Average Error: 35.8 → 27.7
Time: 8.9s
Precision: 64
\[\frac{\tan \left(\frac{x}{y \cdot 2}\right)}{\sin \left(\frac{x}{y \cdot 2}\right)}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{\tan \left(\frac{x}{y \cdot 2}\right)}{\sin \left(\frac{x}{y \cdot 2}\right)} \le 5.551201649719668118621029861969873309135:\\ \;\;\;\;\log \left(\log \left(e^{{\left(e^{1}\right)}^{\left(\frac{1}{\cos \left(\frac{x}{y \cdot 2}\right)}\right)}}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array}\]
\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 5.551201649719668118621029861969873309135:\\
\;\;\;\;\log \left(\log \left(e^{{\left(e^{1}\right)}^{\left(\frac{1}{\cos \left(\frac{x}{y \cdot 2}\right)}\right)}}\right)\right)\\

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

\end{array}
double f(double x, double y) {
        double r529851 = x;
        double r529852 = y;
        double r529853 = 2.0;
        double r529854 = r529852 * r529853;
        double r529855 = r529851 / r529854;
        double r529856 = tan(r529855);
        double r529857 = sin(r529855);
        double r529858 = r529856 / r529857;
        return r529858;
}
↓
double f(double x, double y) {
        double r529859 = x;
        double r529860 = y;
        double r529861 = 2.0;
        double r529862 = r529860 * r529861;
        double r529863 = r529859 / r529862;
        double r529864 = tan(r529863);
        double r529865 = sin(r529863);
        double r529866 = r529864 / r529865;
        double r529867 = 5.551201649719668;
        bool r529868 = r529866 <= r529867;
        double r529869 = 1.0;
        double r529870 = exp(r529869);
        double r529871 = cos(r529863);
        double r529872 = r529869 / r529871;
        double r529873 = pow(r529870, r529872);
        double r529874 = exp(r529873);
        double r529875 = log(r529874);
        double r529876 = log(r529875);
        double r529877 = 1.0;
        double r529878 = r529868 ? r529876 : r529877;
        return r529878;
}

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
Target28.8
Herbie27.7
\[\begin{array}{l} \mathbf{if}\;y \lt -1.230369091130699363447511617672816900781 \cdot 10^{114}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \lt -9.102852406811913849731222630299032206502 \cdot 10^{-222}:\\ \;\;\;\;\frac{\sin \left(\frac{x}{y \cdot 2}\right)}{\sin \left(\frac{x}{y \cdot 2}\right) \cdot \log \left(e^{\cos \left(\frac{x}{y \cdot 2}\right)}\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0)))) < 5.551201649719668

    1. Initial program 25.9

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

    3. Applied tan-quot25.9

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

    4. Applied associate-/l/25.9

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

    6. Applied add-log-exp25.9

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

    7. Simplified25.9

      \[\leadsto \log \color{blue}{\left({\left(e^{1}\right)}^{\left(\frac{1}{\cos \left(\frac{x}{y \cdot 2}\right)}\right)}\right)}\]
    8. Using strategy rm

    9. Applied add-log-exp25.9

      \[\leadsto \log \color{blue}{\left(\log \left(e^{{\left(e^{1}\right)}^{\left(\frac{1}{\cos \left(\frac{x}{y \cdot 2}\right)}\right)}}\right)\right)}\]

    if 5.551201649719668 < (/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))

    1. Initial program 63.3

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

    2. Taylor expanded around 0 32.5

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

  4. Final simplification27.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\tan \left(\frac{x}{y \cdot 2}\right)}{\sin \left(\frac{x}{y \cdot 2}\right)} \le 5.551201649719668118621029861969873309135:\\ \;\;\;\;\log \left(\log \left(e^{{\left(e^{1}\right)}^{\left(\frac{1}{\cos \left(\frac{x}{y \cdot 2}\right)}\right)}}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array}\]

Reproduce

herbie shell --seed 1978988140 
(FPCore (x y)
  :name "Diagrams.TwoD.Layout.CirclePacking:approxRadius from diagrams-contrib-1.3.0.5"
  :precision binary64

  :herbie-target
  (if (< y -1.23036909113069936e114) 1 (if (< y -9.1028524068119138e-222) (/ (sin (/ x (* y 2))) (* (sin (/ x (* y 2))) (log (exp (cos (/ x (* y 2))))))) 1))

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