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

Percentage Accurate: 49.9% → 78.7%

Time: 7.5s

Alternatives: 5

Speedup: 2.6×

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: 49.9% 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: 78.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(y \cdot 4\right)\\ t_1 := \frac{x \cdot x - t_0}{t_0 + x \cdot x}\\ \mathbf{if}\;t_0 \leq 5 \cdot 10^{-128}:\\ \;\;\;\;1\\ \mathbf{elif}\;t_0 \leq 5 \cdot 10^{-63}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_0 \leq 2 \cdot 10^{+21}:\\ \;\;\;\;1\\ \mathbf{elif}\;t_0 \leq 10^{+278}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{log1p}\left(0.5 \cdot {\left(\frac{x}{y}\right)}^{2}\right) + -1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* y (* y 4.0))) (t_1 (/ (- (* x x) t_0) (+ t_0 (* x x)))))
   (if (<= t_0 5e-128)
     1.0
     (if (<= t_0 5e-63)
       t_1
       (if (<= t_0 2e+21)
         1.0
         (if (<= t_0 1e+278)
           t_1
           (+ (log1p (* 0.5 (pow (/ x y) 2.0))) -1.0)))))))

C

double code(double x, double y) {
	double t_0 = y * (y * 4.0);
	double t_1 = ((x * x) - t_0) / (t_0 + (x * x));
	double tmp;
	if (t_0 <= 5e-128) {
		tmp = 1.0;
	} else if (t_0 <= 5e-63) {
		tmp = t_1;
	} else if (t_0 <= 2e+21) {
		tmp = 1.0;
	} else if (t_0 <= 1e+278) {
		tmp = t_1;
	} else {
		tmp = log1p((0.5 * pow((x / y), 2.0))) + -1.0;
	}
	return tmp;
}

Java

public static double code(double x, double y) {
	double t_0 = y * (y * 4.0);
	double t_1 = ((x * x) - t_0) / (t_0 + (x * x));
	double tmp;
	if (t_0 <= 5e-128) {
		tmp = 1.0;
	} else if (t_0 <= 5e-63) {
		tmp = t_1;
	} else if (t_0 <= 2e+21) {
		tmp = 1.0;
	} else if (t_0 <= 1e+278) {
		tmp = t_1;
	} else {
		tmp = Math.log1p((0.5 * Math.pow((x / y), 2.0))) + -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = y * (y * 4.0)
	t_1 = ((x * x) - t_0) / (t_0 + (x * x))
	tmp = 0
	if t_0 <= 5e-128:
		tmp = 1.0
	elif t_0 <= 5e-63:
		tmp = t_1
	elif t_0 <= 2e+21:
		tmp = 1.0
	elif t_0 <= 1e+278:
		tmp = t_1
	else:
		tmp = math.log1p((0.5 * math.pow((x / y), 2.0))) + -1.0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(y * Float64(y * 4.0))
	t_1 = Float64(Float64(Float64(x * x) - t_0) / Float64(t_0 + Float64(x * x)))
	tmp = 0.0
	if (t_0 <= 5e-128)
		tmp = 1.0;
	elseif (t_0 <= 5e-63)
		tmp = t_1;
	elseif (t_0 <= 2e+21)
		tmp = 1.0;
	elseif (t_0 <= 1e+278)
		tmp = t_1;
	else
		tmp = Float64(log1p(Float64(0.5 * (Float64(x / y) ^ 2.0))) + -1.0);
	end
	return tmp
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(y * N[(y * 4.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(N[(x * x), $MachinePrecision] - t$95$0), $MachinePrecision] / N[(t$95$0 + N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, 5e-128], 1.0, If[LessEqual[t$95$0, 5e-63], t$95$1, If[LessEqual[t$95$0, 2e+21], 1.0, If[LessEqual[t$95$0, 1e+278], t$95$1, N[(N[Log[1 + N[(0.5 * N[Power[N[(x / y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] + -1.0), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 y 4) y) < 5.0000000000000001e-128 or 5.0000000000000002e-63 < (*.f64 (*.f64 y 4) y) < 2e21

   1. Initial program 55.7%

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

      1. *-commutative 55.7%

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

      2. fma-def 55.8%

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

      3. *-commutative 55.8%

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

   3. Simplified 55.8%

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

   4. Taylor expanded in x around inf 82.8%

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

   if 5.0000000000000001e-128 < (*.f64 (*.f64 y 4) y) < 5.0000000000000002e-63 or 2e21 < (*.f64 (*.f64 y 4) y) < 9.99999999999999964e277

   1. Initial program 83.8%

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

   if 9.99999999999999964e277 < (*.f64 (*.f64 y 4) y)

