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

Percentage Accurate: 43.9% → 56.6%

Time: 11.9s

Alternatives: 8

Speedup: 244.0×

Specification

Math

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

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ x (* y 2.0)))) (/ (tan t_0) (sin t_0))))

C

double code(double x, double y) {
	double t_0 = x / (y * 2.0);
	return tan(t_0) / sin(t_0);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    t_0 = x / (y * 2.0d0)
    code = tan(t_0) / sin(t_0)
end function

Java

public static double code(double x, double y) {
	double t_0 = x / (y * 2.0);
	return Math.tan(t_0) / Math.sin(t_0);
}

Python

def code(x, y):
	t_0 = x / (y * 2.0)
	return math.tan(t_0) / math.sin(t_0)

Julia

function code(x, y)
	t_0 = Float64(x / Float64(y * 2.0))
	return Float64(tan(t_0) / sin(t_0))
end

MATLAB

function tmp = code(x, y)
	t_0 = x / (y * 2.0);
	tmp = tan(t_0) / sin(t_0);
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(x / N[(y * 2.0), $MachinePrecision]), $MachinePrecision]}, N[(N[Tan[t$95$0], $MachinePrecision] / N[Sin[t$95$0], $MachinePrecision]), $MachinePrecision]]

Initial Program: 43.9% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ x (* y 2.0)))) (/ (tan t_0) (sin t_0))))

C

double code(double x, double y) {
	double t_0 = x / (y * 2.0);
	return tan(t_0) / sin(t_0);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    t_0 = x / (y * 2.0d0)
    code = tan(t_0) / sin(t_0)
end function

Java

public static double code(double x, double y) {
	double t_0 = x / (y * 2.0);
	return Math.tan(t_0) / Math.sin(t_0);
}

Python

def code(x, y):
	t_0 = x / (y * 2.0)
	return math.tan(t_0) / math.sin(t_0)

Julia

function code(x, y)
	t_0 = Float64(x / Float64(y * 2.0))
	return Float64(tan(t_0) / sin(t_0))
end

MATLAB

function tmp = code(x, y)
	t_0 = x / (y * 2.0);
	tmp = tan(t_0) / sin(t_0);
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(x / N[(y * 2.0), $MachinePrecision]), $MachinePrecision]}, N[(N[Tan[t$95$0], $MachinePrecision] / N[Sin[t$95$0], $MachinePrecision]), $MachinePrecision]]

Alternative 1: 56.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ x_m = \left|x\right| \\ \begin{array}{l} t_0 := -0.5 \cdot \frac{x\_m}{y\_m}\\ t_1 := \cos t\_0\\ \mathbf{if}\;\frac{x\_m}{2 \cdot y\_m} \leq 5 \cdot 10^{+264}:\\ \;\;\;\;\frac{{t\_1}^{2} \cdot \frac{-1}{\frac{{\left(\cos \left(\frac{0}{\frac{y\_m}{x\_m}}\right) + \frac{1}{\frac{1}{{t\_1}^{4} - {\sin t\_0}^{4}}}\right)}^{3}}{8}}}{{\left(-t\_1\right)}^{-3}}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

y_m = (fabs.f64 y)
x_m = (fabs.f64 x)
(FPCore (x_m y_m)
 :precision binary64
 (let* ((t_0 (* -0.5 (/ x_m y_m))) (t_1 (cos t_0)))
   (if (<= (/ x_m (* 2.0 y_m)) 5e+264)
     (/
      (*
       (pow t_1 2.0)
       (/
        -1.0
        (/
         (pow
          (+
           (cos (/ 0.0 (/ y_m x_m)))
           (/ 1.0 (/ 1.0 (- (pow t_1 4.0) (pow (sin t_0) 4.0)))))
          3.0)
         8.0)))
      (pow (- t_1) -3.0))
     -1.0)))

C

y_m = fabs(y);
x_m = fabs(x);
double code(double x_m, double y_m) {
	double t_0 = -0.5 * (x_m / y_m);
	double t_1 = cos(t_0);
	double tmp;
	if ((x_m / (2.0 * y_m)) <= 5e+264) {
		tmp = (pow(t_1, 2.0) * (-1.0 / (pow((cos((0.0 / (y_m / x_m))) + (1.0 / (1.0 / (pow(t_1, 4.0) - pow(sin(t_0), 4.0))))), 3.0) / 8.0))) / pow(-t_1, -3.0);
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Fortran

y_m = abs(y)
x_m = abs(x)
real(8) function code(x_m, y_m)
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y_m
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (-0.5d0) * (x_m / y_m)
    t_1 = cos(t_0)
    if ((x_m / (2.0d0 * y_m)) <= 5d+264) then
        tmp = ((t_1 ** 2.0d0) * ((-1.0d0) / (((cos((0.0d0 / (y_m / x_m))) + (1.0d0 / (1.0d0 / ((t_1 ** 4.0d0) - (sin(t_0) ** 4.0d0))))) ** 3.0d0) / 8.0d0))) / (-t_1 ** (-3.0d0))
    else
        tmp = -1.0d0
    end if
    code = tmp
end function

Java

y_m = Math.abs(y);
x_m = Math.abs(x);
public static double code(double x_m, double y_m) {
	double t_0 = -0.5 * (x_m / y_m);
	double t_1 = Math.cos(t_0);
	double tmp;
	if ((x_m / (2.0 * y_m)) <= 5e+264) {
		tmp = (Math.pow(t_1, 2.0) * (-1.0 / (Math.pow((Math.cos((0.0 / (y_m / x_m))) + (1.0 / (1.0 / (Math.pow(t_1, 4.0) - Math.pow(Math.sin(t_0), 4.0))))), 3.0) / 8.0))) / Math.pow(-t_1, -3.0);
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

y_m = math.fabs(y)
x_m = math.fabs(x)
def code(x_m, y_m):
	t_0 = -0.5 * (x_m / y_m)
	t_1 = math.cos(t_0)
	tmp = 0
	if (x_m / (2.0 * y_m)) <= 5e+264:
		tmp = (math.pow(t_1, 2.0) * (-1.0 / (math.pow((math.cos((0.0 / (y_m / x_m))) + (1.0 / (1.0 / (math.pow(t_1, 4.0) - math.pow(math.sin(t_0), 4.0))))), 3.0) / 8.0))) / math.pow(-t_1, -3.0)
	else:
		tmp = -1.0
	return tmp

Julia

y_m = abs(y)
x_m = abs(x)
function code(x_m, y_m)
	t_0 = Float64(-0.5 * Float64(x_m / y_m))
	t_1 = cos(t_0)
	tmp = 0.0
	if (Float64(x_m / Float64(2.0 * y_m)) <= 5e+264)
		tmp = Float64(Float64((t_1 ^ 2.0) * Float64(-1.0 / Float64((Float64(cos(Float64(0.0 / Float64(y_m / x_m))) + Float64(1.0 / Float64(1.0 / Float64((t_1 ^ 4.0) - (sin(t_0) ^ 4.0))))) ^ 3.0) / 8.0))) / (Float64(-t_1) ^ -3.0));
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

y_m = abs(y);
x_m = abs(x);
function tmp_2 = code(x_m, y_m)
	t_0 = -0.5 * (x_m / y_m);
	t_1 = cos(t_0);
	tmp = 0.0;
	if ((x_m / (2.0 * y_m)) <= 5e+264)
		tmp = ((t_1 ^ 2.0) * (-1.0 / (((cos((0.0 / (y_m / x_m))) + (1.0 / (1.0 / ((t_1 ^ 4.0) - (sin(t_0) ^ 4.0))))) ^ 3.0) / 8.0))) / (-t_1 ^ -3.0);
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

y_m = N[Abs[y], $MachinePrecision]
x_m = N[Abs[x], $MachinePrecision]
code[x$95$m_, y$95$m_] := Block[{t$95$0 = N[(-0.5 * N[(x$95$m / y$95$m), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[Cos[t$95$0], $MachinePrecision]}, If[LessEqual[N[(x$95$m / N[(2.0 * y$95$m), $MachinePrecision]), $MachinePrecision], 5e+264], N[(N[(N[Power[t$95$1, 2.0], $MachinePrecision] * N[(-1.0 / N[(N[Power[N[(N[Cos[N[(0.0 / N[(y$95$m / x$95$m), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] + N[(1.0 / N[(1.0 / N[(N[Power[t$95$1, 4.0], $MachinePrecision] - N[Power[N[Sin[t$95$0], $MachinePrecision], 4.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 3.0], $MachinePrecision] / 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[Power[(-t$95$1), -3.0], $MachinePrecision]), $MachinePrecision], -1.0]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (*.f64 y #s(literal 2 binary64))) < 5.00000000000000033e264

   1. Initial program 50.6%

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

   4. Applied rewrites 59.3%

      \[\leadsto \color{blue}{\frac{0 - {\left(\frac{-1}{\cos \left(-0.5 \cdot \frac{x}{y}\right)}\right)}^{3}}{0 + \mathsf{fma}\left(\frac{-1}{\cos \left(-0.5 \cdot \frac{x}{y}\right)}, \frac{-1}{\cos \left(-0.5 \cdot \frac{x}{y}\right)}, 0\right)}} \]

   6. Applied rewrites 59.3%

      \[\leadsto \color{blue}{\frac{\frac{-1}{{\cos \left(\frac{x}{y} \cdot -0.5\right)}^{6}} \cdot {\cos \left(\frac{x}{y} \cdot -0.5\right)}^{2}}{{\left(-\cos \left(\frac{x}{y} \cdot -0.5\right)\right)}^{-3}}} \]
   7. Step-by-step derivation

      1. lift-pow.f64 N/A

         \[\leadsto \frac{\frac{-1}{\color{blue}{{\cos \left(\frac{x}{y} \cdot \frac{-1}{2}\right)}^{6}}} \cdot {\cos \left(\frac{x}{y} \cdot \frac{-1}{2}\right)}^{2}}{{\left(-\cos \left(\frac{x}{y} \cdot \frac{-1}{2}\right)\right)}^{-3}} \]

      2. metadata-eval N/A

         \[\leadsto \frac{\frac{-1}{{\cos \left(\frac{x}{y} \cdot \frac{-1}{2}\right)}^{\color{blue}{\left(2 \cdot 3\right)}}} \cdot {\cos \left(\frac{x}{y} \cdot \frac{-1}{2}\right)}^{2}}{{\left(-\cos \left(\frac{x}{y} \cdot \frac{-1}{2}\right)\right)}^{-3}} \]

      3. pow-sqr N/A

         \[\leadsto \frac{\frac{-1}{\color{blue}{{\cos \left(\frac{x}{y} \cdot \frac{-1}{2}\right)}^{3} \cdot {\cos \left(\frac{x}{y} \cdot \frac{-1}{2}\right)}^{3}}} \cdot {\cos \left(\frac{x}{y} \cdot \frac{-1}{2}\right)}^{2}}{{\left(-\cos \left(\frac{x}{y} \cdot \frac{-1}{2}\right)\right)}^{-3}} \]

