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

Average Error: 36.1 → 28.9

Time: 7.2s

Precision: binary64

Math

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

↓

\[{\left(\sqrt[3]{\frac{1}{\cos \left(\frac{0.5}{y} \cdot x\right)}}\right)}^{3} \]

FPCore

(FPCore (x y)
 :precision binary64
 (/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0)))))

↓

(FPCore (x y)
 :precision binary64
 (pow (cbrt (/ 1.0 (cos (* (/ 0.5 y) x)))) 3.0))

C

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

↓

double code(double x, double y) {
	return pow(cbrt((1.0 / cos(((0.5 / y) * x)))), 3.0);
}

Java

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

↓

public static double code(double x, double y) {
	return Math.pow(Math.cbrt((1.0 / Math.cos(((0.5 / y) * x)))), 3.0);
}

Julia

function code(x, y)
	return Float64(tan(Float64(x / Float64(y * 2.0))) / sin(Float64(x / Float64(y * 2.0))))
end

↓

function code(x, y)
	return cbrt(Float64(1.0 / cos(Float64(Float64(0.5 / y) * x)))) ^ 3.0
end

Wolfram

code[x_, y_] := N[(N[Tan[N[(x / N[(y * 2.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / N[Sin[N[(x / N[(y * 2.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_] := N[Power[N[Power[N[(1.0 / N[Cos[N[(N[(0.5 / y), $MachinePrecision] * x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision], 3.0], $MachinePrecision]

Error

Bits error versus x

Bits error versus y

Target

Original	36.1
Target	29.3
Herbie	28.9

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

Derivation

1. Initial program 36.1

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

2. Applied egg-rr 36.1

   \[\leadsto \color{blue}{{\left(\sqrt[3]{\frac{\tan \left(\frac{x}{y} \cdot 0.5\right)}{\sin \left(\frac{x}{y} \cdot 0.5\right)}}\right)}^{3}} \]

3. Taylor expanded in x around inf 29.0

   \[\leadsto {\left(\sqrt[3]{\color{blue}{\frac{1}{\cos \left(0.5 \cdot \frac{x}{y}\right)}}}\right)}^{3} \]

4. Taylor expanded in x around inf 30.6

   \[\leadsto {\color{blue}{\left({\left(\frac{1}{\cos \left(0.5 \cdot \frac{x}{y}\right)}\right)}^{0.3333333333333333}\right)}}^{3} \]

5. Simplified 28.9

   \[\leadsto {\color{blue}{\left(\sqrt[3]{\frac{1}{\cos \left(\frac{0.5}{y} \cdot x\right)}}\right)}}^{3} \]

6. Final simplification 28.9

   \[\leadsto {\left(\sqrt[3]{\frac{1}{\cos \left(\frac{0.5}{y} \cdot x\right)}}\right)}^{3} \]

Reproduce

herbie shell --seed 2022162 
(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)))))