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

Percentage Accurate: 44.1% → 57.0%

Time: 11.8s

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: 44.1% 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: 57.0% accurate, 1.6× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ x_m = \left|x\right| \\ \begin{array}{l} \mathbf{if}\;\frac{x\_m}{2 \cdot y\_m} \leq 4 \cdot 10^{+48}:\\ \;\;\;\;\frac{1}{\cos \left(x\_m \cdot \frac{0.5}{y\_m}\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

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)) 4e+48) (/ 1.0 (cos (* x_m (/ 0.5 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)) <= 4e+48) {
		tmp = 1.0 / cos((x_m * (0.5 / 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)) <= 4d+48) then
        tmp = 1.0d0 / cos((x_m * (0.5d0 / 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)) <= 4e+48) {
		tmp = 1.0 / Math.cos((x_m * (0.5 / 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)) <= 4e+48:
		tmp = 1.0 / math.cos((x_m * (0.5 / 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)) <= 4e+48)
		tmp = Float64(1.0 / cos(Float64(x_m * Float64(0.5 / 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)) <= 4e+48)
		tmp = 1.0 / cos((x_m * (0.5 / 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], 4e+48], N[(1.0 / N[Cos[N[(x$95$m * N[(0.5 / 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))) < 4.00000000000000018e48

   1. Initial program 52.3%

      \[\frac{\tan \left(\frac{x}{y \cdot 2}\right)}{\sin \left(\frac{x}{y \cdot 2}\right)} \]
   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 65.9

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

   5. Applied rewrites 65.9%

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

   if 4.00000000000000018e48 < (/.f64 x (*.f64 y #s(literal 2 binary64)))

   1. Initial program 7.6%

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

   3. Taylor expanded in y around inf

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

   5. Applied rewrites 9.9%

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

4. Final simplification 53.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{2 \cdot y} \leq 4 \cdot 10^{+48}:\\ \;\;\;\;\frac{1}{\cos \left(x \cdot \frac{0.5}{y}\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 55.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ x_m = \left|x\right| \\ \begin{array}{l} t_0 := \cos \left(\frac{x\_m}{y\_m} \cdot 0.5\right)\\ \frac{\frac{--1}{\cos \left(\frac{x\_m}{y\_m} \cdot -0.5\right)} \cdot \frac{-1}{\cos \left(\frac{\frac{0.5}{y\_m}}{\frac{-1}{x\_m}}\right)}}{\frac{-1}{\frac{{t\_0}^{-1}}{{t\_0}^{-2}}}} \end{array} \end{array} \]

FPCore

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

C

y_m = fabs(y);
x_m = fabs(x);
double code(double x_m, double y_m) {
	double t_0 = cos(((x_m / y_m) * 0.5));
	return ((-(-1.0) / cos(((x_m / y_m) * -0.5))) * (-1.0 / cos(((0.5 / y_m) / (-1.0 / x_m))))) / (-1.0 / (pow(t_0, -1.0) / pow(t_0, -2.0)));
}

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
    real(8) :: t_0
    t_0 = cos(((x_m / y_m) * 0.5d0))
    code = ((-(-1.0d0) / cos(((x_m / y_m) * (-0.5d0)))) * ((-1.0d0) / cos(((0.5d0 / y_m) / ((-1.0d0) / x_m))))) / ((-1.0d0) / ((t_0 ** (-1.0d0)) / (t_0 ** (-2.0d0))))
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(((x_m / y_m) * 0.5));
	return ((-(-1.0) / Math.cos(((x_m / y_m) * -0.5))) * (-1.0 / Math.cos(((0.5 / y_m) / (-1.0 / x_m))))) / (-1.0 / (Math.pow(t_0, -1.0) / Math.pow(t_0, -2.0)));
}

Python

y_m = math.fabs(y)
x_m = math.fabs(x)
def code(x_m, y_m):
	t_0 = math.cos(((x_m / y_m) * 0.5))
	return ((-(-1.0) / math.cos(((x_m / y_m) * -0.5))) * (-1.0 / math.cos(((0.5 / y_m) / (-1.0 / x_m))))) / (-1.0 / (math.pow(t_0, -1.0) / math.pow(t_0, -2.0)))

