Diagrams.TwoD.Layout.CirclePacking:approxRadius from diagrams-contrib-1.3.0.5

Average Error: 35.9 → 27.8

Time: 6.6s

Precision: 64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;\frac{\tan \left(\frac{x}{y \cdot 2}\right)}{\sin \left(\frac{x}{y \cdot 2}\right)} \le 4.5088366999179037:\\ \;\;\;\;\mathsf{log1p}\left(\sqrt[3]{{\left(\mathsf{expm1}\left(\frac{\mathsf{log1p}\left(\mathsf{expm1}\left(\tan \left(\frac{x}{y \cdot 2}\right)\right)\right)}{\sin \left(\frac{x}{y \cdot 2}\right)}\right)\right)}^{3}}\right)\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array}\]

C

double code(double x, double y) {
	return (tan((x / (y * 2.0))) / sin((x / (y * 2.0))));
}

↓

double code(double x, double y) {
	double temp;
	if (((tan((x / (y * 2.0))) / sin((x / (y * 2.0)))) <= 4.508836699917904)) {
		temp = log1p(cbrt(pow(expm1((log1p(expm1(tan((x / (y * 2.0))))) / sin((x / (y * 2.0))))), 3.0)));
	} else {
		temp = 1.0;
	}
	return temp;
}

Error

Bits error versus x

Bits error versus y

Target

Original	35.9
Target	29.1
Herbie	27.8

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

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 log1p-expm1-u 26.0

      \[\leadsto \color{blue}{\mathsf{log1p}\left(\mathsf{expm1}\left(\frac{\tan \left(\frac{x}{y \cdot 2}\right)}{\sin \left(\frac{x}{y \cdot 2}\right)}\right)\right)}\]
   4. Using strategy rm

   5. Applied add-cbrt-cube 26.1

      \[\leadsto \mathsf{log1p}\left(\color{blue}{\sqrt[3]{\left(\mathsf{expm1}\left(\frac{\tan \left(\frac{x}{y \cdot 2}\right)}{\sin \left(\frac{x}{y \cdot 2}\right)}\right) \cdot \mathsf{expm1}\left(\frac{\tan \left(\frac{x}{y \cdot 2}\right)}{\sin \left(\frac{x}{y \cdot 2}\right)}\right)\right) \cdot \mathsf{expm1}\left(\frac{\tan \left(\frac{x}{y \cdot 2}\right)}{\sin \left(\frac{x}{y \cdot 2}\right)}\right)}}\right)\]

   6. Simplified 26.1

      \[\leadsto \mathsf{log1p}\left(\sqrt[3]{\color{blue}{{\left(\mathsf{expm1}\left(\frac{\tan \left(\frac{x}{y \cdot 2}\right)}{\sin \left(\frac{x}{y \cdot 2}\right)}\right)\right)}^{3}}}\right)\]
   7. Using strategy rm

   8. Applied log1p-expm1-u 26.1

      \[\leadsto \mathsf{log1p}\left(\sqrt[3]{{\left(\mathsf{expm1}\left(\frac{\color{blue}{\mathsf{log1p}\left(\mathsf{expm1}\left(\tan \left(\frac{x}{y \cdot 2}\right)\right)\right)}}{\sin \left(\frac{x}{y \cdot 2}\right)}\right)\right)}^{3}}\right)\]

   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 simplification 27.8

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\tan \left(\frac{x}{y \cdot 2}\right)}{\sin \left(\frac{x}{y \cdot 2}\right)} \le 4.5088366999179037:\\ \;\;\;\;\mathsf{log1p}\left(\sqrt[3]{{\left(\mathsf{expm1}\left(\frac{\mathsf{log1p}\left(\mathsf{expm1}\left(\tan \left(\frac{x}{y \cdot 2}\right)\right)\right)}{\sin \left(\frac{x}{y \cdot 2}\right)}\right)\right)}^{3}}\right)\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array}\]

Reproduce

herbie shell --seed 2020049 +o rules:numerics
(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)))))