Average Error: 0.5 → 0.5
Time: 36.1s
Precision: 64
\[\frac{2 + \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x - \cos y\right)}{3 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{3 - \sqrt{5}}{2} \cdot \cos y\right)}\]
↓
\[\frac{\log \left(e^{\sqrt[3]{{\left(\left(\sin x - \frac{\sin y}{16}\right) \cdot \sqrt{2}\right)}^{3}} \cdot \left(\sin y - \frac{\sin x}{16}\right)}\right) \cdot \sqrt[3]{{\left(\cos x - \cos y\right)}^{3}} + 2}{3 \cdot \left(\frac{\frac{{3}^{3} - 5 \cdot \sqrt{5}}{5 + \left(3 + \sqrt{5}\right) \cdot 3}}{2} \cdot \cos y + \left(\frac{\sqrt{5} - 1}{2} \cdot \cos x + 1\right)\right)}\]
\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{\log \left(e^{\sqrt[3]{{\left(\left(\sin x - \frac{\sin y}{16}\right) \cdot \sqrt{2}\right)}^{3}} \cdot \left(\sin y - \frac{\sin x}{16}\right)}\right) \cdot \sqrt[3]{{\left(\cos x - \cos y\right)}^{3}} + 2}{3 \cdot \left(\frac{\frac{{3}^{3} - 5 \cdot \sqrt{5}}{5 + \left(3 + \sqrt{5}\right) \cdot 3}}{2} \cdot \cos y + \left(\frac{\sqrt{5} - 1}{2} \cdot \cos x + 1\right)\right)}
double f(double x, double y) {
        double r182727 = 2.0;
        double r182728 = sqrt(r182727);
        double r182729 = x;
        double r182730 = sin(r182729);
        double r182731 = y;
        double r182732 = sin(r182731);
        double r182733 = 16.0;
        double r182734 = r182732 / r182733;
        double r182735 = r182730 - r182734;
        double r182736 = r182728 * r182735;
        double r182737 = r182730 / r182733;
        double r182738 = r182732 - r182737;
        double r182739 = r182736 * r182738;
        double r182740 = cos(r182729);
        double r182741 = cos(r182731);
        double r182742 = r182740 - r182741;
        double r182743 = r182739 * r182742;
        double r182744 = r182727 + r182743;
        double r182745 = 3.0;
        double r182746 = 1.0;
        double r182747 = 5.0;
        double r182748 = sqrt(r182747);
        double r182749 = r182748 - r182746;
        double r182750 = r182749 / r182727;
        double r182751 = r182750 * r182740;
        double r182752 = r182746 + r182751;
        double r182753 = r182745 - r182748;
        double r182754 = r182753 / r182727;
        double r182755 = r182754 * r182741;
        double r182756 = r182752 + r182755;
        double r182757 = r182745 * r182756;
        double r182758 = r182744 / r182757;
        return r182758;
}
↓
double f(double x, double y) {
        double r182759 = x;
        double r182760 = sin(r182759);
        double r182761 = y;
        double r182762 = sin(r182761);
        double r182763 = 16.0;
        double r182764 = r182762 / r182763;
        double r182765 = r182760 - r182764;
        double r182766 = 2.0;
        double r182767 = sqrt(r182766);
        double r182768 = r182765 * r182767;
        double r182769 = 3.0;
        double r182770 = pow(r182768, r182769);
        double r182771 = cbrt(r182770);
        double r182772 = r182760 / r182763;
        double r182773 = r182762 - r182772;
        double r182774 = r182771 * r182773;
        double r182775 = exp(r182774);
        double r182776 = log(r182775);
        double r182777 = cos(r182759);
        double r182778 = cos(r182761);
        double r182779 = r182777 - r182778;
        double r182780 = pow(r182779, r182769);
        double r182781 = cbrt(r182780);
        double r182782 = r182776 * r182781;
        double r182783 = r182782 + r182766;
        double r182784 = 3.0;
        double r182785 = pow(r182784, r182769);
        double r182786 = 5.0;
        double r182787 = sqrt(r182786);
        double r182788 = r182786 * r182787;
        double r182789 = r182785 - r182788;
        double r182790 = r182784 + r182787;
        double r182791 = r182790 * r182784;
        double r182792 = r182786 + r182791;
        double r182793 = r182789 / r182792;
        double r182794 = r182793 / r182766;
        double r182795 = r182794 * r182778;
        double r182796 = 1.0;
        double r182797 = r182787 - r182796;
        double r182798 = r182797 / r182766;
        double r182799 = r182798 * r182777;
        double r182800 = r182799 + r182796;
        double r182801 = r182795 + r182800;
        double r182802 = r182784 * r182801;
        double r182803 = r182783 / r182802;
        return r182803;
}

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-log-exp0.5

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

  5. Applied flip3--0.5

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

  6. Simplified0.4

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

  7. Simplified0.4

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

  9. Applied add-cbrt-cube0.5

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

  10. Simplified0.5

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

  12. Applied add-cbrt-cube0.5

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

  13. Applied add-cbrt-cube0.5

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

  14. Applied cbrt-unprod0.5

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

  15. Simplified0.5

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

  16. Final simplification0.5

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

Reproduce

herbie shell --seed 2019196 
(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))))))