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

Percentage Accurate: 49.7% → 81.6%

Time: 10.0s

Alternatives: 6

Speedup: 19.0×

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: 49.7% 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: 81.6% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(y \cdot 4\right)\\ t_1 := \mathsf{hypot}\left(x, y \cdot 2\right)\\ \mathbf{if}\;x \cdot x \leq 2 \cdot 10^{-320}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \cdot x \leq 5 \cdot 10^{-281}:\\ \;\;\;\;\frac{x \cdot x - t\_0}{x \cdot x + t\_0}\\ \mathbf{elif}\;x \cdot x \leq 10^{-251}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \cdot x \leq 2 \cdot 10^{+266}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(y, y \cdot -4, {x}^{2}\right)}{t\_1}}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;1 + -8 \cdot \left(\frac{y}{x} \cdot \frac{y}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* y (* y 4.0))) (t_1 (hypot x (* y 2.0))))
   (if (<= (* x x) 2e-320)
     -1.0
     (if (<= (* x x) 5e-281)
       (/ (- (* x x) t_0) (+ (* x x) t_0))
       (if (<= (* x x) 1e-251)
         -1.0
         (if (<= (* x x) 2e+266)
           (/ (/ (fma y (* y -4.0) (pow x 2.0)) t_1) t_1)
           (+ 1.0 (* -8.0 (* (/ y x) (/ y x))))))))))

C

double code(double x, double y) {
	double t_0 = y * (y * 4.0);
	double t_1 = hypot(x, (y * 2.0));
	double tmp;
	if ((x * x) <= 2e-320) {
		tmp = -1.0;
	} else if ((x * x) <= 5e-281) {
		tmp = ((x * x) - t_0) / ((x * x) + t_0);
	} else if ((x * x) <= 1e-251) {
		tmp = -1.0;
	} else if ((x * x) <= 2e+266) {
		tmp = (fma(y, (y * -4.0), pow(x, 2.0)) / t_1) / t_1;
	} else {
		tmp = 1.0 + (-8.0 * ((y / x) * (y / x)));
	}
	return tmp;
}

Julia

function code(x, y)
	t_0 = Float64(y * Float64(y * 4.0))
	t_1 = hypot(x, Float64(y * 2.0))
	tmp = 0.0
	if (Float64(x * x) <= 2e-320)
		tmp = -1.0;
	elseif (Float64(x * x) <= 5e-281)
		tmp = Float64(Float64(Float64(x * x) - t_0) / Float64(Float64(x * x) + t_0));
	elseif (Float64(x * x) <= 1e-251)
		tmp = -1.0;
	elseif (Float64(x * x) <= 2e+266)
		tmp = Float64(Float64(fma(y, Float64(y * -4.0), (x ^ 2.0)) / t_1) / t_1);
	else
		tmp = Float64(1.0 + Float64(-8.0 * Float64(Float64(y / x) * Float64(y / x))));
	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[Sqrt[x ^ 2 + N[(y * 2.0), $MachinePrecision] ^ 2], $MachinePrecision]}, If[LessEqual[N[(x * x), $MachinePrecision], 2e-320], -1.0, If[LessEqual[N[(x * x), $MachinePrecision], 5e-281], N[(N[(N[(x * x), $MachinePrecision] - t$95$0), $MachinePrecision] / N[(N[(x * x), $MachinePrecision] + t$95$0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * x), $MachinePrecision], 1e-251], -1.0, If[LessEqual[N[(x * x), $MachinePrecision], 2e+266], N[(N[(N[(y * N[(y * -4.0), $MachinePrecision] + N[Power[x, 2.0], $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision] / t$95$1), $MachinePrecision], N[(1.0 + N[(-8.0 * N[(N[(y / x), $MachinePrecision] * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x x) < 1.99998e-320 or 4.9999999999999998e-281 < (*.f64 x x) < 1.00000000000000002e-251