      4. pow-prod-down N/A

         \[\leadsto \frac{\frac{-1}{\color{blue}{{\left(\cos \left(\frac{x}{y} \cdot \frac{-1}{2}\right) \cdot \cos \left(\frac{x}{y} \cdot \frac{-1}{2}\right)\right)}^{3}}} \cdot {\cos \left(\frac{x}{y} \cdot \frac{-1}{2}\right)}^{2}}{{\left(-\cos \left(\frac{x}{y} \cdot \frac{-1}{2}\right)\right)}^{-3}} \]

      5. lift-cos.f64 N/A

         \[\leadsto \frac{\frac{-1}{{\left(\color{blue}{\cos \left(\frac{x}{y} \cdot \frac{-1}{2}\right)} \cdot \cos \left(\frac{x}{y} \cdot \frac{-1}{2}\right)\right)}^{3}} \cdot {\cos \left(\frac{x}{y} \cdot \frac{-1}{2}\right)}^{2}}{{\left(-\cos \left(\frac{x}{y} \cdot \frac{-1}{2}\right)\right)}^{-3}} \]

      6. lift-cos.f64 N/A

         \[\leadsto \frac{\frac{-1}{{\left(\cos \left(\frac{x}{y} \cdot \frac{-1}{2}\right) \cdot \color{blue}{\cos \left(\frac{x}{y} \cdot \frac{-1}{2}\right)}\right)}^{3}} \cdot {\cos \left(\frac{x}{y} \cdot \frac{-1}{2}\right)}^{2}}{{\left(-\cos \left(\frac{x}{y} \cdot \frac{-1}{2}\right)\right)}^{-3}} \]

      7. cos-mult N/A

         \[\leadsto \frac{\frac{-1}{{\color{blue}{\left(\frac{\cos \left(\frac{x}{y} \cdot \frac{-1}{2} + \frac{x}{y} \cdot \frac{-1}{2}\right) + \cos \left(\frac{x}{y} \cdot \frac{-1}{2} - \frac{x}{y} \cdot \frac{-1}{2}\right)}{2}\right)}}^{3}} \cdot {\cos \left(\frac{x}{y} \cdot \frac{-1}{2}\right)}^{2}}{{\left(-\cos \left(\frac{x}{y} \cdot \frac{-1}{2}\right)\right)}^{-3}} \]

      8. cube-div N/A

         \[\leadsto \frac{\frac{-1}{\color{blue}{\frac{{\left(\cos \left(\frac{x}{y} \cdot \frac{-1}{2} + \frac{x}{y} \cdot \frac{-1}{2}\right) + \cos \left(\frac{x}{y} \cdot \frac{-1}{2} - \frac{x}{y} \cdot \frac{-1}{2}\right)\right)}^{3}}{{2}^{3}}}} \cdot {\cos \left(\frac{x}{y} \cdot \frac{-1}{2}\right)}^{2}}{{\left(-\cos \left(\frac{x}{y} \cdot \frac{-1}{2}\right)\right)}^{-3}} \]

      9. metadata-eval N/A

         \[\leadsto \frac{\frac{-1}{\frac{{\left(\cos \left(\frac{x}{y} \cdot \frac{-1}{2} + \frac{x}{y} \cdot \frac{-1}{2}\right) + \cos \left(\frac{x}{y} \cdot \frac{-1}{2} - \frac{x}{y} \cdot \frac{-1}{2}\right)\right)}^{3}}{\color{blue}{8}}} \cdot {\cos \left(\frac{x}{y} \cdot \frac{-1}{2}\right)}^{2}}{{\left(-\cos \left(\frac{x}{y} \cdot \frac{-1}{2}\right)\right)}^{-3}} \]

      10. metadata-eval N/A

          \[\leadsto \frac{\frac{-1}{\frac{{\left(\cos \left(\frac{x}{y} \cdot \frac{-1}{2} + \frac{x}{y} \cdot \frac{-1}{2}\right) + \cos \left(\frac{x}{y} \cdot \frac{-1}{2} - \frac{x}{y} \cdot \frac{-1}{2}\right)\right)}^{3}}{\color{blue}{\frac{1}{\frac{1}{8}}}}} \cdot {\cos \left(\frac{x}{y} \cdot \frac{-1}{2}\right)}^{2}}{{\left(-\cos \left(\frac{x}{y} \cdot \frac{-1}{2}\right)\right)}^{-3}} \]

      11. lower-/.f64 N/A

          \[\leadsto \frac{\frac{-1}{\color{blue}{\frac{{\left(\cos \left(\frac{x}{y} \cdot \frac{-1}{2} + \frac{x}{y} \cdot \frac{-1}{2}\right) + \cos \left(\frac{x}{y} \cdot \frac{-1}{2} - \frac{x}{y} \cdot \frac{-1}{2}\right)\right)}^{3}}{\frac{1}{\frac{1}{8}}}}} \cdot {\cos \left(\frac{x}{y} \cdot \frac{-1}{2}\right)}^{2}}{{\left(-\cos \left(\frac{x}{y} \cdot \frac{-1}{2}\right)\right)}^{-3}} \]

   8. Applied rewrites 59.3%

      \[\leadsto \frac{\frac{-1}{\color{blue}{\frac{{\left(\cos \left(2 \cdot \left(-0.5 \cdot \frac{x}{y}\right)\right) + \cos \left(\frac{0}{\frac{y}{x}}\right)\right)}^{3}}{8}}} \cdot {\cos \left(\frac{x}{y} \cdot -0.5\right)}^{2}}{{\left(-\cos \left(\frac{x}{y} \cdot -0.5\right)\right)}^{-3}} \]
   9. Step-by-step derivation

      1. lift-cos.f64 N/A

         \[\leadsto \frac{\frac{-1}{\frac{{\left(\color{blue}{\cos \left(2 \cdot \left(\frac{-1}{2} \cdot \frac{x}{y}\right)\right)} + \cos \left(\frac{0}{\frac{y}{x}}\right)\right)}^{3}}{8}} \cdot {\cos \left(\frac{x}{y} \cdot \frac{-1}{2}\right)}^{2}}{{\left(-\cos \left(\frac{x}{y} \cdot \frac{-1}{2}\right)\right)}^{-3}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\frac{-1}{\frac{{\left(\cos \color{blue}{\left(2 \cdot \left(\frac{-1}{2} \cdot \frac{x}{y}\right)\right)} + \cos \left(\frac{0}{\frac{y}{x}}\right)\right)}^{3}}{8}} \cdot {\cos \left(\frac{x}{y} \cdot \frac{-1}{2}\right)}^{2}}{{\left(-\cos \left(\frac{x}{y} \cdot \frac{-1}{2}\right)\right)}^{-3}} \]

      3. cos-2 N/A

         \[\leadsto \frac{\frac{-1}{\frac{{\left(\color{blue}{\left(\cos \left(\frac{-1}{2} \cdot \frac{x}{y}\right) \cdot \cos \left(\frac{-1}{2} \cdot \frac{x}{y}\right) - \sin \left(\frac{-1}{2} \cdot \frac{x}{y}\right) \cdot \sin \left(\frac{-1}{2} \cdot \frac{x}{y}\right)\right)} + \cos \left(\frac{0}{\frac{y}{x}}\right)\right)}^{3}}{8}} \cdot {\cos \left(\frac{x}{y} \cdot \frac{-1}{2}\right)}^{2}}{{\left(-\cos \left(\frac{x}{y} \cdot \frac{-1}{2}\right)\right)}^{-3}} \]

      4. flip-- N/A

         \[\leadsto \frac{\frac{-1}{\frac{{\left(\color{blue}{\frac{\left(\cos \left(\frac{-1}{2} \cdot \frac{x}{y}\right) \cdot \cos \left(\frac{-1}{2} \cdot \frac{x}{y}\right)\right) \cdot \left(\cos \left(\frac{-1}{2} \cdot \frac{x}{y}\right) \cdot \cos \left(\frac{-1}{2} \cdot \frac{x}{y}\right)\right) - \left(\sin \left(\frac{-1}{2} \cdot \frac{x}{y}\right) \cdot \sin \left(\frac{-1}{2} \cdot \frac{x}{y}\right)\right) \cdot \left(\sin \left(\frac{-1}{2} \cdot \frac{x}{y}\right) \cdot \sin \left(\frac{-1}{2} \cdot \frac{x}{y}\right)\right)}{\cos \left(\frac{-1}{2} \cdot \frac{x}{y}\right) \cdot \cos \left(\frac{-1}{2} \cdot \frac{x}{y}\right) + \sin \left(\frac{-1}{2} \cdot \frac{x}{y}\right) \cdot \sin \left(\frac{-1}{2} \cdot \frac{x}{y}\right)}} + \cos \left(\frac{0}{\frac{y}{x}}\right)\right)}^{3}}{8}} \cdot {\cos \left(\frac{x}{y} \cdot \frac{-1}{2}\right)}^{2}}{{\left(-\cos \left(\frac{x}{y} \cdot \frac{-1}{2}\right)\right)}^{-3}} \]

      5. cos-sin-sum N/A

         \[\leadsto \frac{\frac{-1}{\frac{{\left(\frac{\left(\cos \left(\frac{-1}{2} \cdot \frac{x}{y}\right) \cdot \cos \left(\frac{-1}{2} \cdot \frac{x}{y}\right)\right) \cdot \left(\cos \left(\frac{-1}{2} \cdot \frac{x}{y}\right) \cdot \cos \left(\frac{-1}{2} \cdot \frac{x}{y}\right)\right) - \left(\sin \left(\frac{-1}{2} \cdot \frac{x}{y}\right) \cdot \sin \left(\frac{-1}{2} \cdot \frac{x}{y}\right)\right) \cdot \left(\sin \left(\frac{-1}{2} \cdot \frac{x}{y}\right) \cdot \sin \left(\frac{-1}{2} \cdot \frac{x}{y}\right)\right)}{\color{blue}{1}} + \cos \left(\frac{0}{\frac{y}{x}}\right)\right)}^{3}}{8}} \cdot {\cos \left(\frac{x}{y} \cdot \frac{-1}{2}\right)}^{2}}{{\left(-\cos \left(\frac{x}{y} \cdot \frac{-1}{2}\right)\right)}^{-3}} \]

      6. clear-num N/A

         \[\leadsto \frac{\frac{-1}{\frac{{\left(\color{blue}{\frac{1}{\frac{1}{\left(\cos \left(\frac{-1}{2} \cdot \frac{x}{y}\right) \cdot \cos \left(\frac{-1}{2} \cdot \frac{x}{y}\right)\right) \cdot \left(\cos \left(\frac{-1}{2} \cdot \frac{x}{y}\right) \cdot \cos \left(\frac{-1}{2} \cdot \frac{x}{y}\right)\right) - \left(\sin \left(\frac{-1}{2} \cdot \frac{x}{y}\right) \cdot \sin \left(\frac{-1}{2} \cdot \frac{x}{y}\right)\right) \cdot \left(\sin \left(\frac{-1}{2} \cdot \frac{x}{y}\right) \cdot \sin \left(\frac{-1}{2} \cdot \frac{x}{y}\right)\right)}}} + \cos \left(\frac{0}{\frac{y}{x}}\right)\right)}^{3}}{8}} \cdot {\cos \left(\frac{x}{y} \cdot \frac{-1}{2}\right)}^{2}}{{\left(-\cos \left(\frac{x}{y} \cdot \frac{-1}{2}\right)\right)}^{-3}} \]

