Diagrams.TwoD.Arc:arcBetween from diagrams-lib-1.3.0.3

Percentage Accurate: 50.9% → 80.1%

Time: 5.6s

Alternatives: 4

Speedup: 3.2×

Specification

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(y \cdot 4\right) \cdot y\\ \frac{x \cdot x - t\_0}{x \cdot x + t\_0} \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* (* y 4.0) y))) (/ (- (* x x) t_0) (+ (* x x) t_0))))

C

double code(double x, double y) {
	double t_0 = (y * 4.0) * y;
	return ((x * x) - t_0) / ((x * x) + 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 = (y * 4.0d0) * y
    code = ((x * x) - t_0) / ((x * x) + t_0)
end function

Java

public static double code(double x, double y) {
	double t_0 = (y * 4.0) * y;
	return ((x * x) - t_0) / ((x * x) + t_0);
}

Python

def code(x, y):
	t_0 = (y * 4.0) * y
	return ((x * x) - t_0) / ((x * x) + t_0)

Julia

function code(x, y)
	t_0 = Float64(Float64(y * 4.0) * y)
	return Float64(Float64(Float64(x * x) - t_0) / Float64(Float64(x * x) + t_0))
end

MATLAB

function tmp = code(x, y)
	t_0 = (y * 4.0) * y;
	tmp = ((x * x) - t_0) / ((x * x) + t_0);
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(y * 4.0), $MachinePrecision] * y), $MachinePrecision]}, N[(N[(N[(x * x), $MachinePrecision] - t$95$0), $MachinePrecision] / N[(N[(x * x), $MachinePrecision] + t$95$0), $MachinePrecision]), $MachinePrecision]]

Initial Program: 50.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(y \cdot 4\right) \cdot y\\ \frac{x \cdot x - t\_0}{x \cdot x + t\_0} \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* (* y 4.0) y))) (/ (- (* x x) t_0) (+ (* x x) t_0))))

C

double code(double x, double y) {
	double t_0 = (y * 4.0) * y;
	return ((x * x) - t_0) / ((x * x) + 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 = (y * 4.0d0) * y
    code = ((x * x) - t_0) / ((x * x) + t_0)
end function

Java

public static double code(double x, double y) {
	double t_0 = (y * 4.0) * y;
	return ((x * x) - t_0) / ((x * x) + t_0);
}

Python

def code(x, y):
	t_0 = (y * 4.0) * y
	return ((x * x) - t_0) / ((x * x) + t_0)

Julia

function code(x, y)
	t_0 = Float64(Float64(y * 4.0) * y)
	return Float64(Float64(Float64(x * x) - t_0) / Float64(Float64(x * x) + t_0))
end

MATLAB

function tmp = code(x, y)
	t_0 = (y * 4.0) * y;
	tmp = ((x * x) - t_0) / ((x * x) + t_0);
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(y * 4.0), $MachinePrecision] * y), $MachinePrecision]}, N[(N[(N[(x * x), $MachinePrecision] - t$95$0), $MachinePrecision] / N[(N[(x * x), $MachinePrecision] + t$95$0), $MachinePrecision]), $MachinePrecision]]

Alternative 1: 80.1% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(y \cdot 4\right)\\ \mathbf{if}\;t\_0 \leq 5 \cdot 10^{-285}:\\ \;\;\;\;1\\ \mathbf{elif}\;t\_0 \leq 2 \cdot 10^{+152}:\\ \;\;\;\;{\left(\frac{\mathsf{fma}\left(4, y \cdot y, x \cdot x\right)}{\mathsf{fma}\left(y, y \cdot -4, x \cdot x\right)}\right)}^{-1}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* y (* y 4.0))))
   (if (<= t_0 5e-285)
     1.0
     (if (<= t_0 2e+152)
       (pow (/ (fma 4.0 (* y y) (* x x)) (fma y (* y -4.0) (* x x))) -1.0)
       -1.0))))

