Average Error: 0.5 → 0.5
Time: 10.6s
Precision: 64
\[\frac{2 + \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x - \cos y\right)}{3 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{3 - \sqrt{5}}{2} \cdot \cos y\right)}\]
↓
\[\frac{2 + \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \sqrt[3]{{\left(\sqrt[3]{{\left(\cos x - \cos y\right)}^{3}}\right)}^{3}}}{3 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{\frac{3 \cdot 3 + \left(-5\right)}{3 + \sqrt{5}}}{2} \cdot \cos y\right)}\]
\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 \sqrt[3]{{\left(\sqrt[3]{{\left(\cos x - \cos y\right)}^{3}}\right)}^{3}}}{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)}
double f(double x, double y) {
        double r208578 = 2.0;
        double r208579 = sqrt(r208578);
        double r208580 = x;
        double r208581 = sin(r208580);
        double r208582 = y;
        double r208583 = sin(r208582);
        double r208584 = 16.0;
        double r208585 = r208583 / r208584;
        double r208586 = r208581 - r208585;
        double r208587 = r208579 * r208586;
        double r208588 = r208581 / r208584;
        double r208589 = r208583 - r208588;
        double r208590 = r208587 * r208589;
        double r208591 = cos(r208580);
        double r208592 = cos(r208582);
        double r208593 = r208591 - r208592;
        double r208594 = r208590 * r208593;
        double r208595 = r208578 + r208594;
        double r208596 = 3.0;
        double r208597 = 1.0;
        double r208598 = 5.0;
        double r208599 = sqrt(r208598);
        double r208600 = r208599 - r208597;
        double r208601 = r208600 / r208578;
        double r208602 = r208601 * r208591;
        double r208603 = r208597 + r208602;
        double r208604 = r208596 - r208599;
        double r208605 = r208604 / r208578;
        double r208606 = r208605 * r208592;
        double r208607 = r208603 + r208606;
        double r208608 = r208596 * r208607;
        double r208609 = r208595 / r208608;
        return r208609;
}
↓
double f(double x, double y) {
        double r208610 = 2.0;
        double r208611 = sqrt(r208610);
        double r208612 = x;
        double r208613 = sin(r208612);
        double r208614 = y;
        double r208615 = sin(r208614);
        double r208616 = 16.0;
        double r208617 = r208615 / r208616;
        double r208618 = r208613 - r208617;
        double r208619 = r208611 * r208618;
        double r208620 = r208613 / r208616;
        double r208621 = r208615 - r208620;
        double r208622 = r208619 * r208621;
        double r208623 = cos(r208612);
        double r208624 = cos(r208614);
        double r208625 = r208623 - r208624;
        double r208626 = 3.0;
        double r208627 = pow(r208625, r208626);
        double r208628 = cbrt(r208627);
        double r208629 = pow(r208628, r208626);
        double r208630 = cbrt(r208629);
        double r208631 = r208622 * r208630;
        double r208632 = r208610 + r208631;
        double r208633 = 3.0;
        double r208634 = 1.0;
        double r208635 = 5.0;
        double r208636 = sqrt(r208635);
        double r208637 = r208636 - r208634;
        double r208638 = r208637 / r208610;
        double r208639 = r208638 * r208623;
        double r208640 = r208634 + r208639;
        double r208641 = r208633 * r208633;
        double r208642 = -r208635;
        double r208643 = r208641 + r208642;
        double r208644 = r208633 + r208636;
        double r208645 = r208643 / r208644;
        double r208646 = r208645 / r208610;
        double r208647 = r208646 * r208624;
        double r208648 = r208640 + r208647;
        double r208649 = r208633 * r208648;
        double r208650 = r208632 / r208649;
        return r208650;
}

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-cbrt-cube0.5

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

  4. Simplified0.5

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

  6. Applied add-log-exp0.5

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

  7. Applied add-log-exp0.5

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

  8. Applied diff-log0.5

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

  9. Simplified0.5

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

  11. Applied flip--0.5

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

  12. Simplified0.4

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

  14. Applied add-cbrt-cube0.5

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

  15. Simplified0.5

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

  16. Final simplification0.5

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

Reproduce

herbie shell --seed 2019356 
(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))))))