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

Percentage Accurate: 44.0% → 56.6%

Time: 11.8s

Alternatives: 5

Speedup: 89.2×

Specification

Math

\[\begin{array}{l} t_0 := \frac{x}{y \cdot 2}\\ \frac{\tan t\_0}{\sin t\_0} \end{array} \]

FPCore

(FPCore (x y)
  :precision binary64
  :pre TRUE
  (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)
use fmin_fmax_functions
    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]]

ReFlow

f(x, y):
	x in [-inf, +inf],
	y in [-inf, +inf]
code: THEORY
BEGIN
f(x, y: real): real =
	LET t_0 = (x / (y * (2))) IN
	(tan(t_0)) / (sin(t_0))
END code

Initial Program: 44.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} t_0 := \frac{x}{y \cdot 2}\\ \frac{\tan t\_0}{\sin t\_0} \end{array} \]

FPCore

(FPCore (x y)
  :precision binary64
  :pre TRUE
  (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)
use fmin_fmax_functions
    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]]

ReFlow

f(x, y):
	x in [-inf, +inf],
	y in [-inf, +inf]
code: THEORY
BEGIN
f(x, y: real): real =
	LET t_0 = (x / (y * (2))) IN
	(tan(t_0)) / (sin(t_0))
END code

Alternative 1: 56.6% accurate, 1.5× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\frac{\left|x\right|}{\left|y\right| \cdot 2} \leq 2 \cdot 10^{+32}:\\ \;\;\;\;\frac{1}{\cos \left(\left|x\right| \cdot \frac{0.5}{\left|y\right|}\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

FPCore

(FPCore (x y)
  :precision binary64
  :pre TRUE
  (if (<= (/ (fabs x) (* (fabs y) 2.0)) 2e+32)
  (/ 1.0 (cos (* (fabs x) (/ 0.5 (fabs y)))))
  1.0))

C

double code(double x, double y) {
	double tmp;
	if ((fabs(x) / (fabs(y) * 2.0)) <= 2e+32) {
		tmp = 1.0 / cos((fabs(x) * (0.5 / fabs(y))));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((abs(x) / (abs(y) * 2.0d0)) <= 2d+32) then
        tmp = 1.0d0 / cos((abs(x) * (0.5d0 / abs(y))))
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((Math.abs(x) / (Math.abs(y) * 2.0)) <= 2e+32) {
		tmp = 1.0 / Math.cos((Math.abs(x) * (0.5 / Math.abs(y))));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (math.fabs(x) / (math.fabs(y) * 2.0)) <= 2e+32:
		tmp = 1.0 / math.cos((math.fabs(x) * (0.5 / math.fabs(y))))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (Float64(abs(x) / Float64(abs(y) * 2.0)) <= 2e+32)
		tmp = Float64(1.0 / cos(Float64(abs(x) * Float64(0.5 / abs(y)))));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((abs(x) / (abs(y) * 2.0)) <= 2e+32)
		tmp = 1.0 / cos((abs(x) * (0.5 / abs(y))));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[N[(N[Abs[x], $MachinePrecision] / N[(N[Abs[y], $MachinePrecision] * 2.0), $MachinePrecision]), $MachinePrecision], 2e+32], N[(1.0 / N[Cos[N[(N[Abs[x], $MachinePrecision] * N[(0.5 / N[Abs[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 1.0]

ReFlow

f(x, y):
	x in [-inf, +inf],
	y in [-inf, +inf]
code: THEORY
BEGIN
f(x, y: real): real =
	LET tmp = IF (((abs(x)) / ((abs(y)) * (2))) <= (200000000000000010732324408786944)) THEN ((1) / (cos(((abs(x)) * ((5e-1) / (abs(y))))))) ELSE (1) ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (*.f64 y #s(literal 2 binary64))) < 2.0000000000000001e32

   1. Initial program 44.0%

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

   3. Applied rewrites 54.7%

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

   5. Applied rewrites 54.8%

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

   if 2.0000000000000001e32 < (/.f64 x (*.f64 y #s(literal 2 binary64)))

