Average Error: 0.5 → 0.5
Time: 41.3s
Precision: 64
\[\frac{2 + \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x - \cos y\right)}{3 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{3 - \sqrt{5}}{2} \cdot \cos y\right)}\]
↓
\[\frac{2 + \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x - \cos y\right)}{\left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{\frac{3 \cdot 3 + \left(-5\right)}{3 + \sqrt{5}}}{2} \cdot \cos y\right) \cdot 3}\]
\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{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)}{\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) \cdot 3}
double f(double x, double y) {
        double r188684 = 2.0;
        double r188685 = sqrt(r188684);
        double r188686 = x;
        double r188687 = sin(r188686);
        double r188688 = y;
        double r188689 = sin(r188688);
        double r188690 = 16.0;
        double r188691 = r188689 / r188690;
        double r188692 = r188687 - r188691;
        double r188693 = r188685 * r188692;
        double r188694 = r188687 / r188690;
        double r188695 = r188689 - r188694;
        double r188696 = r188693 * r188695;
        double r188697 = cos(r188686);
        double r188698 = cos(r188688);
        double r188699 = r188697 - r188698;
        double r188700 = r188696 * r188699;
        double r188701 = r188684 + r188700;
        double r188702 = 3.0;
        double r188703 = 1.0;
        double r188704 = 5.0;
        double r188705 = sqrt(r188704);
        double r188706 = r188705 - r188703;
        double r188707 = r188706 / r188684;
        double r188708 = r188707 * r188697;
        double r188709 = r188703 + r188708;
        double r188710 = r188702 - r188705;
        double r188711 = r188710 / r188684;
        double r188712 = r188711 * r188698;
        double r188713 = r188709 + r188712;
        double r188714 = r188702 * r188713;
        double r188715 = r188701 / r188714;
        return r188715;
}
↓
double f(double x, double y) {
        double r188716 = 2.0;
        double r188717 = sqrt(r188716);
        double r188718 = x;
        double r188719 = sin(r188718);
        double r188720 = y;
        double r188721 = sin(r188720);
        double r188722 = 16.0;
        double r188723 = r188721 / r188722;
        double r188724 = r188719 - r188723;
        double r188725 = r188717 * r188724;
        double r188726 = r188719 / r188722;
        double r188727 = r188721 - r188726;
        double r188728 = r188725 * r188727;
        double r188729 = cos(r188718);
        double r188730 = cos(r188720);
        double r188731 = r188729 - r188730;
        double r188732 = r188728 * r188731;
        double r188733 = r188716 + r188732;
        double r188734 = 1.0;
        double r188735 = 5.0;
        double r188736 = sqrt(r188735);
        double r188737 = r188736 - r188734;
        double r188738 = r188737 / r188716;
        double r188739 = r188738 * r188729;
        double r188740 = r188734 + r188739;
        double r188741 = 3.0;
        double r188742 = r188741 * r188741;
        double r188743 = -r188735;
        double r188744 = r188742 + r188743;
        double r188745 = r188741 + r188736;
        double r188746 = r188744 / r188745;
        double r188747 = r188746 / r188716;
        double r188748 = r188747 * r188730;
        double r188749 = r188740 + r188748;
        double r188750 = r188749 * r188741;
        double r188751 = r188733 / r188750;
        return r188751;
}

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 *-un-lft-identity0.5

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

  7. Applied times-frac0.5

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

  8. Final simplification0.5

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

Reproduce

herbie shell --seed 2019294 
(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))))))