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

Percentage Accurate: 43.8% → 57.2%

Time: 24.2s

Alternatives: 7

Speedup: 211.0×

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: 43.8% 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: 57.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ y_m = \left|y\right| \\ \begin{array}{l} \mathbf{if}\;\frac{x\_m}{y\_m \cdot 2} \leq 10^{+199}:\\ \;\;\;\;\frac{1}{e^{\mathsf{log1p}\left(\cos \left(\sqrt{x\_m} \cdot \frac{\sqrt{x\_m}}{y\_m \cdot 2}\right)\right)} + -1}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x\_m}{x\_m \cdot 0.16666666666666666 + e^{\log \left(x\_m \cdot 0.3333333333333333\right)}}\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
y_m = (fabs.f64 y)
(FPCore (x_m y_m)
 :precision binary64
 (if (<= (/ x_m (* y_m 2.0)) 1e+199)
   (/
    1.0
    (+ (exp (log1p (cos (* (sqrt x_m) (/ (sqrt x_m) (* y_m 2.0)))))) -1.0))
   (*
    0.5
    (/
     x_m
     (+ (* x_m 0.16666666666666666) (exp (log (* x_m 0.3333333333333333))))))))

C

x_m = fabs(x);
y_m = fabs(y);
double code(double x_m, double y_m) {
	double tmp;
	if ((x_m / (y_m * 2.0)) <= 1e+199) {
		tmp = 1.0 / (exp(log1p(cos((sqrt(x_m) * (sqrt(x_m) / (y_m * 2.0)))))) + -1.0);
	} else {
		tmp = 0.5 * (x_m / ((x_m * 0.16666666666666666) + exp(log((x_m * 0.3333333333333333)))));
	}
	return tmp;
}

Java

x_m = Math.abs(x);
y_m = Math.abs(y);
public static double code(double x_m, double y_m) {
	double tmp;
	if ((x_m / (y_m * 2.0)) <= 1e+199) {
		tmp = 1.0 / (Math.exp(Math.log1p(Math.cos((Math.sqrt(x_m) * (Math.sqrt(x_m) / (y_m * 2.0)))))) + -1.0);
	} else {
		tmp = 0.5 * (x_m / ((x_m * 0.16666666666666666) + Math.exp(Math.log((x_m * 0.3333333333333333)))));
	}
	return tmp;
}

Python

x_m = math.fabs(x)
y_m = math.fabs(y)
def code(x_m, y_m):
	tmp = 0
	if (x_m / (y_m * 2.0)) <= 1e+199:
		tmp = 1.0 / (math.exp(math.log1p(math.cos((math.sqrt(x_m) * (math.sqrt(x_m) / (y_m * 2.0)))))) + -1.0)
	else:
		tmp = 0.5 * (x_m / ((x_m * 0.16666666666666666) + math.exp(math.log((x_m * 0.3333333333333333)))))
	return tmp

Julia

x_m = abs(x)
y_m = abs(y)
function code(x_m, y_m)
	tmp = 0.0
	if (Float64(x_m / Float64(y_m * 2.0)) <= 1e+199)
		tmp = Float64(1.0 / Float64(exp(log1p(cos(Float64(sqrt(x_m) * Float64(sqrt(x_m) / Float64(y_m * 2.0)))))) + -1.0));
	else
		tmp = Float64(0.5 * Float64(x_m / Float64(Float64(x_m * 0.16666666666666666) + exp(log(Float64(x_m * 0.3333333333333333))))));
	end
	return tmp
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
y_m = N[Abs[y], $MachinePrecision]
code[x$95$m_, y$95$m_] := If[LessEqual[N[(x$95$m / N[(y$95$m * 2.0), $MachinePrecision]), $MachinePrecision], 1e+199], N[(1.0 / N[(N[Exp[N[Log[1 + N[Cos[N[(N[Sqrt[x$95$m], $MachinePrecision] * N[(N[Sqrt[x$95$m], $MachinePrecision] / N[(y$95$m * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]], $MachinePrecision]], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(x$95$m / N[(N[(x$95$m * 0.16666666666666666), $MachinePrecision] + N[Exp[N[Log[N[(x$95$m * 0.3333333333333333), $MachinePrecision]], $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (*.f64 y 2)) < 1.0000000000000001e199

   1. Initial program 49.4%

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

   3. Taylor expanded in x around inf 60.8%

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

      1. associate-*r/ 60.8%

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

   5. Simplified 60.8%

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

      1. expm1-log1p-u 60.8%

         \[\leadsto \frac{1}{\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\cos \left(\frac{0.5 \cdot x}{y}\right)\right)\right)}} \]

      2. expm1-udef 60.8%

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

      3. *-commutative 60.8%

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

      4. associate-*r/ 60.8%

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

   7. Applied egg-rr 60.8%

      \[\leadsto \frac{1}{\color{blue}{e^{\mathsf{log1p}\left(\cos \left(x \cdot \frac{0.5}{y}\right)\right)} - 1}} \]
   8. Step-by-step derivation

      1. associate-*r/ 60.8%

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

      2. associate-/l* 60.8%

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

      3. div-inv 60.8%

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

      4. metadata-eval 60.8%

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

      5. add-sqr-sqrt 30.8%

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

      6. associate-/l* 30.8%

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

   9. Applied egg-rr 30.8%

      \[\leadsto \frac{1}{e^{\mathsf{log1p}\left(\cos \color{blue}{\left(\frac{\sqrt{x}}{\frac{y \cdot 2}{\sqrt{x}}}\right)}\right)} - 1} \]
   10. Step-by-step derivation

       1. associate-/r/ 30.8%

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

       2. *-commutative 30.8%

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

   11. Simplified 30.8%

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

   if 1.0000000000000001e199 < (/.f64 x (*.f64 y 2))

