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

Percentage Accurate: 44.2% → 57.2%

Time: 18.2s

Alternatives: 4

Speedup: 211.0×

Specification

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{y \cdot 2}\\ \frac{\tan t_0}{\sin t_0} \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ x (* y 2.0)))) (/ (tan t_0) (sin t_0))))

C

double code(double x, double y) {
	double t_0 = x / (y * 2.0);
	return tan(t_0) / sin(t_0);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    t_0 = x / (y * 2.0d0)
    code = tan(t_0) / sin(t_0)
end function

Java

public static double code(double x, double y) {
	double t_0 = x / (y * 2.0);
	return Math.tan(t_0) / Math.sin(t_0);
}

Python

def code(x, y):
	t_0 = x / (y * 2.0)
	return math.tan(t_0) / math.sin(t_0)

Julia

function code(x, y)
	t_0 = Float64(x / Float64(y * 2.0))
	return Float64(tan(t_0) / sin(t_0))
end

MATLAB

function tmp = code(x, y)
	t_0 = x / (y * 2.0);
	tmp = tan(t_0) / sin(t_0);
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(x / N[(y * 2.0), $MachinePrecision]), $MachinePrecision]}, N[(N[Tan[t$95$0], $MachinePrecision] / N[Sin[t$95$0], $MachinePrecision]), $MachinePrecision]]

Initial Program: 44.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{y \cdot 2}\\ \frac{\tan t_0}{\sin t_0} \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ x (* y 2.0)))) (/ (tan t_0) (sin t_0))))

C

double code(double x, double y) {
	double t_0 = x / (y * 2.0);
	return tan(t_0) / sin(t_0);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    t_0 = x / (y * 2.0d0)
    code = tan(t_0) / sin(t_0)
end function

Java

public static double code(double x, double y) {
	double t_0 = x / (y * 2.0);
	return Math.tan(t_0) / Math.sin(t_0);
}

Python

def code(x, y):
	t_0 = x / (y * 2.0)
	return math.tan(t_0) / math.sin(t_0)

Julia

function code(x, y)
	t_0 = Float64(x / Float64(y * 2.0))
	return Float64(tan(t_0) / sin(t_0))
end

MATLAB

function tmp = code(x, y)
	t_0 = x / (y * 2.0);
	tmp = tan(t_0) / sin(t_0);
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(x / N[(y * 2.0), $MachinePrecision]), $MachinePrecision]}, N[(N[Tan[t$95$0], $MachinePrecision] / N[Sin[t$95$0], $MachinePrecision]), $MachinePrecision]]

Alternative 1: 57.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} x = |x|\\ y = |y|\\ \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y \cdot 2} \leq 5 \cdot 10^{+66}:\\ \;\;\;\;\sqrt[3]{{\log \left(e^{\cos \left(\sqrt[3]{{\left(x \cdot \frac{0.5}{y}\right)}^{3}}\right)}\right)}^{-3}}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

NOTE: x should be positive before calling this function
NOTE: y should be positive before calling this function
(FPCore (x y)
 :precision binary64
 (if (<= (/ x (* y 2.0)) 5e+66)
   (cbrt (pow (log (exp (cos (cbrt (pow (* x (/ 0.5 y)) 3.0))))) -3.0))
   1.0))

C

x = abs(x);
y = abs(y);
double code(double x, double y) {
	double tmp;
	if ((x / (y * 2.0)) <= 5e+66) {
		tmp = cbrt(pow(log(exp(cos(cbrt(pow((x * (0.5 / y)), 3.0))))), -3.0));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Java

x = Math.abs(x);
y = Math.abs(y);
public static double code(double x, double y) {
	double tmp;
	if ((x / (y * 2.0)) <= 5e+66) {
		tmp = Math.cbrt(Math.pow(Math.log(Math.exp(Math.cos(Math.cbrt(Math.pow((x * (0.5 / y)), 3.0))))), -3.0));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Julia

x = abs(x)
y = abs(y)
function code(x, y)
	tmp = 0.0
	if (Float64(x / Float64(y * 2.0)) <= 5e+66)
		tmp = cbrt((log(exp(cos(cbrt((Float64(x * Float64(0.5 / y)) ^ 3.0))))) ^ -3.0));
	else
		tmp = 1.0;
	end
	return tmp
end

