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

Percentage Accurate: 50.6% → 81.9%

Time: 7.2s

Alternatives: 6

Speedup: 1.2×

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: 50.6% 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: 81.9% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(y \cdot 4\right)\\ \mathbf{if}\;t\_0 \leq 3 \cdot 10^{-177}:\\ \;\;\;\;1 + -8 \cdot \left(\frac{y}{x} \cdot \frac{y}{x}\right)\\ \mathbf{elif}\;t\_0 \leq 4 \cdot 10^{+189}:\\ \;\;\;\;{\left(\frac{{\left(\mathsf{hypot}\left(x, y \cdot 2\right)\right)}^{2}}{\mathsf{fma}\left(y, y \cdot -4, {x}^{2}\right)}\right)}^{-1}\\ \mathbf{else}:\\ \;\;\;\;-1 + 0.5 \cdot \left(\frac{x}{y} \cdot \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* y (* y 4.0))))
   (if (<= t_0 3e-177)
     (+ 1.0 (* -8.0 (* (/ y x) (/ y x))))
     (if (<= t_0 4e+189)
       (pow
        (/ (pow (hypot x (* y 2.0)) 2.0) (fma y (* y -4.0) (pow x 2.0)))
        -1.0)
       (+ -1.0 (* 0.5 (* (/ x y) (/ x y))))))))

C

double code(double x, double y) {
	double t_0 = y * (y * 4.0);
	double tmp;
	if (t_0 <= 3e-177) {
		tmp = 1.0 + (-8.0 * ((y / x) * (y / x)));
	} else if (t_0 <= 4e+189) {
		tmp = pow((pow(hypot(x, (y * 2.0)), 2.0) / fma(y, (y * -4.0), pow(x, 2.0))), -1.0);
	} else {
		tmp = -1.0 + (0.5 * ((x / y) * (x / y)));
	}
	return tmp;
}

Julia

function code(x, y)
	t_0 = Float64(y * Float64(y * 4.0))
	tmp = 0.0
	if (t_0 <= 3e-177)
		tmp = Float64(1.0 + Float64(-8.0 * Float64(Float64(y / x) * Float64(y / x))));
	elseif (t_0 <= 4e+189)
		tmp = Float64((hypot(x, Float64(y * 2.0)) ^ 2.0) / fma(y, Float64(y * -4.0), (x ^ 2.0))) ^ -1.0;
	else
		tmp = Float64(-1.0 + Float64(0.5 * Float64(Float64(x / y) * Float64(x / y))));
	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, 3e-177], N[(1.0 + N[(-8.0 * N[(N[(y / x), $MachinePrecision] * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 4e+189], N[Power[N[(N[Power[N[Sqrt[x ^ 2 + N[(y * 2.0), $MachinePrecision] ^ 2], $MachinePrecision], 2.0], $MachinePrecision] / N[(y * N[(y * -4.0), $MachinePrecision] + N[Power[x, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], -1.0], $MachinePrecision], N[(-1.0 + N[(0.5 * N[(N[(x / y), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 y 4) y) < 3.00000000000000008e-177

   1. Initial program 57.5%

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

   3. Taylor expanded in y around 0 79.6%

      \[\leadsto \color{blue}{1 + -8 \cdot \frac{{y}^{2}}{{x}^{2}}} \]
   4. Step-by-step derivation

      1. unpow2 79.6%

         \[\leadsto 1 + -8 \cdot \frac{\color{blue}{y \cdot y}}{{x}^{2}} \]

      2. unpow2 79.6%

         \[\leadsto 1 + -8 \cdot \frac{y \cdot y}{\color{blue}{x \cdot x}} \]

      3. times-frac 85.9%

         \[\leadsto 1 + -8 \cdot \color{blue}{\left(\frac{y}{x} \cdot \frac{y}{x}\right)} \]

