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

Percentage Accurate: 44.4% → 56.7%

Time: 15.5s

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: 44.4% 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: 56.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{y \cdot 2}\\ \mathbf{if}\;\frac{\tan t_0}{\sin t_0} \leq 5:\\ \;\;\;\;\frac{1}{\cos \left({\left(\frac{1}{\sqrt[3]{\frac{y}{x}}}\right)}^{2} \cdot \left(\sqrt[3]{\frac{x}{y}} \cdot 0.5\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ x (* y 2.0))))
   (if (<= (/ (tan t_0) (sin t_0)) 5.0)
     (/ 1.0 (cos (* (pow (/ 1.0 (cbrt (/ y x))) 2.0) (* (cbrt (/ x y)) 0.5))))
     1.0)))

C

double code(double x, double y) {
	double t_0 = x / (y * 2.0);
	double tmp;
	if ((tan(t_0) / sin(t_0)) <= 5.0) {
		tmp = 1.0 / cos((pow((1.0 / cbrt((y / x))), 2.0) * (cbrt((x / y)) * 0.5)));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Java

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)) <= 5.0) {
		tmp = 1.0 / Math.cos((Math.pow((1.0 / Math.cbrt((y / x))), 2.0) * (Math.cbrt((x / y)) * 0.5)));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Julia

function code(x, y)
	t_0 = Float64(x / Float64(y * 2.0))
	tmp = 0.0
	if (Float64(tan(t_0) / sin(t_0)) <= 5.0)
		tmp = Float64(1.0 / cos(Float64((Float64(1.0 / cbrt(Float64(y / x))) ^ 2.0) * Float64(cbrt(Float64(x / y)) * 0.5))));
	else
		tmp = 1.0;
	end
	return tmp
end

Wolfram

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], 5.0], N[(1.0 / N[Cos[N[(N[Power[N[(1.0 / N[Power[N[(y / x), $MachinePrecision], 1/3], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision] * N[(N[Power[N[(x / y), $MachinePrecision], 1/3], $MachinePrecision] * 0.5), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (tan.f64 (/.f64 x (*.f64 y 2))) (sin.f64 (/.f64 x (*.f64 y 2)))) < 5

   1. Initial program 61.5%

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

   2. Taylor expanded in x around inf 61.4%

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

      1. clear-num 61.3%

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

      2. un-div-inv 61.5%

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

   4. Applied egg-rr 61.5%

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

      1. div-inv 61.3%

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

      2. clear-num 61.4%

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

      3. *-commutative 61.4%

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

      4. add-cbrt-cube 58.5%

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

      5. associate-/r/ 58.1%

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

      6. cbrt-prod 59.1%

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

      7. associate-*l* 59.1%

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

      8. associate-/r/ 59.5%

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

      9. cbrt-prod 60.4%

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

      10. pow2 60.4%

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

   6. Applied egg-rr 60.4%

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

      1. clear-num 60.5%

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

      2. cbrt-div 61.8%

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

      3. metadata-eval 61.8%

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

   8. Applied egg-rr 61.8%

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

   if 5 < (/.f64 (tan.f64 (/.f64 x (*.f64 y 2))) (sin.f64 (/.f64 x (*.f64 y 2))))

   1. Initial program 1.5%

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

   2. Taylor expanded in x around 0 46.7%

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

4. Final simplification 57.7%

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

Alternative 2: 56.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{y \cdot 2}\\ \mathbf{if}\;\frac{\tan t_0}{\sin t_0} \leq 1.16:\\ \;\;\;\;\frac{1}{\cos \left({\left(\sqrt[3]{x \cdot 0.5} \cdot \sqrt[3]{\frac{1}{y}}\right)}^{3}\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ x (* y 2.0))))
   (if (<= (/ (tan t_0) (sin t_0)) 1.16)
     (/ 1.0 (cos (pow (* (cbrt (* x 0.5)) (cbrt (/ 1.0 y))) 3.0)))
     1.0)))

C

double code(double x, double y) {
	double t_0 = x / (y * 2.0);
	double tmp;
	if ((tan(t_0) / sin(t_0)) <= 1.16) {
		tmp = 1.0 / cos(pow((cbrt((x * 0.5)) * cbrt((1.0 / y))), 3.0));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Java

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)) <= 1.16) {
		tmp = 1.0 / Math.cos(Math.pow((Math.cbrt((x * 0.5)) * Math.cbrt((1.0 / y))), 3.0));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Julia

function code(x, y)
	t_0 = Float64(x / Float64(y * 2.0))
	tmp = 0.0
	if (Float64(tan(t_0) / sin(t_0)) <= 1.16)
		tmp = Float64(1.0 / cos((Float64(cbrt(Float64(x * 0.5)) * cbrt(Float64(1.0 / y))) ^ 3.0)));
	else
		tmp = 1.0;
	end
	return tmp
end

Wolfram

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], 1.16], N[(1.0 / N[Cos[N[Power[N[(N[Power[N[(x * 0.5), $MachinePrecision], 1/3], $MachinePrecision] * N[Power[N[(1.0 / y), $MachinePrecision], 1/3], $MachinePrecision]), $MachinePrecision], 3.0], $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (tan.f64 (/.f64 x (*.f64 y 2))) (sin.f64 (/.f64 x (*.f64 y 2)))) < 1.15999999999999992