Julia

y_m = abs(y)
x_m = abs(x)
function code(x_m, y_m)
	t_0 = cos(Float64(Float64(x_m / y_m) * 0.5))
	return Float64(Float64(Float64(Float64(-(-1.0)) / cos(Float64(Float64(x_m / y_m) * -0.5))) * Float64(-1.0 / cos(Float64(Float64(0.5 / y_m) / Float64(-1.0 / x_m))))) / Float64(-1.0 / Float64((t_0 ^ -1.0) / (t_0 ^ -2.0))))
end

MATLAB

y_m = abs(y);
x_m = abs(x);
function tmp = code(x_m, y_m)
	t_0 = cos(((x_m / y_m) * 0.5));
	tmp = ((-(-1.0) / cos(((x_m / y_m) * -0.5))) * (-1.0 / cos(((0.5 / y_m) / (-1.0 / x_m))))) / (-1.0 / ((t_0 ^ -1.0) / (t_0 ^ -2.0)));
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[(N[(x$95$m / y$95$m), $MachinePrecision] * 0.5), $MachinePrecision]], $MachinePrecision]}, N[(N[(N[((--1.0) / N[Cos[N[(N[(x$95$m / y$95$m), $MachinePrecision] * -0.5), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[(-1.0 / N[Cos[N[(N[(0.5 / y$95$m), $MachinePrecision] / N[(-1.0 / x$95$m), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(-1.0 / N[(N[Power[t$95$0, -1.0], $MachinePrecision] / N[Power[t$95$0, -2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Initial program 42.3%

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

4. Applied rewrites 53.3%

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

   1. lift-*.f64 N/A

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

   2. lift-/.f64 N/A

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

   3. clear-num N/A

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

   4. un-div-inv N/A

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

   5. lower-/.f64 N/A

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

   6. lower-/.f64 53.5

      \[\leadsto \frac{0 - \frac{-1}{\cos \left(\frac{-0.5}{\color{blue}{\frac{y}{x}}}\right)} \cdot \frac{-1}{\cos \left(-0.5 \cdot \frac{x}{y}\right)}}{\frac{-1}{\cos \left(-0.5 \cdot \frac{x}{y}\right)}} \]

6. Applied rewrites 53.5%

   \[\leadsto \frac{0 - \frac{-1}{\cos \color{blue}{\left(\frac{-0.5}{\frac{y}{x}}\right)}} \cdot \frac{-1}{\cos \left(-0.5 \cdot \frac{x}{y}\right)}}{\frac{-1}{\cos \left(-0.5 \cdot \frac{x}{y}\right)}} \]

8. Applied rewrites 53.5%

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

   1. lift-/.f64 N/A

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

   2. lift-/.f64 N/A

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

   3. div-inv N/A

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

   4. associate-/r* N/A

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

   5. lift-/.f64 N/A

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

   6. frac-2neg N/A

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

   7. lift-/.f64 N/A

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

   8. distribute-neg-frac N/A

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

   9. metadata-eval N/A

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

   10. clear-num N/A

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

   11. inv-pow N/A

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

   12. div-inv N/A

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

   13. metadata-eval N/A

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

   14. lift-*.f64 N/A

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

   15. metadata-eval N/A

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

   16. pow-pow N/A

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

   17. lift-*.f64 N/A

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

   18. *-commutative N/A

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

   19. lift-*.f64 N/A

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

   20. lift-pow.f64 N/A

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

   21. pow2 N/A

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

   22. mul-1-neg N/A

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

   23. div-inv N/A

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

   24. lift-/.f64 N/A

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

   25. lower-/.f64 N/A

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

10. Applied rewrites 53.5%

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

11. Final simplification 53.5%

    \[\leadsto \frac{\frac{--1}{\cos \left(\frac{x}{y} \cdot -0.5\right)} \cdot \frac{-1}{\cos \left(\frac{\frac{0.5}{y}}{\frac{-1}{x}}\right)}}{\frac{-1}{\frac{{\cos \left(\frac{x}{y} \cdot 0.5\right)}^{-1}}{{\cos \left(\frac{x}{y} \cdot 0.5\right)}^{-2}}}} \]
12. Add Preprocessing