   5. Applied egg-rr 85.9%

      \[\leadsto 1 + -8 \cdot \color{blue}{\left(\frac{y}{x} \cdot \frac{y}{x}\right)} \]

   if 3.00000000000000008e-177 < (*.f64 (*.f64 y 4) y) < 4.0000000000000001e189

   1. Initial program 80.6%

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

      1. clear-num 80.6%

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

      2. inv-pow 80.6%

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

      3. +-commutative 80.6%

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

      4. *-commutative 80.6%

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

      5. associate-*l* 80.6%

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

      6. fma-define 80.6%

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

      7. pow2 80.6%

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

      8. pow2 80.6%

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

      9. sub-neg 80.6%

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

      10. +-commutative 80.6%

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

      11. *-commutative 80.6%

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

      12. distribute-rgt-neg-in 80.6%

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

      13. fma-define 80.6%

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

      14. distribute-rgt-neg-in 80.6%

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

      15. metadata-eval 80.6%

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

      16. pow2 80.6%

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

   4. Applied egg-rr 80.6%

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

      1. fma-undefine 80.6%

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

      2. +-commutative 80.6%

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

   6. Applied egg-rr 80.6%

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

   7. Taylor expanded in x around 0 80.6%

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

      1. +-commutative 80.6%

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

      2. unpow2 80.6%

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

      3. *-commutative 80.6%

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

      4. unpow2 80.6%

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

      5. metadata-eval 80.6%

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

      6. swap-sqr 80.6%

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

      7. rem-square-sqrt 80.6%

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

      8. hypot-undefine 80.6%

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

      9. hypot-undefine 80.6%

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

      10. unpow2 80.6%

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

   9. Simplified 80.6%

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

   if 4.0000000000000001e189 < (*.f64 (*.f64 y 4) y)

   1. Initial program 26.3%

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

   3. Taylor expanded in x around 0 79.1%

      \[\leadsto \color{blue}{0.5 \cdot \frac{{x}^{2}}{{y}^{2}} - 1} \]
   4. Step-by-step derivation

      1. unpow2 79.1%

         \[\leadsto 0.5 \cdot \frac{\color{blue}{x \cdot x}}{{y}^{2}} - 1 \]

      2. unpow2 79.1%

         \[\leadsto 0.5 \cdot \frac{x \cdot x}{\color{blue}{y \cdot y}} - 1 \]

      3. times-frac 87.6%

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

   5. Applied egg-rr 87.6%

      \[\leadsto 0.5 \cdot \color{blue}{\left(\frac{x}{y} \cdot \frac{x}{y}\right)} - 1 \]
3. Recombined 3 regimes into one program.

4. Final simplification 84.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(y \cdot 4\right) \leq 3 \cdot 10^{-177}:\\ \;\;\;\;1 + -8 \cdot \left(\frac{y}{x} \cdot \frac{y}{x}\right)\\ \mathbf{elif}\;y \cdot \left(y \cdot 4\right) \leq 4 \cdot 10^{+189}:\\ \;\;\;\;{\left(\frac{{\left(\mathsf{hypot}\left(x, y \cdot 2\right)\right)}^{2}}{\mathsf{fma}\left(y, y \cdot -4, {x}^{2}\right)}\right)}^{-1}\\ \mathbf{else}:\\ \;\;\;\;-1 + 0.5 \cdot \left(\frac{x}{y} \cdot \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 81.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(y \cdot 4\right)\\ \mathbf{if}\;t\_0 \leq 3 \cdot 10^{-177}:\\ \;\;\;\;1 + -8 \cdot \left(\frac{y}{x} \cdot \frac{y}{x}\right)\\ \mathbf{elif}\;t\_0 \leq 4 \cdot 10^{+189}:\\ \;\;\;\;\frac{x \cdot x - t\_0}{t\_0 + x \cdot x}\\ \mathbf{else}:\\ \;\;\;\;-1 + 0.5 \cdot \left(\frac{x}{y} \cdot \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* y (* y 4.0))))
   (if (<= t_0 3e-177)
     (+ 1.0 (* -8.0 (* (/ y x) (/ y x))))
     (if (<= t_0 4e+189)
       (/ (- (* x x) t_0) (+ t_0 (* x x)))
       (+ -1.0 (* 0.5 (* (/ x y) (/ x y))))))))

