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

Percentage Accurate: 44.4% → 56.8%

Time: 9.8s

Alternatives: 2

Speedup: 244.0×

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: 56.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ x_m = \left|x\right| \\ \begin{array}{l} \mathbf{if}\;\frac{x\_m}{2 \cdot y\_m} \leq 2 \cdot 10^{+73}:\\ \;\;\;\;\frac{-1}{\cos \left(\mathsf{fma}\left(-0.5, {\left({\left(\frac{x\_m}{y\_m}\right)}^{0.5}\right)}^{2}, \mathsf{PI}\left(\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

y_m = (fabs.f64 y)
x_m = (fabs.f64 x)
(FPCore (x_m y_m)
 :precision binary64
 (if (<= (/ x_m (* 2.0 y_m)) 2e+73)
   (/ -1.0 (cos (fma -0.5 (pow (pow (/ x_m y_m) 0.5) 2.0) (PI))))
   1.0))

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (*.f64 y #s(literal 2 binary64))) < 1.99999999999999997e73

   1. Initial program 53.2%

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

      1. lift-/.f64 N/A

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

      2. div-inv N/A

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

      3. lift-tan.f64 N/A

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

      4. tan-quot N/A

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

      5. lift-sin.f64 N/A

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

      6. associate-*l/ N/A

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

      7. frac-2neg N/A

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

      8. rgt-mult-inverse N/A

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

      9. metadata-eval N/A

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

      10. lower-/.f64 N/A

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

      11. cos-neg-rev N/A

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

      12. cos-+PI-rev N/A

          \[\leadsto \frac{-1}{\color{blue}{\cos \left(\left(\mathsf{neg}\left(\frac{x}{y \cdot 2}\right)\right) + \mathsf{PI}\left(\right)\right)}} \]

      13. lower-cos.f64 N/A

          \[\leadsto \frac{-1}{\color{blue}{\cos \left(\left(\mathsf{neg}\left(\frac{x}{y \cdot 2}\right)\right) + \mathsf{PI}\left(\right)\right)}} \]

   4. Applied rewrites 65.9%

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

      1. lift-/.f64 N/A

         \[\leadsto \frac{-1}{\cos \left(\mathsf{fma}\left(\frac{-1}{2}, \color{blue}{\frac{x}{y}}, \mathsf{PI}\left(\right)\right)\right)} \]

      2. clear-num N/A

         \[\leadsto \frac{-1}{\cos \left(\mathsf{fma}\left(\frac{-1}{2}, \color{blue}{\frac{1}{\frac{y}{x}}}, \mathsf{PI}\left(\right)\right)\right)} \]

      3. lower-/.f64 N/A

         \[\leadsto \frac{-1}{\cos \left(\mathsf{fma}\left(\frac{-1}{2}, \color{blue}{\frac{1}{\frac{y}{x}}}, \mathsf{PI}\left(\right)\right)\right)} \]

      4. lower-/.f64 65.9

         \[\leadsto \frac{-1}{\cos \left(\mathsf{fma}\left(-0.5, \frac{1}{\color{blue}{\frac{y}{x}}}, \mathsf{PI}\left(\right)\right)\right)} \]

   6. Applied rewrites 65.9%

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

      1. lift-/.f64 N/A

         \[\leadsto \frac{-1}{\cos \left(\mathsf{fma}\left(\frac{-1}{2}, \color{blue}{\frac{1}{\frac{y}{x}}}, \mathsf{PI}\left(\right)\right)\right)} \]

      2. inv-pow N/A

         \[\leadsto \frac{-1}{\cos \left(\mathsf{fma}\left(\frac{-1}{2}, \color{blue}{{\left(\frac{y}{x}\right)}^{-1}}, \mathsf{PI}\left(\right)\right)\right)} \]

      3. metadata-eval N/A

         \[\leadsto \frac{-1}{\cos \left(\mathsf{fma}\left(\frac{-1}{2}, {\left(\frac{y}{x}\right)}^{\color{blue}{\left(\frac{-1}{2} + \frac{-1}{2}\right)}}, \mathsf{PI}\left(\right)\right)\right)} \]

      4. pow-prod-up N/A

         \[\leadsto \frac{-1}{\cos \left(\mathsf{fma}\left(\frac{-1}{2}, \color{blue}{{\left(\frac{y}{x}\right)}^{\frac{-1}{2}} \cdot {\left(\frac{y}{x}\right)}^{\frac{-1}{2}}}, \mathsf{PI}\left(\right)\right)\right)} \]

      5. pow2 N/A

         \[\leadsto \frac{-1}{\cos \left(\mathsf{fma}\left(\frac{-1}{2}, \color{blue}{{\left({\left(\frac{y}{x}\right)}^{\frac{-1}{2}}\right)}^{2}}, \mathsf{PI}\left(\right)\right)\right)} \]

      6. lower-pow.f64 N/A

         \[\leadsto \frac{-1}{\cos \left(\mathsf{fma}\left(\frac{-1}{2}, \color{blue}{{\left({\left(\frac{y}{x}\right)}^{\frac{-1}{2}}\right)}^{2}}, \mathsf{PI}\left(\right)\right)\right)} \]

      7. remove-double-div N/A

         \[\leadsto \frac{-1}{\cos \left(\mathsf{fma}\left(\frac{-1}{2}, {\left({\color{blue}{\left(\frac{1}{\frac{1}{\frac{y}{x}}}\right)}}^{\frac{-1}{2}}\right)}^{2}, \mathsf{PI}\left(\right)\right)\right)} \]

