Average Error: 35.6 → 28.0
Time: 6.9s
Precision: binary64
\[\frac{\tan \left(\frac{x}{y \cdot 2}\right)}{\sin \left(\frac{x}{y \cdot 2}\right)}\]
↓
\[\sqrt[3]{{\log \left(e^{\frac{1}{\cos \left(\frac{x}{y \cdot 2}\right)}}\right)}^{3}}\]
\frac{\tan \left(\frac{x}{y \cdot 2}\right)}{\sin \left(\frac{x}{y \cdot 2}\right)}
↓
\sqrt[3]{{\log \left(e^{\frac{1}{\cos \left(\frac{x}{y \cdot 2}\right)}}\right)}^{3}}
(FPCore (x y)
 :precision binary64
 (/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0)))))
↓
(FPCore (x y)
 :precision binary64
 (cbrt (pow (log (exp (/ 1.0 (cos (/ x (* y 2.0)))))) 3.0)))
double code(double x, double y) {
	return tan(x / (y * 2.0)) / sin(x / (y * 2.0));
}
↓
double code(double x, double y) {
	return cbrt(pow(log(exp(1.0 / cos(x / (y * 2.0)))), 3.0));
}

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
Target28.3
Herbie28.0
\[\begin{array}{l} \mathbf{if}\;y < -1.2303690911306994 \cdot 10^{+114}:\\ \;\;\;\;1\\ \mathbf{elif}\;y < -9.102852406811914 \cdot 10^{-222}:\\ \;\;\;\;\frac{\sin \left(\frac{x}{y \cdot 2}\right)}{\sin \left(\frac{x}{y \cdot 2}\right) \cdot \log \left(e^{\cos \left(\frac{x}{y \cdot 2}\right)}\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array}\]

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 add-cbrt-cube_binary64_2006735.6

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

  4. Simplified35.6

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

  6. Applied tan-quot_binary64_2019035.6

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

  8. Applied add-log-exp_binary64_2007035.6

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

  9. Simplified28.0

    \[\leadsto \sqrt[3]{{\log \color{blue}{\left(e^{\frac{1}{\cos \left(\frac{x}{y \cdot 2}\right)}}\right)}}^{3}}\]

  10. Final simplification28.0

    \[\leadsto \sqrt[3]{{\log \left(e^{\frac{1}{\cos \left(\frac{x}{y \cdot 2}\right)}}\right)}^{3}}\]

Reproduce

herbie shell --seed 2020280 
(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)))))