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

Average Error: 36.0 → 27.9

Time: 6.7s

Precision: binary64

Math

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

↓

\[\begin{array}{l} t_0 := \sqrt[3]{0.5 \cdot \frac{x}{y}}\\ t_1 := \frac{x}{y \cdot 2}\\ \mathbf{if}\;\frac{\tan t_1}{\sin t_1} \leq 1.9:\\ \;\;\;\;\frac{1}{\cos \left(t_0 \cdot {t_0}^{2}\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

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 (* 0.5 (/ x y)))) (t_1 (/ x (* y 2.0))))
   (if (<= (/ (tan t_1) (sin t_1)) 1.9)
     (/ 1.0 (cos (* t_0 (pow t_0 2.0))))
     1.0)))

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((0.5 * (x / y)));
	double t_1 = x / (y * 2.0);
	double tmp;
	if ((tan(t_1) / sin(t_1)) <= 1.9) {
		tmp = 1.0 / cos((t_0 * pow(t_0, 2.0)));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

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((0.5 * (x / y)));
	double t_1 = x / (y * 2.0);
	double tmp;
	if ((Math.tan(t_1) / Math.sin(t_1)) <= 1.9) {
		tmp = 1.0 / Math.cos((t_0 * Math.pow(t_0, 2.0)));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

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(0.5 * Float64(x / y)))
	t_1 = Float64(x / Float64(y * 2.0))
	tmp = 0.0
	if (Float64(tan(t_1) / sin(t_1)) <= 1.9)
		tmp = Float64(1.0 / cos(Float64(t_0 * (t_0 ^ 2.0))));
	else
		tmp = 1.0;
	end
	return tmp
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[(0.5 * N[(x / y), $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision]}, Block[{t$95$1 = N[(x / N[(y * 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[Tan[t$95$1], $MachinePrecision] / N[Sin[t$95$1], $MachinePrecision]), $MachinePrecision], 1.9], N[(1.0 / N[Cos[N[(t$95$0 * N[Power[t$95$0, 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 1.0]]]

Target

Original	36.0
Target	29.1
Herbie	27.9

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

Derivation

1. Split input into 2 regimes

2. if (/.f64 (tan.f64 (/.f64 x (*.f64 y 2))) (sin.f64 (/.f64 x (*.f64 y 2)))) < 1.8999999999999999

   1. Initial program 24.4

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

   2. Taylor expanded in x around inf 24.4

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

   3. Simplified 24.5

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

   4. Applied egg-rr 24.7

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

   if 1.8999999999999999 < (/.f64 (tan.f64 (/.f64 x (*.f64 y 2))) (sin.f64 (/.f64 x (*.f64 y 2))))

   1. Initial program 61.9

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

   2. Taylor expanded in x around 0 35.4

      \[\leadsto \color{blue}{1} \]
3. Recombined 2 regimes into one program.

4. Final simplification 27.9

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\tan \left(\frac{x}{y \cdot 2}\right)}{\sin \left(\frac{x}{y \cdot 2}\right)} \leq 1.9:\\ \;\;\;\;\frac{1}{\cos \left(\sqrt[3]{0.5 \cdot \frac{x}{y}} \cdot {\left(\sqrt[3]{0.5 \cdot \frac{x}{y}}\right)}^{2}\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Reproduce

herbie shell --seed 2022202 
(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)))))