   1. Initial program 43.1%

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

   3. Taylor expanded in x around 0 90.2%

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

   if 1.99998e-320 < (*.f64 x x) < 4.9999999999999998e-281

   1. Initial program 82.5%

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

   if 1.00000000000000002e-251 < (*.f64 x x) < 2.0000000000000001e266

   1. Initial program 78.3%

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

      1. clear-num 78.3%

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

      2. inv-pow 78.3%

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

      3. +-commutative 78.3%

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

      4. *-commutative 78.3%

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

      5. associate-*l* 78.3%

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

      6. fma-define 78.3%

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

      7. pow2 78.3%

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

      8. pow2 78.3%

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

      9. sub-neg 78.3%

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

      10. +-commutative 78.3%

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

      11. *-commutative 78.3%

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

      12. distribute-rgt-neg-in 78.3%

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

      13. fma-define 78.3%

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

      14. distribute-rgt-neg-in 78.3%

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

      15. metadata-eval 78.3%

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

      16. pow2 78.3%

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

   4. Applied egg-rr 78.3%

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

      1. fma-undefine 78.3%

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

      2. +-commutative 78.3%

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

   6. Applied egg-rr 78.3%

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

      1. unpow-1 78.3%

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

      2. +-commutative 78.3%

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

      3. fma-undefine 78.3%

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

      4. rem-exp-log 71.2%

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

      5. clear-num 71.3%

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

      6. rem-exp-log 78.2%

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

      7. add-sqr-sqrt 78.2%

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

      8. associate-/r* 78.2%

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

   8. Applied egg-rr 78.9%

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

   if 2.0000000000000001e266 < (*.f64 x x)

   1. Initial program 6.8%

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

   3. Taylor expanded in y around 0 76.8%

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

      1. unpow2 76.8%

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

      2. pow2 76.8%

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

      3. times-frac 91.0%

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

   5. Applied egg-rr 91.0%

      \[\leadsto 1 + -8 \cdot \color{blue}{\left(\frac{y}{x} \cdot \frac{y}{x}\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 85.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot x \leq 2 \cdot 10^{-320}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \cdot x \leq 5 \cdot 10^{-281}:\\ \;\;\;\;\frac{x \cdot x - y \cdot \left(y \cdot 4\right)}{x \cdot x + y \cdot \left(y \cdot 4\right)}\\ \mathbf{elif}\;x \cdot x \leq 10^{-251}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \cdot x \leq 2 \cdot 10^{+266}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(y, y \cdot -4, {x}^{2}\right)}{\mathsf{hypot}\left(x, y \cdot 2\right)}}{\mathsf{hypot}\left(x, y \cdot 2\right)}\\ \mathbf{else}:\\ \;\;\;\;1 + -8 \cdot \left(\frac{y}{x} \cdot \frac{y}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 81.3% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(y \cdot 4\right)\\ t_1 := x \cdot x - t\_0\\ \mathbf{if}\;x \cdot x \leq 2 \cdot 10^{-320}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \cdot x \leq 5 \cdot 10^{-281}:\\ \;\;\;\;\frac{t\_1}{x \cdot x + t\_0}\\ \mathbf{elif}\;x \cdot x \leq 10^{-251}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \cdot x \leq 2 \cdot 10^{+266}:\\ \;\;\;\;\frac{t\_1}{\mathsf{fma}\left(y \cdot 4, y, {x}^{2}\right)}\\ \mathbf{else}:\\ \;\;\;\;1 + -8 \cdot \left(\frac{y}{x} \cdot \frac{y}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* y (* y 4.0))) (t_1 (- (* x x) t_0)))
   (if (<= (* x x) 2e-320)
     -1.0
     (if (<= (* x x) 5e-281)
       (/ t_1 (+ (* x x) t_0))
       (if (<= (* x x) 1e-251)
         -1.0
         (if (<= (* x x) 2e+266)
           (/ t_1 (fma (* y 4.0) y (pow x 2.0)))
           (+ 1.0 (* -8.0 (* (/ y x) (/ y x))))))))))

C

double code(double x, double y) {
	double t_0 = y * (y * 4.0);
	double t_1 = (x * x) - t_0;
	double tmp;
	if ((x * x) <= 2e-320) {
		tmp = -1.0;
	} else if ((x * x) <= 5e-281) {
		tmp = t_1 / ((x * x) + t_0);
	} else if ((x * x) <= 1e-251) {
		tmp = -1.0;
	} else if ((x * x) <= 2e+266) {
		tmp = t_1 / fma((y * 4.0), y, pow(x, 2.0));
	} else {
		tmp = 1.0 + (-8.0 * ((y / x) * (y / x)));
	}
	return tmp;
}