      7. lower-/.f64 N/A

         \[\leadsto \frac{\frac{-1}{\frac{{\left(\color{blue}{\frac{1}{\frac{1}{\left(\cos \left(\frac{-1}{2} \cdot \frac{x}{y}\right) \cdot \cos \left(\frac{-1}{2} \cdot \frac{x}{y}\right)\right) \cdot \left(\cos \left(\frac{-1}{2} \cdot \frac{x}{y}\right) \cdot \cos \left(\frac{-1}{2} \cdot \frac{x}{y}\right)\right) - \left(\sin \left(\frac{-1}{2} \cdot \frac{x}{y}\right) \cdot \sin \left(\frac{-1}{2} \cdot \frac{x}{y}\right)\right) \cdot \left(\sin \left(\frac{-1}{2} \cdot \frac{x}{y}\right) \cdot \sin \left(\frac{-1}{2} \cdot \frac{x}{y}\right)\right)}}} + \cos \left(\frac{0}{\frac{y}{x}}\right)\right)}^{3}}{8}} \cdot {\cos \left(\frac{x}{y} \cdot \frac{-1}{2}\right)}^{2}}{{\left(-\cos \left(\frac{x}{y} \cdot \frac{-1}{2}\right)\right)}^{-3}} \]

   10. Applied rewrites 59.3%

       \[\leadsto \frac{\frac{-1}{\frac{{\left(\color{blue}{\frac{1}{\frac{1}{{\cos \left(\frac{x}{y} \cdot -0.5\right)}^{4} - {\sin \left(\frac{x}{y} \cdot -0.5\right)}^{4}}}} + \cos \left(\frac{0}{\frac{y}{x}}\right)\right)}^{3}}{8}} \cdot {\cos \left(\frac{x}{y} \cdot -0.5\right)}^{2}}{{\left(-\cos \left(\frac{x}{y} \cdot -0.5\right)\right)}^{-3}} \]

   if 5.00000000000000033e264 < (/.f64 x (*.f64 y #s(literal 2 binary64)))

   1. Initial program 0.2%

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

   4. Applied rewrites 0.2%

      \[\leadsto \color{blue}{\frac{0 - {\left(\frac{-1}{\cos \left(-0.5 \cdot \frac{x}{y}\right)}\right)}^{3}}{0 + \mathsf{fma}\left(\frac{-1}{\cos \left(-0.5 \cdot \frac{x}{y}\right)}, \frac{-1}{\cos \left(-0.5 \cdot \frac{x}{y}\right)}, 0\right)}} \]

   6. Applied rewrites 2.3%

      \[\leadsto \color{blue}{\frac{0 - {\left({\cos \left(\frac{x}{y} \cdot -0.5\right)}^{-2}\right)}^{2.5}}{{\cos \left(\frac{x}{y} \cdot -0.5\right)}^{-4}}} \]

   7. Taylor expanded in y around inf

      \[\leadsto \color{blue}{-1} \]
   8. Step-by-step derivation

   9. Applied rewrites 13.2%

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

4. Final simplification 54.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{2 \cdot y} \leq 5 \cdot 10^{+264}:\\ \;\;\;\;\frac{{\cos \left(-0.5 \cdot \frac{x}{y}\right)}^{2} \cdot \frac{-1}{\frac{{\left(\cos \left(\frac{0}{\frac{y}{x}}\right) + \frac{1}{\frac{1}{{\cos \left(-0.5 \cdot \frac{x}{y}\right)}^{4} - {\sin \left(-0.5 \cdot \frac{x}{y}\right)}^{4}}}\right)}^{3}}{8}}}{{\left(-\cos \left(-0.5 \cdot \frac{x}{y}\right)\right)}^{-3}}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 56.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ x_m = \left|x\right| \\ \begin{array}{l} t_0 := \cos \left(-0.5 \cdot \frac{x\_m}{y\_m}\right)\\ \mathbf{if}\;\frac{x\_m}{2 \cdot y\_m} \leq 5 \cdot 10^{+264}:\\ \;\;\;\;\frac{\frac{-1}{{t\_0}^{6}} \cdot {t\_0}^{2}}{{\left(-t\_0\right)}^{-3}}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

y_m = (fabs.f64 y)
x_m = (fabs.f64 x)
(FPCore (x_m y_m)
 :precision binary64
 (let* ((t_0 (cos (* -0.5 (/ x_m y_m)))))
   (if (<= (/ x_m (* 2.0 y_m)) 5e+264)
     (/ (* (/ -1.0 (pow t_0 6.0)) (pow t_0 2.0)) (pow (- t_0) -3.0))
     -1.0)))

C

y_m = fabs(y);
x_m = fabs(x);
double code(double x_m, double y_m) {
	double t_0 = cos((-0.5 * (x_m / y_m)));
	double tmp;
	if ((x_m / (2.0 * y_m)) <= 5e+264) {
		tmp = ((-1.0 / pow(t_0, 6.0)) * pow(t_0, 2.0)) / pow(-t_0, -3.0);
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Fortran

y_m = abs(y)
x_m = abs(x)
real(8) function code(x_m, y_m)
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y_m
    real(8) :: t_0
    real(8) :: tmp
    t_0 = cos(((-0.5d0) * (x_m / y_m)))
    if ((x_m / (2.0d0 * y_m)) <= 5d+264) then
        tmp = (((-1.0d0) / (t_0 ** 6.0d0)) * (t_0 ** 2.0d0)) / (-t_0 ** (-3.0d0))
    else
        tmp = -1.0d0
    end if
    code = tmp
end function

Java

y_m = Math.abs(y);
x_m = Math.abs(x);
public static double code(double x_m, double y_m) {
	double t_0 = Math.cos((-0.5 * (x_m / y_m)));
	double tmp;
	if ((x_m / (2.0 * y_m)) <= 5e+264) {
		tmp = ((-1.0 / Math.pow(t_0, 6.0)) * Math.pow(t_0, 2.0)) / Math.pow(-t_0, -3.0);
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

y_m = math.fabs(y)
x_m = math.fabs(x)
def code(x_m, y_m):
	t_0 = math.cos((-0.5 * (x_m / y_m)))
	tmp = 0
	if (x_m / (2.0 * y_m)) <= 5e+264:
		tmp = ((-1.0 / math.pow(t_0, 6.0)) * math.pow(t_0, 2.0)) / math.pow(-t_0, -3.0)
	else:
		tmp = -1.0
	return tmp

Julia

y_m = abs(y)
x_m = abs(x)
function code(x_m, y_m)
	t_0 = cos(Float64(-0.5 * Float64(x_m / y_m)))
	tmp = 0.0
	if (Float64(x_m / Float64(2.0 * y_m)) <= 5e+264)
		tmp = Float64(Float64(Float64(-1.0 / (t_0 ^ 6.0)) * (t_0 ^ 2.0)) / (Float64(-t_0) ^ -3.0));
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

y_m = abs(y);
x_m = abs(x);
function tmp_2 = code(x_m, y_m)
	t_0 = cos((-0.5 * (x_m / y_m)));
	tmp = 0.0;
	if ((x_m / (2.0 * y_m)) <= 5e+264)
		tmp = ((-1.0 / (t_0 ^ 6.0)) * (t_0 ^ 2.0)) / (-t_0 ^ -3.0);
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

y_m = N[Abs[y], $MachinePrecision]
x_m = N[Abs[x], $MachinePrecision]
code[x$95$m_, y$95$m_] := Block[{t$95$0 = N[Cos[N[(-0.5 * N[(x$95$m / y$95$m), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[N[(x$95$m / N[(2.0 * y$95$m), $MachinePrecision]), $MachinePrecision], 5e+264], N[(N[(N[(-1.0 / N[Power[t$95$0, 6.0], $MachinePrecision]), $MachinePrecision] * N[Power[t$95$0, 2.0], $MachinePrecision]), $MachinePrecision] / N[Power[(-t$95$0), -3.0], $MachinePrecision]), $MachinePrecision], -1.0]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (*.f64 y #s(literal 2 binary64))) < 5.00000000000000033e264

   1. Initial program 50.6%

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

   4. Applied rewrites 59.3%

      \[\leadsto \color{blue}{\frac{0 - {\left(\frac{-1}{\cos \left(-0.5 \cdot \frac{x}{y}\right)}\right)}^{3}}{0 + \mathsf{fma}\left(\frac{-1}{\cos \left(-0.5 \cdot \frac{x}{y}\right)}, \frac{-1}{\cos \left(-0.5 \cdot \frac{x}{y}\right)}, 0\right)}} \]

   6. Applied rewrites 59.3%

      \[\leadsto \color{blue}{\frac{\frac{-1}{{\cos \left(\frac{x}{y} \cdot -0.5\right)}^{6}} \cdot {\cos \left(\frac{x}{y} \cdot -0.5\right)}^{2}}{{\left(-\cos \left(\frac{x}{y} \cdot -0.5\right)\right)}^{-3}}} \]

   if 5.00000000000000033e264 < (/.f64 x (*.f64 y #s(literal 2 binary64)))

   1. Initial program 0.2%

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

   4. Applied rewrites 0.2%

      \[\leadsto \color{blue}{\frac{0 - {\left(\frac{-1}{\cos \left(-0.5 \cdot \frac{x}{y}\right)}\right)}^{3}}{0 + \mathsf{fma}\left(\frac{-1}{\cos \left(-0.5 \cdot \frac{x}{y}\right)}, \frac{-1}{\cos \left(-0.5 \cdot \frac{x}{y}\right)}, 0\right)}} \]

   6. Applied rewrites 2.3%

      \[\leadsto \color{blue}{\frac{0 - {\left({\cos \left(\frac{x}{y} \cdot -0.5\right)}^{-2}\right)}^{2.5}}{{\cos \left(\frac{x}{y} \cdot -0.5\right)}^{-4}}} \]

   7. Taylor expanded in y around inf

      \[\leadsto \color{blue}{-1} \]
   8. Step-by-step derivation

   9. Applied rewrites 13.2%

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

4. Final simplification 54.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{2 \cdot y} \leq 5 \cdot 10^{+264}:\\ \;\;\;\;\frac{\frac{-1}{{\cos \left(-0.5 \cdot \frac{x}{y}\right)}^{6}} \cdot {\cos \left(-0.5 \cdot \frac{x}{y}\right)}^{2}}{{\left(-\cos \left(-0.5 \cdot \frac{x}{y}\right)\right)}^{-3}}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 56.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ x_m = \left|x\right| \\ \begin{array}{l} t_0 := \cos \left(-0.5 \cdot \frac{x\_m}{y\_m}\right)\\ \mathbf{if}\;\frac{x\_m}{2 \cdot y\_m} \leq 5 \cdot 10^{+264}:\\ \;\;\;\;\frac{\left(-8 \cdot {\left(1 + \cos \left(\frac{x\_m}{y\_m}\right)\right)}^{-3}\right) \cdot {t\_0}^{2}}{{\left(-t\_0\right)}^{-3}}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

y_m = (fabs.f64 y)
x_m = (fabs.f64 x)
(FPCore (x_m y_m)
 :precision binary64
 (let* ((t_0 (cos (* -0.5 (/ x_m y_m)))))
   (if (<= (/ x_m (* 2.0 y_m)) 5e+264)
     (/
      (* (* -8.0 (pow (+ 1.0 (cos (/ x_m y_m))) -3.0)) (pow t_0 2.0))
      (pow (- t_0) -3.0))
     -1.0)))