   1. Initial program 5.2%

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

      1. add-log-exp 5.2%

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

      2. add-cube-cbrt 5.2%

         \[\leadsto \frac{\tan \left(\frac{x}{y \cdot 2}\right)}{\log \color{blue}{\left(\left(\sqrt[3]{e^{\sin \left(\frac{x}{y \cdot 2}\right)}} \cdot \sqrt[3]{e^{\sin \left(\frac{x}{y \cdot 2}\right)}}\right) \cdot \sqrt[3]{e^{\sin \left(\frac{x}{y \cdot 2}\right)}}\right)}} \]

      3. log-prod 5.2%

         \[\leadsto \frac{\tan \left(\frac{x}{y \cdot 2}\right)}{\color{blue}{\log \left(\sqrt[3]{e^{\sin \left(\frac{x}{y \cdot 2}\right)}} \cdot \sqrt[3]{e^{\sin \left(\frac{x}{y \cdot 2}\right)}}\right) + \log \left(\sqrt[3]{e^{\sin \left(\frac{x}{y \cdot 2}\right)}}\right)}} \]

   4. Applied egg-rr 4.1%

      \[\leadsto \frac{\tan \left(\frac{x}{y \cdot 2}\right)}{\color{blue}{\log \left(\sqrt[3]{e^{\sin \left(x \cdot \frac{0.5}{y}\right)}} \cdot \sqrt[3]{e^{\sin \left(x \cdot \frac{0.5}{y}\right)}}\right) + \log \left(\sqrt[3]{e^{\sin \left(x \cdot \frac{0.5}{y}\right)}}\right)}} \]
   5. Step-by-step derivation

      1. log-prod 4.1%

         \[\leadsto \frac{\tan \left(\frac{x}{y \cdot 2}\right)}{\color{blue}{\left(\log \left(\sqrt[3]{e^{\sin \left(x \cdot \frac{0.5}{y}\right)}}\right) + \log \left(\sqrt[3]{e^{\sin \left(x \cdot \frac{0.5}{y}\right)}}\right)\right)} + \log \left(\sqrt[3]{e^{\sin \left(x \cdot \frac{0.5}{y}\right)}}\right)} \]

      2. count-2 4.1%

         \[\leadsto \frac{\tan \left(\frac{x}{y \cdot 2}\right)}{\color{blue}{2 \cdot \log \left(\sqrt[3]{e^{\sin \left(x \cdot \frac{0.5}{y}\right)}}\right)} + \log \left(\sqrt[3]{e^{\sin \left(x \cdot \frac{0.5}{y}\right)}}\right)} \]

      3. *-commutative 4.1%

         \[\leadsto \frac{\tan \left(\frac{x}{y \cdot 2}\right)}{2 \cdot \log \left(\sqrt[3]{e^{\sin \color{blue}{\left(\frac{0.5}{y} \cdot x\right)}}}\right) + \log \left(\sqrt[3]{e^{\sin \left(x \cdot \frac{0.5}{y}\right)}}\right)} \]

      4. associate-*l/ 4.3%

         \[\leadsto \frac{\tan \left(\frac{x}{y \cdot 2}\right)}{2 \cdot \log \left(\sqrt[3]{e^{\sin \color{blue}{\left(\frac{0.5 \cdot x}{y}\right)}}}\right) + \log \left(\sqrt[3]{e^{\sin \left(x \cdot \frac{0.5}{y}\right)}}\right)} \]

      5. *-commutative 4.3%

         \[\leadsto \frac{\tan \left(\frac{x}{y \cdot 2}\right)}{2 \cdot \log \left(\sqrt[3]{e^{\sin \left(\frac{0.5 \cdot x}{y}\right)}}\right) + \log \left(\sqrt[3]{e^{\sin \color{blue}{\left(\frac{0.5}{y} \cdot x\right)}}}\right)} \]

      6. associate-*l/ 5.2%

         \[\leadsto \frac{\tan \left(\frac{x}{y \cdot 2}\right)}{2 \cdot \log \left(\sqrt[3]{e^{\sin \left(\frac{0.5 \cdot x}{y}\right)}}\right) + \log \left(\sqrt[3]{e^{\sin \color{blue}{\left(\frac{0.5 \cdot x}{y}\right)}}}\right)} \]

   6. Simplified 5.2%

      \[\leadsto \frac{\tan \left(\frac{x}{y \cdot 2}\right)}{\color{blue}{2 \cdot \log \left(\sqrt[3]{e^{\sin \left(\frac{0.5 \cdot x}{y}\right)}}\right) + \log \left(\sqrt[3]{e^{\sin \left(\frac{0.5 \cdot x}{y}\right)}}\right)}} \]

   7. Taylor expanded in y around inf 11.5%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x}{0.16666666666666666 \cdot x + 0.3333333333333333 \cdot x}} \]
   8. Step-by-step derivation

      1. add-exp-log 4.6%

         \[\leadsto 0.5 \cdot \frac{x}{0.16666666666666666 \cdot x + \color{blue}{e^{\log \left(0.3333333333333333 \cdot x\right)}}} \]

      2. *-commutative 4.6%

         \[\leadsto 0.5 \cdot \frac{x}{0.16666666666666666 \cdot x + e^{\log \color{blue}{\left(x \cdot 0.3333333333333333\right)}}} \]

   9. Applied egg-rr 4.6%

      \[\leadsto 0.5 \cdot \frac{x}{0.16666666666666666 \cdot x + \color{blue}{e^{\log \left(x \cdot 0.3333333333333333\right)}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 27.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y \cdot 2} \leq 10^{+199}:\\ \;\;\;\;\frac{1}{e^{\mathsf{log1p}\left(\cos \left(\sqrt{x} \cdot \frac{\sqrt{x}}{y \cdot 2}\right)\right)} + -1}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x}{x \cdot 0.16666666666666666 + e^{\log \left(x \cdot 0.3333333333333333\right)}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 57.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ y_m = \left|y\right| \\ \begin{array}{l} t_0 := \frac{x\_m}{y\_m \cdot 2}\\ \mathbf{if}\;t\_0 \leq 10^{+164}:\\ \;\;\;\;\frac{1}{e^{\mathsf{log1p}\left(\cos \left(e^{\log t\_0}\right)\right)} + -1}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{e^{\log 2 + \frac{{x\_m}^{2}}{{y\_m}^{2}} \cdot -0.0625} + -1}\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
y_m = (fabs.f64 y)
(FPCore (x_m y_m)
 :precision binary64
 (let* ((t_0 (/ x_m (* y_m 2.0))))
   (if (<= t_0 1e+164)
     (/ 1.0 (+ (exp (log1p (cos (exp (log t_0))))) -1.0))
     (/
      1.0
      (+
       (exp (+ (log 2.0) (* (/ (pow x_m 2.0) (pow y_m 2.0)) -0.0625)))
       -1.0)))))

