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

Percentage Accurate: 44.7% → 57.3%

Time: 20.5s

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: 44.7% 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: 57.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} x = |x|\\ y = |y|\\ \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y \cdot 2} \leq 10^{+51}:\\ \;\;\;\;\frac{1}{\cos \left(\frac{{\left(\frac{x}{y}\right)}^{0.16666666666666666} \cdot \sqrt{\frac{x}{y}}}{\frac{2}{\sqrt[3]{\frac{x}{y}}}}\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

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)) 1e+51)
   (/
    1.0
    (cos
     (/
      (* (pow (/ x y) 0.16666666666666666) (sqrt (/ x y)))
      (/ 2.0 (cbrt (/ x y))))))
   1.0))

C

x = abs(x);
y = abs(y);
double code(double x, double y) {
	double tmp;
	if ((x / (y * 2.0)) <= 1e+51) {
		tmp = 1.0 / cos(((pow((x / y), 0.16666666666666666) * sqrt((x / y))) / (2.0 / cbrt((x / y)))));
	} 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)) <= 1e+51) {
		tmp = 1.0 / Math.cos(((Math.pow((x / y), 0.16666666666666666) * Math.sqrt((x / y))) / (2.0 / Math.cbrt((x / y)))));
	} 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)) <= 1e+51)
		tmp = Float64(1.0 / cos(Float64(Float64((Float64(x / y) ^ 0.16666666666666666) * sqrt(Float64(x / y))) / Float64(2.0 / cbrt(Float64(x / y))))));
	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], 1e+51], N[(1.0 / N[Cos[N[(N[(N[Power[N[(x / y), $MachinePrecision], 0.16666666666666666], $MachinePrecision] * N[Sqrt[N[(x / y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / N[(2.0 / N[Power[N[(x / y), $MachinePrecision], 1/3], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 1.0]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (*.f64 y 2)) < 1e51

   1. Initial program 50.9%

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

   2. Taylor expanded in x around inf 67.5%

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

      1. *-commutative 67.5%

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

      2. metadata-eval 67.5%

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

      3. div-inv 67.5%

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

      4. add-cube-cbrt 67.9%

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

      5. associate-/l* 67.7%

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

      6. pow2 67.7%

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

   4. Applied egg-rr 67.7%

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

      1. unpow2 67.7%

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

      2. add-sqr-sqrt 45.3%

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

      3. associate-*r* 45.4%

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

      4. add-sqr-sqrt 45.3%

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

      5. sqrt-prod 45.4%

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

      6. unpow2 45.4%

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

      7. sqrt-prod 45.3%

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

      8. unpow2 45.3%

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

      9. add-cube-cbrt 45.1%

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

      10. pow1/3 45.4%

          \[\leadsto \frac{1}{\cos \left(\frac{\sqrt{\frac{x}{y}} \cdot \sqrt{\color{blue}{{\left(\frac{x}{y}\right)}^{0.3333333333333333}}}}{\frac{2}{\sqrt[3]{\frac{x}{y}}}}\right)} \]

      11. sqrt-pow1 45.6%

          \[\leadsto \frac{1}{\cos \left(\frac{\sqrt{\frac{x}{y}} \cdot \color{blue}{{\left(\frac{x}{y}\right)}^{\left(\frac{0.3333333333333333}{2}\right)}}}{\frac{2}{\sqrt[3]{\frac{x}{y}}}}\right)} \]

      12. metadata-eval 45.6%

          \[\leadsto \frac{1}{\cos \left(\frac{\sqrt{\frac{x}{y}} \cdot {\left(\frac{x}{y}\right)}^{\color{blue}{0.16666666666666666}}}{\frac{2}{\sqrt[3]{\frac{x}{y}}}}\right)} \]

   6. Applied egg-rr 45.6%

      \[\leadsto \frac{1}{\cos \left(\frac{\color{blue}{\sqrt{\frac{x}{y}} \cdot {\left(\frac{x}{y}\right)}^{0.16666666666666666}}}{\frac{2}{\sqrt[3]{\frac{x}{y}}}}\right)} \]
   7. Step-by-step derivation

      1. *-commutative 45.6%

         \[\leadsto \frac{1}{\cos \left(\frac{\color{blue}{{\left(\frac{x}{y}\right)}^{0.16666666666666666} \cdot \sqrt{\frac{x}{y}}}}{\frac{2}{\sqrt[3]{\frac{x}{y}}}}\right)} \]

   8. Simplified 45.6%

      \[\leadsto \frac{1}{\cos \left(\frac{\color{blue}{{\left(\frac{x}{y}\right)}^{0.16666666666666666} \cdot \sqrt{\frac{x}{y}}}}{\frac{2}{\sqrt[3]{\frac{x}{y}}}}\right)} \]

   if 1e51 < (/.f64 x (*.f64 y 2))

   1. Initial program 9.6%

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

   2. Taylor expanded in x around 0 14.1%

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

4. Final simplification 39.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y \cdot 2} \leq 10^{+51}:\\ \;\;\;\;\frac{1}{\cos \left(\frac{{\left(\frac{x}{y}\right)}^{0.16666666666666666} \cdot \sqrt{\frac{x}{y}}}{\frac{2}{\sqrt[3]{\frac{x}{y}}}}\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 2: 55.5% 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 42.9%

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

2. Taylor expanded in x around 0 57.6%

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

3. Final simplification 57.6%

   \[\leadsto 1 \]

Developer target: 55.5% 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 2023274 
(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)))))