   1. Initial program 2.7%

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

      1. *-commutative 2.7%

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

      2. fma-def 2.7%

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

      3. *-commutative 2.7%

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

   3. Simplified 2.7%

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

   4. Taylor expanded in x around 0 74.7%

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

      1. add-log-exp 74.7%

         \[\leadsto 0.5 \cdot \color{blue}{\log \left(e^{\frac{{x}^{2}}{{y}^{2}}}\right)} - 1 \]

      2. log-pow 74.7%

         \[\leadsto \color{blue}{\log \left({\left(e^{\frac{{x}^{2}}{{y}^{2}}}\right)}^{0.5}\right)} - 1 \]

      3. pow1/2 74.7%

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

      4. add-sqr-sqrt 74.7%

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

      5. pow2 74.7%

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

      6. sqrt-div 74.7%

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

      7. unpow2 74.7%

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

      8. sqrt-prod 33.4%

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

      9. add-sqr-sqrt 85.5%

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

      10. unpow2 85.5%

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

      11. sqrt-prod 41.6%

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

      12. add-sqr-sqrt 85.8%

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

   6. Applied egg-rr 85.8%

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

   7. Taylor expanded in x around 0 74.7%

      \[\leadsto \log \color{blue}{\left(1 + 0.5 \cdot \frac{{x}^{2}}{{y}^{2}}\right)} - 1 \]
   8. Step-by-step derivation

      1. +-commutative 74.7%

         \[\leadsto \log \color{blue}{\left(0.5 \cdot \frac{{x}^{2}}{{y}^{2}} + 1\right)} - 1 \]

      2. fma-def 74.7%

         \[\leadsto \log \color{blue}{\left(\mathsf{fma}\left(0.5, \frac{{x}^{2}}{{y}^{2}}, 1\right)\right)} - 1 \]

      3. unpow2 74.7%

         \[\leadsto \log \left(\mathsf{fma}\left(0.5, \frac{\color{blue}{x \cdot x}}{{y}^{2}}, 1\right)\right) - 1 \]

      4. unpow2 74.7%

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

      5. times-frac 87.4%

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

      6. unpow2 87.4%

         \[\leadsto \log \left(\mathsf{fma}\left(0.5, \color{blue}{{\left(\frac{x}{y}\right)}^{2}}, 1\right)\right) - 1 \]

   9. Simplified 87.4%

      \[\leadsto \log \color{blue}{\left(\mathsf{fma}\left(0.5, {\left(\frac{x}{y}\right)}^{2}, 1\right)\right)} - 1 \]
   10. Step-by-step derivation

       1. *-un-lft-identity 87.4%

          \[\leadsto \log \color{blue}{\left(1 \cdot \mathsf{fma}\left(0.5, {\left(\frac{x}{y}\right)}^{2}, 1\right)\right)} - 1 \]

       2. *-commutative 87.4%

          \[\leadsto \log \color{blue}{\left(\mathsf{fma}\left(0.5, {\left(\frac{x}{y}\right)}^{2}, 1\right) \cdot 1\right)} - 1 \]

       3. log-prod 87.4%

          \[\leadsto \color{blue}{\left(\log \left(\mathsf{fma}\left(0.5, {\left(\frac{x}{y}\right)}^{2}, 1\right)\right) + \log 1\right)} - 1 \]

       4. fma-udef 87.4%

          \[\leadsto \left(\log \color{blue}{\left(0.5 \cdot {\left(\frac{x}{y}\right)}^{2} + 1\right)} + \log 1\right) - 1 \]

       5. +-commutative 87.4%

          \[\leadsto \left(\log \color{blue}{\left(1 + 0.5 \cdot {\left(\frac{x}{y}\right)}^{2}\right)} + \log 1\right) - 1 \]

       6. log1p-udef 87.4%

          \[\leadsto \left(\color{blue}{\mathsf{log1p}\left(0.5 \cdot {\left(\frac{x}{y}\right)}^{2}\right)} + \log 1\right) - 1 \]

       7. metadata-eval 87.4%

          \[\leadsto \left(\mathsf{log1p}\left(0.5 \cdot {\left(\frac{x}{y}\right)}^{2}\right) + \color{blue}{0}\right) - 1 \]

   11. Applied egg-rr 87.4%

       \[\leadsto \color{blue}{\left(\mathsf{log1p}\left(0.5 \cdot {\left(\frac{x}{y}\right)}^{2}\right) + 0\right)} - 1 \]
   12. Step-by-step derivation

       1. +-rgt-identity 87.4%

          \[\leadsto \color{blue}{\mathsf{log1p}\left(0.5 \cdot {\left(\frac{x}{y}\right)}^{2}\right)} - 1 \]

   13. Simplified 87.4%

       \[\leadsto \color{blue}{\mathsf{log1p}\left(0.5 \cdot {\left(\frac{x}{y}\right)}^{2}\right)} - 1 \]
3. Recombined 3 regimes into one program.

