) |
N/A | 0.510 | 0.026 | 0.037 | 0.000 | 0.592 | 0.094 | 0.459 | 0.280 |