C

y_m = fabs(y);
x_m = fabs(x);
double code(double x_m, double y_m) {
	double t_0 = cos((-0.5 * (x_m / y_m)));
	double tmp;
	if ((x_m / (2.0 * y_m)) <= 5e+264) {
		tmp = ((-8.0 * pow((1.0 + cos((x_m / y_m))), -3.0)) * pow(t_0, 2.0)) / pow(-t_0, -3.0);
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Fortran

y_m = abs(y)
x_m = abs(x)
real(8) function code(x_m, y_m)
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y_m
    real(8) :: t_0
    real(8) :: tmp
    t_0 = cos(((-0.5d0) * (x_m / y_m)))
    if ((x_m / (2.0d0 * y_m)) <= 5d+264) then
        tmp = (((-8.0d0) * ((1.0d0 + cos((x_m / y_m))) ** (-3.0d0))) * (t_0 ** 2.0d0)) / (-t_0 ** (-3.0d0))
    else
        tmp = -1.0d0
    end if
    code = tmp
end function

Java

y_m = Math.abs(y);
x_m = Math.abs(x);
public static double code(double x_m, double y_m) {
	double t_0 = Math.cos((-0.5 * (x_m / y_m)));
	double tmp;
	if ((x_m / (2.0 * y_m)) <= 5e+264) {
		tmp = ((-8.0 * Math.pow((1.0 + Math.cos((x_m / y_m))), -3.0)) * Math.pow(t_0, 2.0)) / Math.pow(-t_0, -3.0);
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

y_m = math.fabs(y)
x_m = math.fabs(x)
def code(x_m, y_m):
	t_0 = math.cos((-0.5 * (x_m / y_m)))
	tmp = 0
	if (x_m / (2.0 * y_m)) <= 5e+264:
		tmp = ((-8.0 * math.pow((1.0 + math.cos((x_m / y_m))), -3.0)) * math.pow(t_0, 2.0)) / math.pow(-t_0, -3.0)
	else:
		tmp = -1.0
	return tmp

Julia

y_m = abs(y)
x_m = abs(x)
function code(x_m, y_m)
	t_0 = cos(Float64(-0.5 * Float64(x_m / y_m)))
	tmp = 0.0
	if (Float64(x_m / Float64(2.0 * y_m)) <= 5e+264)
		tmp = Float64(Float64(Float64(-8.0 * (Float64(1.0 + cos(Float64(x_m / y_m))) ^ -3.0)) * (t_0 ^ 2.0)) / (Float64(-t_0) ^ -3.0));
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

y_m = abs(y);
x_m = abs(x);
function tmp_2 = code(x_m, y_m)
	t_0 = cos((-0.5 * (x_m / y_m)));
	tmp = 0.0;
	if ((x_m / (2.0 * y_m)) <= 5e+264)
		tmp = ((-8.0 * ((1.0 + cos((x_m / y_m))) ^ -3.0)) * (t_0 ^ 2.0)) / (-t_0 ^ -3.0);
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

y_m = N[Abs[y], $MachinePrecision]
x_m = N[Abs[x], $MachinePrecision]
code[x$95$m_, y$95$m_] := Block[{t$95$0 = N[Cos[N[(-0.5 * N[(x$95$m / y$95$m), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[N[(x$95$m / N[(2.0 * y$95$m), $MachinePrecision]), $MachinePrecision], 5e+264], N[(N[(N[(-8.0 * N[Power[N[(1.0 + N[Cos[N[(x$95$m / y$95$m), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], -3.0], $MachinePrecision]), $MachinePrecision] * N[Power[t$95$0, 2.0], $MachinePrecision]), $MachinePrecision] / N[Power[(-t$95$0), -3.0], $MachinePrecision]), $MachinePrecision], -1.0]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (*.f64 y #s(literal 2 binary64))) < 5.00000000000000033e264

   1. Initial program 50.6%

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

   4. Applied rewrites 59.3%

      \[\leadsto \color{blue}{\frac{0 - {\left(\frac{-1}{\cos \left(-0.5 \cdot \frac{x}{y}\right)}\right)}^{3}}{0 + \mathsf{fma}\left(\frac{-1}{\cos \left(-0.5 \cdot \frac{x}{y}\right)}, \frac{-1}{\cos \left(-0.5 \cdot \frac{x}{y}\right)}, 0\right)}} \]

   6. Applied rewrites 59.3%

      \[\leadsto \color{blue}{\frac{\frac{-1}{{\cos \left(\frac{x}{y} \cdot -0.5\right)}^{6}} \cdot {\cos \left(\frac{x}{y} \cdot -0.5\right)}^{2}}{{\left(-\cos \left(\frac{x}{y} \cdot -0.5\right)\right)}^{-3}}} \]
   7. Step-by-step derivation

      1. lift-pow.f64 N/A

         \[\leadsto \frac{\frac{-1}{\color{blue}{{\cos \left(\frac{x}{y} \cdot \frac{-1}{2}\right)}^{6}}} \cdot {\cos \left(\frac{x}{y} \cdot \frac{-1}{2}\right)}^{2}}{{\left(-\cos \left(\frac{x}{y} \cdot \frac{-1}{2}\right)\right)}^{-3}} \]

      2. metadata-eval N/A

         \[\leadsto \frac{\frac{-1}{{\cos \left(\frac{x}{y} \cdot \frac{-1}{2}\right)}^{\color{blue}{\left(2 \cdot 3\right)}}} \cdot {\cos \left(\frac{x}{y} \cdot \frac{-1}{2}\right)}^{2}}{{\left(-\cos \left(\frac{x}{y} \cdot \frac{-1}{2}\right)\right)}^{-3}} \]

      3. pow-sqr N/A

         \[\leadsto \frac{\frac{-1}{\color{blue}{{\cos \left(\frac{x}{y} \cdot \frac{-1}{2}\right)}^{3} \cdot {\cos \left(\frac{x}{y} \cdot \frac{-1}{2}\right)}^{3}}} \cdot {\cos \left(\frac{x}{y} \cdot \frac{-1}{2}\right)}^{2}}{{\left(-\cos \left(\frac{x}{y} \cdot \frac{-1}{2}\right)\right)}^{-3}} \]

      4. pow-prod-down N/A

         \[\leadsto \frac{\frac{-1}{\color{blue}{{\left(\cos \left(\frac{x}{y} \cdot \frac{-1}{2}\right) \cdot \cos \left(\frac{x}{y} \cdot \frac{-1}{2}\right)\right)}^{3}}} \cdot {\cos \left(\frac{x}{y} \cdot \frac{-1}{2}\right)}^{2}}{{\left(-\cos \left(\frac{x}{y} \cdot \frac{-1}{2}\right)\right)}^{-3}} \]

      5. lift-cos.f64 N/A

         \[\leadsto \frac{\frac{-1}{{\left(\color{blue}{\cos \left(\frac{x}{y} \cdot \frac{-1}{2}\right)} \cdot \cos \left(\frac{x}{y} \cdot \frac{-1}{2}\right)\right)}^{3}} \cdot {\cos \left(\frac{x}{y} \cdot \frac{-1}{2}\right)}^{2}}{{\left(-\cos \left(\frac{x}{y} \cdot \frac{-1}{2}\right)\right)}^{-3}} \]

      6. lift-cos.f64 N/A

         \[\leadsto \frac{\frac{-1}{{\left(\cos \left(\frac{x}{y} \cdot \frac{-1}{2}\right) \cdot \color{blue}{\cos \left(\frac{x}{y} \cdot \frac{-1}{2}\right)}\right)}^{3}} \cdot {\cos \left(\frac{x}{y} \cdot \frac{-1}{2}\right)}^{2}}{{\left(-\cos \left(\frac{x}{y} \cdot \frac{-1}{2}\right)\right)}^{-3}} \]

      7. cos-mult N/A

         \[\leadsto \frac{\frac{-1}{{\color{blue}{\left(\frac{\cos \left(\frac{x}{y} \cdot \frac{-1}{2} + \frac{x}{y} \cdot \frac{-1}{2}\right) + \cos \left(\frac{x}{y} \cdot \frac{-1}{2} - \frac{x}{y} \cdot \frac{-1}{2}\right)}{2}\right)}}^{3}} \cdot {\cos \left(\frac{x}{y} \cdot \frac{-1}{2}\right)}^{2}}{{\left(-\cos \left(\frac{x}{y} \cdot \frac{-1}{2}\right)\right)}^{-3}} \]

      8. cube-div N/A

         \[\leadsto \frac{\frac{-1}{\color{blue}{\frac{{\left(\cos \left(\frac{x}{y} \cdot \frac{-1}{2} + \frac{x}{y} \cdot \frac{-1}{2}\right) + \cos \left(\frac{x}{y} \cdot \frac{-1}{2} - \frac{x}{y} \cdot \frac{-1}{2}\right)\right)}^{3}}{{2}^{3}}}} \cdot {\cos \left(\frac{x}{y} \cdot \frac{-1}{2}\right)}^{2}}{{\left(-\cos \left(\frac{x}{y} \cdot \frac{-1}{2}\right)\right)}^{-3}} \]

      9. metadata-eval N/A

         \[\leadsto \frac{\frac{-1}{\frac{{\left(\cos \left(\frac{x}{y} \cdot \frac{-1}{2} + \frac{x}{y} \cdot \frac{-1}{2}\right) + \cos \left(\frac{x}{y} \cdot \frac{-1}{2} - \frac{x}{y} \cdot \frac{-1}{2}\right)\right)}^{3}}{\color{blue}{8}}} \cdot {\cos \left(\frac{x}{y} \cdot \frac{-1}{2}\right)}^{2}}{{\left(-\cos \left(\frac{x}{y} \cdot \frac{-1}{2}\right)\right)}^{-3}} \]

      10. metadata-eval N/A

          \[\leadsto \frac{\frac{-1}{\frac{{\left(\cos \left(\frac{x}{y} \cdot \frac{-1}{2} + \frac{x}{y} \cdot \frac{-1}{2}\right) + \cos \left(\frac{x}{y} \cdot \frac{-1}{2} - \frac{x}{y} \cdot \frac{-1}{2}\right)\right)}^{3}}{\color{blue}{\frac{1}{\frac{1}{8}}}}} \cdot {\cos \left(\frac{x}{y} \cdot \frac{-1}{2}\right)}^{2}}{{\left(-\cos \left(\frac{x}{y} \cdot \frac{-1}{2}\right)\right)}^{-3}} \]

      11. lower-/.f64 N/A

          \[\leadsto \frac{\frac{-1}{\color{blue}{\frac{{\left(\cos \left(\frac{x}{y} \cdot \frac{-1}{2} + \frac{x}{y} \cdot \frac{-1}{2}\right) + \cos \left(\frac{x}{y} \cdot \frac{-1}{2} - \frac{x}{y} \cdot \frac{-1}{2}\right)\right)}^{3}}{\frac{1}{\frac{1}{8}}}}} \cdot {\cos \left(\frac{x}{y} \cdot \frac{-1}{2}\right)}^{2}}{{\left(-\cos \left(\frac{x}{y} \cdot \frac{-1}{2}\right)\right)}^{-3}} \]