C

double code(double x, double y) {
	double t_0 = y * (y * 4.0);
	double tmp;
	if (t_0 <= 5e-285) {
		tmp = 1.0;
	} else if (t_0 <= 2e+152) {
		tmp = pow((fma(4.0, (y * y), (x * x)) / fma(y, (y * -4.0), (x * x))), -1.0);
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Julia

function code(x, y)
	t_0 = Float64(y * Float64(y * 4.0))
	tmp = 0.0
	if (t_0 <= 5e-285)
		tmp = 1.0;
	elseif (t_0 <= 2e+152)
		tmp = Float64(fma(4.0, Float64(y * y), Float64(x * x)) / fma(y, Float64(y * -4.0), Float64(x * x))) ^ -1.0;
	else
		tmp = -1.0;
	end
	return tmp
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(y * N[(y * 4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, 5e-285], 1.0, If[LessEqual[t$95$0, 2e+152], N[Power[N[(N[(4.0 * N[(y * y), $MachinePrecision] + N[(x * x), $MachinePrecision]), $MachinePrecision] / N[(y * N[(y * -4.0), $MachinePrecision] + N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], -1.0], $MachinePrecision], -1.0]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 y #s(literal 4 binary64)) y) < 5.00000000000000018e-285

   1. Initial program 54.3%

      \[\frac{x \cdot x - \left(y \cdot 4\right) \cdot y}{x \cdot x + \left(y \cdot 4\right) \cdot y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 92.2%

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

   if 5.00000000000000018e-285 < (*.f64 (*.f64 y #s(literal 4 binary64)) y) < 2.0000000000000001e152

   1. Initial program 74.7%

      \[\frac{x \cdot x - \left(y \cdot 4\right) \cdot y}{x \cdot x + \left(y \cdot 4\right) \cdot y} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. clear-num 74.7%

         \[\leadsto \color{blue}{\frac{1}{\frac{x \cdot x + \left(y \cdot 4\right) \cdot y}{x \cdot x - \left(y \cdot 4\right) \cdot y}}} \]

      2. inv-pow 74.7%

         \[\leadsto \color{blue}{{\left(\frac{x \cdot x + \left(y \cdot 4\right) \cdot y}{x \cdot x - \left(y \cdot 4\right) \cdot y}\right)}^{-1}} \]

      3. +-commutative 74.7%

         \[\leadsto {\left(\frac{\color{blue}{\left(y \cdot 4\right) \cdot y + x \cdot x}}{x \cdot x - \left(y \cdot 4\right) \cdot y}\right)}^{-1} \]

      4. *-commutative 74.7%

         \[\leadsto {\left(\frac{\color{blue}{\left(4 \cdot y\right)} \cdot y + x \cdot x}{x \cdot x - \left(y \cdot 4\right) \cdot y}\right)}^{-1} \]

      5. associate-*l* 74.7%

         \[\leadsto {\left(\frac{\color{blue}{4 \cdot \left(y \cdot y\right)} + x \cdot x}{x \cdot x - \left(y \cdot 4\right) \cdot y}\right)}^{-1} \]

      6. fma-define 74.7%

         \[\leadsto {\left(\frac{\color{blue}{\mathsf{fma}\left(4, y \cdot y, x \cdot x\right)}}{x \cdot x - \left(y \cdot 4\right) \cdot y}\right)}^{-1} \]

      7. pow2 74.7%

         \[\leadsto {\left(\frac{\mathsf{fma}\left(4, \color{blue}{{y}^{2}}, x \cdot x\right)}{x \cdot x - \left(y \cdot 4\right) \cdot y}\right)}^{-1} \]

      8. pow2 74.7%

         \[\leadsto {\left(\frac{\mathsf{fma}\left(4, {y}^{2}, \color{blue}{{x}^{2}}\right)}{x \cdot x - \left(y \cdot 4\right) \cdot y}\right)}^{-1} \]

