Average Error: 0.5 → 0.5
Time: 13.1s
Precision: 64
\[\frac{2 + \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x - \cos y\right)}{3 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{3 - \sqrt{5}}{2} \cdot \cos y\right)}\]
↓
\[\frac{2 + \frac{\left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left({\left(\cos x\right)}^{3} - {\left(\cos y\right)}^{3}\right)}{\cos x \cdot \cos x + \left(\sqrt[3]{\frac{1}{2} + \left(\frac{1}{2} \cdot \cos \left(2 \cdot y\right) + \cos x \cdot \cos y\right)} \cdot \sqrt[3]{\frac{1}{2} + \left(\frac{1}{2} \cdot \cos \left(2 \cdot y\right) + \cos x \cdot \cos y\right)}\right) \cdot \sqrt[3]{\frac{1}{2} + \left(\frac{1}{2} \cdot \cos \left(2 \cdot y\right) + \cos x \cdot \cos y\right)}}}{3 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{\frac{3 \cdot 3 + \left(-5\right)}{3 + \sqrt{5}}}{2} \cdot \cos y\right)}\]
\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 + \frac{\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({\left(\cos x\right)}^{3} - {\left(\cos y\right)}^{3}\right)}{\cos x \cdot \cos x + \left(\sqrt[3]{\frac{1}{2} + \left(\frac{1}{2} \cdot \cos \left(2 \cdot y\right) + \cos x \cdot \cos y\right)} \cdot \sqrt[3]{\frac{1}{2} + \left(\frac{1}{2} \cdot \cos \left(2 \cdot y\right) + \cos x \cdot \cos y\right)}\right) \cdot \sqrt[3]{\frac{1}{2} + \left(\frac{1}{2} \cdot \cos \left(2 \cdot y\right) + \cos x \cdot \cos y\right)}}}{3 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{\frac{3 \cdot 3 + \left(-5\right)}{3 + \sqrt{5}}}{2} \cdot \cos y\right)}
double f(double x, double y) {
        double r240870 = 2.0;
        double r240871 = sqrt(r240870);
        double r240872 = x;
        double r240873 = sin(r240872);
        double r240874 = y;
        double r240875 = sin(r240874);
        double r240876 = 16.0;
        double r240877 = r240875 / r240876;
        double r240878 = r240873 - r240877;
        double r240879 = r240871 * r240878;
        double r240880 = r240873 / r240876;
        double r240881 = r240875 - r240880;
        double r240882 = r240879 * r240881;
        double r240883 = cos(r240872);
        double r240884 = cos(r240874);
        double r240885 = r240883 - r240884;
        double r240886 = r240882 * r240885;
        double r240887 = r240870 + r240886;
        double r240888 = 3.0;
        double r240889 = 1.0;
        double r240890 = 5.0;
        double r240891 = sqrt(r240890);
        double r240892 = r240891 - r240889;
        double r240893 = r240892 / r240870;
        double r240894 = r240893 * r240883;
        double r240895 = r240889 + r240894;
        double r240896 = r240888 - r240891;
        double r240897 = r240896 / r240870;
        double r240898 = r240897 * r240884;
        double r240899 = r240895 + r240898;
        double r240900 = r240888 * r240899;
        double r240901 = r240887 / r240900;
        return r240901;
}
↓
double f(double x, double y) {
        double r240902 = 2.0;
        double r240903 = sqrt(r240902);
        double r240904 = x;
        double r240905 = sin(r240904);
        double r240906 = y;
        double r240907 = sin(r240906);
        double r240908 = 16.0;
        double r240909 = r240907 / r240908;
        double r240910 = r240905 - r240909;
        double r240911 = r240903 * r240910;
        double r240912 = r240905 / r240908;
        double r240913 = r240907 - r240912;
        double r240914 = r240911 * r240913;
        double r240915 = cos(r240904);
        double r240916 = 3.0;
        double r240917 = pow(r240915, r240916);
        double r240918 = cos(r240906);
        double r240919 = pow(r240918, r240916);
        double r240920 = r240917 - r240919;
        double r240921 = r240914 * r240920;
        double r240922 = r240915 * r240915;
        double r240923 = 0.5;
        double r240924 = 2.0;
        double r240925 = r240924 * r240906;
        double r240926 = cos(r240925);
        double r240927 = r240923 * r240926;
        double r240928 = r240915 * r240918;
        double r240929 = r240927 + r240928;
        double r240930 = r240923 + r240929;
        double r240931 = cbrt(r240930);
        double r240932 = r240931 * r240931;
        double r240933 = r240932 * r240931;
        double r240934 = r240922 + r240933;
        double r240935 = r240921 / r240934;
        double r240936 = r240902 + r240935;
        double r240937 = 3.0;
        double r240938 = 1.0;
        double r240939 = 5.0;
        double r240940 = sqrt(r240939);
        double r240941 = r240940 - r240938;
        double r240942 = r240941 / r240902;
        double r240943 = r240942 * r240915;
        double r240944 = r240938 + r240943;
        double r240945 = r240937 * r240937;
        double r240946 = -r240939;
        double r240947 = r240945 + r240946;
        double r240948 = r240937 + r240940;
        double r240949 = r240947 / r240948;
        double r240950 = r240949 / r240902;
        double r240951 = r240950 * r240918;
        double r240952 = r240944 + r240951;
        double r240953 = r240937 * r240952;
        double r240954 = r240936 / r240953;
        return r240954;
}

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. Simplified0.5

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

  6. Applied flip3--0.5

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

  7. Applied associate-*r/0.5

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

  9. Applied sqr-cos0.5

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

  10. Applied associate-+l+0.5

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

  12. Applied add-cube-cbrt0.5

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

  13. Final simplification0.5

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

Reproduce

herbie shell --seed 2020003 
(FPCore (x y)
  :name "Diagrams.TwoD.Path.Metafont.Internal:hobbyF from diagrams-contrib-1.3.0.5"
  :precision binary64
  (/ (+ 2 (* (* (* (sqrt 2) (- (sin x) (/ (sin y) 16))) (- (sin y) (/ (sin x) 16))) (- (cos x) (cos y)))) (* 3 (+ (+ 1 (* (/ (- (sqrt 5) 1) 2) (cos x))) (* (/ (- 3 (sqrt 5)) 2) (cos y))))))