C

double code(double x, double y) {
	double t_0 = y * (y * 4.0);
	double tmp;
	if (t_0 <= 3e-177) {
		tmp = 1.0 + (-8.0 * ((y / x) * (y / x)));
	} else if (t_0 <= 4e+189) {
		tmp = ((x * x) - t_0) / (t_0 + (x * x));
	} else {
		tmp = -1.0 + (0.5 * ((x / y) * (x / y)));
	}
	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 <= 3d-177) then
        tmp = 1.0d0 + ((-8.0d0) * ((y / x) * (y / x)))
    else if (t_0 <= 4d+189) then
        tmp = ((x * x) - t_0) / (t_0 + (x * x))
    else
        tmp = (-1.0d0) + (0.5d0 * ((x / y) * (x / y)))
    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 <= 3e-177) {
		tmp = 1.0 + (-8.0 * ((y / x) * (y / x)));
	} else if (t_0 <= 4e+189) {
		tmp = ((x * x) - t_0) / (t_0 + (x * x));
	} else {
		tmp = -1.0 + (0.5 * ((x / y) * (x / y)));
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = y * (y * 4.0)
	tmp = 0
	if t_0 <= 3e-177:
		tmp = 1.0 + (-8.0 * ((y / x) * (y / x)))
	elif t_0 <= 4e+189:
		tmp = ((x * x) - t_0) / (t_0 + (x * x))
	else:
		tmp = -1.0 + (0.5 * ((x / y) * (x / y)))
	return tmp

Julia

function code(x, y)
	t_0 = Float64(y * Float64(y * 4.0))
	tmp = 0.0
	if (t_0 <= 3e-177)
		tmp = Float64(1.0 + Float64(-8.0 * Float64(Float64(y / x) * Float64(y / x))));
	elseif (t_0 <= 4e+189)
		tmp = Float64(Float64(Float64(x * x) - t_0) / Float64(t_0 + Float64(x * x)));
	else
		tmp = Float64(-1.0 + Float64(0.5 * Float64(Float64(x / y) * Float64(x / y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = y * (y * 4.0);
	tmp = 0.0;
	if (t_0 <= 3e-177)
		tmp = 1.0 + (-8.0 * ((y / x) * (y / x)));
	elseif (t_0 <= 4e+189)
		tmp = ((x * x) - t_0) / (t_0 + (x * x));
	else
		tmp = -1.0 + (0.5 * ((x / y) * (x / y)));
	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, 3e-177], N[(1.0 + N[(-8.0 * N[(N[(y / x), $MachinePrecision] * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 4e+189], N[(N[(N[(x * x), $MachinePrecision] - t$95$0), $MachinePrecision] / N[(t$95$0 + N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-1.0 + N[(0.5 * N[(N[(x / y), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 y 4) y) < 3.00000000000000008e-177

   1. Initial program 57.5%

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

   3. Taylor expanded in y around 0 79.6%

      \[\leadsto \color{blue}{1 + -8 \cdot \frac{{y}^{2}}{{x}^{2}}} \]
   4. Step-by-step derivation

      1. unpow2 79.6%

         \[\leadsto 1 + -8 \cdot \frac{\color{blue}{y \cdot y}}{{x}^{2}} \]

      2. unpow2 79.6%

         \[\leadsto 1 + -8 \cdot \frac{y \cdot y}{\color{blue}{x \cdot x}} \]

      3. times-frac 85.9%

         \[\leadsto 1 + -8 \cdot \color{blue}{\left(\frac{y}{x} \cdot \frac{y}{x}\right)} \]

   5. Applied egg-rr 85.9%

      \[\leadsto 1 + -8 \cdot \color{blue}{\left(\frac{y}{x} \cdot \frac{y}{x}\right)} \]

   if 3.00000000000000008e-177 < (*.f64 (*.f64 y 4) y) < 4.0000000000000001e189

   1. Initial program 80.6%

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

   if 4.0000000000000001e189 < (*.f64 (*.f64 y 4) y)

   1. Initial program 26.3%

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

   3. Taylor expanded in x around 0 79.1%

      \[\leadsto \color{blue}{0.5 \cdot \frac{{x}^{2}}{{y}^{2}} - 1} \]
   4. Step-by-step derivation

      1. unpow2 79.1%

         \[\leadsto 0.5 \cdot \frac{\color{blue}{x \cdot x}}{{y}^{2}} - 1 \]

      2. unpow2 79.1%

         \[\leadsto 0.5 \cdot \frac{x \cdot x}{\color{blue}{y \cdot y}} - 1 \]

      3. times-frac 87.6%

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

   5. Applied egg-rr 87.6%

      \[\leadsto 0.5 \cdot \color{blue}{\left(\frac{x}{y} \cdot \frac{x}{y}\right)} - 1 \]
3. Recombined 3 regimes into one program.