Julia

function code(x, y)
	t_0 = Float64(y * Float64(y * 4.0))
	t_1 = Float64(Float64(x * x) - t_0)
	tmp = 0.0
	if (Float64(x * x) <= 2e-320)
		tmp = -1.0;
	elseif (Float64(x * x) <= 5e-281)
		tmp = Float64(t_1 / Float64(Float64(x * x) + t_0));
	elseif (Float64(x * x) <= 1e-251)
		tmp = -1.0;
	elseif (Float64(x * x) <= 2e+266)
		tmp = Float64(t_1 / fma(Float64(y * 4.0), y, (x ^ 2.0)));
	else
		tmp = Float64(1.0 + Float64(-8.0 * Float64(Float64(y / x) * Float64(y / x))));
	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[(x * x), $MachinePrecision] - t$95$0), $MachinePrecision]}, If[LessEqual[N[(x * x), $MachinePrecision], 2e-320], -1.0, If[LessEqual[N[(x * x), $MachinePrecision], 5e-281], N[(t$95$1 / N[(N[(x * x), $MachinePrecision] + t$95$0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * x), $MachinePrecision], 1e-251], -1.0, If[LessEqual[N[(x * x), $MachinePrecision], 2e+266], N[(t$95$1 / N[(N[(y * 4.0), $MachinePrecision] * y + N[Power[x, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(-8.0 * N[(N[(y / x), $MachinePrecision] * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x x) < 1.99998e-320 or 4.9999999999999998e-281 < (*.f64 x x) < 1.00000000000000002e-251

   1. Initial program 43.1%

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

   3. Taylor expanded in x around 0 90.2%

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

   if 1.99998e-320 < (*.f64 x x) < 4.9999999999999998e-281

   1. Initial program 82.5%

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

   if 1.00000000000000002e-251 < (*.f64 x x) < 2.0000000000000001e266

   1. Initial program 78.3%

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

      1. +-commutative 78.3%

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

      2. fma-define 78.3%

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

      3. pow2 78.3%

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

   4. Applied egg-rr 78.3%

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

   if 2.0000000000000001e266 < (*.f64 x x)

   1. Initial program 6.8%

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

   3. Taylor expanded in y around 0 76.8%

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

      1. unpow2 76.8%

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

      2. pow2 76.8%

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

      3. times-frac 91.0%

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

   5. Applied egg-rr 91.0%

      \[\leadsto 1 + -8 \cdot \color{blue}{\left(\frac{y}{x} \cdot \frac{y}{x}\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 85.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot x \leq 2 \cdot 10^{-320}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \cdot x \leq 5 \cdot 10^{-281}:\\ \;\;\;\;\frac{x \cdot x - y \cdot \left(y \cdot 4\right)}{x \cdot x + y \cdot \left(y \cdot 4\right)}\\ \mathbf{elif}\;x \cdot x \leq 10^{-251}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \cdot x \leq 2 \cdot 10^{+266}:\\ \;\;\;\;\frac{x \cdot x - y \cdot \left(y \cdot 4\right)}{\mathsf{fma}\left(y \cdot 4, y, {x}^{2}\right)}\\ \mathbf{else}:\\ \;\;\;\;1 + -8 \cdot \left(\frac{y}{x} \cdot \frac{y}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 81.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(y \cdot 4\right)\\ t_1 := \frac{x \cdot x - t\_0}{x \cdot x + t\_0}\\ \mathbf{if}\;x \cdot x \leq 2 \cdot 10^{-320}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \cdot x \leq 5 \cdot 10^{-281}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot x \leq 10^{-251}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \cdot x \leq 2 \cdot 10^{+266}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;1 + -8 \cdot \left(\frac{y}{x} \cdot \frac{y}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* y (* y 4.0))) (t_1 (/ (- (* x x) t_0) (+ (* x x) t_0))))
   (if (<= (* x x) 2e-320)
     -1.0
     (if (<= (* x x) 5e-281)
       t_1
       (if (<= (* x x) 1e-251)
         -1.0
         (if (<= (* x x) 2e+266) t_1 (+ 1.0 (* -8.0 (* (/ y x) (/ y x))))))))))

