Average Error: 35.8 → 27.9
Time: 8.3s
Precision: 64
\[\frac{\tan \left(\frac{x}{y \cdot 2}\right)}{\sin \left(\frac{x}{y \cdot 2}\right)}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{\tan \left(\frac{x}{y \cdot 2}\right)}{\sin \left(\frac{x}{y \cdot 2}\right)} \le 2.388236677338849:\\ \;\;\;\;\sqrt[3]{{\left(\frac{\frac{\sin \left(\frac{x}{y \cdot 2}\right)}{\log \left(e^{\cos \left(\frac{x}{y \cdot 2}\right)}\right)}}{\sin \left(\frac{x}{y \cdot 2}\right)}\right)}^{3}}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array}\]
\frac{\tan \left(\frac{x}{y \cdot 2}\right)}{\sin \left(\frac{x}{y \cdot 2}\right)}
↓
\begin{array}{l}
\mathbf{if}\;\frac{\tan \left(\frac{x}{y \cdot 2}\right)}{\sin \left(\frac{x}{y \cdot 2}\right)} \le 2.388236677338849:\\
\;\;\;\;\sqrt[3]{{\left(\frac{\frac{\sin \left(\frac{x}{y \cdot 2}\right)}{\log \left(e^{\cos \left(\frac{x}{y \cdot 2}\right)}\right)}}{\sin \left(\frac{x}{y \cdot 2}\right)}\right)}^{3}}\\

\mathbf{else}:\\
\;\;\;\;1\\

\end{array}
double f(double x, double y) {
        double r987644 = x;
        double r987645 = y;
        double r987646 = 2.0;
        double r987647 = r987645 * r987646;
        double r987648 = r987644 / r987647;
        double r987649 = tan(r987648);
        double r987650 = sin(r987648);
        double r987651 = r987649 / r987650;
        return r987651;
}
↓
double f(double x, double y) {
        double r987652 = x;
        double r987653 = y;
        double r987654 = 2.0;
        double r987655 = r987653 * r987654;
        double r987656 = r987652 / r987655;
        double r987657 = tan(r987656);
        double r987658 = sin(r987656);
        double r987659 = r987657 / r987658;
        double r987660 = 2.388236677338849;
        bool r987661 = r987659 <= r987660;
        double r987662 = cos(r987656);
        double r987663 = exp(r987662);
        double r987664 = log(r987663);
        double r987665 = r987658 / r987664;
        double r987666 = r987665 / r987658;
        double r987667 = 3.0;
        double r987668 = pow(r987666, r987667);
        double r987669 = cbrt(r987668);
        double r987670 = 1.0;
        double r987671 = r987661 ? r987669 : r987670;
        return r987671;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original35.8
Target29.0
Herbie27.9
\[\begin{array}{l} \mathbf{if}\;y \lt -1.23036909113069936 \cdot 10^{114}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \lt -9.1028524068119138 \cdot 10^{-222}:\\ \;\;\;\;\frac{\sin \left(\frac{x}{y \cdot 2}\right)}{\sin \left(\frac{x}{y \cdot 2}\right) \cdot \log \left(e^{\cos \left(\frac{x}{y \cdot 2}\right)}\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0)))) < 2.388236677338849

    1. Initial program 24.9

      \[\frac{\tan \left(\frac{x}{y \cdot 2}\right)}{\sin \left(\frac{x}{y \cdot 2}\right)}\]
    2. Using strategy rm

    3. Applied add-cbrt-cube45.6

      \[\leadsto \frac{\tan \left(\frac{x}{y \cdot 2}\right)}{\color{blue}{\sqrt[3]{\left(\sin \left(\frac{x}{y \cdot 2}\right) \cdot \sin \left(\frac{x}{y \cdot 2}\right)\right) \cdot \sin \left(\frac{x}{y \cdot 2}\right)}}}\]

    4. Applied add-cbrt-cube45.2

      \[\leadsto \frac{\color{blue}{\sqrt[3]{\left(\tan \left(\frac{x}{y \cdot 2}\right) \cdot \tan \left(\frac{x}{y \cdot 2}\right)\right) \cdot \tan \left(\frac{x}{y \cdot 2}\right)}}}{\sqrt[3]{\left(\sin \left(\frac{x}{y \cdot 2}\right) \cdot \sin \left(\frac{x}{y \cdot 2}\right)\right) \cdot \sin \left(\frac{x}{y \cdot 2}\right)}}\]

    5. Applied cbrt-undiv45.2

      \[\leadsto \color{blue}{\sqrt[3]{\frac{\left(\tan \left(\frac{x}{y \cdot 2}\right) \cdot \tan \left(\frac{x}{y \cdot 2}\right)\right) \cdot \tan \left(\frac{x}{y \cdot 2}\right)}{\left(\sin \left(\frac{x}{y \cdot 2}\right) \cdot \sin \left(\frac{x}{y \cdot 2}\right)\right) \cdot \sin \left(\frac{x}{y \cdot 2}\right)}}}\]

    6. Simplified24.9

      \[\leadsto \sqrt[3]{\color{blue}{{\left(\frac{\tan \left(\frac{x}{y \cdot 2}\right)}{\sin \left(\frac{x}{y \cdot 2}\right)}\right)}^{3}}}\]
    7. Using strategy rm

    8. Applied tan-quot24.9

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

    10. Applied add-log-exp24.9

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

    if 2.388236677338849 < (/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))

    1. Initial program 62.4

      \[\frac{\tan \left(\frac{x}{y \cdot 2}\right)}{\sin \left(\frac{x}{y \cdot 2}\right)}\]

    2. Taylor expanded around 0 35.0

      \[\leadsto \color{blue}{1}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification27.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\tan \left(\frac{x}{y \cdot 2}\right)}{\sin \left(\frac{x}{y \cdot 2}\right)} \le 2.388236677338849:\\ \;\;\;\;\sqrt[3]{{\left(\frac{\frac{\sin \left(\frac{x}{y \cdot 2}\right)}{\log \left(e^{\cos \left(\frac{x}{y \cdot 2}\right)}\right)}}{\sin \left(\frac{x}{y \cdot 2}\right)}\right)}^{3}}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array}\]

Reproduce

herbie shell --seed 2020047 
(FPCore (x y)
  :name "Diagrams.TwoD.Layout.CirclePacking:approxRadius from diagrams-contrib-1.3.0.5"
  :precision binary64

  :herbie-target
  (if (< y -1.2303690911306994e+114) 1 (if (< y -9.102852406811914e-222) (/ (sin (/ x (* y 2))) (* (sin (/ x (* y 2))) (log (exp (cos (/ x (* y 2))))))) 1))

  (/ (tan (/ x (* y 2))) (sin (/ x (* y 2)))))