Average Error: 0.5 → 0.5
Time: 35.1s
Precision: 64
\[\frac{2 + \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x - \cos y\right)}{3 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{3 - \sqrt{5}}{2} \cdot \cos y\right)}\]
↓
\[\frac{2 + \sqrt[3]{{\left(\cos x - \cos y\right)}^{3}} \cdot \left(\left(\sqrt{\sqrt{2}} \cdot \left(\sqrt{\sqrt{2}} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right)}{3 \cdot \left(\frac{\frac{{3}^{3} - 5 \cdot \sqrt{5}}{\left(3 \cdot 3 + 3 \cdot \sqrt{5}\right) + 5}}{2} \cdot \cos y + \left(\frac{\sqrt{5} - 1}{2} \cdot \cos x + 1\right)\right)}\]
\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{2 + \sqrt[3]{{\left(\cos x - \cos y\right)}^{3}} \cdot \left(\left(\sqrt{\sqrt{2}} \cdot \left(\sqrt{\sqrt{2}} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right)}{3 \cdot \left(\frac{\frac{{3}^{3} - 5 \cdot \sqrt{5}}{\left(3 \cdot 3 + 3 \cdot \sqrt{5}\right) + 5}}{2} \cdot \cos y + \left(\frac{\sqrt{5} - 1}{2} \cdot \cos x + 1\right)\right)}
double f(double x, double y) {
        double r159886 = 2.0;
        double r159887 = sqrt(r159886);
        double r159888 = x;
        double r159889 = sin(r159888);
        double r159890 = y;
        double r159891 = sin(r159890);
        double r159892 = 16.0;
        double r159893 = r159891 / r159892;
        double r159894 = r159889 - r159893;
        double r159895 = r159887 * r159894;
        double r159896 = r159889 / r159892;
        double r159897 = r159891 - r159896;
        double r159898 = r159895 * r159897;
        double r159899 = cos(r159888);
        double r159900 = cos(r159890);
        double r159901 = r159899 - r159900;
        double r159902 = r159898 * r159901;
        double r159903 = r159886 + r159902;
        double r159904 = 3.0;
        double r159905 = 1.0;
        double r159906 = 5.0;
        double r159907 = sqrt(r159906);
        double r159908 = r159907 - r159905;
        double r159909 = r159908 / r159886;
        double r159910 = r159909 * r159899;
        double r159911 = r159905 + r159910;
        double r159912 = r159904 - r159907;
        double r159913 = r159912 / r159886;
        double r159914 = r159913 * r159900;
        double r159915 = r159911 + r159914;
        double r159916 = r159904 * r159915;
        double r159917 = r159903 / r159916;
        return r159917;
}
↓
double f(double x, double y) {
        double r159918 = 2.0;
        double r159919 = x;
        double r159920 = cos(r159919);
        double r159921 = y;
        double r159922 = cos(r159921);
        double r159923 = r159920 - r159922;
        double r159924 = 3.0;
        double r159925 = pow(r159923, r159924);
        double r159926 = cbrt(r159925);
        double r159927 = sqrt(r159918);
        double r159928 = sqrt(r159927);
        double r159929 = sin(r159919);
        double r159930 = sin(r159921);
        double r159931 = 16.0;
        double r159932 = r159930 / r159931;
        double r159933 = r159929 - r159932;
        double r159934 = r159928 * r159933;
        double r159935 = r159928 * r159934;
        double r159936 = r159929 / r159931;
        double r159937 = r159930 - r159936;
        double r159938 = r159935 * r159937;
        double r159939 = r159926 * r159938;
        double r159940 = r159918 + r159939;
        double r159941 = 3.0;
        double r159942 = pow(r159941, r159924);
        double r159943 = 5.0;
        double r159944 = sqrt(r159943);
        double r159945 = r159943 * r159944;
        double r159946 = r159942 - r159945;
        double r159947 = r159941 * r159941;
        double r159948 = r159941 * r159944;
        double r159949 = r159947 + r159948;
        double r159950 = r159949 + r159943;
        double r159951 = r159946 / r159950;
        double r159952 = r159951 / r159918;
        double r159953 = r159952 * r159922;
        double r159954 = 1.0;
        double r159955 = r159944 - r159954;
        double r159956 = r159955 / r159918;
        double r159957 = r159956 * r159920;
        double r159958 = r159957 + r159954;
        double r159959 = r159953 + r159958;
        double r159960 = r159941 * r159959;
        double r159961 = r159940 / r159960;
        return r159961;
}

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 add-sqr-sqrt0.5

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

  4. Applied sqrt-prod0.5

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

  5. Applied associate-*l*0.5

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

  6. Simplified0.5

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

  8. Applied flip3--0.5

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

  9. Simplified0.4

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

  10. Simplified0.4

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

  12. Applied add-cbrt-cube0.5

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

  13. Simplified0.5

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

  14. Final simplification0.5

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

Reproduce

herbie shell --seed 2019195 
(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))))))