      9. sub-neg 74.7%

         \[\leadsto {\left(\frac{\mathsf{fma}\left(4, {y}^{2}, {x}^{2}\right)}{\color{blue}{x \cdot x + \left(-\left(y \cdot 4\right) \cdot y\right)}}\right)}^{-1} \]

      10. +-commutative 74.7%

          \[\leadsto {\left(\frac{\mathsf{fma}\left(4, {y}^{2}, {x}^{2}\right)}{\color{blue}{\left(-\left(y \cdot 4\right) \cdot y\right) + x \cdot x}}\right)}^{-1} \]

      11. *-commutative 74.7%

          \[\leadsto {\left(\frac{\mathsf{fma}\left(4, {y}^{2}, {x}^{2}\right)}{\left(-\color{blue}{y \cdot \left(y \cdot 4\right)}\right) + x \cdot x}\right)}^{-1} \]

      12. distribute-rgt-neg-in 74.7%

          \[\leadsto {\left(\frac{\mathsf{fma}\left(4, {y}^{2}, {x}^{2}\right)}{\color{blue}{y \cdot \left(-y \cdot 4\right)} + x \cdot x}\right)}^{-1} \]

      13. fma-define 74.7%

          \[\leadsto {\left(\frac{\mathsf{fma}\left(4, {y}^{2}, {x}^{2}\right)}{\color{blue}{\mathsf{fma}\left(y, -y \cdot 4, x \cdot x\right)}}\right)}^{-1} \]

      14. distribute-rgt-neg-in 74.7%

          \[\leadsto {\left(\frac{\mathsf{fma}\left(4, {y}^{2}, {x}^{2}\right)}{\mathsf{fma}\left(y, \color{blue}{y \cdot \left(-4\right)}, x \cdot x\right)}\right)}^{-1} \]

      15. metadata-eval 74.7%

          \[\leadsto {\left(\frac{\mathsf{fma}\left(4, {y}^{2}, {x}^{2}\right)}{\mathsf{fma}\left(y, y \cdot \color{blue}{-4}, x \cdot x\right)}\right)}^{-1} \]

      16. pow2 74.7%

          \[\leadsto {\left(\frac{\mathsf{fma}\left(4, {y}^{2}, {x}^{2}\right)}{\mathsf{fma}\left(y, y \cdot -4, \color{blue}{{x}^{2}}\right)}\right)}^{-1} \]

   4. Applied egg-rr 74.7%

      \[\leadsto \color{blue}{{\left(\frac{\mathsf{fma}\left(4, {y}^{2}, {x}^{2}\right)}{\mathsf{fma}\left(y, y \cdot -4, {x}^{2}\right)}\right)}^{-1}} \]
   5. Step-by-step derivation

      1. unpow2 74.7%

         \[\leadsto {\left(\frac{\mathsf{fma}\left(4, {y}^{2}, {x}^{2}\right)}{\mathsf{fma}\left(y, y \cdot -4, \color{blue}{x \cdot x}\right)}\right)}^{-1} \]

   6. Applied egg-rr 74.7%

      \[\leadsto {\left(\frac{\mathsf{fma}\left(4, {y}^{2}, {x}^{2}\right)}{\mathsf{fma}\left(y, y \cdot -4, \color{blue}{x \cdot x}\right)}\right)}^{-1} \]
   7. Step-by-step derivation

      1. unpow2 74.7%

         \[\leadsto {\left(\frac{\mathsf{fma}\left(4, {y}^{2}, {x}^{2}\right)}{\mathsf{fma}\left(y, y \cdot -4, \color{blue}{x \cdot x}\right)}\right)}^{-1} \]

   8. Applied egg-rr 74.7%

      \[\leadsto {\left(\frac{\mathsf{fma}\left(4, {y}^{2}, \color{blue}{x \cdot x}\right)}{\mathsf{fma}\left(y, y \cdot -4, x \cdot x\right)}\right)}^{-1} \]
   9. Step-by-step derivation