C

x_m = fabs(x);
y_m = fabs(y);
double code(double x_m, double y_m) {
	double t_0 = x_m / (y_m * 2.0);
	double tmp;
	if (t_0 <= 1e+164) {
		tmp = 1.0 / (exp(log1p(cos(exp(log(t_0))))) + -1.0);
	} else {
		tmp = 1.0 / (exp((log(2.0) + ((pow(x_m, 2.0) / pow(y_m, 2.0)) * -0.0625))) + -1.0);
	}
	return tmp;
}

Java

x_m = Math.abs(x);
y_m = Math.abs(y);
public static double code(double x_m, double y_m) {
	double t_0 = x_m / (y_m * 2.0);
	double tmp;
	if (t_0 <= 1e+164) {
		tmp = 1.0 / (Math.exp(Math.log1p(Math.cos(Math.exp(Math.log(t_0))))) + -1.0);
	} else {
		tmp = 1.0 / (Math.exp((Math.log(2.0) + ((Math.pow(x_m, 2.0) / Math.pow(y_m, 2.0)) * -0.0625))) + -1.0);
	}
	return tmp;
}

Python

x_m = math.fabs(x)
y_m = math.fabs(y)
def code(x_m, y_m):
	t_0 = x_m / (y_m * 2.0)
	tmp = 0
	if t_0 <= 1e+164:
		tmp = 1.0 / (math.exp(math.log1p(math.cos(math.exp(math.log(t_0))))) + -1.0)
	else:
		tmp = 1.0 / (math.exp((math.log(2.0) + ((math.pow(x_m, 2.0) / math.pow(y_m, 2.0)) * -0.0625))) + -1.0)
	return tmp

Julia

x_m = abs(x)
y_m = abs(y)
function code(x_m, y_m)
	t_0 = Float64(x_m / Float64(y_m * 2.0))
	tmp = 0.0
	if (t_0 <= 1e+164)
		tmp = Float64(1.0 / Float64(exp(log1p(cos(exp(log(t_0))))) + -1.0));
	else
		tmp = Float64(1.0 / Float64(exp(Float64(log(2.0) + Float64(Float64((x_m ^ 2.0) / (y_m ^ 2.0)) * -0.0625))) + -1.0));
	end
	return tmp
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
y_m = N[Abs[y], $MachinePrecision]
code[x$95$m_, y$95$m_] := Block[{t$95$0 = N[(x$95$m / N[(y$95$m * 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, 1e+164], N[(1.0 / N[(N[Exp[N[Log[1 + N[Cos[N[Exp[N[Log[t$95$0], $MachinePrecision]], $MachinePrecision]], $MachinePrecision]], $MachinePrecision]], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision], N[(1.0 / N[(N[Exp[N[(N[Log[2.0], $MachinePrecision] + N[(N[(N[Power[x$95$m, 2.0], $MachinePrecision] / N[Power[y$95$m, 2.0], $MachinePrecision]), $MachinePrecision] * -0.0625), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (*.f64 y 2)) < 1e164

   1. Initial program 50.7%

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

   3. Taylor expanded in x around inf 62.5%

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

      1. associate-*r/ 62.5%

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

   5. Simplified 62.5%

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

      1. expm1-log1p-u 62.5%

         \[\leadsto \frac{1}{\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\cos \left(\frac{0.5 \cdot x}{y}\right)\right)\right)}} \]

      2. expm1-udef 62.5%

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

      3. *-commutative 62.5%

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

      4. associate-*r/ 62.5%

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

   7. Applied egg-rr 62.5%

      \[\leadsto \frac{1}{\color{blue}{e^{\mathsf{log1p}\left(\cos \left(x \cdot \frac{0.5}{y}\right)\right)} - 1}} \]
   8. Step-by-step derivation

      1. associate-*r/ 62.5%

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

      2. associate-/l* 62.5%

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

      3. div-inv 62.5%

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

      4. metadata-eval 62.5%

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

      5. add-exp-log 37.9%

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

   9. Applied egg-rr 37.9%

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

   if 1e164 < (/.f64 x (*.f64 y 2))

   1. Initial program 7.0%

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

   3. Taylor expanded in x around inf 7.0%

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

      1. associate-*r/ 7.0%

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

   5. Simplified 7.0%

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

      1. expm1-log1p-u 7.0%

         \[\leadsto \frac{1}{\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\cos \left(\frac{0.5 \cdot x}{y}\right)\right)\right)}} \]

      2. expm1-udef 7.0%

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

      3. *-commutative 7.0%

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

      4. associate-*r/ 7.6%

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

   7. Applied egg-rr 7.6%

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

   8. Taylor expanded in x around 0 12.7%

      \[\leadsto \frac{1}{e^{\color{blue}{\log 2 + -0.0625 \cdot \frac{{x}^{2}}{{y}^{2}}}} - 1} \]
   9. Step-by-step derivation

      1. *-commutative 12.7%

         \[\leadsto \frac{1}{e^{\log 2 + \color{blue}{\frac{{x}^{2}}{{y}^{2}} \cdot -0.0625}} - 1} \]

   10. Simplified 12.7%

       \[\leadsto \frac{1}{e^{\color{blue}{\log 2 + \frac{{x}^{2}}{{y}^{2}} \cdot -0.0625}} - 1} \]
3. Recombined 2 regimes into one program.

