Average Error: 0.5 → 0.5
Time: 21.9s
Precision: 64
\[\frac{2 + \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x - \cos y\right)}{3 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{3 - \sqrt{5}}{2} \cdot \cos y\right)}\]
↓
\[\frac{2 + \left(\log \left(e^{\sqrt{\sqrt{2}} \cdot \left(\sqrt{\sqrt{2}} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right)}\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x - \cos y\right)}{3 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{\frac{3 \cdot 3 - 5}{3 + \sqrt{5}}}{2} \cdot \cos y\right)}\]
\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(\log \left(e^{\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{\frac{3 \cdot 3 - 5}{3 + \sqrt{5}}}{2} \cdot \cos y\right)}
double f(double x, double y) {
        double r229613 = 2.0;
        double r229614 = sqrt(r229613);
        double r229615 = x;
        double r229616 = sin(r229615);
        double r229617 = y;
        double r229618 = sin(r229617);
        double r229619 = 16.0;
        double r229620 = r229618 / r229619;
        double r229621 = r229616 - r229620;
        double r229622 = r229614 * r229621;
        double r229623 = r229616 / r229619;
        double r229624 = r229618 - r229623;
        double r229625 = r229622 * r229624;
        double r229626 = cos(r229615);
        double r229627 = cos(r229617);
        double r229628 = r229626 - r229627;
        double r229629 = r229625 * r229628;
        double r229630 = r229613 + r229629;
        double r229631 = 3.0;
        double r229632 = 1.0;
        double r229633 = 5.0;
        double r229634 = sqrt(r229633);
        double r229635 = r229634 - r229632;
        double r229636 = r229635 / r229613;
        double r229637 = r229636 * r229626;
        double r229638 = r229632 + r229637;
        double r229639 = r229631 - r229634;
        double r229640 = r229639 / r229613;
        double r229641 = r229640 * r229627;
        double r229642 = r229638 + r229641;
        double r229643 = r229631 * r229642;
        double r229644 = r229630 / r229643;
        return r229644;
}
↓
double f(double x, double y) {
        double r229645 = 2.0;
        double r229646 = sqrt(r229645);
        double r229647 = sqrt(r229646);
        double r229648 = x;
        double r229649 = sin(r229648);
        double r229650 = y;
        double r229651 = sin(r229650);
        double r229652 = 16.0;
        double r229653 = r229651 / r229652;
        double r229654 = r229649 - r229653;
        double r229655 = r229647 * r229654;
        double r229656 = r229647 * r229655;
        double r229657 = exp(r229656);
        double r229658 = log(r229657);
        double r229659 = r229649 / r229652;
        double r229660 = r229651 - r229659;
        double r229661 = r229658 * r229660;
        double r229662 = cos(r229648);
        double r229663 = cos(r229650);
        double r229664 = r229662 - r229663;
        double r229665 = r229661 * r229664;
        double r229666 = r229645 + r229665;
        double r229667 = 3.0;
        double r229668 = 1.0;
        double r229669 = 5.0;
        double r229670 = sqrt(r229669);
        double r229671 = r229670 - r229668;
        double r229672 = r229671 / r229645;
        double r229673 = r229672 * r229662;
        double r229674 = r229668 + r229673;
        double r229675 = r229667 * r229667;
        double r229676 = r229675 - r229669;
        double r229677 = r229667 + r229670;
        double r229678 = r229676 / r229677;
        double r229679 = r229678 / r229645;
        double r229680 = r229679 * r229663;
        double r229681 = r229674 + r229680;
        double r229682 = r229667 * r229681;
        double r229683 = r229666 / r229682;
        return r229683;
}

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

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

  6. Applied add-log-exp0.5

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

  8. Applied add-sqr-sqrt0.5

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

  9. Applied sqrt-prod0.5

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

  10. Applied associate-*l*0.5

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

  11. Final simplification0.5

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

Reproduce

herbie shell --seed 2020047 
(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))))))