Average Error: 35.4 → 27.4
Time: 5.1s
Precision: 64
\[\frac{\tan \left(\frac{x}{y \cdot 2}\right)}{\sin \left(\frac{x}{y \cdot 2}\right)}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{\tan \left(\frac{x}{y \cdot 2}\right)}{\sin \left(\frac{x}{y \cdot 2}\right)} \le 10.123476350845582:\\ \;\;\;\;\frac{\sqrt[3]{\tan \left(\frac{x}{y \cdot 2}\right)} \cdot \sqrt[3]{\tan \left(\frac{x}{y \cdot 2}\right)}}{\sqrt[3]{\sin \left(\frac{x}{y \cdot 2}\right)} \cdot \sqrt[3]{\sin \left(\frac{x}{y \cdot 2}\right)}} \cdot \frac{\sqrt[3]{\tan \left(\frac{x}{y \cdot 2}\right)}}{\sqrt[3]{\sin \left(\frac{x}{y \cdot 2}\right)}}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array}\]
\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 10.123476350845582:\\
\;\;\;\;\frac{\sqrt[3]{\tan \left(\frac{x}{y \cdot 2}\right)} \cdot \sqrt[3]{\tan \left(\frac{x}{y \cdot 2}\right)}}{\sqrt[3]{\sin \left(\frac{x}{y \cdot 2}\right)} \cdot \sqrt[3]{\sin \left(\frac{x}{y \cdot 2}\right)}} \cdot \frac{\sqrt[3]{\tan \left(\frac{x}{y \cdot 2}\right)}}{\sqrt[3]{\sin \left(\frac{x}{y \cdot 2}\right)}}\\

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

\end{array}
double f(double x, double y) {
        double r614986 = x;
        double r614987 = y;
        double r614988 = 2.0;
        double r614989 = r614987 * r614988;
        double r614990 = r614986 / r614989;
        double r614991 = tan(r614990);
        double r614992 = sin(r614990);
        double r614993 = r614991 / r614992;
        return r614993;
}
↓
double f(double x, double y) {
        double r614994 = x;
        double r614995 = y;
        double r614996 = 2.0;
        double r614997 = r614995 * r614996;
        double r614998 = r614994 / r614997;
        double r614999 = tan(r614998);
        double r615000 = sin(r614998);
        double r615001 = r614999 / r615000;
        double r615002 = 10.123476350845582;
        bool r615003 = r615001 <= r615002;
        double r615004 = cbrt(r614999);
        double r615005 = r615004 * r615004;
        double r615006 = cbrt(r615000);
        double r615007 = r615006 * r615006;
        double r615008 = r615005 / r615007;
        double r615009 = r615004 / r615006;
        double r615010 = r615008 * r615009;
        double r615011 = 1.0;
        double r615012 = r615003 ? r615010 : r615011;
        return r615012;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original35.4
Target28.8
Herbie27.4
\[\begin{array}{l} \mathbf{if}\;y \lt -1.23036909113069936 \cdot 10^{114}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \lt -9.1028524068119138 \cdot 10^{-222}:\\ \;\;\;\;\frac{\sin \left(\frac{x}{y \cdot 2}\right)}{\sin \left(\frac{x}{y \cdot 2}\right) \cdot \log \left(e^{\cos \left(\frac{x}{y \cdot 2}\right)}\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0)))) < 10.123476350845582

    1. Initial program 26.1

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

    3. Applied add-cube-cbrt26.8

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

    4. Applied add-cube-cbrt26.1

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

    5. Applied times-frac26.1

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

    if 10.123476350845582 < (/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))

    1. Initial program 63.5

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

    2. Taylor expanded around 0 31.4

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

  4. Final simplification27.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\tan \left(\frac{x}{y \cdot 2}\right)}{\sin \left(\frac{x}{y \cdot 2}\right)} \le 10.123476350845582:\\ \;\;\;\;\frac{\sqrt[3]{\tan \left(\frac{x}{y \cdot 2}\right)} \cdot \sqrt[3]{\tan \left(\frac{x}{y \cdot 2}\right)}}{\sqrt[3]{\sin \left(\frac{x}{y \cdot 2}\right)} \cdot \sqrt[3]{\sin \left(\frac{x}{y \cdot 2}\right)}} \cdot \frac{\sqrt[3]{\tan \left(\frac{x}{y \cdot 2}\right)}}{\sqrt[3]{\sin \left(\frac{x}{y \cdot 2}\right)}}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array}\]

Reproduce

herbie shell --seed 2020064 
(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)))))