      1. unpow2 74.7%

         \[\leadsto {\left(\frac{\mathsf{fma}\left(4, \color{blue}{y \cdot y}, x \cdot x\right)}{\mathsf{fma}\left(y, y \cdot -4, x \cdot x\right)}\right)}^{-1} \]

   10. Applied egg-rr 74.7%

       \[\leadsto {\left(\frac{\mathsf{fma}\left(4, \color{blue}{y \cdot y}, x \cdot x\right)}{\mathsf{fma}\left(y, y \cdot -4, x \cdot x\right)}\right)}^{-1} \]

   if 2.0000000000000001e152 < (*.f64 (*.f64 y #s(literal 4 binary64)) y)

   1. Initial program 22.0%

      \[\frac{x \cdot x - \left(y \cdot 4\right) \cdot y}{x \cdot x + \left(y \cdot 4\right) \cdot y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 86.3%

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

4. Final simplification 83.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(y \cdot 4\right) \leq 5 \cdot 10^{-285}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \cdot \left(y \cdot 4\right) \leq 2 \cdot 10^{+152}:\\ \;\;\;\;{\left(\frac{\mathsf{fma}\left(4, y \cdot y, x \cdot x\right)}{\mathsf{fma}\left(y, y \cdot -4, x \cdot x\right)}\right)}^{-1}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 80.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(y \cdot 4\right)\\ \mathbf{if}\;t\_0 \leq 1.15 \cdot 10^{-284}:\\ \;\;\;\;1\\ \mathbf{elif}\;t\_0 \leq 4.1 \cdot 10^{+166}:\\ \;\;\;\;\frac{x \cdot x - t\_0}{t\_0 + x \cdot x}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* y (* y 4.0))))
   (if (<= t_0 1.15e-284)
     1.0
     (if (<= t_0 4.1e+166) (/ (- (* x x) t_0) (+ t_0 (* x x))) -1.0))))

C

double code(double x, double y) {
	double t_0 = y * (y * 4.0);
	double tmp;
	if (t_0 <= 1.15e-284) {
		tmp = 1.0;
	} else if (t_0 <= 4.1e+166) {
		tmp = ((x * x) - t_0) / (t_0 + (x * x));
	} 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) :: tmp
    t_0 = y * (y * 4.0d0)
    if (t_0 <= 1.15d-284) then
        tmp = 1.0d0
    else if (t_0 <= 4.1d+166) then
        tmp = ((x * x) - t_0) / (t_0 + (x * x))
    else
        tmp = -1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = y * (y * 4.0);
	double tmp;
	if (t_0 <= 1.15e-284) {
		tmp = 1.0;
	} else if (t_0 <= 4.1e+166) {
		tmp = ((x * x) - t_0) / (t_0 + (x * x));
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = y * (y * 4.0)
	tmp = 0
	if t_0 <= 1.15e-284:
		tmp = 1.0
	elif t_0 <= 4.1e+166:
		tmp = ((x * x) - t_0) / (t_0 + (x * x))
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(y * Float64(y * 4.0))
	tmp = 0.0
	if (t_0 <= 1.15e-284)
		tmp = 1.0;
	elseif (t_0 <= 4.1e+166)
		tmp = Float64(Float64(Float64(x * x) - t_0) / Float64(t_0 + Float64(x * x)));
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = y * (y * 4.0);
	tmp = 0.0;
	if (t_0 <= 1.15e-284)
		tmp = 1.0;
	elseif (t_0 <= 4.1e+166)
		tmp = ((x * x) - t_0) / (t_0 + (x * x));
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(y * N[(y * 4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, 1.15e-284], 1.0, If[LessEqual[t$95$0, 4.1e+166], N[(N[(N[(x * x), $MachinePrecision] - t$95$0), $MachinePrecision] / N[(t$95$0 + N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], -1.0]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 y #s(literal 4 binary64)) y) < 1.15e-284

