Average Error: 0.5 → 0.5
Time: 11.4s
Precision: 64
\[\frac{2 + \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x - \cos y\right)}{3 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{3 - \sqrt{5}}{2} \cdot \cos y\right)}\]
↓
\[\frac{2 + \left(\frac{\sqrt{2} \cdot \left(\sin x \cdot \sin x - \frac{\sin y}{16} \cdot \frac{\sin y}{16}\right)}{\sin x + \frac{\sin y}{16}} \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \sqrt[3]{\sqrt[3]{{\left({\left(\cos x - \cos y\right)}^{3}\right)}^{3}}}}{3 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{\frac{3 \cdot 3 + \left(-5\right)}{3 + \sqrt{5}}}{2} \cdot \cos y\right)}\]
\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 + \left(\frac{\sqrt{2} \cdot \left(\sin x \cdot \sin x - \frac{\sin y}{16} \cdot \frac{\sin y}{16}\right)}{\sin x + \frac{\sin y}{16}} \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \sqrt[3]{\sqrt[3]{{\left({\left(\cos x - \cos y\right)}^{3}\right)}^{3}}}}{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 r223920 = 2.0;
        double r223921 = sqrt(r223920);
        double r223922 = x;
        double r223923 = sin(r223922);
        double r223924 = y;
        double r223925 = sin(r223924);
        double r223926 = 16.0;
        double r223927 = r223925 / r223926;
        double r223928 = r223923 - r223927;
        double r223929 = r223921 * r223928;
        double r223930 = r223923 / r223926;
        double r223931 = r223925 - r223930;
        double r223932 = r223929 * r223931;
        double r223933 = cos(r223922);
        double r223934 = cos(r223924);
        double r223935 = r223933 - r223934;
        double r223936 = r223932 * r223935;
        double r223937 = r223920 + r223936;
        double r223938 = 3.0;
        double r223939 = 1.0;
        double r223940 = 5.0;
        double r223941 = sqrt(r223940);
        double r223942 = r223941 - r223939;
        double r223943 = r223942 / r223920;
        double r223944 = r223943 * r223933;
        double r223945 = r223939 + r223944;
        double r223946 = r223938 - r223941;
        double r223947 = r223946 / r223920;
        double r223948 = r223947 * r223934;
        double r223949 = r223945 + r223948;
        double r223950 = r223938 * r223949;
        double r223951 = r223937 / r223950;
        return r223951;
}
↓
double f(double x, double y) {
        double r223952 = 2.0;
        double r223953 = sqrt(r223952);
        double r223954 = x;
        double r223955 = sin(r223954);
        double r223956 = r223955 * r223955;
        double r223957 = y;
        double r223958 = sin(r223957);
        double r223959 = 16.0;
        double r223960 = r223958 / r223959;
        double r223961 = r223960 * r223960;
        double r223962 = r223956 - r223961;
        double r223963 = r223953 * r223962;
        double r223964 = r223955 + r223960;
        double r223965 = r223963 / r223964;
        double r223966 = r223955 / r223959;
        double r223967 = r223958 - r223966;
        double r223968 = r223965 * r223967;
        double r223969 = cos(r223954);
        double r223970 = cos(r223957);
        double r223971 = r223969 - r223970;
        double r223972 = 3.0;
        double r223973 = pow(r223971, r223972);
        double r223974 = pow(r223973, r223972);
        double r223975 = cbrt(r223974);
        double r223976 = cbrt(r223975);
        double r223977 = r223968 * r223976;
        double r223978 = r223952 + r223977;
        double r223979 = 3.0;
        double r223980 = 1.0;
        double r223981 = 5.0;
        double r223982 = sqrt(r223981);
        double r223983 = r223982 - r223980;
        double r223984 = r223983 / r223952;
        double r223985 = r223984 * r223969;
        double r223986 = r223980 + r223985;
        double r223987 = r223979 * r223979;
        double r223988 = -r223981;
        double r223989 = r223987 + r223988;
        double r223990 = r223979 + r223982;
        double r223991 = r223989 / r223990;
        double r223992 = r223991 / r223952;
        double r223993 = r223992 * r223970;
        double r223994 = r223986 + r223993;
        double r223995 = r223979 * r223994;
        double r223996 = r223978 / r223995;
        return r223996;
}

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-cbrt-cube0.5

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

  4. Simplified0.5

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

  6. Applied flip--0.5

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

  7. Simplified0.5

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

  9. Applied flip--0.5

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

  10. Applied associate-*r/0.5

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

  12. Applied add-cbrt-cube0.5

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

  13. Simplified0.5

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

  14. Final simplification0.5

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

Reproduce

herbie shell --seed 2020049 
(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))))))