4. Final simplification 34.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y \cdot 2} \leq 10^{+164}:\\ \;\;\;\;\frac{1}{e^{\mathsf{log1p}\left(\cos \left(e^{\log \left(\frac{x}{y \cdot 2}\right)}\right)\right)} + -1}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{e^{\log 2 + \frac{{x}^{2}}{{y}^{2}} \cdot -0.0625} + -1}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 57.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ y_m = \left|y\right| \\ \begin{array}{l} \mathbf{if}\;\frac{x\_m}{y\_m \cdot 2} \leq 5 \cdot 10^{+168}:\\ \;\;\;\;\frac{1}{e^{\mathsf{log1p}\left(\cos \left(x\_m \cdot \frac{0.5}{y\_m}\right)\right)} + -1}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{e^{\log 2 + \frac{{x\_m}^{2}}{{y\_m}^{2}} \cdot -0.0625} + -1}\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
y_m = (fabs.f64 y)
(FPCore (x_m y_m)
 :precision binary64
 (if (<= (/ x_m (* y_m 2.0)) 5e+168)
   (/ 1.0 (+ (exp (log1p (cos (* x_m (/ 0.5 y_m))))) -1.0))
   (/
    1.0
    (+ (exp (+ (log 2.0) (* (/ (pow x_m 2.0) (pow y_m 2.0)) -0.0625))) -1.0))))

C

x_m = fabs(x);
y_m = fabs(y);
double code(double x_m, double y_m) {
	double tmp;
	if ((x_m / (y_m * 2.0)) <= 5e+168) {
		tmp = 1.0 / (exp(log1p(cos((x_m * (0.5 / y_m))))) + -1.0);
	} else {
		tmp = 1.0 / (exp((log(2.0) + ((pow(x_m, 2.0) / pow(y_m, 2.0)) * -0.0625))) + -1.0);
	}
	return tmp;
}

Java

x_m = Math.abs(x);
y_m = Math.abs(y);
public static double code(double x_m, double y_m) {
	double tmp;
	if ((x_m / (y_m * 2.0)) <= 5e+168) {
		tmp = 1.0 / (Math.exp(Math.log1p(Math.cos((x_m * (0.5 / y_m))))) + -1.0);
	} else {
		tmp = 1.0 / (Math.exp((Math.log(2.0) + ((Math.pow(x_m, 2.0) / Math.pow(y_m, 2.0)) * -0.0625))) + -1.0);
	}
	return tmp;
}

Python

x_m = math.fabs(x)
y_m = math.fabs(y)
def code(x_m, y_m):
	tmp = 0
	if (x_m / (y_m * 2.0)) <= 5e+168:
		tmp = 1.0 / (math.exp(math.log1p(math.cos((x_m * (0.5 / y_m))))) + -1.0)
	else:
		tmp = 1.0 / (math.exp((math.log(2.0) + ((math.pow(x_m, 2.0) / math.pow(y_m, 2.0)) * -0.0625))) + -1.0)
	return tmp

Julia

x_m = abs(x)
y_m = abs(y)
function code(x_m, y_m)
	tmp = 0.0
	if (Float64(x_m / Float64(y_m * 2.0)) <= 5e+168)
		tmp = Float64(1.0 / Float64(exp(log1p(cos(Float64(x_m * Float64(0.5 / y_m))))) + -1.0));
	else
		tmp = Float64(1.0 / Float64(exp(Float64(log(2.0) + Float64(Float64((x_m ^ 2.0) / (y_m ^ 2.0)) * -0.0625))) + -1.0));
	end
	return tmp
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
y_m = N[Abs[y], $MachinePrecision]
code[x$95$m_, y$95$m_] := If[LessEqual[N[(x$95$m / N[(y$95$m * 2.0), $MachinePrecision]), $MachinePrecision], 5e+168], N[(1.0 / N[(N[Exp[N[Log[1 + N[Cos[N[(x$95$m * N[(0.5 / y$95$m), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]], $MachinePrecision]], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision], N[(1.0 / N[(N[Exp[N[(N[Log[2.0], $MachinePrecision] + N[(N[(N[Power[x$95$m, 2.0], $MachinePrecision] / N[Power[y$95$m, 2.0], $MachinePrecision]), $MachinePrecision] * -0.0625), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (*.f64 y 2)) < 4.99999999999999967e168

   1. Initial program 50.7%

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

   3. Taylor expanded in x around inf 62.5%

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

      1. associate-*r/ 62.5%

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

   5. Simplified 62.5%

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

      1. expm1-log1p-u 62.5%

         \[\leadsto \frac{1}{\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\cos \left(\frac{0.5 \cdot x}{y}\right)\right)\right)}} \]

      2. expm1-udef 62.5%

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

      3. *-commutative 62.5%

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

      4. associate-*r/ 62.5%

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

   7. Applied egg-rr 62.5%

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

   if 4.99999999999999967e168 < (/.f64 x (*.f64 y 2))

   1. Initial program 7.0%

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

   3. Taylor expanded in x around inf 7.0%

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

      1. associate-*r/ 7.0%

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

   5. Simplified 7.0%

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

      1. expm1-log1p-u 7.0%

         \[\leadsto \frac{1}{\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\cos \left(\frac{0.5 \cdot x}{y}\right)\right)\right)}} \]

      2. expm1-udef 7.0%

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

      3. *-commutative 7.0%

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

      4. associate-*r/ 7.6%

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

   7. Applied egg-rr 7.6%

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

   8. Taylor expanded in x around 0 12.7%

      \[\leadsto \frac{1}{e^{\color{blue}{\log 2 + -0.0625 \cdot \frac{{x}^{2}}{{y}^{2}}}} - 1} \]
   9. Step-by-step derivation

      1. *-commutative 12.7%

         \[\leadsto \frac{1}{e^{\log 2 + \color{blue}{\frac{{x}^{2}}{{y}^{2}} \cdot -0.0625}} - 1} \]

   10. Simplified 12.7%

       \[\leadsto \frac{1}{e^{\color{blue}{\log 2 + \frac{{x}^{2}}{{y}^{2}} \cdot -0.0625}} - 1} \]
3. Recombined 2 regimes into one program.