Alternative 3: 55.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ x_m = \left|x\right| \\ \begin{array}{l} t_0 := \frac{-1}{\cos \left(\frac{x\_m}{y\_m} \cdot -0.5\right)}\\ \frac{\frac{--1}{\cos \left(\frac{-0.5}{\frac{y\_m}{x\_m}}\right)} \cdot t\_0}{t\_0} \end{array} \end{array} \]

FPCore

y_m = (fabs.f64 y)
x_m = (fabs.f64 x)
(FPCore (x_m y_m)
 :precision binary64
 (let* ((t_0 (/ -1.0 (cos (* (/ x_m y_m) -0.5)))))
   (/ (* (/ (- -1.0) (cos (/ -0.5 (/ y_m x_m)))) t_0) t_0)))

C

y_m = fabs(y);
x_m = fabs(x);
double code(double x_m, double y_m) {
	double t_0 = -1.0 / cos(((x_m / y_m) * -0.5));
	return ((-(-1.0) / cos((-0.5 / (y_m / x_m)))) * t_0) / t_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
    real(8) :: t_0
    t_0 = (-1.0d0) / cos(((x_m / y_m) * (-0.5d0)))
    code = ((-(-1.0d0) / cos(((-0.5d0) / (y_m / x_m)))) * t_0) / t_0
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 = -1.0 / Math.cos(((x_m / y_m) * -0.5));
	return ((-(-1.0) / Math.cos((-0.5 / (y_m / x_m)))) * t_0) / t_0;
}

Python

y_m = math.fabs(y)
x_m = math.fabs(x)
def code(x_m, y_m):
	t_0 = -1.0 / math.cos(((x_m / y_m) * -0.5))
	return ((-(-1.0) / math.cos((-0.5 / (y_m / x_m)))) * t_0) / t_0

Julia

y_m = abs(y)
x_m = abs(x)
function code(x_m, y_m)
	t_0 = Float64(-1.0 / cos(Float64(Float64(x_m / y_m) * -0.5)))
	return Float64(Float64(Float64(Float64(-(-1.0)) / cos(Float64(-0.5 / Float64(y_m / x_m)))) * t_0) / t_0)
end

MATLAB

y_m = abs(y);
x_m = abs(x);
function tmp = code(x_m, y_m)
	t_0 = -1.0 / cos(((x_m / y_m) * -0.5));
	tmp = ((-(-1.0) / cos((-0.5 / (y_m / x_m)))) * t_0) / t_0;
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[(-1.0 / N[Cos[N[(N[(x$95$m / y$95$m), $MachinePrecision] * -0.5), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, N[(N[(N[((--1.0) / N[Cos[N[(-0.5 / N[(y$95$m / x$95$m), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * t$95$0), $MachinePrecision] / t$95$0), $MachinePrecision]]

Derivation

1. Initial program 42.3%

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

4. Applied rewrites 53.3%

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

   1. lift-*.f64 N/A

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

   2. lift-/.f64 N/A

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

   3. clear-num N/A

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

   4. un-div-inv N/A

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

   5. lower-/.f64 N/A

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

   6. lower-/.f64 53.5

      \[\leadsto \frac{0 - \frac{-1}{\cos \left(\frac{-0.5}{\color{blue}{\frac{y}{x}}}\right)} \cdot \frac{-1}{\cos \left(-0.5 \cdot \frac{x}{y}\right)}}{\frac{-1}{\cos \left(-0.5 \cdot \frac{x}{y}\right)}} \]

6. Applied rewrites 53.5%

   \[\leadsto \frac{0 - \frac{-1}{\cos \color{blue}{\left(\frac{-0.5}{\frac{y}{x}}\right)}} \cdot \frac{-1}{\cos \left(-0.5 \cdot \frac{x}{y}\right)}}{\frac{-1}{\cos \left(-0.5 \cdot \frac{x}{y}\right)}} \]