   1. Initial program 44.0%

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

   2. Taylor expanded in x around 0

      \[\leadsto 1 \]
   3. Step-by-step derivation

   4. Applied rewrites 54.8%

      \[\leadsto 1 \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 2: 56.6% accurate, 1.5× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\frac{\left|x\right|}{\left|y\right| \cdot 2} \leq 10^{+31}:\\ \;\;\;\;\frac{1}{\cos \left(\frac{\left|x\right|}{\left|y\right| + \left|y\right|}\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

FPCore

(FPCore (x y)
  :precision binary64
  :pre TRUE
  (if (<= (/ (fabs x) (* (fabs y) 2.0)) 1e+31)
  (/ 1.0 (cos (/ (fabs x) (+ (fabs y) (fabs y)))))
  1.0))

C

double code(double x, double y) {
	double tmp;
	if ((fabs(x) / (fabs(y) * 2.0)) <= 1e+31) {
		tmp = 1.0 / cos((fabs(x) / (fabs(y) + fabs(y))));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((abs(x) / (abs(y) * 2.0d0)) <= 1d+31) then
        tmp = 1.0d0 / cos((abs(x) / (abs(y) + abs(y))))
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((Math.abs(x) / (Math.abs(y) * 2.0)) <= 1e+31) {
		tmp = 1.0 / Math.cos((Math.abs(x) / (Math.abs(y) + Math.abs(y))));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (math.fabs(x) / (math.fabs(y) * 2.0)) <= 1e+31:
		tmp = 1.0 / math.cos((math.fabs(x) / (math.fabs(y) + math.fabs(y))))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (Float64(abs(x) / Float64(abs(y) * 2.0)) <= 1e+31)
		tmp = Float64(1.0 / cos(Float64(abs(x) / Float64(abs(y) + abs(y)))));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((abs(x) / (abs(y) * 2.0)) <= 1e+31)
		tmp = 1.0 / cos((abs(x) / (abs(y) + abs(y))));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[N[(N[Abs[x], $MachinePrecision] / N[(N[Abs[y], $MachinePrecision] * 2.0), $MachinePrecision]), $MachinePrecision], 1e+31], N[(1.0 / N[Cos[N[(N[Abs[x], $MachinePrecision] / N[(N[Abs[y], $MachinePrecision] + N[Abs[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 1.0]

ReFlow

f(x, y):
	x in [-inf, +inf],
	y in [-inf, +inf]
code: THEORY
BEGIN
f(x, y: real): real =
	LET tmp = IF (((abs(x)) / ((abs(y)) * (2))) <= (9999999999999999635896294965248)) THEN ((1) / (cos(((abs(x)) / ((abs(y)) + (abs(y))))))) ELSE (1) ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (*.f64 y #s(literal 2 binary64))) < 9.9999999999999996e30

   1. Initial program 44.0%

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

   3. Applied rewrites 54.7%

      \[\leadsto \frac{1}{\cos \left(\frac{x}{y + y}\right)} \]

   if 9.9999999999999996e30 < (/.f64 x (*.f64 y #s(literal 2 binary64)))

   1. Initial program 44.0%

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

   2. Taylor expanded in x around 0

      \[\leadsto 1 \]
   3. Step-by-step derivation

   4. Applied rewrites 54.8%

      \[\leadsto 1 \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 54.8% accurate, 1.7× speedup

Math

\[\frac{1}{\sin \left(0.5 \cdot \left(\pi - \frac{1}{\frac{\left|y\right|}{\left|x\right|}}\right)\right)} \]

FPCore

(FPCore (x y)
  :precision binary64
  :pre TRUE
  (/ 1.0 (sin (* 0.5 (- PI (/ 1.0 (/ (fabs y) (fabs x))))))))

C

double code(double x, double y) {
	return 1.0 / sin((0.5 * (((double) M_PI) - (1.0 / (fabs(y) / fabs(x))))));
}

Java

public static double code(double x, double y) {
	return 1.0 / Math.sin((0.5 * (Math.PI - (1.0 / (Math.abs(y) / Math.abs(x))))));
}

Python

def code(x, y):
	return 1.0 / math.sin((0.5 * (math.pi - (1.0 / (math.fabs(y) / math.fabs(x))))))

