Average Error: 35.3 → 27.6
Time: 11.2s
Precision: binary64
\[\frac{\tan \left(\frac{x}{y \cdot 2}\right)}{\sin \left(\frac{x}{y \cdot 2}\right)}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{x}{y \cdot 2} \le 0.0:\\ \;\;\;\;1\\ \mathbf{elif}\;\frac{x}{y \cdot 2} \le 2.72673292042630212 \cdot 10^{26}:\\ \;\;\;\;\frac{\sin \left(\frac{x}{y \cdot 2}\right)}{\sin \left(\frac{x}{y \cdot 2}\right) \cdot \log \left(e^{\cos \left(\frac{x}{y \cdot 2}\right)}\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array}\]
\frac{\tan \left(\frac{x}{y \cdot 2}\right)}{\sin \left(\frac{x}{y \cdot 2}\right)}
↓
\begin{array}{l}
\mathbf{if}\;\frac{x}{y \cdot 2} \le 0.0:\\
\;\;\;\;1\\

\mathbf{elif}\;\frac{x}{y \cdot 2} \le 2.72673292042630212 \cdot 10^{26}:\\
\;\;\;\;\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}
double code(double x, double y) {
	return ((double) (((double) tan(((double) (x / ((double) (y * 2.0)))))) / ((double) sin(((double) (x / ((double) (y * 2.0))))))));
}
↓
double code(double x, double y) {
	double VAR;
	if ((((double) (x / ((double) (y * 2.0)))) <= 0.0)) {
		VAR = 1.0;
	} else {
		double VAR_1;
		if ((((double) (x / ((double) (y * 2.0)))) <= 2.726732920426302e+26)) {
			VAR_1 = ((double) (((double) sin(((double) (x / ((double) (y * 2.0)))))) / ((double) (((double) sin(((double) (x / ((double) (y * 2.0)))))) * ((double) log(((double) exp(((double) cos(((double) (x / ((double) (y * 2.0))))))))))))));
		} else {
			VAR_1 = 1.0;
		}
		VAR = VAR_1;
	}
	return VAR;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original35.3
Target28.5
Herbie27.6
\[\begin{array}{l} \mathbf{if}\;y \lt -1.23036909113069936 \cdot 10^{114}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \lt -9.1028524068119138 \cdot 10^{-222}:\\ \;\;\;\;\frac{\sin \left(\frac{x}{y \cdot 2}\right)}{\sin \left(\frac{x}{y \cdot 2}\right) \cdot \log \left(e^{\cos \left(\frac{x}{y \cdot 2}\right)}\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (/ x (* y 2.0)) < 0.0 or 2.72673292042630212e26 < (/ x (* y 2.0))

    1. Initial program 44.5

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

    2. Taylor expanded around 0 34.6

      \[\leadsto \color{blue}{1}\]

    if 0.0 < (/ x (* y 2.0)) < 2.72673292042630212e26

    1. Initial program 3.1

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

    3. Applied tan-quot3.1

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

    4. Applied associate-/l/3.0

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

    6. Applied add-log-exp3.1

      \[\leadsto \frac{\sin \left(\frac{x}{y \cdot 2}\right)}{\sin \left(\frac{x}{y \cdot 2}\right) \cdot \color{blue}{\log \left(e^{\cos \left(\frac{x}{y \cdot 2}\right)}\right)}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification27.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y \cdot 2} \le 0.0:\\ \;\;\;\;1\\ \mathbf{elif}\;\frac{x}{y \cdot 2} \le 2.72673292042630212 \cdot 10^{26}:\\ \;\;\;\;\frac{\sin \left(\frac{x}{y \cdot 2}\right)}{\sin \left(\frac{x}{y \cdot 2}\right) \cdot \log \left(e^{\cos \left(\frac{x}{y \cdot 2}\right)}\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array}\]

Reproduce

herbie shell --seed 2020169 
(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) 1.0 (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)))))