4. Final simplification 84.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(y \cdot 4\right) \leq 3 \cdot 10^{-177}:\\ \;\;\;\;1 + -8 \cdot \left(\frac{y}{x} \cdot \frac{y}{x}\right)\\ \mathbf{elif}\;y \cdot \left(y \cdot 4\right) \leq 4 \cdot 10^{+189}:\\ \;\;\;\;\frac{x \cdot x - y \cdot \left(y \cdot 4\right)}{y \cdot \left(y \cdot 4\right) + x \cdot x}\\ \mathbf{else}:\\ \;\;\;\;-1 + 0.5 \cdot \left(\frac{x}{y} \cdot \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 63.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 5.6 \cdot 10^{-78}:\\ \;\;\;\;1 + -8 \cdot \left(\frac{y}{x} \cdot \frac{y}{x}\right)\\ \mathbf{elif}\;y \leq 10^{+84} \lor \neg \left(y \leq 1.5 \cdot 10^{+96}\right):\\ \;\;\;\;-1 + 0.5 \cdot \left(\frac{x}{y} \cdot \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y 5.6e-78)
   (+ 1.0 (* -8.0 (* (/ y x) (/ y x))))
   (if (or (<= y 1e+84) (not (<= y 1.5e+96)))
     (+ -1.0 (* 0.5 (* (/ x y) (/ x y))))
     1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= 5.6e-78) {
		tmp = 1.0 + (-8.0 * ((y / x) * (y / x)));
	} else if ((y <= 1e+84) || !(y <= 1.5e+96)) {
		tmp = -1.0 + (0.5 * ((x / y) * (x / y)));
	} 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 <= 5.6d-78) then
        tmp = 1.0d0 + ((-8.0d0) * ((y / x) * (y / x)))
    else if ((y <= 1d+84) .or. (.not. (y <= 1.5d+96))) then
        tmp = (-1.0d0) + (0.5d0 * ((x / y) * (x / y)))
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= 5.6e-78) {
		tmp = 1.0 + (-8.0 * ((y / x) * (y / x)));
	} else if ((y <= 1e+84) || !(y <= 1.5e+96)) {
		tmp = -1.0 + (0.5 * ((x / y) * (x / y)));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 5.6e-78:
		tmp = 1.0 + (-8.0 * ((y / x) * (y / x)))
	elif (y <= 1e+84) or not (y <= 1.5e+96):
		tmp = -1.0 + (0.5 * ((x / y) * (x / y)))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 5.6e-78)
		tmp = Float64(1.0 + Float64(-8.0 * Float64(Float64(y / x) * Float64(y / x))));
	elseif ((y <= 1e+84) || !(y <= 1.5e+96))
		tmp = Float64(-1.0 + Float64(0.5 * Float64(Float64(x / y) * Float64(x / y))));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= 5.6e-78)
		tmp = 1.0 + (-8.0 * ((y / x) * (y / x)));
	elseif ((y <= 1e+84) || ~((y <= 1.5e+96)))
		tmp = -1.0 + (0.5 * ((x / y) * (x / y)));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 5.6e-78], N[(1.0 + N[(-8.0 * N[(N[(y / x), $MachinePrecision] * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 1e+84], N[Not[LessEqual[y, 1.5e+96]], $MachinePrecision]], N[(-1.0 + N[(0.5 * N[(N[(x / y), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 3 regimes

2. if y < 5.60000000000000047e-78

   1. Initial program 57.7%

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

   3. Taylor expanded in y around 0 54.1%

      \[\leadsto \color{blue}{1 + -8 \cdot \frac{{y}^{2}}{{x}^{2}}} \]
   4. Step-by-step derivation

      1. unpow2 54.1%

         \[\leadsto 1 + -8 \cdot \frac{\color{blue}{y \cdot y}}{{x}^{2}} \]