4. Final simplification 55.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y \cdot 2} \leq 5 \cdot 10^{+168}:\\ \;\;\;\;\frac{1}{e^{\mathsf{log1p}\left(\cos \left(x \cdot \frac{0.5}{y}\right)\right)} + -1}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{e^{\log 2 + \frac{{x}^{2}}{{y}^{2}} \cdot -0.0625} + -1}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 57.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ y_m = \left|y\right| \\ \begin{array}{l} \mathbf{if}\;\frac{x\_m}{y\_m \cdot 2} \leq 10^{+199}:\\ \;\;\;\;\frac{1}{e^{\mathsf{log1p}\left(\cos \left(x\_m \cdot \frac{0.5}{y\_m}\right)\right)} + -1}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x\_m}{x\_m \cdot 0.16666666666666666 + e^{\log \left(x\_m \cdot 0.3333333333333333\right)}}\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
y_m = (fabs.f64 y)
(FPCore (x_m y_m)
 :precision binary64
 (if (<= (/ x_m (* y_m 2.0)) 1e+199)
   (/ 1.0 (+ (exp (log1p (cos (* x_m (/ 0.5 y_m))))) -1.0))
   (*
    0.5
    (/
     x_m
     (+ (* x_m 0.16666666666666666) (exp (log (* x_m 0.3333333333333333))))))))

C

x_m = fabs(x);
y_m = fabs(y);
double code(double x_m, double y_m) {
	double tmp;
	if ((x_m / (y_m * 2.0)) <= 1e+199) {
		tmp = 1.0 / (exp(log1p(cos((x_m * (0.5 / y_m))))) + -1.0);
	} else {
		tmp = 0.5 * (x_m / ((x_m * 0.16666666666666666) + exp(log((x_m * 0.3333333333333333)))));
	}
	return tmp;
}

Java

x_m = Math.abs(x);
y_m = Math.abs(y);
public static double code(double x_m, double y_m) {
	double tmp;
	if ((x_m / (y_m * 2.0)) <= 1e+199) {
		tmp = 1.0 / (Math.exp(Math.log1p(Math.cos((x_m * (0.5 / y_m))))) + -1.0);
	} else {
		tmp = 0.5 * (x_m / ((x_m * 0.16666666666666666) + Math.exp(Math.log((x_m * 0.3333333333333333)))));
	}
	return tmp;
}

Python

x_m = math.fabs(x)
y_m = math.fabs(y)
def code(x_m, y_m):
	tmp = 0
	if (x_m / (y_m * 2.0)) <= 1e+199:
		tmp = 1.0 / (math.exp(math.log1p(math.cos((x_m * (0.5 / y_m))))) + -1.0)
	else:
		tmp = 0.5 * (x_m / ((x_m * 0.16666666666666666) + math.exp(math.log((x_m * 0.3333333333333333)))))
	return tmp

Julia

x_m = abs(x)
y_m = abs(y)
function code(x_m, y_m)
	tmp = 0.0
	if (Float64(x_m / Float64(y_m * 2.0)) <= 1e+199)
		tmp = Float64(1.0 / Float64(exp(log1p(cos(Float64(x_m * Float64(0.5 / y_m))))) + -1.0));
	else
		tmp = Float64(0.5 * Float64(x_m / Float64(Float64(x_m * 0.16666666666666666) + exp(log(Float64(x_m * 0.3333333333333333))))));
	end
	return tmp
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
y_m = N[Abs[y], $MachinePrecision]
code[x$95$m_, y$95$m_] := If[LessEqual[N[(x$95$m / N[(y$95$m * 2.0), $MachinePrecision]), $MachinePrecision], 1e+199], N[(1.0 / N[(N[Exp[N[Log[1 + N[Cos[N[(x$95$m * N[(0.5 / y$95$m), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]], $MachinePrecision]], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(x$95$m / N[(N[(x$95$m * 0.16666666666666666), $MachinePrecision] + N[Exp[N[Log[N[(x$95$m * 0.3333333333333333), $MachinePrecision]], $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (*.f64 y 2)) < 1.0000000000000001e199

   1. Initial program 49.4%

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

   3. Taylor expanded in x around inf 60.8%

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

      1. associate-*r/ 60.8%

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

   5. Simplified 60.8%

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

      1. expm1-log1p-u 60.8%

         \[\leadsto \frac{1}{\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\cos \left(\frac{0.5 \cdot x}{y}\right)\right)\right)}} \]

      2. expm1-udef 60.8%

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

      3. *-commutative 60.8%

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

      4. associate-*r/ 60.8%

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

   7. Applied egg-rr 60.8%

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

   if 1.0000000000000001e199 < (/.f64 x (*.f64 y 2))

   1. Initial program 5.2%

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

      1. add-log-exp 5.2%

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

      2. add-cube-cbrt 5.2%

         \[\leadsto \frac{\tan \left(\frac{x}{y \cdot 2}\right)}{\log \color{blue}{\left(\left(\sqrt[3]{e^{\sin \left(\frac{x}{y \cdot 2}\right)}} \cdot \sqrt[3]{e^{\sin \left(\frac{x}{y \cdot 2}\right)}}\right) \cdot \sqrt[3]{e^{\sin \left(\frac{x}{y \cdot 2}\right)}}\right)}} \]

      3. log-prod 5.2%

         \[\leadsto \frac{\tan \left(\frac{x}{y \cdot 2}\right)}{\color{blue}{\log \left(\sqrt[3]{e^{\sin \left(\frac{x}{y \cdot 2}\right)}} \cdot \sqrt[3]{e^{\sin \left(\frac{x}{y \cdot 2}\right)}}\right) + \log \left(\sqrt[3]{e^{\sin \left(\frac{x}{y \cdot 2}\right)}}\right)}} \]