C

double code(double x, double y) {
	double t_0 = y * (y * 4.0);
	double t_1 = ((x * x) - t_0) / ((x * x) + t_0);
	double tmp;
	if ((x * x) <= 2e-320) {
		tmp = -1.0;
	} else if ((x * x) <= 5e-281) {
		tmp = t_1;
	} else if ((x * x) <= 1e-251) {
		tmp = -1.0;
	} else if ((x * x) <= 2e+266) {
		tmp = t_1;
	} else {
		tmp = 1.0 + (-8.0 * ((y / x) * (y / x)));
	}
	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) / ((x * x) + t_0)
    if ((x * x) <= 2d-320) then
        tmp = -1.0d0
    else if ((x * x) <= 5d-281) then
        tmp = t_1
    else if ((x * x) <= 1d-251) then
        tmp = -1.0d0
    else if ((x * x) <= 2d+266) then
        tmp = t_1
    else
        tmp = 1.0d0 + ((-8.0d0) * ((y / x) * (y / x)))
    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) / ((x * x) + t_0);
	double tmp;
	if ((x * x) <= 2e-320) {
		tmp = -1.0;
	} else if ((x * x) <= 5e-281) {
		tmp = t_1;
	} else if ((x * x) <= 1e-251) {
		tmp = -1.0;
	} else if ((x * x) <= 2e+266) {
		tmp = t_1;
	} else {
		tmp = 1.0 + (-8.0 * ((y / x) * (y / x)));
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = y * (y * 4.0)
	t_1 = ((x * x) - t_0) / ((x * x) + t_0)
	tmp = 0
	if (x * x) <= 2e-320:
		tmp = -1.0
	elif (x * x) <= 5e-281:
		tmp = t_1
	elif (x * x) <= 1e-251:
		tmp = -1.0
	elif (x * x) <= 2e+266:
		tmp = t_1
	else:
		tmp = 1.0 + (-8.0 * ((y / x) * (y / x)))
	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(Float64(x * x) + t_0))
	tmp = 0.0
	if (Float64(x * x) <= 2e-320)
		tmp = -1.0;
	elseif (Float64(x * x) <= 5e-281)
		tmp = t_1;
	elseif (Float64(x * x) <= 1e-251)
		tmp = -1.0;
	elseif (Float64(x * x) <= 2e+266)
		tmp = t_1;
	else
		tmp = Float64(1.0 + Float64(-8.0 * Float64(Float64(y / x) * Float64(y / x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = y * (y * 4.0);
	t_1 = ((x * x) - t_0) / ((x * x) + t_0);
	tmp = 0.0;
	if ((x * x) <= 2e-320)
		tmp = -1.0;
	elseif ((x * x) <= 5e-281)
		tmp = t_1;
	elseif ((x * x) <= 1e-251)
		tmp = -1.0;
	elseif ((x * x) <= 2e+266)
		tmp = t_1;
	else
		tmp = 1.0 + (-8.0 * ((y / x) * (y / x)));
	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[(N[(x * x), $MachinePrecision] + t$95$0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * x), $MachinePrecision], 2e-320], -1.0, If[LessEqual[N[(x * x), $MachinePrecision], 5e-281], t$95$1, If[LessEqual[N[(x * x), $MachinePrecision], 1e-251], -1.0, If[LessEqual[N[(x * x), $MachinePrecision], 2e+266], t$95$1, N[(1.0 + N[(-8.0 * N[(N[(y / x), $MachinePrecision] * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x x) < 1.99998e-320 or 4.9999999999999998e-281 < (*.f64 x x) < 1.00000000000000002e-251

   1. Initial program 43.1%

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

   3. Taylor expanded in x around 0 90.2%

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

   if 1.99998e-320 < (*.f64 x x) < 4.9999999999999998e-281 or 1.00000000000000002e-251 < (*.f64 x x) < 2.0000000000000001e266

   1. Initial program 78.7%

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

   if 2.0000000000000001e266 < (*.f64 x x)

   1. Initial program 6.8%

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

   3. Taylor expanded in y around 0 76.8%

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

      1. unpow2 76.8%

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

      2. pow2 76.8%

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

      3. times-frac 91.0%

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

   5. Applied egg-rr 91.0%

      \[\leadsto 1 + -8 \cdot \color{blue}{\left(\frac{y}{x} \cdot \frac{y}{x}\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 85.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot x \leq 2 \cdot 10^{-320}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \cdot x \leq 5 \cdot 10^{-281}:\\ \;\;\;\;\frac{x \cdot x - y \cdot \left(y \cdot 4\right)}{x \cdot x + y \cdot \left(y \cdot 4\right)}\\ \mathbf{elif}\;x \cdot x \leq 10^{-251}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \cdot x \leq 2 \cdot 10^{+266}:\\ \;\;\;\;\frac{x \cdot x - y \cdot \left(y \cdot 4\right)}{x \cdot x + y \cdot \left(y \cdot 4\right)}\\ \mathbf{else}:\\ \;\;\;\;1 + -8 \cdot \left(\frac{y}{x} \cdot \frac{y}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 63.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 5.2 \cdot 10^{-151}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 5.1 \cdot 10^{-141}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 2.05 \cdot 10^{+32}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x 5.2e-151)
   -1.0
   (if (<= x 5.1e-141) 1.0 (if (<= x 2.05e+32) -1.0 1.0))))