Wolfram

NOTE: x should be positive before calling this function
NOTE: y should be positive before calling this function
code[x_, y_] := If[LessEqual[N[(x / N[(y * 2.0), $MachinePrecision]), $MachinePrecision], 5e+66], N[Power[N[Power[N[Log[N[Exp[N[Cos[N[Power[N[Power[N[(x * N[(0.5 / y), $MachinePrecision]), $MachinePrecision], 3.0], $MachinePrecision], 1/3], $MachinePrecision]], $MachinePrecision]], $MachinePrecision]], $MachinePrecision], -3.0], $MachinePrecision], 1/3], $MachinePrecision], 1.0]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (*.f64 y 2)) < 4.99999999999999991e66

   1. Initial program 50.2%

      \[\frac{\tan \left(\frac{x}{y \cdot 2}\right)}{\sin \left(\frac{x}{y \cdot 2}\right)} \]
   2. Step-by-step derivation

      1. add-cbrt-cube 50.2%

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

      2. pow3 50.2%

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

      3. clear-num 50.2%

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

      4. inv-pow 50.2%

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

      5. metadata-eval 50.2%

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

      6. pow-pow 50.2%

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

   3. Applied egg-rr 65.7%

      \[\leadsto \color{blue}{\sqrt[3]{{\cos \left(x \cdot \frac{0.5}{y}\right)}^{-3}}} \]
   4. Step-by-step derivation

      1. add-log-exp 65.7%

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

   5. Applied egg-rr 65.7%

      \[\leadsto \sqrt[3]{{\color{blue}{\log \left(e^{\cos \left(x \cdot \frac{0.5}{y}\right)}\right)}}^{-3}} \]
   6. Step-by-step derivation

      1. add-cbrt-cube 63.9%

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

      2. pow3 64.0%

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

   7. Applied egg-rr 64.0%

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

   if 4.99999999999999991e66 < (/.f64 x (*.f64 y 2))

   1. Initial program 7.5%

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

   2. Taylor expanded in x around 0 12.3%

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

4. Final simplification 54.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y \cdot 2} \leq 5 \cdot 10^{+66}:\\ \;\;\;\;\sqrt[3]{{\log \left(e^{\cos \left(\sqrt[3]{{\left(x \cdot \frac{0.5}{y}\right)}^{3}}\right)}\right)}^{-3}}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 2: 57.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} x = |x|\\ y = |y|\\ \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y \cdot 2} \leq 5 \cdot 10^{+66}:\\ \;\;\;\;\sqrt[3]{{\cos \left(\sqrt[3]{{\left(x \cdot \frac{0.5}{y}\right)}^{3}}\right)}^{-3}}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

NOTE: x should be positive before calling this function
NOTE: y should be positive before calling this function
(FPCore (x y)
 :precision binary64
 (if (<= (/ x (* y 2.0)) 5e+66)
   (cbrt (pow (cos (cbrt (pow (* x (/ 0.5 y)) 3.0))) -3.0))
   1.0))

C

x = abs(x);
y = abs(y);
double code(double x, double y) {
	double tmp;
	if ((x / (y * 2.0)) <= 5e+66) {
		tmp = cbrt(pow(cos(cbrt(pow((x * (0.5 / y)), 3.0))), -3.0));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Java

x = Math.abs(x);
y = Math.abs(y);
public static double code(double x, double y) {
	double tmp;
	if ((x / (y * 2.0)) <= 5e+66) {
		tmp = Math.cbrt(Math.pow(Math.cos(Math.cbrt(Math.pow((x * (0.5 / y)), 3.0))), -3.0));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Julia

x = abs(x)
y = abs(y)
function code(x, y)
	tmp = 0.0
	if (Float64(x / Float64(y * 2.0)) <= 5e+66)
		tmp = cbrt((cos(cbrt((Float64(x * Float64(0.5 / y)) ^ 3.0))) ^ -3.0));
	else
		tmp = 1.0;
	end
	return tmp
end

Wolfram

NOTE: x should be positive before calling this function
NOTE: y should be positive before calling this function
code[x_, y_] := If[LessEqual[N[(x / N[(y * 2.0), $MachinePrecision]), $MachinePrecision], 5e+66], N[Power[N[Power[N[Cos[N[Power[N[Power[N[(x * N[(0.5 / y), $MachinePrecision]), $MachinePrecision], 3.0], $MachinePrecision], 1/3], $MachinePrecision]], $MachinePrecision], -3.0], $MachinePrecision], 1/3], $MachinePrecision], 1.0]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (*.f64 y 2)) < 4.99999999999999991e66

   1. Initial program 50.2%

      \[\frac{\tan \left(\frac{x}{y \cdot 2}\right)}{\sin \left(\frac{x}{y \cdot 2}\right)} \]
   2. Step-by-step derivation