   8. Applied rewrites 59.3%

      \[\leadsto \frac{\frac{-1}{\color{blue}{\frac{{\left(\cos \left(2 \cdot \left(-0.5 \cdot \frac{x}{y}\right)\right) + \cos \left(\frac{0}{\frac{y}{x}}\right)\right)}^{3}}{8}}} \cdot {\cos \left(\frac{x}{y} \cdot -0.5\right)}^{2}}{{\left(-\cos \left(\frac{x}{y} \cdot -0.5\right)\right)}^{-3}} \]
   9. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{\color{blue}{\frac{-1}{\frac{{\left(\cos \left(2 \cdot \left(\frac{-1}{2} \cdot \frac{x}{y}\right)\right) + \cos \left(\frac{0}{\frac{y}{x}}\right)\right)}^{3}}{8}}} \cdot {\cos \left(\frac{x}{y} \cdot \frac{-1}{2}\right)}^{2}}{{\left(-\cos \left(\frac{x}{y} \cdot \frac{-1}{2}\right)\right)}^{-3}} \]

      2. lift-/.f64 N/A

         \[\leadsto \frac{\frac{-1}{\color{blue}{\frac{{\left(\cos \left(2 \cdot \left(\frac{-1}{2} \cdot \frac{x}{y}\right)\right) + \cos \left(\frac{0}{\frac{y}{x}}\right)\right)}^{3}}{8}}} \cdot {\cos \left(\frac{x}{y} \cdot \frac{-1}{2}\right)}^{2}}{{\left(-\cos \left(\frac{x}{y} \cdot \frac{-1}{2}\right)\right)}^{-3}} \]

      3. frac-2neg N/A

         \[\leadsto \frac{\frac{-1}{\color{blue}{\frac{\mathsf{neg}\left({\left(\cos \left(2 \cdot \left(\frac{-1}{2} \cdot \frac{x}{y}\right)\right) + \cos \left(\frac{0}{\frac{y}{x}}\right)\right)}^{3}\right)}{\mathsf{neg}\left(8\right)}}} \cdot {\cos \left(\frac{x}{y} \cdot \frac{-1}{2}\right)}^{2}}{{\left(-\cos \left(\frac{x}{y} \cdot \frac{-1}{2}\right)\right)}^{-3}} \]

      4. associate-/r/ N/A

         \[\leadsto \frac{\color{blue}{\left(\frac{-1}{\mathsf{neg}\left({\left(\cos \left(2 \cdot \left(\frac{-1}{2} \cdot \frac{x}{y}\right)\right) + \cos \left(\frac{0}{\frac{y}{x}}\right)\right)}^{3}\right)} \cdot \left(\mathsf{neg}\left(8\right)\right)\right)} \cdot {\cos \left(\frac{x}{y} \cdot \frac{-1}{2}\right)}^{2}}{{\left(-\cos \left(\frac{x}{y} \cdot \frac{-1}{2}\right)\right)}^{-3}} \]

      5. metadata-eval N/A

         \[\leadsto \frac{\left(\frac{\color{blue}{\mathsf{neg}\left(1\right)}}{\mathsf{neg}\left({\left(\cos \left(2 \cdot \left(\frac{-1}{2} \cdot \frac{x}{y}\right)\right) + \cos \left(\frac{0}{\frac{y}{x}}\right)\right)}^{3}\right)} \cdot \left(\mathsf{neg}\left(8\right)\right)\right) \cdot {\cos \left(\frac{x}{y} \cdot \frac{-1}{2}\right)}^{2}}{{\left(-\cos \left(\frac{x}{y} \cdot \frac{-1}{2}\right)\right)}^{-3}} \]

      6. frac-2neg N/A

         \[\leadsto \frac{\left(\color{blue}{\frac{1}{{\left(\cos \left(2 \cdot \left(\frac{-1}{2} \cdot \frac{x}{y}\right)\right) + \cos \left(\frac{0}{\frac{y}{x}}\right)\right)}^{3}}} \cdot \left(\mathsf{neg}\left(8\right)\right)\right) \cdot {\cos \left(\frac{x}{y} \cdot \frac{-1}{2}\right)}^{2}}{{\left(-\cos \left(\frac{x}{y} \cdot \frac{-1}{2}\right)\right)}^{-3}} \]

      7. lower-*.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(\frac{1}{{\left(\cos \left(2 \cdot \left(\frac{-1}{2} \cdot \frac{x}{y}\right)\right) + \cos \left(\frac{0}{\frac{y}{x}}\right)\right)}^{3}} \cdot \left(\mathsf{neg}\left(8\right)\right)\right)} \cdot {\cos \left(\frac{x}{y} \cdot \frac{-1}{2}\right)}^{2}}{{\left(-\cos \left(\frac{x}{y} \cdot \frac{-1}{2}\right)\right)}^{-3}} \]

   10. Applied rewrites 59.3%

       \[\leadsto \frac{\color{blue}{\left({\left(1 + \cos \left(\frac{x}{y}\right)\right)}^{-3} \cdot -8\right)} \cdot {\cos \left(\frac{x}{y} \cdot -0.5\right)}^{2}}{{\left(-\cos \left(\frac{x}{y} \cdot -0.5\right)\right)}^{-3}} \]

   if 5.00000000000000033e264 < (/.f64 x (*.f64 y #s(literal 2 binary64)))

   1. Initial program 0.2%

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

   4. Applied rewrites 0.2%

      \[\leadsto \color{blue}{\frac{0 - {\left(\frac{-1}{\cos \left(-0.5 \cdot \frac{x}{y}\right)}\right)}^{3}}{0 + \mathsf{fma}\left(\frac{-1}{\cos \left(-0.5 \cdot \frac{x}{y}\right)}, \frac{-1}{\cos \left(-0.5 \cdot \frac{x}{y}\right)}, 0\right)}} \]

   6. Applied rewrites 2.3%

      \[\leadsto \color{blue}{\frac{0 - {\left({\cos \left(\frac{x}{y} \cdot -0.5\right)}^{-2}\right)}^{2.5}}{{\cos \left(\frac{x}{y} \cdot -0.5\right)}^{-4}}} \]

   7. Taylor expanded in y around inf

      \[\leadsto \color{blue}{-1} \]
   8. Step-by-step derivation

   9. Applied rewrites 13.2%

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

4. Final simplification 54.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{2 \cdot y} \leq 5 \cdot 10^{+264}:\\ \;\;\;\;\frac{\left(-8 \cdot {\left(1 + \cos \left(\frac{x}{y}\right)\right)}^{-3}\right) \cdot {\cos \left(-0.5 \cdot \frac{x}{y}\right)}^{2}}{{\left(-\cos \left(-0.5 \cdot \frac{x}{y}\right)\right)}^{-3}}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 56.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ x_m = \left|x\right| \\ \begin{array}{l} t_0 := \cos \left(-0.5 \cdot \frac{x\_m}{y\_m}\right)\\ t_1 := \frac{-1}{t\_0}\\ \mathbf{if}\;\frac{x\_m}{2 \cdot y\_m} \leq 5 \cdot 10^{+264}:\\ \;\;\;\;\frac{\frac{{t\_0}^{-2}}{t\_0}}{\mathsf{fma}\left(t\_1, t\_1, 0\right)}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

y_m = (fabs.f64 y)
x_m = (fabs.f64 x)
(FPCore (x_m y_m)
 :precision binary64
 (let* ((t_0 (cos (* -0.5 (/ x_m y_m)))) (t_1 (/ -1.0 t_0)))
   (if (<= (/ x_m (* 2.0 y_m)) 5e+264)
     (/ (/ (pow t_0 -2.0) t_0) (fma t_1 t_1 0.0))
     -1.0)))

C

y_m = fabs(y);
x_m = fabs(x);
double code(double x_m, double y_m) {
	double t_0 = cos((-0.5 * (x_m / y_m)));
	double t_1 = -1.0 / t_0;
	double tmp;
	if ((x_m / (2.0 * y_m)) <= 5e+264) {
		tmp = (pow(t_0, -2.0) / t_0) / fma(t_1, t_1, 0.0);
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Julia

y_m = abs(y)
x_m = abs(x)
function code(x_m, y_m)
	t_0 = cos(Float64(-0.5 * Float64(x_m / y_m)))
	t_1 = Float64(-1.0 / t_0)
	tmp = 0.0
	if (Float64(x_m / Float64(2.0 * y_m)) <= 5e+264)
		tmp = Float64(Float64((t_0 ^ -2.0) / t_0) / fma(t_1, t_1, 0.0));
	else
		tmp = -1.0;
	end
	return tmp
end

Wolfram

y_m = N[Abs[y], $MachinePrecision]
x_m = N[Abs[x], $MachinePrecision]
code[x$95$m_, y$95$m_] := Block[{t$95$0 = N[Cos[N[(-0.5 * N[(x$95$m / y$95$m), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[(-1.0 / t$95$0), $MachinePrecision]}, If[LessEqual[N[(x$95$m / N[(2.0 * y$95$m), $MachinePrecision]), $MachinePrecision], 5e+264], N[(N[(N[Power[t$95$0, -2.0], $MachinePrecision] / t$95$0), $MachinePrecision] / N[(t$95$1 * t$95$1 + 0.0), $MachinePrecision]), $MachinePrecision], -1.0]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (*.f64 y #s(literal 2 binary64))) < 5.00000000000000033e264

   1. Initial program 50.6%

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

   4. Applied rewrites 59.3%

      \[\leadsto \color{blue}{\frac{0 - {\left(\frac{-1}{\cos \left(-0.5 \cdot \frac{x}{y}\right)}\right)}^{3}}{0 + \mathsf{fma}\left(\frac{-1}{\cos \left(-0.5 \cdot \frac{x}{y}\right)}, \frac{-1}{\cos \left(-0.5 \cdot \frac{x}{y}\right)}, 0\right)}} \]
   5. Step-by-step derivation

      1. lift-pow.f64 N/A

         \[\leadsto \frac{0 - \color{blue}{{\left(\frac{-1}{\cos \left(\frac{-1}{2} \cdot \frac{x}{y}\right)}\right)}^{3}}}{0 + \mathsf{fma}\left(\frac{-1}{\cos \left(\frac{-1}{2} \cdot \frac{x}{y}\right)}, \frac{-1}{\cos \left(\frac{-1}{2} \cdot \frac{x}{y}\right)}, 0\right)} \]

      2. unpow3 N/A

         \[\leadsto \frac{0 - \color{blue}{\left(\frac{-1}{\cos \left(\frac{-1}{2} \cdot \frac{x}{y}\right)} \cdot \frac{-1}{\cos \left(\frac{-1}{2} \cdot \frac{x}{y}\right)}\right) \cdot \frac{-1}{\cos \left(\frac{-1}{2} \cdot \frac{x}{y}\right)}}}{0 + \mathsf{fma}\left(\frac{-1}{\cos \left(\frac{-1}{2} \cdot \frac{x}{y}\right)}, \frac{-1}{\cos \left(\frac{-1}{2} \cdot \frac{x}{y}\right)}, 0\right)} \]