      2. unpow2 54.1%

         \[\leadsto 1 + -8 \cdot \frac{y \cdot y}{\color{blue}{x \cdot x}} \]

      3. times-frac 58.5%

         \[\leadsto 1 + -8 \cdot \color{blue}{\left(\frac{y}{x} \cdot \frac{y}{x}\right)} \]

   5. Applied egg-rr 58.5%

      \[\leadsto 1 + -8 \cdot \color{blue}{\left(\frac{y}{x} \cdot \frac{y}{x}\right)} \]

   if 5.60000000000000047e-78 < y < 1.00000000000000006e84 or 1.5e96 < y

   1. Initial program 54.4%

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

   3. Taylor expanded in x around 0 65.6%

      \[\leadsto \color{blue}{0.5 \cdot \frac{{x}^{2}}{{y}^{2}} - 1} \]
   4. Step-by-step derivation

      1. unpow2 65.6%

         \[\leadsto 0.5 \cdot \frac{\color{blue}{x \cdot x}}{{y}^{2}} - 1 \]

      2. unpow2 65.6%

         \[\leadsto 0.5 \cdot \frac{x \cdot x}{\color{blue}{y \cdot y}} - 1 \]

      3. times-frac 72.2%

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

   5. Applied egg-rr 72.2%

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

   if 1.00000000000000006e84 < y < 1.5e96

   1. Initial program 50.0%

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

   3. Taylor expanded in x around inf 100.0%

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

4. Final simplification 63.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 5.6 \cdot 10^{-78}:\\ \;\;\;\;1 + -8 \cdot \left(\frac{y}{x} \cdot \frac{y}{x}\right)\\ \mathbf{elif}\;y \leq 10^{+84} \lor \neg \left(y \leq 1.5 \cdot 10^{+96}\right):\\ \;\;\;\;-1 + 0.5 \cdot \left(\frac{x}{y} \cdot \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 62.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 5.2 \cdot 10^{-78}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 10^{+85}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+96}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y 5.2e-78) 1.0 (if (<= y 1e+85) -1.0 (if (<= y 2e+96) 1.0 -1.0))))

C

double code(double x, double y) {
	double tmp;
	if (y <= 5.2e-78) {
		tmp = 1.0;
	} else if (y <= 1e+85) {
		tmp = -1.0;
	} else if (y <= 2e+96) {
		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 <= 5.2d-78) then
        tmp = 1.0d0
    else if (y <= 1d+85) then
        tmp = -1.0d0
    else if (y <= 2d+96) 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 <= 5.2e-78) {
		tmp = 1.0;
	} else if (y <= 1e+85) {
		tmp = -1.0;
	} else if (y <= 2e+96) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 5.2e-78:
		tmp = 1.0
	elif y <= 1e+85:
		tmp = -1.0
	elif y <= 2e+96:
		tmp = 1.0
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 5.2e-78)
		tmp = 1.0;
	elseif (y <= 1e+85)
		tmp = -1.0;
	elseif (y <= 2e+96)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= 5.2e-78)
		tmp = 1.0;
	elseif (y <= 1e+85)
		tmp = -1.0;
	elseif (y <= 2e+96)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 5.2e-78], 1.0, If[LessEqual[y, 1e+85], -1.0, If[LessEqual[y, 2e+96], 1.0, -1.0]]]

Derivation

1. Split input into 2 regimes

2. if y < 5.2000000000000002e-78 or 1e85 < y < 2.0000000000000001e96

   1. Initial program 57.6%

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

   3. Taylor expanded in x around inf 57.4%

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

   if 5.2000000000000002e-78 < y < 1e85 or 2.0000000000000001e96 < y

   1. Initial program 54.4%

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

   3. Taylor expanded in x around 0 70.6%

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

4. Final simplification 61.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 5.2 \cdot 10^{-78}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 10^{+85}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+96}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 62.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 5.6 \cdot 10^{-78}:\\ \;\;\;\;1 + -8 \cdot \left(\frac{y}{x} \cdot \frac{y}{x}\right)\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+81}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{+96}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y 5.6e-78)
   (+ 1.0 (* -8.0 (* (/ y x) (/ y x))))
   (if (<= y 2e+81) -1.0 (if (<= y 1.5e+96) 1.0 -1.0))))

