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

Percentage Accurate: 44.4% → 55.1%

Time: 19.2s

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: 55.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ \begin{array}{l} t_0 := \sqrt{x\_m \cdot 0.5}\\ \frac{1}{\cos \left(t\_0 \cdot \frac{t\_0}{y}\right)} \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
(FPCore (x_m y)
 :precision binary64
 (let* ((t_0 (sqrt (* x_m 0.5)))) (/ 1.0 (cos (* t_0 (/ t_0 y))))))

C

x_m = fabs(x);
double code(double x_m, double y) {
	double t_0 = sqrt((x_m * 0.5));
	return 1.0 / cos((t_0 * (t_0 / y)));
}

Fortran

x_m = abs(x)
real(8) function code(x_m, y)
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8) :: t_0
    t_0 = sqrt((x_m * 0.5d0))
    code = 1.0d0 / cos((t_0 * (t_0 / y)))
end function

Java

x_m = Math.abs(x);
public static double code(double x_m, double y) {
	double t_0 = Math.sqrt((x_m * 0.5));
	return 1.0 / Math.cos((t_0 * (t_0 / y)));
}

Python

x_m = math.fabs(x)
def code(x_m, y):
	t_0 = math.sqrt((x_m * 0.5))
	return 1.0 / math.cos((t_0 * (t_0 / y)))

Julia

x_m = abs(x)
function code(x_m, y)
	t_0 = sqrt(Float64(x_m * 0.5))
	return Float64(1.0 / cos(Float64(t_0 * Float64(t_0 / y))))
end

MATLAB

x_m = abs(x);
function tmp = code(x_m, y)
	t_0 = sqrt((x_m * 0.5));
	tmp = 1.0 / cos((t_0 * (t_0 / y)));
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
code[x$95$m_, y_] := Block[{t$95$0 = N[Sqrt[N[(x$95$m * 0.5), $MachinePrecision]], $MachinePrecision]}, N[(1.0 / N[Cos[N[(t$95$0 * N[(t$95$0 / y), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Initial program 41.7%

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

3. Taylor expanded in x around inf 51.5%

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

   1. associate-*r/ 51.5%

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

5. Simplified 51.5%

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

6. Taylor expanded in x around inf 51.5%

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

   1. associate-*r/ 51.5%

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

   2. *-commutative 51.5%

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

   3. associate-*r/ 51.8%

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

8. Simplified 51.8%

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

   1. associate-*r/ 51.5%

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

   2. clear-num 51.3%

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

10. Applied egg-rr 51.3%

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

    1. clear-num 51.5%

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

    2. add-sqr-sqrt 27.7%

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

    3. *-un-lft-identity 27.7%

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

    4. times-frac 27.4%

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

12. Applied egg-rr 27.4%

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

13. Final simplification 27.4%

    \[\leadsto \frac{1}{\cos \left(\sqrt{x \cdot 0.5} \cdot \frac{\sqrt{x \cdot 0.5}}{y}\right)} \]
14. Add Preprocessing

Alternative 2: 55.1% accurate, 0.7× speedup

Math

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

FPCore

x_m = (fabs.f64 x)
(FPCore (x_m y)
 :precision binary64
 (cbrt (pow (/ 1.0 (cos (* x_m (/ 0.5 y)))) 3.0)))

C

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

Java

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

Julia

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

Wolfram

x_m = N[Abs[x], $MachinePrecision]
code[x$95$m_, y_] := N[Power[N[Power[N[(1.0 / N[Cos[N[(x$95$m * N[(0.5 / y), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 3.0], $MachinePrecision], 1/3], $MachinePrecision]

Derivation

1. Initial program 41.7%

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

3. Taylor expanded in x around inf 51.5%

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

   1. associate-*r/ 51.5%

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

5. Simplified 51.5%

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

   1. add-cbrt-cube 51.5%

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

   2. pow3 51.5%

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

   3. *-commutative 51.5%

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

   4. associate-*r/ 51.8%

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

7. Applied egg-rr 51.8%

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

8. Final simplification 51.8%

   \[\leadsto \sqrt[3]{{\left(\frac{1}{\cos \left(x \cdot \frac{0.5}{y}\right)}\right)}^{3}} \]
9. Add Preprocessing

Alternative 3: 55.1% accurate, 2.0× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ \frac{1}{\cos \left(x\_m \cdot \frac{0.5}{y}\right)} \end{array} \]

FPCore

x_m = (fabs.f64 x)
(FPCore (x_m y) :precision binary64 (/ 1.0 (cos (* x_m (/ 0.5 y)))))

C

x_m = fabs(x);
double code(double x_m, double y) {
	return 1.0 / cos((x_m * (0.5 / y)));
}

Fortran

x_m = abs(x)
real(8) function code(x_m, y)
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    code = 1.0d0 / cos((x_m * (0.5d0 / y)))
end function

Java

x_m = Math.abs(x);
public static double code(double x_m, double y) {
	return 1.0 / Math.cos((x_m * (0.5 / y)));
}

Python

x_m = math.fabs(x)
def code(x_m, y):
	return 1.0 / math.cos((x_m * (0.5 / y)))

Julia

x_m = abs(x)
function code(x_m, y)
	return Float64(1.0 / cos(Float64(x_m * Float64(0.5 / y))))
end

MATLAB

x_m = abs(x);
function tmp = code(x_m, y)
	tmp = 1.0 / cos((x_m * (0.5 / y)));
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
code[x$95$m_, y_] := N[(1.0 / N[Cos[N[(x$95$m * N[(0.5 / y), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 41.7%

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

3. Taylor expanded in x around inf 51.5%

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

   1. associate-*r/ 51.5%

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

5. Simplified 51.5%

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

6. Taylor expanded in x around inf 51.5%

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

   1. associate-*r/ 51.5%

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

   2. *-commutative 51.5%

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

   3. associate-*r/ 51.8%

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

8. Simplified 51.8%

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

9. Final simplification 51.8%

   \[\leadsto \frac{1}{\cos \left(x \cdot \frac{0.5}{y}\right)} \]
10. Add Preprocessing

Alternative 4: 55.2% accurate, 211.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

x_m = N[Abs[x], $MachinePrecision]
code[x$95$m_, y_] := 1.0

Derivation

1. Initial program 41.7%

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

3. Taylor expanded in x around 0 51.2%

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

4. Final simplification 51.2%

   \[\leadsto 1 \]
5. Add Preprocessing

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 2024033 
(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)))))