      1. add-cbrt-cube 50.2%

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

      2. pow3 50.2%

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

      3. clear-num 50.2%

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

      4. inv-pow 50.2%

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

      5. metadata-eval 50.2%

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

      6. pow-pow 50.2%

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

   3. Applied egg-rr 65.7%

      \[\leadsto \color{blue}{\sqrt[3]{{\cos \left(x \cdot \frac{0.5}{y}\right)}^{-3}}} \]
   4. Step-by-step derivation

      1. add-cbrt-cube 63.9%

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

      2. pow3 64.0%

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

   5. Applied egg-rr 64.0%

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

   if 4.99999999999999991e66 < (/.f64 x (*.f64 y 2))

   1. Initial program 7.5%

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

   2. Taylor expanded in x around 0 12.3%

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

4. Final simplification 54.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y \cdot 2} \leq 5 \cdot 10^{+66}:\\ \;\;\;\;\sqrt[3]{{\cos \left(\sqrt[3]{{\left(x \cdot \frac{0.5}{y}\right)}^{3}}\right)}^{-3}}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 3: 57.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} x = |x|\\ y = |y|\\ \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y \cdot 2} \leq 5 \cdot 10^{+66}:\\ \;\;\;\;\frac{1}{\cos \left(\sqrt[3]{{\left(x \cdot \frac{0.5}{y}\right)}^{3}}\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

NOTE: x should be positive before calling this function
NOTE: y should be positive before calling this function
(FPCore (x y)
 :precision binary64
 (if (<= (/ x (* y 2.0)) 5e+66)
   (/ 1.0 (cos (cbrt (pow (* x (/ 0.5 y)) 3.0))))
   1.0))

C

x = abs(x);
y = abs(y);
double code(double x, double y) {
	double tmp;
	if ((x / (y * 2.0)) <= 5e+66) {
		tmp = 1.0 / cos(cbrt(pow((x * (0.5 / y)), 3.0)));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Java

x = Math.abs(x);
y = Math.abs(y);
public static double code(double x, double y) {
	double tmp;
	if ((x / (y * 2.0)) <= 5e+66) {
		tmp = 1.0 / Math.cos(Math.cbrt(Math.pow((x * (0.5 / y)), 3.0)));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Julia

x = abs(x)
y = abs(y)
function code(x, y)
	tmp = 0.0
	if (Float64(x / Float64(y * 2.0)) <= 5e+66)
		tmp = Float64(1.0 / cos(cbrt((Float64(x * Float64(0.5 / y)) ^ 3.0))));
	else
		tmp = 1.0;
	end
	return tmp
end

Wolfram

NOTE: x should be positive before calling this function
NOTE: y should be positive before calling this function
code[x_, y_] := If[LessEqual[N[(x / N[(y * 2.0), $MachinePrecision]), $MachinePrecision], 5e+66], N[(1.0 / N[Cos[N[Power[N[Power[N[(x * N[(0.5 / y), $MachinePrecision]), $MachinePrecision], 3.0], $MachinePrecision], 1/3], $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 1.0]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (*.f64 y 2)) < 4.99999999999999991e66

   1. Initial program 50.2%

      \[\frac{\tan \left(\frac{x}{y \cdot 2}\right)}{\sin \left(\frac{x}{y \cdot 2}\right)} \]
   2. Step-by-step derivation

      1. add-cbrt-cube 50.2%

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

      2. pow3 50.2%

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

      3. clear-num 50.2%

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

      4. inv-pow 50.2%

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

      5. metadata-eval 50.2%

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

      6. pow-pow 50.2%

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

   3. Applied egg-rr 65.7%

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

   4. Taylor expanded in x around inf 65.4%

      \[\leadsto \color{blue}{\frac{1}{\cos \left(0.5 \cdot \frac{x}{y}\right)}} \]
   5. Step-by-step derivation

      1. associate-*r/ 65.4%

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

      2. associate-*l/ 65.7%

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

      3. *-commutative 65.7%

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

   6. Simplified 65.7%

      \[\leadsto \color{blue}{\frac{1}{\cos \left(x \cdot \frac{0.5}{y}\right)}} \]
   7. Step-by-step derivation

      1. add-cbrt-cube 63.9%

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

      2. pow3 64.0%

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

   8. Applied egg-rr 64.0%

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

   if 4.99999999999999991e66 < (/.f64 x (*.f64 y 2))

