Average Error: 0.5 → 0.5
Time: 11.4s
Precision: 64
\[\frac{2 + \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x - \cos y\right)}{3 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{3 - \sqrt{5}}{2} \cdot \cos y\right)}\]
↓
\[\frac{2 + \left(\left(\sqrt[3]{\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)} \cdot \sqrt[3]{\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)}\right) \cdot \sqrt[3]{\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)}\right) \cdot \left(\cos x - \cos y\right)}{3 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{3 - \sqrt{5}}{2} \cdot \cos y\right)}\]
\frac{2 + \left(\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(\left(\sqrt[3]{\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)} \cdot \sqrt[3]{\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(\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)}
double f(double x, double y) {
        double r261762 = 2.0;
        double r261763 = sqrt(r261762);
        double r261764 = x;
        double r261765 = sin(r261764);
        double r261766 = y;
        double r261767 = sin(r261766);
        double r261768 = 16.0;
        double r261769 = r261767 / r261768;
        double r261770 = r261765 - r261769;
        double r261771 = r261763 * r261770;
        double r261772 = r261765 / r261768;
        double r261773 = r261767 - r261772;
        double r261774 = r261771 * r261773;
        double r261775 = cos(r261764);
        double r261776 = cos(r261766);
        double r261777 = r261775 - r261776;
        double r261778 = r261774 * r261777;
        double r261779 = r261762 + r261778;
        double r261780 = 3.0;
        double r261781 = 1.0;
        double r261782 = 5.0;
        double r261783 = sqrt(r261782);
        double r261784 = r261783 - r261781;
        double r261785 = r261784 / r261762;
        double r261786 = r261785 * r261775;
        double r261787 = r261781 + r261786;
        double r261788 = r261780 - r261783;
        double r261789 = r261788 / r261762;
        double r261790 = r261789 * r261776;
        double r261791 = r261787 + r261790;
        double r261792 = r261780 * r261791;
        double r261793 = r261779 / r261792;
        return r261793;
}
↓
double f(double x, double y) {
        double r261794 = 2.0;
        double r261795 = sqrt(r261794);
        double r261796 = x;
        double r261797 = sin(r261796);
        double r261798 = y;
        double r261799 = sin(r261798);
        double r261800 = 16.0;
        double r261801 = r261799 / r261800;
        double r261802 = r261797 - r261801;
        double r261803 = r261795 * r261802;
        double r261804 = r261797 / r261800;
        double r261805 = r261799 - r261804;
        double r261806 = r261803 * r261805;
        double r261807 = cbrt(r261806);
        double r261808 = r261807 * r261807;
        double r261809 = r261808 * r261807;
        double r261810 = cos(r261796);
        double r261811 = cos(r261798);
        double r261812 = r261810 - r261811;
        double r261813 = r261809 * r261812;
        double r261814 = r261794 + r261813;
        double r261815 = 3.0;
        double r261816 = 1.0;
        double r261817 = 5.0;
        double r261818 = sqrt(r261817);
        double r261819 = r261818 - r261816;
        double r261820 = r261819 / r261794;
        double r261821 = r261820 * r261810;
        double r261822 = r261816 + r261821;
        double r261823 = r261815 - r261818;
        double r261824 = r261823 / r261794;
        double r261825 = r261824 * r261811;
        double r261826 = r261822 + r261825;
        double r261827 = r261815 * r261826;
        double r261828 = r261814 / r261827;
        return r261828;
}

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-cube-cbrt0.5

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

  4. Final simplification0.5

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

Reproduce

herbie shell --seed 2020060 
(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))))))