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

Percentage Accurate: 44.4% → 56.1%

Time: 18.5s

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: 44.4% 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: 56.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \frac{1}{e^{\mathsf{fma}\left({\left(\frac{x}{y}\right)}^{2}, -0.0625, \log 2\right)} + -1} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (/ 1.0 (+ (exp (fma (pow (/ x y) 2.0) -0.0625 (log 2.0))) -1.0)))

C

double code(double x, double y) {
	return 1.0 / (exp(fma(pow((x / y), 2.0), -0.0625, log(2.0))) + -1.0);
}

Julia

function code(x, y)
	return Float64(1.0 / Float64(exp(fma((Float64(x / y) ^ 2.0), -0.0625, log(2.0))) + -1.0))
end

Wolfram

code[x_, y_] := N[(1.0 / N[(N[Exp[N[(N[Power[N[(x / y), $MachinePrecision], 2.0], $MachinePrecision] * -0.0625 + N[Log[2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 47.9%

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

3. Taylor expanded in x around inf 57.9%

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

   1. associate-*r/ 58.0%

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

5. Simplified 58.0%

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

   1. *-commutative 58.0%

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

   2. associate-*r/ 58.2%

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

   3. expm1-log1p-u 58.2%

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

   4. expm1-udef 58.2%

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

   5. *-commutative 58.2%

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

   6. associate-/r/ 58.1%

      \[\leadsto \frac{1}{e^{\mathsf{log1p}\left(\cos \color{blue}{\left(\frac{0.5}{\frac{y}{x}}\right)}\right)} - 1} \]

   7. div-inv 57.9%

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

   8. clear-num 58.0%

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

7. Applied egg-rr 58.0%

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

8. Taylor expanded in x around 0 50.4%

   \[\leadsto \frac{1}{e^{\color{blue}{\log 2 + -0.0625 \cdot \frac{{x}^{2}}{{y}^{2}}}} - 1} \]
9. Step-by-step derivation

   1. +-commutative 50.4%

      \[\leadsto \frac{1}{e^{\color{blue}{-0.0625 \cdot \frac{{x}^{2}}{{y}^{2}} + \log 2}} - 1} \]

   2. *-commutative 50.4%

      \[\leadsto \frac{1}{e^{\color{blue}{\frac{{x}^{2}}{{y}^{2}} \cdot -0.0625} + \log 2} - 1} \]

   3. fma-def 50.4%

      \[\leadsto \frac{1}{e^{\color{blue}{\mathsf{fma}\left(\frac{{x}^{2}}{{y}^{2}}, -0.0625, \log 2\right)}} - 1} \]

   4. unpow2 50.4%

      \[\leadsto \frac{1}{e^{\mathsf{fma}\left(\frac{\color{blue}{x \cdot x}}{{y}^{2}}, -0.0625, \log 2\right)} - 1} \]

   5. unpow2 50.4%

      \[\leadsto \frac{1}{e^{\mathsf{fma}\left(\frac{x \cdot x}{\color{blue}{y \cdot y}}, -0.0625, \log 2\right)} - 1} \]

   6. times-frac 59.3%

      \[\leadsto \frac{1}{e^{\mathsf{fma}\left(\color{blue}{\frac{x}{y} \cdot \frac{x}{y}}, -0.0625, \log 2\right)} - 1} \]

   7. unpow2 59.3%

      \[\leadsto \frac{1}{e^{\mathsf{fma}\left(\color{blue}{{\left(\frac{x}{y}\right)}^{2}}, -0.0625, \log 2\right)} - 1} \]

10. Simplified 59.3%

    \[\leadsto \frac{1}{e^{\color{blue}{\mathsf{fma}\left({\left(\frac{x}{y}\right)}^{2}, -0.0625, \log 2\right)}} - 1} \]

11. Final simplification 59.3%

    \[\leadsto \frac{1}{e^{\mathsf{fma}\left({\left(\frac{x}{y}\right)}^{2}, -0.0625, \log 2\right)} + -1} \]
12. Add Preprocessing

Alternative 2: 55.8% 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 47.9%

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

3. Taylor expanded in x around 0 58.7%

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

4. Final simplification 58.7%

   \[\leadsto 1 \]
5. Add Preprocessing

Developer target: 55.2% 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 2024029 
(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)))))