Average Error: 35.2 → 27.5
Time: 13.8s
Precision: 64
\[\frac{\tan \left(\frac{x}{y \cdot 2.0}\right)}{\sin \left(\frac{x}{y \cdot 2.0}\right)}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{\tan \left(\frac{x}{2.0 \cdot y}\right)}{\sin \left(\frac{x}{2.0 \cdot y}\right)} \le 16.799894871361925:\\ \;\;\;\;\sqrt[3]{\frac{\tan \left(\frac{x}{2.0 \cdot y}\right)}{\sin \left(\frac{x}{2.0 \cdot y}\right)}} \cdot \left(\sqrt[3]{\frac{\tan \left(\frac{x}{2.0 \cdot y}\right)}{\sin \left(\frac{x}{2.0 \cdot y}\right)}} \cdot \sqrt[3]{\frac{\tan \left(\frac{x}{2.0 \cdot y}\right)}{\sin \left(\frac{x}{2.0 \cdot y}\right)}}\right)\\ \mathbf{else}:\\ \;\;\;\;1.0\\ \end{array}\]
\frac{\tan \left(\frac{x}{y \cdot 2.0}\right)}{\sin \left(\frac{x}{y \cdot 2.0}\right)}
↓
\begin{array}{l}
\mathbf{if}\;\frac{\tan \left(\frac{x}{2.0 \cdot y}\right)}{\sin \left(\frac{x}{2.0 \cdot y}\right)} \le 16.799894871361925:\\
\;\;\;\;\sqrt[3]{\frac{\tan \left(\frac{x}{2.0 \cdot y}\right)}{\sin \left(\frac{x}{2.0 \cdot y}\right)}} \cdot \left(\sqrt[3]{\frac{\tan \left(\frac{x}{2.0 \cdot y}\right)}{\sin \left(\frac{x}{2.0 \cdot y}\right)}} \cdot \sqrt[3]{\frac{\tan \left(\frac{x}{2.0 \cdot y}\right)}{\sin \left(\frac{x}{2.0 \cdot y}\right)}}\right)\\

\mathbf{else}:\\
\;\;\;\;1.0\\

\end{array}
double f(double x, double y) {
        double r13235391 = x;
        double r13235392 = y;
        double r13235393 = 2.0;
        double r13235394 = r13235392 * r13235393;
        double r13235395 = r13235391 / r13235394;
        double r13235396 = tan(r13235395);
        double r13235397 = sin(r13235395);
        double r13235398 = r13235396 / r13235397;
        return r13235398;
}
↓
double f(double x, double y) {
        double r13235399 = x;
        double r13235400 = 2.0;
        double r13235401 = y;
        double r13235402 = r13235400 * r13235401;
        double r13235403 = r13235399 / r13235402;
        double r13235404 = tan(r13235403);
        double r13235405 = sin(r13235403);
        double r13235406 = r13235404 / r13235405;
        double r13235407 = 16.799894871361925;
        bool r13235408 = r13235406 <= r13235407;
        double r13235409 = cbrt(r13235406);
        double r13235410 = r13235409 * r13235409;
        double r13235411 = r13235409 * r13235410;
        double r13235412 = 1.0;
        double r13235413 = r13235408 ? r13235411 : r13235412;
        return r13235413;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original35.2
Target28.9
Herbie27.5
\[\begin{array}{l} \mathbf{if}\;y \lt -1.2303690911306994 \cdot 10^{+114}:\\ \;\;\;\;1.0\\ \mathbf{elif}\;y \lt -9.102852406811914 \cdot 10^{-222}:\\ \;\;\;\;\frac{\sin \left(\frac{x}{y \cdot 2.0}\right)}{\sin \left(\frac{x}{y \cdot 2.0}\right) \cdot \log \left(e^{\cos \left(\frac{x}{y \cdot 2.0}\right)}\right)}\\ \mathbf{else}:\\ \;\;\;\;1.0\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0)))) < 16.799894871361925

    1. Initial program 26.4

      \[\frac{\tan \left(\frac{x}{y \cdot 2.0}\right)}{\sin \left(\frac{x}{y \cdot 2.0}\right)}\]
    2. Using strategy rm

    3. Applied add-cube-cbrt26.4

      \[\leadsto \color{blue}{\left(\sqrt[3]{\frac{\tan \left(\frac{x}{y \cdot 2.0}\right)}{\sin \left(\frac{x}{y \cdot 2.0}\right)}} \cdot \sqrt[3]{\frac{\tan \left(\frac{x}{y \cdot 2.0}\right)}{\sin \left(\frac{x}{y \cdot 2.0}\right)}}\right) \cdot \sqrt[3]{\frac{\tan \left(\frac{x}{y \cdot 2.0}\right)}{\sin \left(\frac{x}{y \cdot 2.0}\right)}}}\]

    if 16.799894871361925 < (/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))

    1. Initial program 62.2

      \[\frac{\tan \left(\frac{x}{y \cdot 2.0}\right)}{\sin \left(\frac{x}{y \cdot 2.0}\right)}\]

    2. Taylor expanded around 0 30.8

      \[\leadsto \color{blue}{1.0}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification27.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\tan \left(\frac{x}{2.0 \cdot y}\right)}{\sin \left(\frac{x}{2.0 \cdot y}\right)} \le 16.799894871361925:\\ \;\;\;\;\sqrt[3]{\frac{\tan \left(\frac{x}{2.0 \cdot y}\right)}{\sin \left(\frac{x}{2.0 \cdot y}\right)}} \cdot \left(\sqrt[3]{\frac{\tan \left(\frac{x}{2.0 \cdot y}\right)}{\sin \left(\frac{x}{2.0 \cdot y}\right)}} \cdot \sqrt[3]{\frac{\tan \left(\frac{x}{2.0 \cdot y}\right)}{\sin \left(\frac{x}{2.0 \cdot y}\right)}}\right)\\ \mathbf{else}:\\ \;\;\;\;1.0\\ \end{array}\]

Reproduce

herbie shell --seed 2019156 
(FPCore (x y)
  :name "Diagrams.TwoD.Layout.CirclePacking:approxRadius from diagrams-contrib-1.3.0.5"

  :herbie-target
  (if (< y -1.2303690911306994e+114) 1.0 (if (< y -9.102852406811914e-222) (/ (sin (/ x (* y 2.0))) (* (sin (/ x (* y 2.0))) (log (exp (cos (/ x (* y 2.0))))))) 1.0))

  (/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0)))))