   1. Initial program 54.3%

      \[\frac{x \cdot x - \left(y \cdot 4\right) \cdot y}{x \cdot x + \left(y \cdot 4\right) \cdot y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 92.2%

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

   if 1.15e-284 < (*.f64 (*.f64 y #s(literal 4 binary64)) y) < 4.1000000000000003e166

   1. Initial program 74.7%

      \[\frac{x \cdot x - \left(y \cdot 4\right) \cdot y}{x \cdot x + \left(y \cdot 4\right) \cdot y} \]
   2. Add Preprocessing

   if 4.1000000000000003e166 < (*.f64 (*.f64 y #s(literal 4 binary64)) y)

   1. Initial program 22.0%

      \[\frac{x \cdot x - \left(y \cdot 4\right) \cdot y}{x \cdot x + \left(y \cdot 4\right) \cdot y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 86.3%

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

4. Final simplification 83.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(y \cdot 4\right) \leq 1.15 \cdot 10^{-284}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \cdot \left(y \cdot 4\right) \leq 4.1 \cdot 10^{+166}:\\ \;\;\;\;\frac{x \cdot x - y \cdot \left(y \cdot 4\right)}{y \cdot \left(y \cdot 4\right) + x \cdot x}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 62.0% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 8 \cdot 10^{-40}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= y 8e-40) 1.0 -1.0))

C

double code(double x, double y) {
	double tmp;
	if (y <= 8e-40) {
		tmp = 1.0;
	} 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) :: tmp
    if (y <= 8d-40) then
        tmp = 1.0d0
    else
        tmp = -1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= 8e-40) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 8e-40:
		tmp = 1.0
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 8e-40)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= 8e-40)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 8e-40], 1.0, -1.0]

Derivation

1. Split input into 2 regimes

2. if y < 7.9999999999999994e-40

   1. Initial program 54.0%

      \[\frac{x \cdot x - \left(y \cdot 4\right) \cdot y}{x \cdot x + \left(y \cdot 4\right) \cdot y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 58.5%

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

   if 7.9999999999999994e-40 < y

   1. Initial program 37.9%

      \[\frac{x \cdot x - \left(y \cdot 4\right) \cdot y}{x \cdot x + \left(y \cdot 4\right) \cdot y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 76.8%

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

Alternative 4: 49.9% accurate, 19.0× 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 50.4%

   \[\frac{x \cdot x - \left(y \cdot 4\right) \cdot y}{x \cdot x + \left(y \cdot 4\right) \cdot y} \]
2. Add Preprocessing

3. Taylor expanded in x around 0 50.3%

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

Developer Target 1: 51.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(y \cdot y\right) \cdot 4\\ t_1 := x \cdot x + t\_0\\ t_2 := \frac{t\_0}{t\_1}\\ t_3 := \left(y \cdot 4\right) \cdot y\\ \mathbf{if}\;\frac{x \cdot x - t\_3}{x \cdot x + t\_3} < 0.9743233849626781:\\ \;\;\;\;\frac{x \cdot x}{t\_1} - t\_2\\ \mathbf{else}:\\ \;\;\;\;{\left(\frac{x}{\sqrt{t\_1}}\right)}^{2} - t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* (* y y) 4.0))
        (t_1 (+ (* x x) t_0))
        (t_2 (/ t_0 t_1))
        (t_3 (* (* y 4.0) y)))
   (if (< (/ (- (* x x) t_3) (+ (* x x) t_3)) 0.9743233849626781)
     (- (/ (* x x) t_1) t_2)
     (- (pow (/ x (sqrt t_1)) 2.0) t_2))))

