Average Error: 0.5 → 0.5
Time: 35.3s
Precision: 64
\[\frac{2 + \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x - \cos y\right)}{3 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{3 - \sqrt{5}}{2} \cdot \cos y\right)}\]
↓
\[\left(2 + \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x - \cos y\right)\right) \cdot \frac{1}{3 \cdot \left(\left(1 + \sqrt{\frac{\sqrt{5} - 1}{2}} \cdot \left(\sqrt{\frac{\sqrt{5} - 1}{2}} \cdot \cos x\right)\right) + \frac{\frac{3 \cdot 3 - 5}{3 + \sqrt{5}}}{2} \cdot \cos y\right)}\]
\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)}
↓
\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) \cdot \frac{1}{3 \cdot \left(\left(1 + \sqrt{\frac{\sqrt{5} - 1}{2}} \cdot \left(\sqrt{\frac{\sqrt{5} - 1}{2}} \cdot \cos x\right)\right) + \frac{\frac{3 \cdot 3 - 5}{3 + \sqrt{5}}}{2} \cdot \cos y\right)}
double f(double x, double y) {
        double r213573 = 2.0;
        double r213574 = sqrt(r213573);
        double r213575 = x;
        double r213576 = sin(r213575);
        double r213577 = y;
        double r213578 = sin(r213577);
        double r213579 = 16.0;
        double r213580 = r213578 / r213579;
        double r213581 = r213576 - r213580;
        double r213582 = r213574 * r213581;
        double r213583 = r213576 / r213579;
        double r213584 = r213578 - r213583;
        double r213585 = r213582 * r213584;
        double r213586 = cos(r213575);
        double r213587 = cos(r213577);
        double r213588 = r213586 - r213587;
        double r213589 = r213585 * r213588;
        double r213590 = r213573 + r213589;
        double r213591 = 3.0;
        double r213592 = 1.0;
        double r213593 = 5.0;
        double r213594 = sqrt(r213593);
        double r213595 = r213594 - r213592;
        double r213596 = r213595 / r213573;
        double r213597 = r213596 * r213586;
        double r213598 = r213592 + r213597;
        double r213599 = r213591 - r213594;
        double r213600 = r213599 / r213573;
        double r213601 = r213600 * r213587;
        double r213602 = r213598 + r213601;
        double r213603 = r213591 * r213602;
        double r213604 = r213590 / r213603;
        return r213604;
}
↓
double f(double x, double y) {
        double r213605 = 2.0;
        double r213606 = sqrt(r213605);
        double r213607 = x;
        double r213608 = sin(r213607);
        double r213609 = y;
        double r213610 = sin(r213609);
        double r213611 = 16.0;
        double r213612 = r213610 / r213611;
        double r213613 = r213608 - r213612;
        double r213614 = r213606 * r213613;
        double r213615 = r213608 / r213611;
        double r213616 = r213610 - r213615;
        double r213617 = r213614 * r213616;
        double r213618 = cos(r213607);
        double r213619 = cos(r213609);
        double r213620 = r213618 - r213619;
        double r213621 = r213617 * r213620;
        double r213622 = r213605 + r213621;
        double r213623 = 1.0;
        double r213624 = 3.0;
        double r213625 = 1.0;
        double r213626 = 5.0;
        double r213627 = sqrt(r213626);
        double r213628 = r213627 - r213625;
        double r213629 = r213628 / r213605;
        double r213630 = sqrt(r213629);
        double r213631 = r213630 * r213618;
        double r213632 = r213630 * r213631;
        double r213633 = r213625 + r213632;
        double r213634 = r213624 * r213624;
        double r213635 = r213634 - r213626;
        double r213636 = r213624 + r213627;
        double r213637 = r213635 / r213636;
        double r213638 = r213637 / r213605;
        double r213639 = r213638 * r213619;
        double r213640 = r213633 + r213639;
        double r213641 = r213624 * r213640;
        double r213642 = r213623 / r213641;
        double r213643 = r213622 * r213642;
        return r213643;
}

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 div-inv0.5

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

  8. Applied add-sqr-sqrt0.5

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

  9. Applied associate-*l*0.5

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

  10. Final simplification0.5

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

Reproduce

herbie shell --seed 2019326 
(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))))))