      3. +-rgt-identity N/A

         \[\leadsto \frac{0 - \color{blue}{\left(\frac{-1}{\cos \left(\frac{-1}{2} \cdot \frac{x}{y}\right)} \cdot \frac{-1}{\cos \left(\frac{-1}{2} \cdot \frac{x}{y}\right)} + 0\right)} \cdot \frac{-1}{\cos \left(\frac{-1}{2} \cdot \frac{x}{y}\right)}}{0 + \mathsf{fma}\left(\frac{-1}{\cos \left(\frac{-1}{2} \cdot \frac{x}{y}\right)}, \frac{-1}{\cos \left(\frac{-1}{2} \cdot \frac{x}{y}\right)}, 0\right)} \]

      4. lift-fma.f64 N/A

         \[\leadsto \frac{0 - \color{blue}{\mathsf{fma}\left(\frac{-1}{\cos \left(\frac{-1}{2} \cdot \frac{x}{y}\right)}, \frac{-1}{\cos \left(\frac{-1}{2} \cdot \frac{x}{y}\right)}, 0\right)} \cdot \frac{-1}{\cos \left(\frac{-1}{2} \cdot \frac{x}{y}\right)}}{0 + \mathsf{fma}\left(\frac{-1}{\cos \left(\frac{-1}{2} \cdot \frac{x}{y}\right)}, \frac{-1}{\cos \left(\frac{-1}{2} \cdot \frac{x}{y}\right)}, 0\right)} \]

      5. +-lft-identity N/A

         \[\leadsto \frac{0 - \color{blue}{\left(0 + \mathsf{fma}\left(\frac{-1}{\cos \left(\frac{-1}{2} \cdot \frac{x}{y}\right)}, \frac{-1}{\cos \left(\frac{-1}{2} \cdot \frac{x}{y}\right)}, 0\right)\right)} \cdot \frac{-1}{\cos \left(\frac{-1}{2} \cdot \frac{x}{y}\right)}}{0 + \mathsf{fma}\left(\frac{-1}{\cos \left(\frac{-1}{2} \cdot \frac{x}{y}\right)}, \frac{-1}{\cos \left(\frac{-1}{2} \cdot \frac{x}{y}\right)}, 0\right)} \]

      6. lift-+.f64 N/A

         \[\leadsto \frac{0 - \color{blue}{\left(0 + \mathsf{fma}\left(\frac{-1}{\cos \left(\frac{-1}{2} \cdot \frac{x}{y}\right)}, \frac{-1}{\cos \left(\frac{-1}{2} \cdot \frac{x}{y}\right)}, 0\right)\right)} \cdot \frac{-1}{\cos \left(\frac{-1}{2} \cdot \frac{x}{y}\right)}}{0 + \mathsf{fma}\left(\frac{-1}{\cos \left(\frac{-1}{2} \cdot \frac{x}{y}\right)}, \frac{-1}{\cos \left(\frac{-1}{2} \cdot \frac{x}{y}\right)}, 0\right)} \]

      7. lift-/.f64 N/A

         \[\leadsto \frac{0 - \left(0 + \mathsf{fma}\left(\frac{-1}{\cos \left(\frac{-1}{2} \cdot \frac{x}{y}\right)}, \frac{-1}{\cos \left(\frac{-1}{2} \cdot \frac{x}{y}\right)}, 0\right)\right) \cdot \color{blue}{\frac{-1}{\cos \left(\frac{-1}{2} \cdot \frac{x}{y}\right)}}}{0 + \mathsf{fma}\left(\frac{-1}{\cos \left(\frac{-1}{2} \cdot \frac{x}{y}\right)}, \frac{-1}{\cos \left(\frac{-1}{2} \cdot \frac{x}{y}\right)}, 0\right)} \]

      8. frac-2neg N/A

         \[\leadsto \frac{0 - \left(0 + \mathsf{fma}\left(\frac{-1}{\cos \left(\frac{-1}{2} \cdot \frac{x}{y}\right)}, \frac{-1}{\cos \left(\frac{-1}{2} \cdot \frac{x}{y}\right)}, 0\right)\right) \cdot \color{blue}{\frac{\mathsf{neg}\left(-1\right)}{\mathsf{neg}\left(\cos \left(\frac{-1}{2} \cdot \frac{x}{y}\right)\right)}}}{0 + \mathsf{fma}\left(\frac{-1}{\cos \left(\frac{-1}{2} \cdot \frac{x}{y}\right)}, \frac{-1}{\cos \left(\frac{-1}{2} \cdot \frac{x}{y}\right)}, 0\right)} \]

      9. metadata-eval N/A

         \[\leadsto \frac{0 - \left(0 + \mathsf{fma}\left(\frac{-1}{\cos \left(\frac{-1}{2} \cdot \frac{x}{y}\right)}, \frac{-1}{\cos \left(\frac{-1}{2} \cdot \frac{x}{y}\right)}, 0\right)\right) \cdot \frac{\color{blue}{1}}{\mathsf{neg}\left(\cos \left(\frac{-1}{2} \cdot \frac{x}{y}\right)\right)}}{0 + \mathsf{fma}\left(\frac{-1}{\cos \left(\frac{-1}{2} \cdot \frac{x}{y}\right)}, \frac{-1}{\cos \left(\frac{-1}{2} \cdot \frac{x}{y}\right)}, 0\right)} \]

      10. un-div-inv N/A

          \[\leadsto \frac{0 - \color{blue}{\frac{0 + \mathsf{fma}\left(\frac{-1}{\cos \left(\frac{-1}{2} \cdot \frac{x}{y}\right)}, \frac{-1}{\cos \left(\frac{-1}{2} \cdot \frac{x}{y}\right)}, 0\right)}{\mathsf{neg}\left(\cos \left(\frac{-1}{2} \cdot \frac{x}{y}\right)\right)}}}{0 + \mathsf{fma}\left(\frac{-1}{\cos \left(\frac{-1}{2} \cdot \frac{x}{y}\right)}, \frac{-1}{\cos \left(\frac{-1}{2} \cdot \frac{x}{y}\right)}, 0\right)} \]

      11. lower-/.f64 N/A

          \[\leadsto \frac{0 - \color{blue}{\frac{0 + \mathsf{fma}\left(\frac{-1}{\cos \left(\frac{-1}{2} \cdot \frac{x}{y}\right)}, \frac{-1}{\cos \left(\frac{-1}{2} \cdot \frac{x}{y}\right)}, 0\right)}{\mathsf{neg}\left(\cos \left(\frac{-1}{2} \cdot \frac{x}{y}\right)\right)}}}{0 + \mathsf{fma}\left(\frac{-1}{\cos \left(\frac{-1}{2} \cdot \frac{x}{y}\right)}, \frac{-1}{\cos \left(\frac{-1}{2} \cdot \frac{x}{y}\right)}, 0\right)} \]

   6. Applied rewrites 59.3%

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

   if 5.00000000000000033e264 < (/.f64 x (*.f64 y #s(literal 2 binary64)))

   1. Initial program 0.2%

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

   4. Applied rewrites 0.2%

      \[\leadsto \color{blue}{\frac{0 - {\left(\frac{-1}{\cos \left(-0.5 \cdot \frac{x}{y}\right)}\right)}^{3}}{0 + \mathsf{fma}\left(\frac{-1}{\cos \left(-0.5 \cdot \frac{x}{y}\right)}, \frac{-1}{\cos \left(-0.5 \cdot \frac{x}{y}\right)}, 0\right)}} \]

   6. Applied rewrites 2.3%

      \[\leadsto \color{blue}{\frac{0 - {\left({\cos \left(\frac{x}{y} \cdot -0.5\right)}^{-2}\right)}^{2.5}}{{\cos \left(\frac{x}{y} \cdot -0.5\right)}^{-4}}} \]

   7. Taylor expanded in y around inf

      \[\leadsto \color{blue}{-1} \]
   8. Step-by-step derivation

   9. Applied rewrites 13.2%

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

4. Final simplification 54.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{2 \cdot y} \leq 5 \cdot 10^{+264}:\\ \;\;\;\;\frac{\frac{{\cos \left(-0.5 \cdot \frac{x}{y}\right)}^{-2}}{\cos \left(-0.5 \cdot \frac{x}{y}\right)}}{\mathsf{fma}\left(\frac{-1}{\cos \left(-0.5 \cdot \frac{x}{y}\right)}, \frac{-1}{\cos \left(-0.5 \cdot \frac{x}{y}\right)}, 0\right)}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 56.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ x_m = \left|x\right| \\ \begin{array}{l} t_0 := \cos \left(-0.5 \cdot \frac{x\_m}{y\_m}\right)\\ \mathbf{if}\;\frac{x\_m}{2 \cdot y\_m} \leq 5 \cdot 10^{+264}:\\ \;\;\;\;\frac{{t\_0}^{-2}}{\frac{1}{t\_0}}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

y_m = (fabs.f64 y)
x_m = (fabs.f64 x)
(FPCore (x_m y_m)
 :precision binary64
 (let* ((t_0 (cos (* -0.5 (/ x_m y_m)))))
   (if (<= (/ x_m (* 2.0 y_m)) 5e+264) (/ (pow t_0 -2.0) (/ 1.0 t_0)) -1.0)))

C

y_m = fabs(y);
x_m = fabs(x);
double code(double x_m, double y_m) {
	double t_0 = cos((-0.5 * (x_m / y_m)));
	double tmp;
	if ((x_m / (2.0 * y_m)) <= 5e+264) {
		tmp = pow(t_0, -2.0) / (1.0 / t_0);
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Fortran

y_m = abs(y)
x_m = abs(x)
real(8) function code(x_m, y_m)
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y_m
    real(8) :: t_0
    real(8) :: tmp
    t_0 = cos(((-0.5d0) * (x_m / y_m)))
    if ((x_m / (2.0d0 * y_m)) <= 5d+264) then
        tmp = (t_0 ** (-2.0d0)) / (1.0d0 / t_0)
    else
        tmp = -1.0d0
    end if
    code = tmp
end function

Java

y_m = Math.abs(y);
x_m = Math.abs(x);
public static double code(double x_m, double y_m) {
	double t_0 = Math.cos((-0.5 * (x_m / y_m)));
	double tmp;
	if ((x_m / (2.0 * y_m)) <= 5e+264) {
		tmp = Math.pow(t_0, -2.0) / (1.0 / t_0);
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

y_m = math.fabs(y)
x_m = math.fabs(x)
def code(x_m, y_m):
	t_0 = math.cos((-0.5 * (x_m / y_m)))
	tmp = 0
	if (x_m / (2.0 * y_m)) <= 5e+264:
		tmp = math.pow(t_0, -2.0) / (1.0 / t_0)
	else:
		tmp = -1.0
	return tmp