Julia

function code(x, y)
	return Float64(1.0 / sin(Float64(0.5 * Float64(pi - Float64(1.0 / Float64(abs(y) / abs(x)))))))
end

MATLAB

function tmp = code(x, y)
	tmp = 1.0 / sin((0.5 * (pi - (1.0 / (abs(y) / abs(x))))));
end

Wolfram

code[x_, y_] := N[(1.0 / N[Sin[N[(0.5 * N[(Pi - N[(1.0 / N[(N[Abs[y], $MachinePrecision] / N[Abs[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

ReFlow

f(x, y):
	x in [-inf, +inf],
	y in [-inf, +inf]
code: THEORY
BEGIN
f(x, y: real): real =
	(1) / (sin(((5e-1) * ((4 * atan(1)) - ((1) / ((abs(y)) / (abs(x))))))))
END code

Derivation

1. Initial program 44.0%

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

3. Applied rewrites 54.7%

   \[\leadsto \frac{1}{\cos \left(\frac{x}{y + y}\right)} \]

5. Applied rewrites 54.7%

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

7. Applied rewrites 54.7%

   \[\leadsto \frac{1}{\sin \left(0.5 \cdot \left(\pi - \frac{1}{\frac{y}{x}}\right)\right)} \]
8. Add Preprocessing

Alternative 4: 54.8% accurate, 1.8× speedup

Math

\[\frac{1}{\sin \left(0.5 \cdot \left(\pi - \frac{\left|x\right|}{\left|y\right|}\right)\right)} \]

FPCore

(FPCore (x y)
  :precision binary64
  :pre TRUE
  (/ 1.0 (sin (* 0.5 (- PI (/ (fabs x) (fabs y)))))))

C

double code(double x, double y) {
	return 1.0 / sin((0.5 * (((double) M_PI) - (fabs(x) / fabs(y)))));
}

Java

public static double code(double x, double y) {
	return 1.0 / Math.sin((0.5 * (Math.PI - (Math.abs(x) / Math.abs(y)))));
}

Python

def code(x, y):
	return 1.0 / math.sin((0.5 * (math.pi - (math.fabs(x) / math.fabs(y)))))

Julia

function code(x, y)
	return Float64(1.0 / sin(Float64(0.5 * Float64(pi - Float64(abs(x) / abs(y))))))
end

MATLAB

function tmp = code(x, y)
	tmp = 1.0 / sin((0.5 * (pi - (abs(x) / abs(y)))));
end

Wolfram

code[x_, y_] := N[(1.0 / N[Sin[N[(0.5 * N[(Pi - N[(N[Abs[x], $MachinePrecision] / N[Abs[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

ReFlow

f(x, y):
	x in [-inf, +inf],
	y in [-inf, +inf]
code: THEORY
BEGIN
f(x, y: real): real =
	(1) / (sin(((5e-1) * ((4 * atan(1)) - ((abs(x)) / (abs(y)))))))
END code

Derivation

1. Initial program 44.0%

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

3. Applied rewrites 54.7%

   \[\leadsto \frac{1}{\cos \left(\frac{x}{y + y}\right)} \]

5. Applied rewrites 54.7%

   \[\leadsto \frac{1}{\sin \left(0.5 \cdot \left(\pi - \frac{x}{y}\right)\right)} \]
6. Add Preprocessing

Alternative 5: 54.7% accurate, 89.2× speedup

Math

\[1 \]

FPCore

(FPCore (x y)
  :precision binary64
  :pre TRUE
  1.0)

C

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

Fortran

real(8) function code(x, y)
use fmin_fmax_functions
    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

ReFlow

f(x, y):
	x in [-inf, +inf],
	y in [-inf, +inf]
code: THEORY
BEGIN
f(x, y: real): real =
	1
END code

Derivation

1. Initial program 44.0%

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

2. Taylor expanded in x around 0

   \[\leadsto 1 \]
3. Step-by-step derivation

4. Applied rewrites 54.8%

   \[\leadsto 1 \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2026092 
(FPCore (x y)
  :name "Diagrams.TwoD.Layout.CirclePacking:approxRadius from diagrams-contrib-1.3.0.5"
  :precision binary64
  (/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0)))))