Average Error: 0.5 → 0.5
Time: 41.2s
Precision: 64
\[\frac{2 + \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x - \cos y\right)}{3 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{3 - \sqrt{5}}{2} \cdot \cos y\right)}\]
↓
\[\frac{1}{3 \cdot \left(\cos y \cdot \frac{\frac{3 \cdot 3 - 5}{\sqrt{5} + 3}}{2} + \left(1 + \cos x \cdot \frac{\sqrt{5} - 1}{2}\right)\right)} \cdot \left(\left(\cos x - \cos y\right) \cdot \left(\left(\sin y - \frac{\sin x}{16}\right) \cdot \left(\left(\sin x - \frac{\sin y}{16}\right) \cdot \sqrt{2}\right)\right) + 2\right)\]
\frac{2 + \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x - \cos y\right)}{3 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{3 - \sqrt{5}}{2} \cdot \cos y\right)}
↓
\frac{1}{3 \cdot \left(\cos y \cdot \frac{\frac{3 \cdot 3 - 5}{\sqrt{5} + 3}}{2} + \left(1 + \cos x \cdot \frac{\sqrt{5} - 1}{2}\right)\right)} \cdot \left(\left(\cos x - \cos y\right) \cdot \left(\left(\sin y - \frac{\sin x}{16}\right) \cdot \left(\left(\sin x - \frac{\sin y}{16}\right) \cdot \sqrt{2}\right)\right) + 2\right)
double f(double x, double y) {
        double r10797822 = 2.0;
        double r10797823 = sqrt(r10797822);
        double r10797824 = x;
        double r10797825 = sin(r10797824);
        double r10797826 = y;
        double r10797827 = sin(r10797826);
        double r10797828 = 16.0;
        double r10797829 = r10797827 / r10797828;
        double r10797830 = r10797825 - r10797829;
        double r10797831 = r10797823 * r10797830;
        double r10797832 = r10797825 / r10797828;
        double r10797833 = r10797827 - r10797832;
        double r10797834 = r10797831 * r10797833;
        double r10797835 = cos(r10797824);
        double r10797836 = cos(r10797826);
        double r10797837 = r10797835 - r10797836;
        double r10797838 = r10797834 * r10797837;
        double r10797839 = r10797822 + r10797838;
        double r10797840 = 3.0;
        double r10797841 = 1.0;
        double r10797842 = 5.0;
        double r10797843 = sqrt(r10797842);
        double r10797844 = r10797843 - r10797841;
        double r10797845 = r10797844 / r10797822;
        double r10797846 = r10797845 * r10797835;
        double r10797847 = r10797841 + r10797846;
        double r10797848 = r10797840 - r10797843;
        double r10797849 = r10797848 / r10797822;
        double r10797850 = r10797849 * r10797836;
        double r10797851 = r10797847 + r10797850;
        double r10797852 = r10797840 * r10797851;
        double r10797853 = r10797839 / r10797852;
        return r10797853;
}
↓
double f(double x, double y) {
        double r10797854 = 1.0;
        double r10797855 = 3.0;
        double r10797856 = y;
        double r10797857 = cos(r10797856);
        double r10797858 = r10797855 * r10797855;
        double r10797859 = 5.0;
        double r10797860 = r10797858 - r10797859;
        double r10797861 = sqrt(r10797859);
        double r10797862 = r10797861 + r10797855;
        double r10797863 = r10797860 / r10797862;
        double r10797864 = 2.0;
        double r10797865 = r10797863 / r10797864;
        double r10797866 = r10797857 * r10797865;
        double r10797867 = 1.0;
        double r10797868 = x;
        double r10797869 = cos(r10797868);
        double r10797870 = r10797861 - r10797867;
        double r10797871 = r10797870 / r10797864;
        double r10797872 = r10797869 * r10797871;
        double r10797873 = r10797867 + r10797872;
        double r10797874 = r10797866 + r10797873;
        double r10797875 = r10797855 * r10797874;
        double r10797876 = r10797854 / r10797875;
        double r10797877 = r10797869 - r10797857;
        double r10797878 = sin(r10797856);
        double r10797879 = sin(r10797868);
        double r10797880 = 16.0;
        double r10797881 = r10797879 / r10797880;
        double r10797882 = r10797878 - r10797881;
        double r10797883 = r10797878 / r10797880;
        double r10797884 = r10797879 - r10797883;
        double r10797885 = sqrt(r10797864);
        double r10797886 = r10797884 * r10797885;
        double r10797887 = r10797882 * r10797886;
        double r10797888 = r10797877 * r10797887;
        double r10797889 = r10797888 + r10797864;
        double r10797890 = r10797876 * r10797889;
        return r10797890;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.5

    \[\frac{2 + \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x - \cos y\right)}{3 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{3 - \sqrt{5}}{2} \cdot \cos y\right)}\]
  2. Using strategy rm

  3. Applied flip--0.5

    \[\leadsto \frac{2 + \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x - \cos y\right)}{3 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{\color{blue}{\frac{3 \cdot 3 - \sqrt{5} \cdot \sqrt{5}}{3 + \sqrt{5}}}}{2} \cdot \cos y\right)}\]

  4. Simplified0.4

    \[\leadsto \frac{2 + \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x - \cos y\right)}{3 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{\frac{\color{blue}{3 \cdot 3 - 5}}{3 + \sqrt{5}}}{2} \cdot \cos y\right)}\]
  5. Using strategy rm

  6. Applied div-inv0.5

    \[\leadsto \color{blue}{\left(2 + \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x - \cos y\right)\right) \cdot \frac{1}{3 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{\frac{3 \cdot 3 - 5}{3 + \sqrt{5}}}{2} \cdot \cos y\right)}}\]

  7. Final simplification0.5

    \[\leadsto \frac{1}{3 \cdot \left(\cos y \cdot \frac{\frac{3 \cdot 3 - 5}{\sqrt{5} + 3}}{2} + \left(1 + \cos x \cdot \frac{\sqrt{5} - 1}{2}\right)\right)} \cdot \left(\left(\cos x - \cos y\right) \cdot \left(\left(\sin y - \frac{\sin x}{16}\right) \cdot \left(\left(\sin x - \frac{\sin y}{16}\right) \cdot \sqrt{2}\right)\right) + 2\right)\]

Reproduce

herbie shell --seed 2019192 
(FPCore (x y)
  :name "Diagrams.TwoD.Path.Metafont.Internal:hobbyF from diagrams-contrib-1.3.0.5"
  (/ (+ 2.0 (* (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y)))) (* 3.0 (+ (+ 1.0 (* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))) (* (/ (- 3.0 (sqrt 5.0)) 2.0) (cos y))))))