Average Error: 0.5 → 0.5
Time: 34.9s
Precision: 64
\[\frac{2 + \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x - \cos y\right)}{3 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{3 - \sqrt{5}}{2} \cdot \cos y\right)}\]
↓
\[\frac{\left(\left(\sin y - \frac{\sin x}{16}\right) \cdot \left(\cos x - \cos y\right)\right) \cdot \left(\left(\sqrt[3]{\sin x - \frac{\sin y}{16}} \cdot \sqrt{2}\right) \cdot \left(\sqrt[3]{\sin x - \frac{\sin y}{16}} \cdot \sqrt[3]{\sin x - \frac{\sin y}{16}}\right)\right) + 2}{\left(\cos y \cdot \frac{\frac{3 \cdot 3 - 5}{3 + \sqrt{5}}}{2} + \left(\cos x \cdot \frac{\sqrt{5} - 1}{2} + 1\right)\right) \cdot 3}\]
\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{\left(\left(\sin y - \frac{\sin x}{16}\right) \cdot \left(\cos x - \cos y\right)\right) \cdot \left(\left(\sqrt[3]{\sin x - \frac{\sin y}{16}} \cdot \sqrt{2}\right) \cdot \left(\sqrt[3]{\sin x - \frac{\sin y}{16}} \cdot \sqrt[3]{\sin x - \frac{\sin y}{16}}\right)\right) + 2}{\left(\cos y \cdot \frac{\frac{3 \cdot 3 - 5}{3 + \sqrt{5}}}{2} + \left(\cos x \cdot \frac{\sqrt{5} - 1}{2} + 1\right)\right) \cdot 3}
double f(double x, double y) {
        double r239910 = 2.0;
        double r239911 = sqrt(r239910);
        double r239912 = x;
        double r239913 = sin(r239912);
        double r239914 = y;
        double r239915 = sin(r239914);
        double r239916 = 16.0;
        double r239917 = r239915 / r239916;
        double r239918 = r239913 - r239917;
        double r239919 = r239911 * r239918;
        double r239920 = r239913 / r239916;
        double r239921 = r239915 - r239920;
        double r239922 = r239919 * r239921;
        double r239923 = cos(r239912);
        double r239924 = cos(r239914);
        double r239925 = r239923 - r239924;
        double r239926 = r239922 * r239925;
        double r239927 = r239910 + r239926;
        double r239928 = 3.0;
        double r239929 = 1.0;
        double r239930 = 5.0;
        double r239931 = sqrt(r239930);
        double r239932 = r239931 - r239929;
        double r239933 = r239932 / r239910;
        double r239934 = r239933 * r239923;
        double r239935 = r239929 + r239934;
        double r239936 = r239928 - r239931;
        double r239937 = r239936 / r239910;
        double r239938 = r239937 * r239924;
        double r239939 = r239935 + r239938;
        double r239940 = r239928 * r239939;
        double r239941 = r239927 / r239940;
        return r239941;
}
↓
double f(double x, double y) {
        double r239942 = y;
        double r239943 = sin(r239942);
        double r239944 = x;
        double r239945 = sin(r239944);
        double r239946 = 16.0;
        double r239947 = r239945 / r239946;
        double r239948 = r239943 - r239947;
        double r239949 = cos(r239944);
        double r239950 = cos(r239942);
        double r239951 = r239949 - r239950;
        double r239952 = r239948 * r239951;
        double r239953 = r239943 / r239946;
        double r239954 = r239945 - r239953;
        double r239955 = cbrt(r239954);
        double r239956 = 2.0;
        double r239957 = sqrt(r239956);
        double r239958 = r239955 * r239957;
        double r239959 = r239955 * r239955;
        double r239960 = r239958 * r239959;
        double r239961 = r239952 * r239960;
        double r239962 = r239961 + r239956;
        double r239963 = 3.0;
        double r239964 = r239963 * r239963;
        double r239965 = 5.0;
        double r239966 = r239964 - r239965;
        double r239967 = sqrt(r239965);
        double r239968 = r239963 + r239967;
        double r239969 = r239966 / r239968;
        double r239970 = r239969 / r239956;
        double r239971 = r239950 * r239970;
        double r239972 = 1.0;
        double r239973 = r239967 - r239972;
        double r239974 = r239973 / r239956;
        double r239975 = r239949 * r239974;
        double r239976 = r239975 + r239972;
        double r239977 = r239971 + r239976;
        double r239978 = r239977 * r239963;
        double r239979 = r239962 / r239978;
        return r239979;
}

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. Simplified0.5

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

  4. Applied add-cube-cbrt0.5

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

  5. Applied associate-*l*0.5

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

  7. Applied flip--0.6

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

  8. Simplified0.5

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

  9. Final simplification0.5

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

Reproduce

herbie shell --seed 2019174 
(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))))))