4. Final simplification 84.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(y \cdot 4\right) \leq 5 \cdot 10^{-128}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \cdot \left(y \cdot 4\right) \leq 5 \cdot 10^{-63}:\\ \;\;\;\;\frac{x \cdot x - y \cdot \left(y \cdot 4\right)}{y \cdot \left(y \cdot 4\right) + x \cdot x}\\ \mathbf{elif}\;y \cdot \left(y \cdot 4\right) \leq 2 \cdot 10^{+21}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \cdot \left(y \cdot 4\right) \leq 10^{+278}:\\ \;\;\;\;\frac{x \cdot x - y \cdot \left(y \cdot 4\right)}{y \cdot \left(y \cdot 4\right) + x \cdot x}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{log1p}\left(0.5 \cdot {\left(\frac{x}{y}\right)}^{2}\right) + -1\\ \end{array} \]

Alternative 2: 78.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(y \cdot 4\right)\\ t_1 := \frac{x \cdot x - t_0}{t_0 + x \cdot x}\\ \mathbf{if}\;t_0 \leq 5 \cdot 10^{-128}:\\ \;\;\;\;1\\ \mathbf{elif}\;t_0 \leq 5 \cdot 10^{-63}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_0 \leq 2 \cdot 10^{+21}:\\ \;\;\;\;1\\ \mathbf{elif}\;t_0 \leq 10^{+278}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(\frac{x}{y} \cdot \frac{x}{y}\right) + -1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* y (* y 4.0))) (t_1 (/ (- (* x x) t_0) (+ t_0 (* x x)))))
   (if (<= t_0 5e-128)
     1.0
     (if (<= t_0 5e-63)
       t_1
       (if (<= t_0 2e+21)
         1.0
         (if (<= t_0 1e+278) t_1 (+ (* 0.5 (* (/ x y) (/ x y))) -1.0)))))))

C

double code(double x, double y) {
	double t_0 = y * (y * 4.0);
	double t_1 = ((x * x) - t_0) / (t_0 + (x * x));
	double tmp;
	if (t_0 <= 5e-128) {
		tmp = 1.0;
	} else if (t_0 <= 5e-63) {
		tmp = t_1;
	} else if (t_0 <= 2e+21) {
		tmp = 1.0;
	} else if (t_0 <= 1e+278) {
		tmp = t_1;
	} else {
		tmp = (0.5 * ((x / y) * (x / y))) + -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 = y * (y * 4.0d0)
    t_1 = ((x * x) - t_0) / (t_0 + (x * x))
    if (t_0 <= 5d-128) then
        tmp = 1.0d0
    else if (t_0 <= 5d-63) then
        tmp = t_1
    else if (t_0 <= 2d+21) then
        tmp = 1.0d0
    else if (t_0 <= 1d+278) then
        tmp = t_1
    else
        tmp = (0.5d0 * ((x / y) * (x / y))) + (-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 t_1 = ((x * x) - t_0) / (t_0 + (x * x));
	double tmp;
	if (t_0 <= 5e-128) {
		tmp = 1.0;
	} else if (t_0 <= 5e-63) {
		tmp = t_1;
	} else if (t_0 <= 2e+21) {
		tmp = 1.0;
	} else if (t_0 <= 1e+278) {
		tmp = t_1;
	} else {
		tmp = (0.5 * ((x / y) * (x / y))) + -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = y * (y * 4.0)
	t_1 = ((x * x) - t_0) / (t_0 + (x * x))
	tmp = 0
	if t_0 <= 5e-128:
		tmp = 1.0
	elif t_0 <= 5e-63:
		tmp = t_1
	elif t_0 <= 2e+21:
		tmp = 1.0
	elif t_0 <= 1e+278:
		tmp = t_1
	else:
		tmp = (0.5 * ((x / y) * (x / y))) + -1.0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(y * Float64(y * 4.0))
	t_1 = Float64(Float64(Float64(x * x) - t_0) / Float64(t_0 + Float64(x * x)))
	tmp = 0.0
	if (t_0 <= 5e-128)
		tmp = 1.0;
	elseif (t_0 <= 5e-63)
		tmp = t_1;
	elseif (t_0 <= 2e+21)
		tmp = 1.0;
	elseif (t_0 <= 1e+278)
		tmp = t_1;
	else
		tmp = Float64(Float64(0.5 * Float64(Float64(x / y) * Float64(x / y))) + -1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = y * (y * 4.0);
	t_1 = ((x * x) - t_0) / (t_0 + (x * x));
	tmp = 0.0;
	if (t_0 <= 5e-128)
		tmp = 1.0;
	elseif (t_0 <= 5e-63)
		tmp = t_1;
	elseif (t_0 <= 2e+21)
		tmp = 1.0;
	elseif (t_0 <= 1e+278)
		tmp = t_1;
	else
		tmp = (0.5 * ((x / y) * (x / y))) + -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(y * N[(y * 4.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(N[(x * x), $MachinePrecision] - t$95$0), $MachinePrecision] / N[(t$95$0 + N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, 5e-128], 1.0, If[LessEqual[t$95$0, 5e-63], t$95$1, If[LessEqual[t$95$0, 2e+21], 1.0, If[LessEqual[t$95$0, 1e+278], t$95$1, N[(N[(0.5 * N[(N[(x / y), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 y 4) y) < 5.0000000000000001e-128 or 5.0000000000000002e-63 < (*.f64 (*.f64 y 4) y) < 2e21