   1. Initial program 69.5%

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

   2. Taylor expanded in x around inf 69.4%

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

      1. clear-num 69.5%

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

      2. un-div-inv 69.8%

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

   4. Applied egg-rr 69.8%

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

      1. associate-/l* 69.5%

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

      2. *-commutative 69.5%

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

      3. associate-/l* 69.5%

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

      4. div-inv 69.5%

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

      5. metadata-eval 69.5%

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

      6. add-cube-cbrt 69.9%

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

      7. pow3 69.7%

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

      8. *-commutative 69.7%

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

      9. associate-/r* 69.7%

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

   6. Applied egg-rr 69.7%

      \[\leadsto \frac{1}{\cos \color{blue}{\left({\left(\sqrt[3]{\frac{\frac{x}{2}}{y}}\right)}^{3}\right)}} \]
   7. Step-by-step derivation

      1. div-inv 69.6%

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

      2. cbrt-prod 69.9%

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

      3. div-inv 69.9%

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

      4. metadata-eval 69.9%

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

   8. Applied egg-rr 69.9%

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

   if 1.15999999999999992 < (/.f64 (tan.f64 (/.f64 x (*.f64 y 2))) (sin.f64 (/.f64 x (*.f64 y 2))))

   1. Initial program 5.1%

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

   2. Taylor expanded in x around 0 37.3%

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

4. Final simplification 57.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\tan \left(\frac{x}{y \cdot 2}\right)}{\sin \left(\frac{x}{y \cdot 2}\right)} \leq 1.16:\\ \;\;\;\;\frac{1}{\cos \left({\left(\sqrt[3]{x \cdot 0.5} \cdot \sqrt[3]{\frac{1}{y}}\right)}^{3}\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 3: 56.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{y \cdot 2}\\ \mathbf{if}\;\frac{\tan t_0}{\sin t_0} \leq 5:\\ \;\;\;\;\frac{1}{\cos \left(\frac{0.5}{\frac{y}{x}}\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ x (* y 2.0))))
   (if (<= (/ (tan t_0) (sin t_0)) 5.0) (/ 1.0 (cos (/ 0.5 (/ y x)))) 1.0)))

C

double code(double x, double y) {
	double t_0 = x / (y * 2.0);
	double tmp;
	if ((tan(t_0) / sin(t_0)) <= 5.0) {
		tmp = 1.0 / cos((0.5 / (y / x)));
	} 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) :: tmp
    t_0 = x / (y * 2.0d0)
    if ((tan(t_0) / sin(t_0)) <= 5.0d0) then
        tmp = 1.0d0 / cos((0.5d0 / (y / x)))
    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 tmp;
	if ((Math.tan(t_0) / Math.sin(t_0)) <= 5.0) {
		tmp = 1.0 / Math.cos((0.5 / (y / x)));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x / (y * 2.0)
	tmp = 0
	if (math.tan(t_0) / math.sin(t_0)) <= 5.0:
		tmp = 1.0 / math.cos((0.5 / (y / x)))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(x / Float64(y * 2.0))
	tmp = 0.0
	if (Float64(tan(t_0) / sin(t_0)) <= 5.0)
		tmp = Float64(1.0 / cos(Float64(0.5 / Float64(y / x))));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = x / (y * 2.0);
	tmp = 0.0;
	if ((tan(t_0) / sin(t_0)) <= 5.0)
		tmp = 1.0 / cos((0.5 / (y / x)));
	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]}, If[LessEqual[N[(N[Tan[t$95$0], $MachinePrecision] / N[Sin[t$95$0], $MachinePrecision]), $MachinePrecision], 5.0], N[(1.0 / N[Cos[N[(0.5 / N[(y / x), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (tan.f64 (/.f64 x (*.f64 y 2))) (sin.f64 (/.f64 x (*.f64 y 2)))) < 5

   1. Initial program 61.5%

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

   2. Taylor expanded in x around inf 61.4%

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

      1. clear-num 61.3%

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

      2. un-div-inv 61.5%

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

   4. Applied egg-rr 61.5%

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

   if 5 < (/.f64 (tan.f64 (/.f64 x (*.f64 y 2))) (sin.f64 (/.f64 x (*.f64 y 2))))

   1. Initial program 1.5%

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

   2. Taylor expanded in x around 0 46.7%

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

4. Final simplification 57.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\tan \left(\frac{x}{y \cdot 2}\right)}{\sin \left(\frac{x}{y \cdot 2}\right)} \leq 5:\\ \;\;\;\;\frac{1}{\cos \left(\frac{0.5}{\frac{y}{x}}\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 4: 55.1% accurate, 211.0× speedup

Math

\[\begin{array}{l} \\ 1 \end{array} \]

FPCore

(FPCore (x y) :precision binary64 1.0)

C

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

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 1.0d0
end function

Java

public static double code(double x, double y) {
	return 1.0;
}

Python

def code(x, y):
	return 1.0

Julia

function code(x, y)
	return 1.0
end

MATLAB

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

Wolfram

code[x_, y_] := 1.0

Derivation

1. Initial program 45.1%

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

2. Taylor expanded in x around 0 55.7%

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

3. Final simplification 55.7%

   \[\leadsto 1 \]

Developer target: 54.6% 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 2023185 
(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)))))