C

double code(double x, double y) {
	double tmp;
	if (x <= 5.2e-151) {
		tmp = -1.0;
	} else if (x <= 5.1e-141) {
		tmp = 1.0;
	} else if (x <= 2.05e+32) {
		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 (x <= 5.2d-151) then
        tmp = -1.0d0
    else if (x <= 5.1d-141) then
        tmp = 1.0d0
    else if (x <= 2.05d+32) 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 (x <= 5.2e-151) {
		tmp = -1.0;
	} else if (x <= 5.1e-141) {
		tmp = 1.0;
	} else if (x <= 2.05e+32) {
		tmp = -1.0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 5.2e-151:
		tmp = -1.0
	elif x <= 5.1e-141:
		tmp = 1.0
	elif x <= 2.05e+32:
		tmp = -1.0
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= 5.2e-151)
		tmp = -1.0;
	elseif (x <= 5.1e-141)
		tmp = 1.0;
	elseif (x <= 2.05e+32)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= 5.2e-151)
		tmp = -1.0;
	elseif (x <= 5.1e-141)
		tmp = 1.0;
	elseif (x <= 2.05e+32)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 5.2e-151], -1.0, If[LessEqual[x, 5.1e-141], 1.0, If[LessEqual[x, 2.05e+32], -1.0, 1.0]]]

Derivation

1. Split input into 2 regimes

2. if x < 5.2000000000000001e-151 or 5.09999999999999977e-141 < x < 2.0499999999999999e32

   1. Initial program 52.0%

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

   3. Taylor expanded in x around 0 55.7%

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

   if 5.2000000000000001e-151 < x < 5.09999999999999977e-141 or 2.0499999999999999e32 < x

   1. Initial program 40.0%

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

   3. Taylor expanded in x around inf 82.0%

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

4. Final simplification 61.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 5.2 \cdot 10^{-151}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 5.1 \cdot 10^{-141}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 2.05 \cdot 10^{+32}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 62.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.6 \cdot 10^{+68}:\\ \;\;\;\;1 + -8 \cdot \left(\frac{y}{x} \cdot \frac{y}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y 1.6e+68) (+ 1.0 (* -8.0 (* (/ y x) (/ y x)))) -1.0))

C

double code(double x, double y) {
	double tmp;
	if (y <= 1.6e+68) {
		tmp = 1.0 + (-8.0 * ((y / x) * (y / 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) :: tmp
    if (y <= 1.6d+68) then
        tmp = 1.0d0 + ((-8.0d0) * ((y / x) * (y / x)))
    else
        tmp = -1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= 1.6e+68) {
		tmp = 1.0 + (-8.0 * ((y / x) * (y / x)));
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 1.6e+68:
		tmp = 1.0 + (-8.0 * ((y / x) * (y / x)))
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 1.6e+68)
		tmp = Float64(1.0 + Float64(-8.0 * Float64(Float64(y / x) * Float64(y / x))));
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= 1.6e+68)
		tmp = 1.0 + (-8.0 * ((y / x) * (y / x)));
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 1.6e+68], N[(1.0 + N[(-8.0 * N[(N[(y / x), $MachinePrecision] * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], -1.0]

Derivation

1. Split input into 2 regimes

2. if y < 1.59999999999999997e68

   1. Initial program 53.7%

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

   3. Taylor expanded in y around 0 57.8%

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

      1. unpow2 57.8%

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

      2. pow2 57.8%

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

      3. times-frac 63.5%

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

   5. Applied egg-rr 63.5%

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

   if 1.59999999999999997e68 < y

   1. Initial program 32.7%

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

   3. Taylor expanded in x around 0 82.8%

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

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.6 \cdot 10^{+68}:\\ \;\;\;\;1 + -8 \cdot \left(\frac{y}{x} \cdot \frac{y}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 50.3% 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 49.2%

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

3. Taylor expanded in x around 0 47.2%

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

4. Final simplification 47.2%

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

Developer target: 50.2% 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 2024085 
(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))))