Average Error: 35.9 → 27.8
Time: 5.3s
Precision: 64
\[\frac{\tan \left(\frac{x}{y \cdot 2}\right)}{\sin \left(\frac{x}{y \cdot 2}\right)}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{\tan \left(\frac{x}{y \cdot 2}\right)}{\sin \left(\frac{x}{y \cdot 2}\right)} \le 4.5088366999179037:\\ \;\;\;\;\frac{1}{\log \left(e^{\frac{\sin \left(\frac{x}{y \cdot 2}\right)}{\tan \left(\frac{x}{y \cdot 2}\right)}}\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array}\]
\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 4.5088366999179037:\\
\;\;\;\;\frac{1}{\log \left(e^{\frac{\sin \left(\frac{x}{y \cdot 2}\right)}{\tan \left(\frac{x}{y \cdot 2}\right)}}\right)}\\

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

\end{array}
double f(double x, double y) {
        double r740282 = x;
        double r740283 = y;
        double r740284 = 2.0;
        double r740285 = r740283 * r740284;
        double r740286 = r740282 / r740285;
        double r740287 = tan(r740286);
        double r740288 = sin(r740286);
        double r740289 = r740287 / r740288;
        return r740289;
}
↓
double f(double x, double y) {
        double r740290 = x;
        double r740291 = y;
        double r740292 = 2.0;
        double r740293 = r740291 * r740292;
        double r740294 = r740290 / r740293;
        double r740295 = tan(r740294);
        double r740296 = sin(r740294);
        double r740297 = r740295 / r740296;
        double r740298 = 4.508836699917904;
        bool r740299 = r740297 <= r740298;
        double r740300 = 1.0;
        double r740301 = r740296 / r740295;
        double r740302 = exp(r740301);
        double r740303 = log(r740302);
        double r740304 = r740300 / r740303;
        double r740305 = 1.0;
        double r740306 = r740299 ? r740304 : r740305;
        return r740306;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

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

Derivation

  1. Split input into 2 regimes

  2. if (/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0)))) < 4.508836699917904

    1. Initial program 26.0

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

    3. Applied clear-num26.0

      \[\leadsto \color{blue}{\frac{1}{\frac{\sin \left(\frac{x}{y \cdot 2}\right)}{\tan \left(\frac{x}{y \cdot 2}\right)}}}\]
    4. Using strategy rm

    5. Applied add-log-exp26.0

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

    if 4.508836699917904 < (/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0))))

    1. Initial program 63.0

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

    2. Taylor expanded around 0 32.5

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

  4. Final simplification27.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\tan \left(\frac{x}{y \cdot 2}\right)}{\sin \left(\frac{x}{y \cdot 2}\right)} \le 4.5088366999179037:\\ \;\;\;\;\frac{1}{\log \left(e^{\frac{\sin \left(\frac{x}{y \cdot 2}\right)}{\tan \left(\frac{x}{y \cdot 2}\right)}}\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array}\]

Reproduce

herbie shell --seed 2020049 
(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)))))