7. Final simplification 53.5%

   \[\leadsto \frac{\frac{--1}{\cos \left(\frac{-0.5}{\frac{y}{x}}\right)} \cdot \frac{-1}{\cos \left(\frac{x}{y} \cdot -0.5\right)}}{\frac{-1}{\cos \left(\frac{x}{y} \cdot -0.5\right)}} \]
8. Add Preprocessing

Alternative 4: 55.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ x_m = \left|x\right| \\ \begin{array}{l} t_0 := \cos \left(\frac{x\_m}{y\_m} \cdot -0.5\right)\\ \frac{\frac{--1}{t\_0} \cdot \frac{-1}{t\_0}}{\frac{-1}{\cos \left(\frac{-0.5}{\frac{y\_m}{x\_m}}\right)}} \end{array} \end{array} \]

FPCore

y_m = (fabs.f64 y)
x_m = (fabs.f64 x)
(FPCore (x_m y_m)
 :precision binary64
 (let* ((t_0 (cos (* (/ x_m y_m) -0.5))))
   (/ (* (/ (- -1.0) t_0) (/ -1.0 t_0)) (/ -1.0 (cos (/ -0.5 (/ y_m x_m)))))))

C

y_m = fabs(y);
x_m = fabs(x);
double code(double x_m, double y_m) {
	double t_0 = cos(((x_m / y_m) * -0.5));
	return ((-(-1.0) / t_0) * (-1.0 / t_0)) / (-1.0 / cos((-0.5 / (y_m / x_m))));
}

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
    t_0 = cos(((x_m / y_m) * (-0.5d0)))
    code = ((-(-1.0d0) / t_0) * ((-1.0d0) / t_0)) / ((-1.0d0) / cos(((-0.5d0) / (y_m / x_m))))
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(((x_m / y_m) * -0.5));
	return ((-(-1.0) / t_0) * (-1.0 / t_0)) / (-1.0 / Math.cos((-0.5 / (y_m / x_m))));
}

Python

y_m = math.fabs(y)
x_m = math.fabs(x)
def code(x_m, y_m):
	t_0 = math.cos(((x_m / y_m) * -0.5))
	return ((-(-1.0) / t_0) * (-1.0 / t_0)) / (-1.0 / math.cos((-0.5 / (y_m / x_m))))

Julia

y_m = abs(y)
x_m = abs(x)
function code(x_m, y_m)
	t_0 = cos(Float64(Float64(x_m / y_m) * -0.5))
	return Float64(Float64(Float64(Float64(-(-1.0)) / t_0) * Float64(-1.0 / t_0)) / Float64(-1.0 / cos(Float64(-0.5 / Float64(y_m / x_m)))))
end

MATLAB

y_m = abs(y);
x_m = abs(x);
function tmp = code(x_m, y_m)
	t_0 = cos(((x_m / y_m) * -0.5));
	tmp = ((-(-1.0) / t_0) * (-1.0 / t_0)) / (-1.0 / cos((-0.5 / (y_m / x_m))));
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[(N[(x$95$m / y$95$m), $MachinePrecision] * -0.5), $MachinePrecision]], $MachinePrecision]}, N[(N[(N[((--1.0) / t$95$0), $MachinePrecision] * N[(-1.0 / t$95$0), $MachinePrecision]), $MachinePrecision] / N[(-1.0 / N[Cos[N[(-0.5 / N[(y$95$m / x$95$m), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Initial program 42.3%

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

4. Applied rewrites 53.3%

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

   1. lift-*.f64 N/A

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

   2. lift-/.f64 N/A

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

   3. clear-num N/A

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

   4. un-div-inv N/A

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

   5. lower-/.f64 N/A

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

   6. lower-/.f64 53.4

      \[\leadsto \frac{0 - \frac{-1}{\cos \left(-0.5 \cdot \frac{x}{y}\right)} \cdot \frac{-1}{\cos \left(-0.5 \cdot \frac{x}{y}\right)}}{\frac{-1}{\cos \left(\frac{-0.5}{\color{blue}{\frac{y}{x}}}\right)}} \]