   4. Applied egg-rr 4.1%

      \[\leadsto \frac{\tan \left(\frac{x}{y \cdot 2}\right)}{\color{blue}{\log \left(\sqrt[3]{e^{\sin \left(x \cdot \frac{0.5}{y}\right)}} \cdot \sqrt[3]{e^{\sin \left(x \cdot \frac{0.5}{y}\right)}}\right) + \log \left(\sqrt[3]{e^{\sin \left(x \cdot \frac{0.5}{y}\right)}}\right)}} \]
   5. Step-by-step derivation

      1. log-prod 4.1%

         \[\leadsto \frac{\tan \left(\frac{x}{y \cdot 2}\right)}{\color{blue}{\left(\log \left(\sqrt[3]{e^{\sin \left(x \cdot \frac{0.5}{y}\right)}}\right) + \log \left(\sqrt[3]{e^{\sin \left(x \cdot \frac{0.5}{y}\right)}}\right)\right)} + \log \left(\sqrt[3]{e^{\sin \left(x \cdot \frac{0.5}{y}\right)}}\right)} \]

      2. count-2 4.1%

         \[\leadsto \frac{\tan \left(\frac{x}{y \cdot 2}\right)}{\color{blue}{2 \cdot \log \left(\sqrt[3]{e^{\sin \left(x \cdot \frac{0.5}{y}\right)}}\right)} + \log \left(\sqrt[3]{e^{\sin \left(x \cdot \frac{0.5}{y}\right)}}\right)} \]

      3. *-commutative 4.1%

         \[\leadsto \frac{\tan \left(\frac{x}{y \cdot 2}\right)}{2 \cdot \log \left(\sqrt[3]{e^{\sin \color{blue}{\left(\frac{0.5}{y} \cdot x\right)}}}\right) + \log \left(\sqrt[3]{e^{\sin \left(x \cdot \frac{0.5}{y}\right)}}\right)} \]

      4. associate-*l/ 4.3%

         \[\leadsto \frac{\tan \left(\frac{x}{y \cdot 2}\right)}{2 \cdot \log \left(\sqrt[3]{e^{\sin \color{blue}{\left(\frac{0.5 \cdot x}{y}\right)}}}\right) + \log \left(\sqrt[3]{e^{\sin \left(x \cdot \frac{0.5}{y}\right)}}\right)} \]

      5. *-commutative 4.3%

         \[\leadsto \frac{\tan \left(\frac{x}{y \cdot 2}\right)}{2 \cdot \log \left(\sqrt[3]{e^{\sin \left(\frac{0.5 \cdot x}{y}\right)}}\right) + \log \left(\sqrt[3]{e^{\sin \color{blue}{\left(\frac{0.5}{y} \cdot x\right)}}}\right)} \]

      6. associate-*l/ 5.2%

         \[\leadsto \frac{\tan \left(\frac{x}{y \cdot 2}\right)}{2 \cdot \log \left(\sqrt[3]{e^{\sin \left(\frac{0.5 \cdot x}{y}\right)}}\right) + \log \left(\sqrt[3]{e^{\sin \color{blue}{\left(\frac{0.5 \cdot x}{y}\right)}}}\right)} \]

   6. Simplified 5.2%

      \[\leadsto \frac{\tan \left(\frac{x}{y \cdot 2}\right)}{\color{blue}{2 \cdot \log \left(\sqrt[3]{e^{\sin \left(\frac{0.5 \cdot x}{y}\right)}}\right) + \log \left(\sqrt[3]{e^{\sin \left(\frac{0.5 \cdot x}{y}\right)}}\right)}} \]

   7. Taylor expanded in y around inf 11.5%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x}{0.16666666666666666 \cdot x + 0.3333333333333333 \cdot x}} \]
   8. Step-by-step derivation

      1. add-exp-log 4.6%

         \[\leadsto 0.5 \cdot \frac{x}{0.16666666666666666 \cdot x + \color{blue}{e^{\log \left(0.3333333333333333 \cdot x\right)}}} \]

      2. *-commutative 4.6%

         \[\leadsto 0.5 \cdot \frac{x}{0.16666666666666666 \cdot x + e^{\log \color{blue}{\left(x \cdot 0.3333333333333333\right)}}} \]

   9. Applied egg-rr 4.6%

      \[\leadsto 0.5 \cdot \frac{x}{0.16666666666666666 \cdot x + \color{blue}{e^{\log \left(x \cdot 0.3333333333333333\right)}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 54.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y \cdot 2} \leq 10^{+199}:\\ \;\;\;\;\frac{1}{e^{\mathsf{log1p}\left(\cos \left(x \cdot \frac{0.5}{y}\right)\right)} + -1}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x}{x \cdot 0.16666666666666666 + e^{\log \left(x \cdot 0.3333333333333333\right)}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 57.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ y_m = \left|y\right| \\ \begin{array}{l} \mathbf{if}\;\frac{x\_m}{y\_m \cdot 2} \leq 10^{+199}:\\ \;\;\;\;\frac{1}{\cos \left(x\_m \cdot \frac{0.5}{y\_m}\right)}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x\_m}{x\_m \cdot 0.16666666666666666 + e^{\log \left(x\_m \cdot 0.3333333333333333\right)}}\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
y_m = (fabs.f64 y)
(FPCore (x_m y_m)
 :precision binary64
 (if (<= (/ x_m (* y_m 2.0)) 1e+199)
   (/ 1.0 (cos (* x_m (/ 0.5 y_m))))
   (*
    0.5
    (/
     x_m
     (+ (* x_m 0.16666666666666666) (exp (log (* x_m 0.3333333333333333))))))))

C

x_m = fabs(x);
y_m = fabs(y);
double code(double x_m, double y_m) {
	double tmp;
	if ((x_m / (y_m * 2.0)) <= 1e+199) {
		tmp = 1.0 / cos((x_m * (0.5 / y_m)));
	} else {
		tmp = 0.5 * (x_m / ((x_m * 0.16666666666666666) + exp(log((x_m * 0.3333333333333333)))));
	}
	return tmp;
}

