Average Error: 0.5 → 0.5
Time: 50.2s
Precision: 64
\[\frac{2 + \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x - \cos y\right)}{3 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{3 - \sqrt{5}}{2} \cdot \cos y\right)}\]
↓
\[\frac{2 \cdot 2 - \left(\left(\left(\sqrt{\sqrt{2}} \cdot \left(\sqrt{\sqrt{2}} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x - \cos y\right)\right) \cdot \left(\left(\left(\sqrt{\sqrt{2}} \cdot \left(\sqrt{\sqrt{2}} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x - \cos y\right)\right)}{\left(3 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{3 - \sqrt{5}}{2} \cdot \cos y\right)\right) \cdot \left(2 - \left(\left(\sqrt{\sqrt{2}} \cdot \left(\sqrt{\sqrt{2}} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x - \cos y\right)\right)}\]
\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{2 \cdot 2 - \left(\left(\left(\sqrt{\sqrt{2}} \cdot \left(\sqrt{\sqrt{2}} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x - \cos y\right)\right) \cdot \left(\left(\left(\sqrt{\sqrt{2}} \cdot \left(\sqrt{\sqrt{2}} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x - \cos y\right)\right)}{\left(3 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{3 - \sqrt{5}}{2} \cdot \cos y\right)\right) \cdot \left(2 - \left(\left(\sqrt{\sqrt{2}} \cdot \left(\sqrt{\sqrt{2}} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x - \cos y\right)\right)}
double f(double x, double y) {
        double r27775660 = 2.0;
        double r27775661 = sqrt(r27775660);
        double r27775662 = x;
        double r27775663 = sin(r27775662);
        double r27775664 = y;
        double r27775665 = sin(r27775664);
        double r27775666 = 16.0;
        double r27775667 = r27775665 / r27775666;
        double r27775668 = r27775663 - r27775667;
        double r27775669 = r27775661 * r27775668;
        double r27775670 = r27775663 / r27775666;
        double r27775671 = r27775665 - r27775670;
        double r27775672 = r27775669 * r27775671;
        double r27775673 = cos(r27775662);
        double r27775674 = cos(r27775664);
        double r27775675 = r27775673 - r27775674;
        double r27775676 = r27775672 * r27775675;
        double r27775677 = r27775660 + r27775676;
        double r27775678 = 3.0;
        double r27775679 = 1.0;
        double r27775680 = 5.0;
        double r27775681 = sqrt(r27775680);
        double r27775682 = r27775681 - r27775679;
        double r27775683 = r27775682 / r27775660;
        double r27775684 = r27775683 * r27775673;
        double r27775685 = r27775679 + r27775684;
        double r27775686 = r27775678 - r27775681;
        double r27775687 = r27775686 / r27775660;
        double r27775688 = r27775687 * r27775674;
        double r27775689 = r27775685 + r27775688;
        double r27775690 = r27775678 * r27775689;
        double r27775691 = r27775677 / r27775690;
        return r27775691;
}
↓
double f(double x, double y) {
        double r27775692 = 2.0;
        double r27775693 = r27775692 * r27775692;
        double r27775694 = sqrt(r27775692);
        double r27775695 = sqrt(r27775694);
        double r27775696 = x;
        double r27775697 = sin(r27775696);
        double r27775698 = y;
        double r27775699 = sin(r27775698);
        double r27775700 = 16.0;
        double r27775701 = r27775699 / r27775700;
        double r27775702 = r27775697 - r27775701;
        double r27775703 = r27775695 * r27775702;
        double r27775704 = r27775695 * r27775703;
        double r27775705 = r27775697 / r27775700;
        double r27775706 = r27775699 - r27775705;
        double r27775707 = r27775704 * r27775706;
        double r27775708 = cos(r27775696);
        double r27775709 = cos(r27775698);
        double r27775710 = r27775708 - r27775709;
        double r27775711 = r27775707 * r27775710;
        double r27775712 = r27775711 * r27775711;
        double r27775713 = r27775693 - r27775712;
        double r27775714 = 3.0;
        double r27775715 = 1.0;
        double r27775716 = 5.0;
        double r27775717 = sqrt(r27775716);
        double r27775718 = r27775717 - r27775715;
        double r27775719 = r27775718 / r27775692;
        double r27775720 = r27775719 * r27775708;
        double r27775721 = r27775715 + r27775720;
        double r27775722 = r27775714 - r27775717;
        double r27775723 = r27775722 / r27775692;
        double r27775724 = r27775723 * r27775709;
        double r27775725 = r27775721 + r27775724;
        double r27775726 = r27775714 * r27775725;
        double r27775727 = r27775692 - r27775711;
        double r27775728 = r27775726 * r27775727;
        double r27775729 = r27775713 / r27775728;
        return r27775729;
}

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-sqr-sqrt0.5

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

  4. Applied sqrt-prod0.5

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

  5. Applied associate-*l*0.5

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

  7. Applied flip-+0.5

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

  8. Applied associate-/l/0.5

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

  9. Final simplification0.5

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

Reproduce

herbie shell --seed 2019173 
(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))))))