6. Applied rewrites 53.4%

   \[\leadsto \frac{0 - \frac{-1}{\cos \left(-0.5 \cdot \frac{x}{y}\right)} \cdot \frac{-1}{\cos \left(-0.5 \cdot \frac{x}{y}\right)}}{\frac{-1}{\cos \color{blue}{\left(\frac{-0.5}{\frac{y}{x}}\right)}}} \]

7. Final simplification 53.4%

   \[\leadsto \frac{\frac{--1}{\cos \left(\frac{x}{y} \cdot -0.5\right)} \cdot \frac{-1}{\cos \left(\frac{x}{y} \cdot -0.5\right)}}{\frac{-1}{\cos \left(\frac{-0.5}{\frac{y}{x}}\right)}} \]
8. Add Preprocessing

Alternative 5: 55.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ x_m = \left|x\right| \\ \begin{array}{l} t_0 := \cos \left(\frac{x\_m}{y\_m} \cdot -0.5\right)\\ \frac{{\left(\frac{-1}{t\_0}\right)}^{2}}{\frac{--1}{t\_0}} \end{array} \end{array} \]

FPCore

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

C

y_m = fabs(y);
x_m = fabs(x);
double code(double x_m, double y_m) {
	double t_0 = cos(((x_m / y_m) * -0.5));
	return pow((-1.0 / t_0), 2.0) / (-(-1.0) / t_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
    real(8) :: t_0
    t_0 = cos(((x_m / y_m) * (-0.5d0)))
    code = (((-1.0d0) / t_0) ** 2.0d0) / (-(-1.0d0) / t_0)
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(((x_m / y_m) * -0.5));
	return Math.pow((-1.0 / t_0), 2.0) / (-(-1.0) / t_0);
}

Python

y_m = math.fabs(y)
x_m = math.fabs(x)
def code(x_m, y_m):
	t_0 = math.cos(((x_m / y_m) * -0.5))
	return math.pow((-1.0 / t_0), 2.0) / (-(-1.0) / t_0)

Julia

y_m = abs(y)
x_m = abs(x)
function code(x_m, y_m)
	t_0 = cos(Float64(Float64(x_m / y_m) * -0.5))
	return Float64((Float64(-1.0 / t_0) ^ 2.0) / Float64(Float64(-(-1.0)) / t_0))
end

MATLAB

y_m = abs(y);
x_m = abs(x);
function tmp = code(x_m, y_m)
	t_0 = cos(((x_m / y_m) * -0.5));
	tmp = ((-1.0 / t_0) ^ 2.0) / (-(-1.0) / t_0);
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[(N[(x$95$m / y$95$m), $MachinePrecision] * -0.5), $MachinePrecision]], $MachinePrecision]}, N[(N[Power[N[(-1.0 / t$95$0), $MachinePrecision], 2.0], $MachinePrecision] / N[((--1.0) / t$95$0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Initial program 42.3%

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

4. Applied rewrites 53.3%

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

   1. lift-*.f64 N/A

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

   2. pow2 N/A

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

   3. lower-pow.f64 53.3

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

   4. lift-*.f64 N/A

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

   5. *-commutative N/A

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

   6. lower-*.f64 53.3

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

6. Applied rewrites 53.3%

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

7. Final simplification 53.3%

   \[\leadsto \frac{{\left(\frac{-1}{\cos \left(\frac{x}{y} \cdot -0.5\right)}\right)}^{2}}{\frac{--1}{\cos \left(\frac{x}{y} \cdot -0.5\right)}} \]
8. Add Preprocessing

Alternative 6: 55.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ x_m = \left|x\right| \\ \begin{array}{l} t_0 := \cos \left(\frac{x\_m}{y\_m} \cdot -0.5\right)\\ \left(-t\_0\right) \cdot \frac{-1}{{t\_0}^{2}} \end{array} \end{array} \]

FPCore

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

C

y_m = fabs(y);
x_m = fabs(x);
double code(double x_m, double y_m) {
	double t_0 = cos(((x_m / y_m) * -0.5));
	return -t_0 * (-1.0 / pow(t_0, 2.0));
}