   1. Initial program 7.5%

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

   2. Taylor expanded in x around 0 12.3%

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

4. Final simplification 54.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y \cdot 2} \leq 5 \cdot 10^{+66}:\\ \;\;\;\;\frac{1}{\cos \left(\sqrt[3]{{\left(x \cdot \frac{0.5}{y}\right)}^{3}}\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 4: 55.7% accurate, 211.0× speedup

Math

\[\begin{array}{l} x = |x|\\ y = |y|\\ \\ 1 \end{array} \]

FPCore

NOTE: x should be positive before calling this function
NOTE: y should be positive before calling this function
(FPCore (x y) :precision binary64 1.0)

C

x = abs(x);
y = abs(y);
double code(double x, double y) {
	return 1.0;
}

Fortran

NOTE: x should be positive before calling this function
NOTE: y should be positive before calling this function
real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 1.0d0
end function

Java

x = Math.abs(x);
y = Math.abs(y);
public static double code(double x, double y) {
	return 1.0;
}

Python

x = abs(x)
y = abs(y)
def code(x, y):
	return 1.0

Julia

x = abs(x)
y = abs(y)
function code(x, y)
	return 1.0
end

MATLAB

x = abs(x)
y = abs(y)
function tmp = code(x, y)
	tmp = 1.0;
end

Wolfram

NOTE: x should be positive before calling this function
NOTE: y should be positive before calling this function
code[x_, y_] := 1.0

Derivation

1. Initial program 42.5%

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

2. Taylor expanded in x around 0 55.7%

   \[\leadsto \color{blue}{1} \]

3. Final simplification 55.7%

   \[\leadsto 1 \]

Developer target: 55.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{y \cdot 2}\\ t_1 := \sin t_0\\ \mathbf{if}\;y < -1.2303690911306994 \cdot 10^{+114}:\\ \;\;\;\;1\\ \mathbf{elif}\;y < -9.102852406811914 \cdot 10^{-222}:\\ \;\;\;\;\frac{t_1}{t_1 \cdot \log \left(e^{\cos t_0}\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ x (* y 2.0))) (t_1 (sin t_0)))
   (if (< y -1.2303690911306994e+114)
     1.0
     (if (< y -9.102852406811914e-222)
       (/ t_1 (* t_1 (log (exp (cos t_0)))))
       1.0))))

C

double code(double x, double y) {
	double t_0 = x / (y * 2.0);
	double t_1 = sin(t_0);
	double tmp;
	if (y < -1.2303690911306994e+114) {
		tmp = 1.0;
	} else if (y < -9.102852406811914e-222) {
		tmp = t_1 / (t_1 * log(exp(cos(t_0))));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = x / (y * 2.0d0)
    t_1 = sin(t_0)
    if (y < (-1.2303690911306994d+114)) then
        tmp = 1.0d0
    else if (y < (-9.102852406811914d-222)) then
        tmp = t_1 / (t_1 * log(exp(cos(t_0))))
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = x / (y * 2.0);
	double t_1 = Math.sin(t_0);
	double tmp;
	if (y < -1.2303690911306994e+114) {
		tmp = 1.0;
	} else if (y < -9.102852406811914e-222) {
		tmp = t_1 / (t_1 * Math.log(Math.exp(Math.cos(t_0))));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x / (y * 2.0)
	t_1 = math.sin(t_0)
	tmp = 0
	if y < -1.2303690911306994e+114:
		tmp = 1.0
	elif y < -9.102852406811914e-222:
		tmp = t_1 / (t_1 * math.log(math.exp(math.cos(t_0))))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(x / Float64(y * 2.0))
	t_1 = sin(t_0)
	tmp = 0.0
	if (y < -1.2303690911306994e+114)
		tmp = 1.0;
	elseif (y < -9.102852406811914e-222)
		tmp = Float64(t_1 / Float64(t_1 * log(exp(cos(t_0)))));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = x / (y * 2.0);
	t_1 = sin(t_0);
	tmp = 0.0;
	if (y < -1.2303690911306994e+114)
		tmp = 1.0;
	elseif (y < -9.102852406811914e-222)
		tmp = t_1 / (t_1 * log(exp(cos(t_0))));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(x / N[(y * 2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[Sin[t$95$0], $MachinePrecision]}, If[Less[y, -1.2303690911306994e+114], 1.0, If[Less[y, -9.102852406811914e-222], N[(t$95$1 / N[(t$95$1 * N[Log[N[Exp[N[Cos[t$95$0], $MachinePrecision]], $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]]]

Reproduce

herbie shell --seed 2023271 
(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)))))