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

Average Accuracy: 43.9% → 55.4%

Time: 14.3s

Precision: binary64

Cost: 26496

Math

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

↓

\[\begin{array}{l} t_0 := \sqrt[3]{\frac{x \cdot 0.5}{y}}\\ \frac{1}{\cos \left(t_0 \cdot {t_0}^{2}\right)} \end{array} \]

FPCore

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

↓

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (cbrt (/ (* x 0.5) y)))) (/ 1.0 (cos (* t_0 (pow t_0 2.0))))))

C

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

↓

double code(double x, double y) {
	double t_0 = cbrt(((x * 0.5) / y));
	return 1.0 / cos((t_0 * pow(t_0, 2.0)));
}

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) {
	double t_0 = Math.cbrt(((x * 0.5) / y));
	return 1.0 / Math.cos((t_0 * Math.pow(t_0, 2.0)));
}

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)
	t_0 = cbrt(Float64(Float64(x * 0.5) / y))
	return Float64(1.0 / cos(Float64(t_0 * (t_0 ^ 2.0))))
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_] := Block[{t$95$0 = N[Power[N[(N[(x * 0.5), $MachinePrecision] / y), $MachinePrecision], 1/3], $MachinePrecision]}, N[(1.0 / N[Cos[N[(t$95$0 * N[Power[t$95$0, 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Target

Original	43.9%
Target	54.6%
Herbie	55.4%

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

Derivation

1. Initial program 43.9%

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

2. Applied egg-rr 55.6%

   \[\leadsto \color{blue}{0 + \frac{1}{\cos \left(x \cdot \frac{0.5}{y}\right)}} \]
   Proof

   [Start] 43.9	\[ \frac{\tan \left(\frac{x}{y \cdot 2}\right)}{\sin \left(\frac{x}{y \cdot 2}\right)} \]
   add-log-exp [=>] 43.9	\[ \color{blue}{\log \left(e^{\frac{\tan \left(\frac{x}{y \cdot 2}\right)}{\sin \left(\frac{x}{y \cdot 2}\right)}}\right)} \]
   *-un-lft-identity [=>] 43.9	\[ \log \color{blue}{\left(1 \cdot e^{\frac{\tan \left(\frac{x}{y \cdot 2}\right)}{\sin \left(\frac{x}{y \cdot 2}\right)}}\right)} \]
   log-prod [=>] 43.9	\[ \color{blue}{\log 1 + \log \left(e^{\frac{\tan \left(\frac{x}{y \cdot 2}\right)}{\sin \left(\frac{x}{y \cdot 2}\right)}}\right)} \]
   metadata-eval [=>] 43.9	\[ \color{blue}{0} + \log \left(e^{\frac{\tan \left(\frac{x}{y \cdot 2}\right)}{\sin \left(\frac{x}{y \cdot 2}\right)}}\right) \]
   add-log-exp [<=] 43.9	\[ 0 + \color{blue}{\frac{\tan \left(\frac{x}{y \cdot 2}\right)}{\sin \left(\frac{x}{y \cdot 2}\right)}} \]
   div-inv [=>] 42.3	\[ 0 + \color{blue}{\tan \left(\frac{x}{y \cdot 2}\right) \cdot \frac{1}{\sin \left(\frac{x}{y \cdot 2}\right)}} \]
   tan-quot [=>] 42.3	\[ 0 + \color{blue}{\frac{\sin \left(\frac{x}{y \cdot 2}\right)}{\cos \left(\frac{x}{y \cdot 2}\right)}} \cdot \frac{1}{\sin \left(\frac{x}{y \cdot 2}\right)} \]
   associate-*l/ [=>] 42.3	\[ 0 + \color{blue}{\frac{\sin \left(\frac{x}{y \cdot 2}\right) \cdot \frac{1}{\sin \left(\frac{x}{y \cdot 2}\right)}}{\cos \left(\frac{x}{y \cdot 2}\right)}} \]
   pow1 [=>] 42.3	\[ 0 + \frac{\color{blue}{{\sin \left(\frac{x}{y \cdot 2}\right)}^{1}} \cdot \frac{1}{\sin \left(\frac{x}{y \cdot 2}\right)}}{\cos \left(\frac{x}{y \cdot 2}\right)} \]
   inv-pow [=>] 42.3	\[ 0 + \frac{{\sin \left(\frac{x}{y \cdot 2}\right)}^{1} \cdot \color{blue}{{\sin \left(\frac{x}{y \cdot 2}\right)}^{-1}}}{\cos \left(\frac{x}{y \cdot 2}\right)} \]
   pow-prod-up [=>] 55.5	\[ 0 + \frac{\color{blue}{{\sin \left(\frac{x}{y \cdot 2}\right)}^{\left(1 + -1\right)}}}{\cos \left(\frac{x}{y \cdot 2}\right)} \]
   metadata-eval [=>] 55.5	\[ 0 + \frac{{\sin \left(\frac{x}{y \cdot 2}\right)}^{\color{blue}{0}}}{\cos \left(\frac{x}{y \cdot 2}\right)} \]
   metadata-eval [=>] 55.5	\[ 0 + \frac{\color{blue}{1}}{\cos \left(\frac{x}{y \cdot 2}\right)} \]
   div-inv [=>] 55.6	\[ 0 + \frac{1}{\cos \color{blue}{\left(x \cdot \frac{1}{y \cdot 2}\right)}} \]
   *-commutative [=>] 55.6	\[ 0 + \frac{1}{\cos \left(x \cdot \frac{1}{\color{blue}{2 \cdot y}}\right)} \]
   associate-/r* [=>] 55.6	\[ 0 + \frac{1}{\cos \left(x \cdot \color{blue}{\frac{\frac{1}{2}}{y}}\right)} \]
   metadata-eval [=>] 55.6	\[ 0 + \frac{1}{\cos \left(x \cdot \frac{\color{blue}{0.5}}{y}\right)} \]