Fortran

x_m = abs(x)
y_m = abs(y)
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 / (y_m * 2.0d0)) <= 1d+199) then
        tmp = 1.0d0 / cos((x_m * (0.5d0 / y_m)))
    else
        tmp = 0.5d0 * (x_m / ((x_m * 0.16666666666666666d0) + exp(log((x_m * 0.3333333333333333d0)))))
    end if
    code = tmp
end function

Java

x_m = Math.abs(x);
y_m = Math.abs(y);
public static double code(double x_m, double y_m) {
	double tmp;
	if ((x_m / (y_m * 2.0)) <= 1e+199) {
		tmp = 1.0 / Math.cos((x_m * (0.5 / y_m)));
	} else {
		tmp = 0.5 * (x_m / ((x_m * 0.16666666666666666) + Math.exp(Math.log((x_m * 0.3333333333333333)))));
	}
	return tmp;
}

Python

x_m = math.fabs(x)
y_m = math.fabs(y)
def code(x_m, y_m):
	tmp = 0
	if (x_m / (y_m * 2.0)) <= 1e+199:
		tmp = 1.0 / math.cos((x_m * (0.5 / y_m)))
	else:
		tmp = 0.5 * (x_m / ((x_m * 0.16666666666666666) + math.exp(math.log((x_m * 0.3333333333333333)))))
	return tmp

Julia

x_m = abs(x)
y_m = abs(y)
function code(x_m, y_m)
	tmp = 0.0
	if (Float64(x_m / Float64(y_m * 2.0)) <= 1e+199)
		tmp = Float64(1.0 / cos(Float64(x_m * Float64(0.5 / y_m))));
	else
		tmp = Float64(0.5 * Float64(x_m / Float64(Float64(x_m * 0.16666666666666666) + exp(log(Float64(x_m * 0.3333333333333333))))));
	end
	return tmp
end

MATLAB

x_m = abs(x);
y_m = abs(y);
function tmp_2 = code(x_m, y_m)
	tmp = 0.0;
	if ((x_m / (y_m * 2.0)) <= 1e+199)
		tmp = 1.0 / cos((x_m * (0.5 / y_m)));
	else
		tmp = 0.5 * (x_m / ((x_m * 0.16666666666666666) + exp(log((x_m * 0.3333333333333333)))));
	end
	tmp_2 = tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
y_m = N[Abs[y], $MachinePrecision]
code[x$95$m_, y$95$m_] := If[LessEqual[N[(x$95$m / N[(y$95$m * 2.0), $MachinePrecision]), $MachinePrecision], 1e+199], N[(1.0 / N[Cos[N[(x$95$m * N[(0.5 / y$95$m), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(x$95$m / N[(N[(x$95$m * 0.16666666666666666), $MachinePrecision] + N[Exp[N[Log[N[(x$95$m * 0.3333333333333333), $MachinePrecision]], $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (*.f64 y 2)) < 1.0000000000000001e199

   1. Initial program 49.4%

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

   3. Taylor expanded in x around inf 60.8%

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

      1. associate-*r/ 60.8%

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

   5. Simplified 60.8%

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

      1. expm1-log1p-u 60.8%

         \[\leadsto \frac{1}{\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\cos \left(\frac{0.5 \cdot x}{y}\right)\right)\right)}} \]

      2. expm1-udef 60.8%

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

      3. *-commutative 60.8%

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

      4. associate-*r/ 60.8%

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

   7. Applied egg-rr 60.8%

      \[\leadsto \frac{1}{\color{blue}{e^{\mathsf{log1p}\left(\cos \left(x \cdot \frac{0.5}{y}\right)\right)} - 1}} \]
   8. Step-by-step derivation

      1. expm1-def 60.8%

         \[\leadsto \frac{1}{\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\cos \left(x \cdot \frac{0.5}{y}\right)\right)\right)}} \]

      2. expm1-log1p 60.8%

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

   9. Simplified 60.8%

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

   if 1.0000000000000001e199 < (/.f64 x (*.f64 y 2))

   1. Initial program 5.2%

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

      1. add-log-exp 5.2%

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

      2. add-cube-cbrt 5.2%

         \[\leadsto \frac{\tan \left(\frac{x}{y \cdot 2}\right)}{\log \color{blue}{\left(\left(\sqrt[3]{e^{\sin \left(\frac{x}{y \cdot 2}\right)}} \cdot \sqrt[3]{e^{\sin \left(\frac{x}{y \cdot 2}\right)}}\right) \cdot \sqrt[3]{e^{\sin \left(\frac{x}{y \cdot 2}\right)}}\right)}} \]

      3. log-prod 5.2%

         \[\leadsto \frac{\tan \left(\frac{x}{y \cdot 2}\right)}{\color{blue}{\log \left(\sqrt[3]{e^{\sin \left(\frac{x}{y \cdot 2}\right)}} \cdot \sqrt[3]{e^{\sin \left(\frac{x}{y \cdot 2}\right)}}\right) + \log \left(\sqrt[3]{e^{\sin \left(\frac{x}{y \cdot 2}\right)}}\right)}} \]

   4. Applied egg-rr 4.1%

      \[\leadsto \frac{\tan \left(\frac{x}{y \cdot 2}\right)}{\color{blue}{\log \left(\sqrt[3]{e^{\sin \left(x \cdot \frac{0.5}{y}\right)}} \cdot \sqrt[3]{e^{\sin \left(x \cdot \frac{0.5}{y}\right)}}\right) + \log \left(\sqrt[3]{e^{\sin \left(x \cdot \frac{0.5}{y}\right)}}\right)}} \]
   5. Step-by-step derivation

      1. log-prod 4.1%

         \[\leadsto \frac{\tan \left(\frac{x}{y \cdot 2}\right)}{\color{blue}{\left(\log \left(\sqrt[3]{e^{\sin \left(x \cdot \frac{0.5}{y}\right)}}\right) + \log \left(\sqrt[3]{e^{\sin \left(x \cdot \frac{0.5}{y}\right)}}\right)\right)} + \log \left(\sqrt[3]{e^{\sin \left(x \cdot \frac{0.5}{y}\right)}}\right)} \]

