Average Error: 35.8 → 27.9
Time: 5.8s
Precision: 64
\[\frac{\tan \left(\frac{x}{y \cdot 2}\right)}{\sin \left(\frac{x}{y \cdot 2}\right)}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{\tan \left(\frac{x}{y \cdot 2}\right)}{\sin \left(\frac{x}{y \cdot 2}\right)} \le 2.388236677338849:\\ \;\;\;\;\sqrt[3]{{\left(\frac{\sin \left(\frac{x}{y \cdot 2}\right)}{\sin \left(\frac{x}{y \cdot 2}\right) \cdot \log \left(e^{\cos \left(\frac{x}{y \cdot 2}\right)}\right)}\right)}^{3}}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array}\]
\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{\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)}\right)}^{3}}\\

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

\end{array}
double f(double x, double y) {
        double r705370 = x;
        double r705371 = y;
        double r705372 = 2.0;
        double r705373 = r705371 * r705372;
        double r705374 = r705370 / r705373;
        double r705375 = tan(r705374);
        double r705376 = sin(r705374);
        double r705377 = r705375 / r705376;
        return r705377;
}
↓
double f(double x, double y) {
        double r705378 = x;
        double r705379 = y;
        double r705380 = 2.0;
        double r705381 = r705379 * r705380;
        double r705382 = r705378 / r705381;
        double r705383 = tan(r705382);
        double r705384 = sin(r705382);
        double r705385 = r705383 / r705384;
        double r705386 = 2.388236677338849;
        bool r705387 = r705385 <= r705386;
        double r705388 = cos(r705382);
        double r705389 = exp(r705388);
        double r705390 = log(r705389);
        double r705391 = r705384 * r705390;
        double r705392 = r705384 / r705391;
        double r705393 = 3.0;
        double r705394 = pow(r705392, r705393);
        double r705395 = cbrt(r705394);
        double r705396 = 1.0;
        double r705397 = r705387 ? r705395 : r705396;
        return r705397;
}

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. Applied associate-/l/24.9

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

    11. Applied add-log-exp24.9

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

    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

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

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)))))