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

Percentage Accurate: 44.1% → 55.3%

Time: 23.4s

Alternatives: 2

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: 44.1% 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: 55.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} x = |x|\\ y = |y|\\ \\ {\left(\frac{1}{\sqrt[3]{\cos \left({\left(\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{\sqrt[3]{x \cdot 0.5}}{\sqrt[3]{y}}\right)\right)\right)}^{3}\right)}}\right)}^{3} \end{array} \]

FPCore

NOTE: x should be positive before calling this function
NOTE: y should be positive before calling this function
(FPCore (x y)
 :precision binary64
 (pow
  (/ 1.0 (cbrt (cos (pow (expm1 (log1p (/ (cbrt (* x 0.5)) (cbrt y)))) 3.0))))
  3.0))

C

x = abs(x);
y = abs(y);
double code(double x, double y) {
	return pow((1.0 / cbrt(cos(pow(expm1(log1p((cbrt((x * 0.5)) / cbrt(y)))), 3.0)))), 3.0);
}

Java

x = Math.abs(x);
y = Math.abs(y);
public static double code(double x, double y) {
	return Math.pow((1.0 / Math.cbrt(Math.cos(Math.pow(Math.expm1(Math.log1p((Math.cbrt((x * 0.5)) / Math.cbrt(y)))), 3.0)))), 3.0);
}

Julia

x = abs(x)
y = abs(y)
function code(x, y)
	return Float64(1.0 / cbrt(cos((expm1(log1p(Float64(cbrt(Float64(x * 0.5)) / cbrt(y)))) ^ 3.0)))) ^ 3.0
end

Wolfram

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

Derivation

1. Initial program 43.7%

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

   1. add-cube-cbrt 43.6%

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

   2. pow3 43.6%

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

3. Applied egg-rr 54.1%

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

   1. add-cube-cbrt 54.0%

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

   2. pow3 53.8%

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

5. Applied egg-rr 53.8%

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

   1. expm1-log1p-u 52.0%

      \[\leadsto {\left(\frac{1}{\sqrt[3]{\cos \left({\color{blue}{\left(\mathsf{expm1}\left(\mathsf{log1p}\left(\sqrt[3]{x \cdot \frac{0.5}{y}}\right)\right)\right)}}^{3}\right)}}\right)}^{3} \]

7. Applied egg-rr 52.0%

   \[\leadsto {\left(\frac{1}{\sqrt[3]{\cos \left({\color{blue}{\left(\mathsf{expm1}\left(\mathsf{log1p}\left(\sqrt[3]{x \cdot \frac{0.5}{y}}\right)\right)\right)}}^{3}\right)}}\right)}^{3} \]
8. Step-by-step derivation

   1. associate-*r/ 52.0%

      \[\leadsto {\left(\frac{1}{\sqrt[3]{\cos \left({\left(\mathsf{expm1}\left(\mathsf{log1p}\left(\sqrt[3]{\color{blue}{\frac{x \cdot 0.5}{y}}}\right)\right)\right)}^{3}\right)}}\right)}^{3} \]

   2. cbrt-div 52.1%

      \[\leadsto {\left(\frac{1}{\sqrt[3]{\cos \left({\left(\mathsf{expm1}\left(\mathsf{log1p}\left(\color{blue}{\frac{\sqrt[3]{x \cdot 0.5}}{\sqrt[3]{y}}}\right)\right)\right)}^{3}\right)}}\right)}^{3} \]

9. Applied egg-rr 52.1%

   \[\leadsto {\left(\frac{1}{\sqrt[3]{\cos \left({\left(\mathsf{expm1}\left(\mathsf{log1p}\left(\color{blue}{\frac{\sqrt[3]{x \cdot 0.5}}{\sqrt[3]{y}}}\right)\right)\right)}^{3}\right)}}\right)}^{3} \]

10. Final simplification 52.1%

    \[\leadsto {\left(\frac{1}{\sqrt[3]{\cos \left({\left(\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{\sqrt[3]{x \cdot 0.5}}{\sqrt[3]{y}}\right)\right)\right)}^{3}\right)}}\right)}^{3} \]

Alternative 2: 55.4% 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 43.7%

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

2. Taylor expanded in x around 0 54.7%

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

3. Final simplification 54.7%

   \[\leadsto 1 \]

Developer target: 55.4% 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 2023279 
(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)))))