   1. Initial program 55.7%

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

      1. *-commutative 55.7%

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

      2. fma-def 55.8%

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

      3. *-commutative 55.8%

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

   3. Simplified 55.8%

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

   4. Taylor expanded in x around inf 82.8%

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

   if 5.0000000000000001e-128 < (*.f64 (*.f64 y 4) y) < 5.0000000000000002e-63 or 2e21 < (*.f64 (*.f64 y 4) y) < 9.99999999999999964e277

   1. Initial program 83.8%

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

   if 9.99999999999999964e277 < (*.f64 (*.f64 y 4) y)

   1. Initial program 2.7%

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

      1. *-commutative 2.7%

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

      2. fma-def 2.7%

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

      3. *-commutative 2.7%

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

   3. Simplified 2.7%

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

   4. Taylor expanded in x around 0 74.7%

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

      1. unpow2 74.7%

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

      2. unpow2 74.7%

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

      3. times-frac 86.3%

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

   6. Applied egg-rr 86.3%

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

4. Final simplification 84.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(y \cdot 4\right) \leq 5 \cdot 10^{-128}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \cdot \left(y \cdot 4\right) \leq 5 \cdot 10^{-63}:\\ \;\;\;\;\frac{x \cdot x - y \cdot \left(y \cdot 4\right)}{y \cdot \left(y \cdot 4\right) + x \cdot x}\\ \mathbf{elif}\;y \cdot \left(y \cdot 4\right) \leq 2 \cdot 10^{+21}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \cdot \left(y \cdot 4\right) \leq 10^{+278}:\\ \;\;\;\;\frac{x \cdot x - y \cdot \left(y \cdot 4\right)}{y \cdot \left(y \cdot 4\right) + x \cdot x}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(\frac{x}{y} \cdot \frac{x}{y}\right) + -1\\ \end{array} \]

Alternative 3: 61.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 5.5 \cdot 10^{-63}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{-32} \lor \neg \left(y \leq 32000000000\right):\\ \;\;\;\;0.5 \cdot \left(\frac{x}{y} \cdot \frac{x}{y}\right) + -1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y 5.5e-63)
   1.0
   (if (or (<= y 5.8e-32) (not (<= y 32000000000.0)))
     (+ (* 0.5 (* (/ x y) (/ x y))) -1.0)
     1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= 5.5e-63) {
		tmp = 1.0;
	} else if ((y <= 5.8e-32) || !(y <= 32000000000.0)) {
		tmp = (0.5 * ((x / y) * (x / y))) + -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 <= 5.5d-63) then
        tmp = 1.0d0
    else if ((y <= 5.8d-32) .or. (.not. (y <= 32000000000.0d0))) then
        tmp = (0.5d0 * ((x / y) * (x / y))) + (-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 <= 5.5e-63) {
		tmp = 1.0;
	} else if ((y <= 5.8e-32) || !(y <= 32000000000.0)) {
		tmp = (0.5 * ((x / y) * (x / y))) + -1.0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 5.5e-63:
		tmp = 1.0
	elif (y <= 5.8e-32) or not (y <= 32000000000.0):
		tmp = (0.5 * ((x / y) * (x / y))) + -1.0
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 5.5e-63)
		tmp = 1.0;
	elseif ((y <= 5.8e-32) || !(y <= 32000000000.0))
		tmp = Float64(Float64(0.5 * Float64(Float64(x / y) * Float64(x / y))) + -1.0);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= 5.5e-63)
		tmp = 1.0;
	elseif ((y <= 5.8e-32) || ~((y <= 32000000000.0)))
		tmp = (0.5 * ((x / y) * (x / y))) + -1.0;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 5.5e-63], 1.0, If[Or[LessEqual[y, 5.8e-32], N[Not[LessEqual[y, 32000000000.0]], $MachinePrecision]], N[(N[(0.5 * N[(N[(x / y), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < 5.50000000000000043e-63 or 5.79999999999999991e-32 < y < 3.2e10