      2. count-2 4.1%

         \[\leadsto \frac{\tan \left(\frac{x}{y \cdot 2}\right)}{\color{blue}{2 \cdot \log \left(\sqrt[3]{e^{\sin \left(x \cdot \frac{0.5}{y}\right)}}\right)} + \log \left(\sqrt[3]{e^{\sin \left(x \cdot \frac{0.5}{y}\right)}}\right)} \]

      3. *-commutative 4.1%

         \[\leadsto \frac{\tan \left(\frac{x}{y \cdot 2}\right)}{2 \cdot \log \left(\sqrt[3]{e^{\sin \color{blue}{\left(\frac{0.5}{y} \cdot x\right)}}}\right) + \log \left(\sqrt[3]{e^{\sin \left(x \cdot \frac{0.5}{y}\right)}}\right)} \]

      4. associate-*l/ 4.3%

         \[\leadsto \frac{\tan \left(\frac{x}{y \cdot 2}\right)}{2 \cdot \log \left(\sqrt[3]{e^{\sin \color{blue}{\left(\frac{0.5 \cdot x}{y}\right)}}}\right) + \log \left(\sqrt[3]{e^{\sin \left(x \cdot \frac{0.5}{y}\right)}}\right)} \]

      5. *-commutative 4.3%

         \[\leadsto \frac{\tan \left(\frac{x}{y \cdot 2}\right)}{2 \cdot \log \left(\sqrt[3]{e^{\sin \left(\frac{0.5 \cdot x}{y}\right)}}\right) + \log \left(\sqrt[3]{e^{\sin \color{blue}{\left(\frac{0.5}{y} \cdot x\right)}}}\right)} \]

      6. associate-*l/ 5.2%

         \[\leadsto \frac{\tan \left(\frac{x}{y \cdot 2}\right)}{2 \cdot \log \left(\sqrt[3]{e^{\sin \left(\frac{0.5 \cdot x}{y}\right)}}\right) + \log \left(\sqrt[3]{e^{\sin \color{blue}{\left(\frac{0.5 \cdot x}{y}\right)}}}\right)} \]

   6. Simplified 5.2%

      \[\leadsto \frac{\tan \left(\frac{x}{y \cdot 2}\right)}{\color{blue}{2 \cdot \log \left(\sqrt[3]{e^{\sin \left(\frac{0.5 \cdot x}{y}\right)}}\right) + \log \left(\sqrt[3]{e^{\sin \left(\frac{0.5 \cdot x}{y}\right)}}\right)}} \]

   7. Taylor expanded in y around inf 11.5%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x}{0.16666666666666666 \cdot x + 0.3333333333333333 \cdot x}} \]
   8. Step-by-step derivation

      1. add-exp-log 4.6%

         \[\leadsto 0.5 \cdot \frac{x}{0.16666666666666666 \cdot x + \color{blue}{e^{\log \left(0.3333333333333333 \cdot x\right)}}} \]

      2. *-commutative 4.6%

         \[\leadsto 0.5 \cdot \frac{x}{0.16666666666666666 \cdot x + e^{\log \color{blue}{\left(x \cdot 0.3333333333333333\right)}}} \]

   9. Applied egg-rr 4.6%

      \[\leadsto 0.5 \cdot \frac{x}{0.16666666666666666 \cdot x + \color{blue}{e^{\log \left(x \cdot 0.3333333333333333\right)}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 54.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y \cdot 2} \leq 10^{+199}:\\ \;\;\;\;\frac{1}{\cos \left(x \cdot \frac{0.5}{y}\right)}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x}{x \cdot 0.16666666666666666 + e^{\log \left(x \cdot 0.3333333333333333\right)}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 55.8% accurate, 2.0× speedup

Math

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

FPCore

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

C

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

Fortran

x_m = abs(x)
y_m = abs(y)
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 * (0.5d0 / y_m)))
end function

Java

x_m = Math.abs(x);
y_m = Math.abs(y);
public static double code(double x_m, double y_m) {
	return 1.0 / Math.cos((x_m * (0.5 / y_m)));
}

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 44.6%

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

3. Taylor expanded in x around inf 54.7%

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

   1. associate-*r/ 54.7%

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

5. Simplified 54.7%

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

   1. expm1-log1p-u 54.7%

      \[\leadsto \frac{1}{\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\cos \left(\frac{0.5 \cdot x}{y}\right)\right)\right)}} \]

   2. expm1-udef 54.7%

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

   3. *-commutative 54.7%

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

   4. associate-*r/ 54.8%

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

7. Applied egg-rr 54.8%

   \[\leadsto \frac{1}{\color{blue}{e^{\mathsf{log1p}\left(\cos \left(x \cdot \frac{0.5}{y}\right)\right)} - 1}} \]
8. Step-by-step derivation

   1. expm1-def 54.8%

      \[\leadsto \frac{1}{\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\cos \left(x \cdot \frac{0.5}{y}\right)\right)\right)}} \]

   2. expm1-log1p 54.8%

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

9. Simplified 54.8%

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

10. Final simplification 54.8%

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

Alternative 7: 55.7% accurate, 211.0× speedup

Math

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

FPCore

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

C

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

Fortran

x_m = abs(x)
y_m = abs(y)
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

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 44.6%

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

3. Taylor expanded in x around 0 54.6%

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

4. Final simplification 54.6%

   \[\leadsto 1 \]
5. Add Preprocessing

Developer target: 55.7% 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 2024027 
(FPCore (x y)
  :name "Diagrams.TwoD.Layout.CirclePacking:approxRadius from diagrams-contrib-1.3.0.5"
  :precision binary64

  :herbie-target
  (if (< y -1.2303690911306994e+114) 1.0 (if (< y -9.102852406811914e-222) (/ (sin (/ x (* y 2.0))) (* (sin (/ x (* y 2.0))) (log (exp (cos (/ x (* y 2.0))))))) 1.0))

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