Julia

y_m = abs(y)
x_m = abs(x)
function code(x_m, y_m)
	t_0 = cos(Float64(-0.5 * Float64(x_m / y_m)))
	tmp = 0.0
	if (Float64(x_m / Float64(2.0 * y_m)) <= 5e+264)
		tmp = Float64((t_0 ^ -2.0) / Float64(1.0 / t_0));
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

y_m = abs(y);
x_m = abs(x);
function tmp_2 = code(x_m, y_m)
	t_0 = cos((-0.5 * (x_m / y_m)));
	tmp = 0.0;
	if ((x_m / (2.0 * y_m)) <= 5e+264)
		tmp = (t_0 ^ -2.0) / (1.0 / t_0);
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

y_m = N[Abs[y], $MachinePrecision]
x_m = N[Abs[x], $MachinePrecision]
code[x$95$m_, y$95$m_] := Block[{t$95$0 = N[Cos[N[(-0.5 * N[(x$95$m / y$95$m), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[N[(x$95$m / N[(2.0 * y$95$m), $MachinePrecision]), $MachinePrecision], 5e+264], N[(N[Power[t$95$0, -2.0], $MachinePrecision] / N[(1.0 / t$95$0), $MachinePrecision]), $MachinePrecision], -1.0]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (*.f64 y #s(literal 2 binary64))) < 5.00000000000000033e264

   1. Initial program 50.6%

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

   4. Applied rewrites 59.3%

      \[\leadsto \color{blue}{\frac{0 - {\left(\frac{-1}{\cos \left(-0.5 \cdot \frac{x}{y}\right)}\right)}^{3}}{0 + \mathsf{fma}\left(\frac{-1}{\cos \left(-0.5 \cdot \frac{x}{y}\right)}, \frac{-1}{\cos \left(-0.5 \cdot \frac{x}{y}\right)}, 0\right)}} \]

   6. Applied rewrites 59.3%

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

   if 5.00000000000000033e264 < (/.f64 x (*.f64 y #s(literal 2 binary64)))

   1. Initial program 0.2%

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

   4. Applied rewrites 0.2%

      \[\leadsto \color{blue}{\frac{0 - {\left(\frac{-1}{\cos \left(-0.5 \cdot \frac{x}{y}\right)}\right)}^{3}}{0 + \mathsf{fma}\left(\frac{-1}{\cos \left(-0.5 \cdot \frac{x}{y}\right)}, \frac{-1}{\cos \left(-0.5 \cdot \frac{x}{y}\right)}, 0\right)}} \]

   6. Applied rewrites 2.3%

      \[\leadsto \color{blue}{\frac{0 - {\left({\cos \left(\frac{x}{y} \cdot -0.5\right)}^{-2}\right)}^{2.5}}{{\cos \left(\frac{x}{y} \cdot -0.5\right)}^{-4}}} \]

   7. Taylor expanded in y around inf

      \[\leadsto \color{blue}{-1} \]
   8. Step-by-step derivation

   9. Applied rewrites 13.2%

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

4. Final simplification 54.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{2 \cdot y} \leq 5 \cdot 10^{+264}:\\ \;\;\;\;\frac{{\cos \left(-0.5 \cdot \frac{x}{y}\right)}^{-2}}{\frac{1}{\cos \left(-0.5 \cdot \frac{x}{y}\right)}}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 56.7% accurate, 1.6× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ x_m = \left|x\right| \\ \begin{array}{l} \mathbf{if}\;\frac{x\_m}{2 \cdot y\_m} \leq 5 \cdot 10^{+264}:\\ \;\;\;\;\frac{1}{\cos \left(-0.5 \cdot \frac{x\_m}{y\_m}\right)}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

y_m = (fabs.f64 y)
x_m = (fabs.f64 x)
(FPCore (x_m y_m)
 :precision binary64
 (if (<= (/ x_m (* 2.0 y_m)) 5e+264) (/ 1.0 (cos (* -0.5 (/ x_m y_m)))) -1.0))

C

y_m = fabs(y);
x_m = fabs(x);
double code(double x_m, double y_m) {
	double tmp;
	if ((x_m / (2.0 * y_m)) <= 5e+264) {
		tmp = 1.0 / cos((-0.5 * (x_m / y_m)));
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Fortran

y_m = abs(y)
x_m = abs(x)
real(8) function code(x_m, y_m)
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y_m
    real(8) :: tmp
    if ((x_m / (2.0d0 * y_m)) <= 5d+264) then
        tmp = 1.0d0 / cos(((-0.5d0) * (x_m / y_m)))
    else
        tmp = -1.0d0
    end if
    code = tmp
end function

Java

y_m = Math.abs(y);
x_m = Math.abs(x);
public static double code(double x_m, double y_m) {
	double tmp;
	if ((x_m / (2.0 * y_m)) <= 5e+264) {
		tmp = 1.0 / Math.cos((-0.5 * (x_m / y_m)));
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

y_m = math.fabs(y)
x_m = math.fabs(x)
def code(x_m, y_m):
	tmp = 0
	if (x_m / (2.0 * y_m)) <= 5e+264:
		tmp = 1.0 / math.cos((-0.5 * (x_m / y_m)))
	else:
		tmp = -1.0
	return tmp

Julia

y_m = abs(y)
x_m = abs(x)
function code(x_m, y_m)
	tmp = 0.0
	if (Float64(x_m / Float64(2.0 * y_m)) <= 5e+264)
		tmp = Float64(1.0 / cos(Float64(-0.5 * Float64(x_m / y_m))));
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

y_m = abs(y);
x_m = abs(x);
function tmp_2 = code(x_m, y_m)
	tmp = 0.0;
	if ((x_m / (2.0 * y_m)) <= 5e+264)
		tmp = 1.0 / cos((-0.5 * (x_m / y_m)));
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

y_m = N[Abs[y], $MachinePrecision]
x_m = N[Abs[x], $MachinePrecision]
code[x$95$m_, y$95$m_] := If[LessEqual[N[(x$95$m / N[(2.0 * y$95$m), $MachinePrecision]), $MachinePrecision], 5e+264], N[(1.0 / N[Cos[N[(-0.5 * N[(x$95$m / y$95$m), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], -1.0]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (*.f64 y #s(literal 2 binary64))) < 5.00000000000000033e264

   1. Initial program 50.6%

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

      1. lift-/.f64 N/A

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

      2. clear-num N/A

         \[\leadsto \color{blue}{\frac{1}{\frac{\sin \left(\frac{x}{y \cdot 2}\right)}{\tan \left(\frac{x}{y \cdot 2}\right)}}} \]

      3. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{1}{\frac{\sin \left(\frac{x}{y \cdot 2}\right)}{\tan \left(\frac{x}{y \cdot 2}\right)}}} \]

      4. lift-tan.f64 N/A

         \[\leadsto \frac{1}{\frac{\sin \left(\frac{x}{y \cdot 2}\right)}{\color{blue}{\tan \left(\frac{x}{y \cdot 2}\right)}}} \]

      5. tan-quot N/A

         \[\leadsto \frac{1}{\frac{\sin \left(\frac{x}{y \cdot 2}\right)}{\color{blue}{\frac{\sin \left(\frac{x}{y \cdot 2}\right)}{\cos \left(\frac{x}{y \cdot 2}\right)}}}} \]

      6. lift-sin.f64 N/A

         \[\leadsto \frac{1}{\frac{\sin \left(\frac{x}{y \cdot 2}\right)}{\frac{\color{blue}{\sin \left(\frac{x}{y \cdot 2}\right)}}{\cos \left(\frac{x}{y \cdot 2}\right)}}} \]

      7. associate-/r/ N/A

         \[\leadsto \frac{1}{\color{blue}{\frac{\sin \left(\frac{x}{y \cdot 2}\right)}{\sin \left(\frac{x}{y \cdot 2}\right)} \cdot \cos \left(\frac{x}{y \cdot 2}\right)}} \]

      8. *-inverses N/A

         \[\leadsto \frac{1}{\color{blue}{1} \cdot \cos \left(\frac{x}{y \cdot 2}\right)} \]

      9. remove-double-neg N/A

         \[\leadsto \frac{1}{1 \cdot \color{blue}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\cos \left(\frac{x}{y \cdot 2}\right)\right)\right)\right)\right)}} \]

      10. distribute-rgt-neg-in N/A

          \[\leadsto \frac{1}{\color{blue}{\mathsf{neg}\left(1 \cdot \left(\mathsf{neg}\left(\cos \left(\frac{x}{y \cdot 2}\right)\right)\right)\right)}} \]

      11. distribute-lft-neg-in N/A

          \[\leadsto \frac{1}{\color{blue}{\left(\mathsf{neg}\left(1\right)\right) \cdot \left(\mathsf{neg}\left(\cos \left(\frac{x}{y \cdot 2}\right)\right)\right)}} \]

      12. metadata-eval N/A

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

      13. neg-mul-1 N/A

          \[\leadsto \frac{1}{\color{blue}{\mathsf{neg}\left(\left(\mathsf{neg}\left(\cos \left(\frac{x}{y \cdot 2}\right)\right)\right)\right)}} \]

      14. remove-double-neg N/A

          \[\leadsto \frac{1}{\color{blue}{\cos \left(\frac{x}{y \cdot 2}\right)}} \]

      15. cos-neg N/A

          \[\leadsto \frac{1}{\color{blue}{\cos \left(\mathsf{neg}\left(\frac{x}{y \cdot 2}\right)\right)}} \]

      16. lift-/.f64 N/A

          \[\leadsto \frac{1}{\cos \left(\mathsf{neg}\left(\color{blue}{\frac{x}{y \cdot 2}}\right)\right)} \]

      17. distribute-frac-neg2 N/A

          \[\leadsto \frac{1}{\cos \color{blue}{\left(\frac{x}{\mathsf{neg}\left(y \cdot 2\right)}\right)}} \]

      18. lower-cos.f64 N/A

          \[\leadsto \frac{1}{\color{blue}{\cos \left(\frac{x}{\mathsf{neg}\left(y \cdot 2\right)}\right)}} \]

      19. distribute-frac-neg2 N/A

          \[\leadsto \frac{1}{\cos \color{blue}{\left(\mathsf{neg}\left(\frac{x}{y \cdot 2}\right)\right)}} \]

      20. lift-*.f64 N/A

          \[\leadsto \frac{1}{\cos \left(\mathsf{neg}\left(\frac{x}{\color{blue}{y \cdot 2}}\right)\right)} \]

   4. Applied rewrites 59.3%

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

   if 5.00000000000000033e264 < (/.f64 x (*.f64 y #s(literal 2 binary64)))

   1. Initial program 0.2%

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

   4. Applied rewrites 0.2%

      \[\leadsto \color{blue}{\frac{0 - {\left(\frac{-1}{\cos \left(-0.5 \cdot \frac{x}{y}\right)}\right)}^{3}}{0 + \mathsf{fma}\left(\frac{-1}{\cos \left(-0.5 \cdot \frac{x}{y}\right)}, \frac{-1}{\cos \left(-0.5 \cdot \frac{x}{y}\right)}, 0\right)}} \]

   6. Applied rewrites 2.3%

      \[\leadsto \color{blue}{\frac{0 - {\left({\cos \left(\frac{x}{y} \cdot -0.5\right)}^{-2}\right)}^{2.5}}{{\cos \left(\frac{x}{y} \cdot -0.5\right)}^{-4}}} \]