   1. Initial program 49.7%

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

      1. *-commutative 49.7%

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

      2. fma-def 49.7%

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

      3. *-commutative 49.7%

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

   3. Simplified 49.7%

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

   4. Taylor expanded in x around inf 60.7%

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

   if 5.50000000000000043e-63 < y < 5.79999999999999991e-32 or 3.2e10 < y

   1. Initial program 42.5%

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

      1. *-commutative 42.5%

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

      2. fma-def 42.5%

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

      3. *-commutative 42.5%

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

   3. Simplified 42.5%

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

   4. Taylor expanded in x around 0 78.4%

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

      1. unpow2 78.4%

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

      2. unpow2 78.4%

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

      3. times-frac 81.7%

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

   6. Applied egg-rr 81.7%

      \[\leadsto 0.5 \cdot \color{blue}{\left(\frac{x}{y} \cdot \frac{x}{y}\right)} - 1 \]
3. Recombined 2 regimes into one program.

4. Final simplification 66.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 5.5 \cdot 10^{-63}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{-32} \lor \neg \left(y \leq 32000000000\right):\\ \;\;\;\;0.5 \cdot \left(\frac{x}{y} \cdot \frac{x}{y}\right) + -1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 4: 61.5% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 4 \cdot 10^{-62}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-32}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 23000000000:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y 4e-62)
   1.0
   (if (<= y 4e-32) -1.0 (if (<= y 23000000000.0) 1.0 -1.0))))

C

double code(double x, double y) {
	double tmp;
	if (y <= 4e-62) {
		tmp = 1.0;
	} else if (y <= 4e-32) {
		tmp = -1.0;
	} else if (y <= 23000000000.0) {
		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 <= 4d-62) then
        tmp = 1.0d0
    else if (y <= 4d-32) then
        tmp = -1.0d0
    else if (y <= 23000000000.0d0) 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 <= 4e-62) {
		tmp = 1.0;
	} else if (y <= 4e-32) {
		tmp = -1.0;
	} else if (y <= 23000000000.0) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 4e-62:
		tmp = 1.0
	elif y <= 4e-32:
		tmp = -1.0
	elif y <= 23000000000.0:
		tmp = 1.0
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 4e-62)
		tmp = 1.0;
	elseif (y <= 4e-32)
		tmp = -1.0;
	elseif (y <= 23000000000.0)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= 4e-62)
		tmp = 1.0;
	elseif (y <= 4e-32)
		tmp = -1.0;
	elseif (y <= 23000000000.0)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 4e-62], 1.0, If[LessEqual[y, 4e-32], -1.0, If[LessEqual[y, 23000000000.0], 1.0, -1.0]]]

Derivation

1. Split input into 2 regimes

2. if y < 4.0000000000000002e-62 or 4.00000000000000022e-32 < y < 2.3e10

   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. Step-by-step derivation

      1. *-commutative 50.0%

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

      2. fma-def 50.0%

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

      3. *-commutative 50.0%

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

   3. Simplified 50.0%

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

   4. Taylor expanded in x around inf 60.9%

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

   if 4.0000000000000002e-62 < y < 4.00000000000000022e-32 or 2.3e10 < y

   1. Initial program 41.7%

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

      1. *-commutative 41.7%

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

      2. fma-def 41.7%

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

      3. *-commutative 41.7%

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

   3. Simplified 41.7%

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

   4. Taylor expanded in x around 0 82.2%

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

4. Final simplification 66.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 4 \cdot 10^{-62}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-32}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 23000000000:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 5: 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 47.6%

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

   1. *-commutative 47.6%

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

   2. fma-def 47.7%

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

   3. *-commutative 47.7%

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

3. Simplified 47.7%

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

4. Taylor expanded in x around 0 51.4%

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

5. Final simplification 51.4%

   \[\leadsto -1 \]

Developer target: 50.4% 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 2023310 
(FPCore (x y)
  :name "Diagrams.TwoD.Arc:arcBetween from diagrams-lib-1.3.0.3"
  :precision binary64

  :herbie-target
  (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))))