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
    real(8) :: t_0
    t_0 = cos(((x_m / y_m) * (-0.5d0)))
    code = -t_0 * ((-1.0d0) / (t_0 ** 2.0d0))
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(((x_m / y_m) * -0.5));
	return -t_0 * (-1.0 / Math.pow(t_0, 2.0));
}

Python

y_m = math.fabs(y)
x_m = math.fabs(x)
def code(x_m, y_m):
	t_0 = math.cos(((x_m / y_m) * -0.5))
	return -t_0 * (-1.0 / math.pow(t_0, 2.0))

Julia

y_m = abs(y)
x_m = abs(x)
function code(x_m, y_m)
	t_0 = cos(Float64(Float64(x_m / y_m) * -0.5))
	return Float64(Float64(-t_0) * Float64(-1.0 / (t_0 ^ 2.0)))
end

MATLAB

y_m = abs(y);
x_m = abs(x);
function tmp = code(x_m, y_m)
	t_0 = cos(((x_m / y_m) * -0.5));
	tmp = -t_0 * (-1.0 / (t_0 ^ 2.0));
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[(N[(x$95$m / y$95$m), $MachinePrecision] * -0.5), $MachinePrecision]], $MachinePrecision]}, N[((-t$95$0) * N[(-1.0 / N[Power[t$95$0, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Initial program 42.3%

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

4. Applied rewrites 53.3%

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

   1. lift-/.f64 N/A

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

   2. div-inv N/A

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

   3. lift-/.f64 N/A

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

   4. clear-num N/A

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

   5. lower-*.f64 N/A

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

6. Applied rewrites 53.3%

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

7. Final simplification 53.3%

   \[\leadsto \left(-\cos \left(\frac{x}{y} \cdot -0.5\right)\right) \cdot \frac{-1}{{\cos \left(\frac{x}{y} \cdot -0.5\right)}^{2}} \]
8. Add Preprocessing

Alternative 7: 55.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ x_m = \left|x\right| \\ \frac{1}{\cos \left(\frac{x\_m}{y\_m} \cdot -0.5\right)} \end{array} \]

FPCore

y_m = (fabs.f64 y)
x_m = (fabs.f64 x)
(FPCore (x_m y_m) :precision binary64 (/ 1.0 (cos (* (/ x_m y_m) -0.5))))

C

y_m = fabs(y);
x_m = fabs(x);
double code(double x_m, double y_m) {
	return 1.0 / cos(((x_m / y_m) * -0.5));
}

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 / cos(((x_m / y_m) * (-0.5d0)))
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 / Math.cos(((x_m / y_m) * -0.5));
}

Python

y_m = math.fabs(y)
x_m = math.fabs(x)
def code(x_m, y_m):
	return 1.0 / math.cos(((x_m / y_m) * -0.5))

Julia

y_m = abs(y)
x_m = abs(x)
function code(x_m, y_m)
	return Float64(1.0 / cos(Float64(Float64(x_m / y_m) * -0.5)))
end

MATLAB

y_m = abs(y);
x_m = abs(x);
function tmp = code(x_m, y_m)
	tmp = 1.0 / cos(((x_m / y_m) * -0.5));
end

Wolfram

y_m = N[Abs[y], $MachinePrecision]
x_m = N[Abs[x], $MachinePrecision]
code[x$95$m_, y$95$m_] := N[(1.0 / N[Cos[N[(N[(x$95$m / y$95$m), $MachinePrecision] * -0.5), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 42.3%

   \[\frac{\tan \left(\frac{x}{y \cdot 2}\right)}{\sin \left(\frac{x}{y \cdot 2}\right)} \]
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 53.3%

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

5. Final simplification 53.3%

   \[\leadsto \frac{1}{\cos \left(\frac{x}{y} \cdot -0.5\right)} \]
6. Add Preprocessing

Alternative 8: 55.2% 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 42.3%

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

3. Taylor expanded in y around inf

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

5. Applied rewrites 52.6%

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

Developer Target 1: 55.2% 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 2024266 
(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)))))