Average Error: 35.6 → 28.3
Time: 12.7s
Precision: binary64
\[\frac{\tan \left(\frac{x}{y \cdot 2}\right)}{\sin \left(\frac{x}{y \cdot 2}\right)}\]
↓
\[\frac{1}{\cos \left(\frac{x}{y \cdot 2}\right)}\]
\frac{\tan \left(\frac{x}{y \cdot 2}\right)}{\sin \left(\frac{x}{y \cdot 2}\right)}
↓
\frac{1}{\cos \left(\frac{x}{y \cdot 2}\right)}
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) {
	return ((double) (1.0 / ((double) cos(((double) (x / ((double) (y * 2.0))))))));
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original35.6
Target28.6
Herbie28.3
\[\begin{array}{l} \mathbf{if}\;y \lt -1.23036909113069936 \cdot 10^{114}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \lt -9.1028524068119138 \cdot 10^{-222}:\\ \;\;\;\;\frac{\sin \left(\frac{x}{y \cdot 2}\right)}{\sin \left(\frac{x}{y \cdot 2}\right) \cdot \log \left(e^{\cos \left(\frac{x}{y \cdot 2}\right)}\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array}\]

Derivation

  1. Initial program 35.6

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

  3. Applied tan-quot35.6

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

  5. Applied clear-num35.6

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

  6. Simplified28.3

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

  7. Final simplification28.3

    \[\leadsto \frac{1}{\cos \left(\frac{x}{y \cdot 2}\right)}\]

Reproduce

herbie shell --seed 2020162 
(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)))))