   7. Taylor expanded in y around inf

      \[\leadsto \color{blue}{-1} \]
   8. Step-by-step derivation

   9. Applied rewrites 13.2%

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

4. Final simplification 54.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{2 \cdot y} \leq 5 \cdot 10^{+264}:\\ \;\;\;\;\frac{1}{\cos \left(-0.5 \cdot \frac{x}{y}\right)}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 56.8% accurate, 1.6× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ x_m = \left|x\right| \\ \begin{array}{l} \mathbf{if}\;\frac{x\_m}{2 \cdot y\_m} \leq 5 \cdot 10^{+35}:\\ \;\;\;\;\frac{1}{\cos \left(\frac{0.5}{y\_m} \cdot x\_m\right)}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

y_m = (fabs.f64 y)
x_m = (fabs.f64 x)
(FPCore (x_m y_m)
 :precision binary64
 (if (<= (/ x_m (* 2.0 y_m)) 5e+35) (/ 1.0 (cos (* (/ 0.5 y_m) x_m))) -1.0))

C

y_m = fabs(y);
x_m = fabs(x);
double code(double x_m, double y_m) {
	double tmp;
	if ((x_m / (2.0 * y_m)) <= 5e+35) {
		tmp = 1.0 / cos(((0.5 / y_m) * x_m));
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Fortran

y_m = abs(y)
x_m = abs(x)
real(8) function code(x_m, y_m)
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y_m
    real(8) :: tmp
    if ((x_m / (2.0d0 * y_m)) <= 5d+35) then
        tmp = 1.0d0 / cos(((0.5d0 / y_m) * x_m))
    else
        tmp = -1.0d0
    end if
    code = tmp
end function

Java

y_m = Math.abs(y);
x_m = Math.abs(x);
public static double code(double x_m, double y_m) {
	double tmp;
	if ((x_m / (2.0 * y_m)) <= 5e+35) {
		tmp = 1.0 / Math.cos(((0.5 / y_m) * x_m));
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

y_m = math.fabs(y)
x_m = math.fabs(x)
def code(x_m, y_m):
	tmp = 0
	if (x_m / (2.0 * y_m)) <= 5e+35:
		tmp = 1.0 / math.cos(((0.5 / y_m) * x_m))
	else:
		tmp = -1.0
	return tmp

Julia

y_m = abs(y)
x_m = abs(x)
function code(x_m, y_m)
	tmp = 0.0
	if (Float64(x_m / Float64(2.0 * y_m)) <= 5e+35)
		tmp = Float64(1.0 / cos(Float64(Float64(0.5 / y_m) * x_m)));
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

y_m = abs(y);
x_m = abs(x);
function tmp_2 = code(x_m, y_m)
	tmp = 0.0;
	if ((x_m / (2.0 * y_m)) <= 5e+35)
		tmp = 1.0 / cos(((0.5 / y_m) * x_m));
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

y_m = N[Abs[y], $MachinePrecision]
x_m = N[Abs[x], $MachinePrecision]
code[x$95$m_, y$95$m_] := If[LessEqual[N[(x$95$m / N[(2.0 * y$95$m), $MachinePrecision]), $MachinePrecision], 5e+35], N[(1.0 / N[Cos[N[(N[(0.5 / y$95$m), $MachinePrecision] * x$95$m), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], -1.0]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (*.f64 y #s(literal 2 binary64))) < 5.00000000000000021e35

   1. Initial program 56.8%

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

   3. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{1}{\cos \left(\frac{1}{2} \cdot \frac{x}{y}\right)}} \]

      2. associate-*r/ N/A

         \[\leadsto \frac{1}{\cos \color{blue}{\left(\frac{\frac{1}{2} \cdot x}{y}\right)}} \]

      3. *-commutative N/A

         \[\leadsto \frac{1}{\cos \left(\frac{\color{blue}{x \cdot \frac{1}{2}}}{y}\right)} \]

      4. associate-*r/ N/A

         \[\leadsto \frac{1}{\cos \color{blue}{\left(x \cdot \frac{\frac{1}{2}}{y}\right)}} \]

      5. metadata-eval N/A

         \[\leadsto \frac{1}{\cos \left(x \cdot \frac{\color{blue}{\frac{1}{2} \cdot 1}}{y}\right)} \]

      6. associate-*r/ N/A

         \[\leadsto \frac{1}{\cos \left(x \cdot \color{blue}{\left(\frac{1}{2} \cdot \frac{1}{y}\right)}\right)} \]

      7. lower-cos.f64 N/A

         \[\leadsto \frac{1}{\color{blue}{\cos \left(x \cdot \left(\frac{1}{2} \cdot \frac{1}{y}\right)\right)}} \]

      8. *-commutative N/A

         \[\leadsto \frac{1}{\cos \color{blue}{\left(\left(\frac{1}{2} \cdot \frac{1}{y}\right) \cdot x\right)}} \]

      9. lower-*.f64 N/A

         \[\leadsto \frac{1}{\cos \color{blue}{\left(\left(\frac{1}{2} \cdot \frac{1}{y}\right) \cdot x\right)}} \]

      10. associate-*r/ N/A

          \[\leadsto \frac{1}{\cos \left(\color{blue}{\frac{\frac{1}{2} \cdot 1}{y}} \cdot x\right)} \]

      11. metadata-eval N/A

          \[\leadsto \frac{1}{\cos \left(\frac{\color{blue}{\frac{1}{2}}}{y} \cdot x\right)} \]

      12. lower-/.f64 66.9

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

   5. Applied rewrites 66.9%

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

   if 5.00000000000000021e35 < (/.f64 x (*.f64 y #s(literal 2 binary64)))

   1. Initial program 5.7%

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

   4. Applied rewrites 5.7%

      \[\leadsto \color{blue}{\frac{0 - {\left(\frac{-1}{\cos \left(-0.5 \cdot \frac{x}{y}\right)}\right)}^{3}}{0 + \mathsf{fma}\left(\frac{-1}{\cos \left(-0.5 \cdot \frac{x}{y}\right)}, \frac{-1}{\cos \left(-0.5 \cdot \frac{x}{y}\right)}, 0\right)}} \]

   6. Applied rewrites 6.1%

      \[\leadsto \color{blue}{\frac{0 - {\left({\cos \left(\frac{x}{y} \cdot -0.5\right)}^{-2}\right)}^{2.5}}{{\cos \left(\frac{x}{y} \cdot -0.5\right)}^{-4}}} \]

   7. Taylor expanded in y around inf

      \[\leadsto \color{blue}{-1} \]
   8. Step-by-step derivation

   9. Applied rewrites 12.1%

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

4. Final simplification 54.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{2 \cdot y} \leq 5 \cdot 10^{+35}:\\ \;\;\;\;\frac{1}{\cos \left(\frac{0.5}{y} \cdot x\right)}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 55.5% accurate, 244.0× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ x_m = \left|x\right| \\ 1 \end{array} \]

FPCore

y_m = (fabs.f64 y)
x_m = (fabs.f64 x)
(FPCore (x_m y_m) :precision binary64 1.0)

C

y_m = fabs(y);
x_m = fabs(x);
double code(double x_m, double y_m) {
	return 1.0;
}

Fortran

y_m = abs(y)
x_m = abs(x)
real(8) function code(x_m, y_m)
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y_m
    code = 1.0d0
end function

Java

y_m = Math.abs(y);
x_m = Math.abs(x);
public static double code(double x_m, double y_m) {
	return 1.0;
}

Python

y_m = math.fabs(y)
x_m = math.fabs(x)
def code(x_m, y_m):
	return 1.0

Julia

y_m = abs(y)
x_m = abs(x)
function code(x_m, y_m)
	return 1.0
end

MATLAB

y_m = abs(y);
x_m = abs(x);
function tmp = code(x_m, y_m)
	tmp = 1.0;
end

Wolfram

y_m = N[Abs[y], $MachinePrecision]
x_m = N[Abs[x], $MachinePrecision]
code[x$95$m_, y$95$m_] := 1.0

Derivation

1. Initial program 45.5%

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

3. Taylor expanded in y around inf

   \[\leadsto \color{blue}{1} \]
4. Step-by-step derivation

5. Applied rewrites 52.3%

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

Developer Target 1: 55.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{y \cdot 2}\\ t_1 := \sin t\_0\\ \mathbf{if}\;y < -1.2303690911306994 \cdot 10^{+114}:\\ \;\;\;\;1\\ \mathbf{elif}\;y < -9.102852406811914 \cdot 10^{-222}:\\ \;\;\;\;\frac{t\_1}{t\_1 \cdot \log \left(e^{\cos t\_0}\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ x (* y 2.0))) (t_1 (sin t_0)))
   (if (< y -1.2303690911306994e+114)
     1.0
     (if (< y -9.102852406811914e-222)
       (/ t_1 (* t_1 (log (exp (cos t_0)))))
       1.0))))

C

double code(double x, double y) {
	double t_0 = x / (y * 2.0);
	double t_1 = sin(t_0);
	double tmp;
	if (y < -1.2303690911306994e+114) {
		tmp = 1.0;
	} else if (y < -9.102852406811914e-222) {
		tmp = t_1 / (t_1 * log(exp(cos(t_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) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = x / (y * 2.0d0)
    t_1 = sin(t_0)
    if (y < (-1.2303690911306994d+114)) then
        tmp = 1.0d0
    else if (y < (-9.102852406811914d-222)) then
        tmp = t_1 / (t_1 * log(exp(cos(t_0))))
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = x / (y * 2.0);
	double t_1 = Math.sin(t_0);
	double tmp;
	if (y < -1.2303690911306994e+114) {
		tmp = 1.0;
	} else if (y < -9.102852406811914e-222) {
		tmp = t_1 / (t_1 * Math.log(Math.exp(Math.cos(t_0))));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x / (y * 2.0)
	t_1 = math.sin(t_0)
	tmp = 0
	if y < -1.2303690911306994e+114:
		tmp = 1.0
	elif y < -9.102852406811914e-222:
		tmp = t_1 / (t_1 * math.log(math.exp(math.cos(t_0))))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(x / Float64(y * 2.0))
	t_1 = sin(t_0)
	tmp = 0.0
	if (y < -1.2303690911306994e+114)
		tmp = 1.0;
	elseif (y < -9.102852406811914e-222)
		tmp = Float64(t_1 / Float64(t_1 * log(exp(cos(t_0)))));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = x / (y * 2.0);
	t_1 = sin(t_0);
	tmp = 0.0;
	if (y < -1.2303690911306994e+114)
		tmp = 1.0;
	elseif (y < -9.102852406811914e-222)
		tmp = t_1 / (t_1 * log(exp(cos(t_0))));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(x / N[(y * 2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[Sin[t$95$0], $MachinePrecision]}, If[Less[y, -1.2303690911306994e+114], 1.0, If[Less[y, -9.102852406811914e-222], N[(t$95$1 / N[(t$95$1 * N[Log[N[Exp[N[Cos[t$95$0], $MachinePrecision]], $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]]]

Reproduce

herbie shell --seed 2024243 
(FPCore (x y)
  :name "Diagrams.TwoD.Layout.CirclePacking:approxRadius from diagrams-contrib-1.3.0.5"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< y -1230369091130699400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) 1 (if (< y -4551426203405957/500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (/ (sin (/ x (* y 2))) (* (sin (/ x (* y 2))) (log (exp (cos (/ x (* y 2))))))) 1)))

  (/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0)))))