      8. lift-/.f64 N/A

         \[\leadsto \frac{-1}{\cos \left(\mathsf{fma}\left(\frac{-1}{2}, {\left({\left(\frac{1}{\color{blue}{\frac{1}{\frac{y}{x}}}}\right)}^{\frac{-1}{2}}\right)}^{2}, \mathsf{PI}\left(\right)\right)\right)} \]

      9. inv-pow N/A

         \[\leadsto \frac{-1}{\cos \left(\mathsf{fma}\left(\frac{-1}{2}, {\left({\color{blue}{\left({\left(\frac{1}{\frac{y}{x}}\right)}^{-1}\right)}}^{\frac{-1}{2}}\right)}^{2}, \mathsf{PI}\left(\right)\right)\right)} \]

      10. pow-pow N/A

          \[\leadsto \frac{-1}{\cos \left(\mathsf{fma}\left(\frac{-1}{2}, {\color{blue}{\left({\left(\frac{1}{\frac{y}{x}}\right)}^{\left(-1 \cdot \frac{-1}{2}\right)}\right)}}^{2}, \mathsf{PI}\left(\right)\right)\right)} \]

      11. metadata-eval N/A

          \[\leadsto \frac{-1}{\cos \left(\mathsf{fma}\left(\frac{-1}{2}, {\left({\left(\frac{1}{\frac{y}{x}}\right)}^{\color{blue}{\frac{1}{2}}}\right)}^{2}, \mathsf{PI}\left(\right)\right)\right)} \]

      12. lower-pow.f64 40.2

          \[\leadsto \frac{-1}{\cos \left(\mathsf{fma}\left(-0.5, {\color{blue}{\left({\left(\frac{1}{\frac{y}{x}}\right)}^{0.5}\right)}}^{2}, \mathsf{PI}\left(\right)\right)\right)} \]

      13. lift-/.f64 N/A

          \[\leadsto \frac{-1}{\cos \left(\mathsf{fma}\left(\frac{-1}{2}, {\left({\color{blue}{\left(\frac{1}{\frac{y}{x}}\right)}}^{\frac{1}{2}}\right)}^{2}, \mathsf{PI}\left(\right)\right)\right)} \]

      14. lift-/.f64 N/A

          \[\leadsto \frac{-1}{\cos \left(\mathsf{fma}\left(\frac{-1}{2}, {\left({\left(\frac{1}{\color{blue}{\frac{y}{x}}}\right)}^{\frac{1}{2}}\right)}^{2}, \mathsf{PI}\left(\right)\right)\right)} \]

      15. clear-num-rev N/A

          \[\leadsto \frac{-1}{\cos \left(\mathsf{fma}\left(\frac{-1}{2}, {\left({\color{blue}{\left(\frac{x}{y}\right)}}^{\frac{1}{2}}\right)}^{2}, \mathsf{PI}\left(\right)\right)\right)} \]

      16. lift-/.f64 38.7

          \[\leadsto \frac{-1}{\cos \left(\mathsf{fma}\left(-0.5, {\left({\color{blue}{\left(\frac{x}{y}\right)}}^{0.5}\right)}^{2}, \mathsf{PI}\left(\right)\right)\right)} \]

   8. Applied rewrites 38.7%

      \[\leadsto \frac{-1}{\cos \left(\mathsf{fma}\left(-0.5, \color{blue}{{\left({\left(\frac{x}{y}\right)}^{0.5}\right)}^{2}}, \mathsf{PI}\left(\right)\right)\right)} \]

   if 1.99999999999999997e73 < (/.f64 x (*.f64 y #s(literal 2 binary64)))

   1. Initial program 6.7%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{1} \]
   4. Step-by-step derivation

   5. Applied rewrites 15.3%

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

4. Final simplification 34.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{2 \cdot y} \leq 2 \cdot 10^{+73}:\\ \;\;\;\;\frac{-1}{\cos \left(\mathsf{fma}\left(-0.5, {\left({\left(\frac{x}{y}\right)}^{0.5}\right)}^{2}, \mathsf{PI}\left(\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 55.1% accurate, 244.0× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ x_m = \left|x\right| \\ 1 \end{array} \]

FPCore

y_m = (fabs.f64 y)
x_m = (fabs.f64 x)
(FPCore (x_m y_m) :precision binary64 1.0)

C

y_m = fabs(y);
x_m = fabs(x);
double code(double x_m, double y_m) {
	return 1.0;
}

Fortran

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

Java

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

Python

y_m = math.fabs(y)
x_m = math.fabs(x)
def code(x_m, y_m):
	return 1.0

Julia

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

MATLAB

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

Wolfram

y_m = N[Abs[y], $MachinePrecision]
x_m = N[Abs[x], $MachinePrecision]
code[x$95$m_, y$95$m_] := 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. Add Preprocessing

3. Taylor expanded in x around 0

   \[\leadsto \color{blue}{1} \]
4. Step-by-step derivation

5. Applied rewrites 56.2%

   \[\leadsto \color{blue}{1} \]
6. Add Preprocessing

Developer Target 1: 55.1% 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 2024298 
(FPCore (x y)
  :name "Diagrams.TwoD.Layout.CirclePacking:approxRadius from diagrams-contrib-1.3.0.5"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< y -1230369091130699400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) 1 (if (< y -4551426203405957/500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (/ (sin (/ x (* y 2))) (* (sin (/ x (* y 2))) (log (exp (cos (/ x (* y 2))))))) 1)))

  (/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0)))))