C

double code(double x, double y) {
	double t_0 = (y * y) * 4.0;
	double t_1 = (x * x) + t_0;
	double t_2 = t_0 / t_1;
	double t_3 = (y * 4.0) * y;
	double tmp;
	if ((((x * x) - t_3) / ((x * x) + t_3)) < 0.9743233849626781) {
		tmp = ((x * x) / t_1) - t_2;
	} else {
		tmp = pow((x / sqrt(t_1)), 2.0) - t_2;
	}
	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) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_0 = (y * y) * 4.0d0
    t_1 = (x * x) + t_0
    t_2 = t_0 / t_1
    t_3 = (y * 4.0d0) * y
    if ((((x * x) - t_3) / ((x * x) + t_3)) < 0.9743233849626781d0) then
        tmp = ((x * x) / t_1) - t_2
    else
        tmp = ((x / sqrt(t_1)) ** 2.0d0) - t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = (y * y) * 4.0;
	double t_1 = (x * x) + t_0;
	double t_2 = t_0 / t_1;
	double t_3 = (y * 4.0) * y;
	double tmp;
	if ((((x * x) - t_3) / ((x * x) + t_3)) < 0.9743233849626781) {
		tmp = ((x * x) / t_1) - t_2;
	} else {
		tmp = Math.pow((x / Math.sqrt(t_1)), 2.0) - t_2;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = (y * y) * 4.0
	t_1 = (x * x) + t_0
	t_2 = t_0 / t_1
	t_3 = (y * 4.0) * y
	tmp = 0
	if (((x * x) - t_3) / ((x * x) + t_3)) < 0.9743233849626781:
		tmp = ((x * x) / t_1) - t_2
	else:
		tmp = math.pow((x / math.sqrt(t_1)), 2.0) - t_2
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(y * y) * 4.0)
	t_1 = Float64(Float64(x * x) + t_0)
	t_2 = Float64(t_0 / t_1)
	t_3 = Float64(Float64(y * 4.0) * y)
	tmp = 0.0
	if (Float64(Float64(Float64(x * x) - t_3) / Float64(Float64(x * x) + t_3)) < 0.9743233849626781)
		tmp = Float64(Float64(Float64(x * x) / t_1) - t_2);
	else
		tmp = Float64((Float64(x / sqrt(t_1)) ^ 2.0) - t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = (y * y) * 4.0;
	t_1 = (x * x) + t_0;
	t_2 = t_0 / t_1;
	t_3 = (y * 4.0) * y;
	tmp = 0.0;
	if ((((x * x) - t_3) / ((x * x) + t_3)) < 0.9743233849626781)
		tmp = ((x * x) / t_1) - t_2;
	else
		tmp = ((x / sqrt(t_1)) ^ 2.0) - t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(y * y), $MachinePrecision] * 4.0), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x * x), $MachinePrecision] + t$95$0), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$0 / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y * 4.0), $MachinePrecision] * y), $MachinePrecision]}, If[Less[N[(N[(N[(x * x), $MachinePrecision] - t$95$3), $MachinePrecision] / N[(N[(x * x), $MachinePrecision] + t$95$3), $MachinePrecision]), $MachinePrecision], 0.9743233849626781], N[(N[(N[(x * x), $MachinePrecision] / t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision], N[(N[Power[N[(x / N[Sqrt[t$95$1], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision] - t$95$2), $MachinePrecision]]]]]]

Reproduce

herbie shell --seed 2024139 
(FPCore (x y)
  :name "Diagrams.TwoD.Arc:arcBetween from diagrams-lib-1.3.0.3"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< (/ (- (* x x) (* (* y 4) y)) (+ (* x x) (* (* y 4) y))) 9743233849626781/10000000000000000) (- (/ (* x x) (+ (* x x) (* (* y y) 4))) (/ (* (* y y) 4) (+ (* x x) (* (* y y) 4)))) (- (pow (/ x (sqrt (+ (* x x) (* (* y y) 4)))) 2) (/ (* (* y y) 4) (+ (* x x) (* (* y y) 4))))))

  (/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y))))