C

double code(double x, double y) {
	double tmp;
	if (y <= 5.6e-78) {
		tmp = 1.0 + (-8.0 * ((y / x) * (y / x)));
	} else if (y <= 2e+81) {
		tmp = -1.0;
	} else if (y <= 1.5e+96) {
		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 <= 5.6d-78) then
        tmp = 1.0d0 + ((-8.0d0) * ((y / x) * (y / x)))
    else if (y <= 2d+81) then
        tmp = -1.0d0
    else if (y <= 1.5d+96) 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 <= 5.6e-78) {
		tmp = 1.0 + (-8.0 * ((y / x) * (y / x)));
	} else if (y <= 2e+81) {
		tmp = -1.0;
	} else if (y <= 1.5e+96) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 5.6e-78:
		tmp = 1.0 + (-8.0 * ((y / x) * (y / x)))
	elif y <= 2e+81:
		tmp = -1.0
	elif y <= 1.5e+96:
		tmp = 1.0
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 5.6e-78)
		tmp = Float64(1.0 + Float64(-8.0 * Float64(Float64(y / x) * Float64(y / x))));
	elseif (y <= 2e+81)
		tmp = -1.0;
	elseif (y <= 1.5e+96)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= 5.6e-78)
		tmp = 1.0 + (-8.0 * ((y / x) * (y / x)));
	elseif (y <= 2e+81)
		tmp = -1.0;
	elseif (y <= 1.5e+96)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 5.6e-78], N[(1.0 + N[(-8.0 * N[(N[(y / x), $MachinePrecision] * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2e+81], -1.0, If[LessEqual[y, 1.5e+96], 1.0, -1.0]]]

Derivation

1. Split input into 3 regimes

2. if y < 5.60000000000000047e-78

   1. Initial program 57.7%

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

   3. Taylor expanded in y around 0 54.1%

      \[\leadsto \color{blue}{1 + -8 \cdot \frac{{y}^{2}}{{x}^{2}}} \]
   4. Step-by-step derivation

      1. unpow2 54.1%

         \[\leadsto 1 + -8 \cdot \frac{\color{blue}{y \cdot y}}{{x}^{2}} \]

      2. unpow2 54.1%

         \[\leadsto 1 + -8 \cdot \frac{y \cdot y}{\color{blue}{x \cdot x}} \]

      3. times-frac 58.5%

         \[\leadsto 1 + -8 \cdot \color{blue}{\left(\frac{y}{x} \cdot \frac{y}{x}\right)} \]

   5. Applied egg-rr 58.5%

      \[\leadsto 1 + -8 \cdot \color{blue}{\left(\frac{y}{x} \cdot \frac{y}{x}\right)} \]

   if 5.60000000000000047e-78 < y < 1.99999999999999984e81 or 1.5e96 < y

   1. Initial program 54.4%

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

   3. Taylor expanded in x around 0 70.6%

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

   if 1.99999999999999984e81 < y < 1.5e96

   1. Initial program 50.0%

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

   3. Taylor expanded in x around inf 100.0%

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

4. Final simplification 62.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 5.6 \cdot 10^{-78}:\\ \;\;\;\;1 + -8 \cdot \left(\frac{y}{x} \cdot \frac{y}{x}\right)\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+81}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{+96}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 50.5% 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 56.6%

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

3. Taylor expanded in x around 0 51.8%

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

4. Final simplification 51.8%

   \[\leadsto -1 \]
5. Add Preprocessing

Developer target: 51.1% 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 2024051 
(FPCore (x y)
  :name "Diagrams.TwoD.Arc:arcBetween from diagrams-lib-1.3.0.3"
  :precision binary64

  :alt
  (if (< (/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y))) 0.9743233849626781) (- (/ (* x x) (+ (* x x) (* (* y y) 4.0))) (/ (* (* y y) 4.0) (+ (* x x) (* (* y y) 4.0)))) (- (pow (/ x (sqrt (+ (* x x) (* (* y y) 4.0)))) 2.0) (/ (* (* y y) 4.0) (+ (* x x) (* (* y y) 4.0)))))

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