3. Applied egg-rr 33.8%

   \[\leadsto 0 + \frac{1}{\cos \color{blue}{\left(e^{\left(3 \cdot \log \left(x \cdot \frac{0.5}{y}\right)\right) \cdot 0.3333333333333333}\right)}} \]
   Proof

   [Start] 55.6	\[ 0 + \frac{1}{\cos \left(x \cdot \frac{0.5}{y}\right)} \]
   add-cbrt-cube [=>] 53.0	\[ 0 + \frac{1}{\cos \color{blue}{\left(\sqrt[3]{\left(\left(x \cdot \frac{0.5}{y}\right) \cdot \left(x \cdot \frac{0.5}{y}\right)\right) \cdot \left(x \cdot \frac{0.5}{y}\right)}\right)}} \]
   pow1/3 [=>] 43.8	\[ 0 + \frac{1}{\cos \color{blue}{\left({\left(\left(\left(x \cdot \frac{0.5}{y}\right) \cdot \left(x \cdot \frac{0.5}{y}\right)\right) \cdot \left(x \cdot \frac{0.5}{y}\right)\right)}^{0.3333333333333333}\right)}} \]
   pow-to-exp [=>] 43.8	\[ 0 + \frac{1}{\cos \color{blue}{\left(e^{\log \left(\left(\left(x \cdot \frac{0.5}{y}\right) \cdot \left(x \cdot \frac{0.5}{y}\right)\right) \cdot \left(x \cdot \frac{0.5}{y}\right)\right) \cdot 0.3333333333333333}\right)}} \]
   pow3 [=>] 43.8	\[ 0 + \frac{1}{\cos \left(e^{\log \color{blue}{\left({\left(x \cdot \frac{0.5}{y}\right)}^{3}\right)} \cdot 0.3333333333333333}\right)} \]
   log-pow [=>] 33.8	\[ 0 + \frac{1}{\cos \left(e^{\color{blue}{\left(3 \cdot \log \left(x \cdot \frac{0.5}{y}\right)\right)} \cdot 0.3333333333333333}\right)} \]

4. Applied egg-rr 55.4%

   \[\leadsto 0 + \frac{1}{\cos \color{blue}{\left({\left(\sqrt[3]{\frac{x \cdot 0.5}{y}}\right)}^{2} \cdot \sqrt[3]{\frac{x \cdot 0.5}{y}}\right)}} \]
   Proof

   [Start] 33.8	\[ 0 + \frac{1}{\cos \left(e^{\left(3 \cdot \log \left(x \cdot \frac{0.5}{y}\right)\right) \cdot 0.3333333333333333}\right)} \]
   add-cube-cbrt [=>] 33.7	\[ 0 + \frac{1}{\cos \color{blue}{\left(\left(\sqrt[3]{e^{\left(3 \cdot \log \left(x \cdot \frac{0.5}{y}\right)\right) \cdot 0.3333333333333333}} \cdot \sqrt[3]{e^{\left(3 \cdot \log \left(x \cdot \frac{0.5}{y}\right)\right) \cdot 0.3333333333333333}}\right) \cdot \sqrt[3]{e^{\left(3 \cdot \log \left(x \cdot \frac{0.5}{y}\right)\right) \cdot 0.3333333333333333}}\right)}} \]

5. Final simplification 55.4%

   \[\leadsto \frac{1}{\cos \left(\sqrt[3]{\frac{x \cdot 0.5}{y}} \cdot {\left(\sqrt[3]{\frac{x \cdot 0.5}{y}}\right)}^{2}\right)} \]

Alternatives

Alternative 1
Accuracy	55.2%
Cost	64

\[1 \]

Reproduce

herbie shell --seed 2023147 
(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)))))