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

Average Error: 35.6 → 27.5

Time: 16.9s

Precision: binary64

Cost: 59332

Math

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

↓

\[\begin{array}{l} t_0 := \frac{x}{y \cdot 2}\\ \mathbf{if}\;\frac{\tan t_0}{\sin t_0} \leq 10:\\ \;\;\;\;\sqrt[3]{{\cos \left({\left(\frac{1}{\frac{\sqrt[3]{y}}{\sqrt[3]{x \cdot 0.5}}}\right)}^{2} \cdot \sqrt[3]{\frac{x \cdot 0.5}{y}}\right)}^{-3}}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

FPCore

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

↓

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ x (* y 2.0))))
   (if (<= (/ (tan t_0) (sin t_0)) 10.0)
     (cbrt
      (pow
       (cos
        (*
         (pow (/ 1.0 (/ (cbrt y) (cbrt (* x 0.5)))) 2.0)
         (cbrt (/ (* x 0.5) y))))
       -3.0))
     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 = x / (y * 2.0);
	double tmp;
	if ((tan(t_0) / sin(t_0)) <= 10.0) {
		tmp = cbrt(pow(cos((pow((1.0 / (cbrt(y) / cbrt((x * 0.5)))), 2.0) * cbrt(((x * 0.5) / y)))), -3.0));
	} 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 = x / (y * 2.0);
	double tmp;
	if ((Math.tan(t_0) / Math.sin(t_0)) <= 10.0) {
		tmp = Math.cbrt(Math.pow(Math.cos((Math.pow((1.0 / (Math.cbrt(y) / Math.cbrt((x * 0.5)))), 2.0) * Math.cbrt(((x * 0.5) / y)))), -3.0));
	} 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 = Float64(x / Float64(y * 2.0))
	tmp = 0.0
	if (Float64(tan(t_0) / sin(t_0)) <= 10.0)
		tmp = cbrt((cos(Float64((Float64(1.0 / Float64(cbrt(y) / cbrt(Float64(x * 0.5)))) ^ 2.0) * cbrt(Float64(Float64(x * 0.5) / y)))) ^ -3.0));
	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[(x / N[(y * 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[Tan[t$95$0], $MachinePrecision] / N[Sin[t$95$0], $MachinePrecision]), $MachinePrecision], 10.0], N[Power[N[Power[N[Cos[N[(N[Power[N[(1.0 / N[(N[Power[y, 1/3], $MachinePrecision] / N[Power[N[(x * 0.5), $MachinePrecision], 1/3], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision] * N[Power[N[(N[(x * 0.5), $MachinePrecision] / y), $MachinePrecision], 1/3], $MachinePrecision]), $MachinePrecision]], $MachinePrecision], -3.0], $MachinePrecision], 1/3], $MachinePrecision], 1.0]]

Target

Original	35.6
Target	28.8
Herbie	27.5

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

Derivation

1. Split input into 2 regimes

2. if (/.f64 (tan.f64 (/.f64 x (*.f64 y 2))) (sin.f64 (/.f64 x (*.f64 y 2)))) < 10

   1. Initial program 26.3

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

   2. Applied egg-rr 26.3

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

   3. Applied egg-rr 26.4

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

   4. Applied egg-rr 26.4

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

   5. Applied egg-rr 26.4

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

   if 10 < (/.f64 (tan.f64 (/.f64 x (*.f64 y 2))) (sin.f64 (/.f64 x (*.f64 y 2))))

   1. Initial program 63.6

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

   2. Taylor expanded in x around 0 30.6

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

4. Final simplification 27.5

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\tan \left(\frac{x}{y \cdot 2}\right)}{\sin \left(\frac{x}{y \cdot 2}\right)} \leq 10:\\ \;\;\;\;\sqrt[3]{{\cos \left({\left(\frac{1}{\frac{\sqrt[3]{y}}{\sqrt[3]{x \cdot 0.5}}}\right)}^{2} \cdot \sqrt[3]{\frac{x \cdot 0.5}{y}}\right)}^{-3}}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternatives

Alternative 1
Error	27.5
Cost	40068

\[\begin{array}{l} t_0 := \sqrt[3]{x \cdot \frac{0.5}{y}}\\ t_1 := \frac{x}{y \cdot 2}\\ \mathbf{if}\;\frac{\tan t_1}{\sin t_1} \leq 8:\\ \;\;\;\;\frac{1}{\cos \left(t_0 \cdot {t_0}^{2}\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 2
Error	28.3
Cost	64

\[1 \]

Reproduce

herbie shell --seed 2022316 
(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)))))