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

Percentage Accurate: 44.1% → 56.9%

Time: 24.8s

Alternatives: 10

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: 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: 56.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ y_m = \left|y\right| \\ \begin{array}{l} t_0 := \sqrt[3]{\frac{x\_m}{y\_m}}\\ \mathbf{if}\;\frac{x\_m}{2 \cdot y\_m} \leq 5 \cdot 10^{+125}:\\ \;\;\;\;\frac{1}{\cos \left({t\_0}^{2} \cdot \left(0.5 \cdot t\_0\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
y_m = (fabs.f64 y)
(FPCore (x_m y_m)
 :precision binary64
 (let* ((t_0 (cbrt (/ x_m y_m))))
   (if (<= (/ x_m (* 2.0 y_m)) 5e+125)
     (/ 1.0 (cos (* (pow t_0 2.0) (* 0.5 t_0))))
     1.0)))

C

x_m = fabs(x);
y_m = fabs(y);
double code(double x_m, double y_m) {
	double t_0 = cbrt((x_m / y_m));
	double tmp;
	if ((x_m / (2.0 * y_m)) <= 5e+125) {
		tmp = 1.0 / cos((pow(t_0, 2.0) * (0.5 * t_0)));
	} else {
		tmp = 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 = Math.cbrt((x_m / y_m));
	double tmp;
	if ((x_m / (2.0 * y_m)) <= 5e+125) {
		tmp = 1.0 / Math.cos((Math.pow(t_0, 2.0) * (0.5 * t_0)));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Julia

x_m = abs(x)
y_m = abs(y)
function code(x_m, y_m)
	t_0 = cbrt(Float64(x_m / y_m))
	tmp = 0.0
	if (Float64(x_m / Float64(2.0 * y_m)) <= 5e+125)
		tmp = Float64(1.0 / cos(Float64((t_0 ^ 2.0) * Float64(0.5 * t_0))));
	else
		tmp = 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[Power[N[(x$95$m / y$95$m), $MachinePrecision], 1/3], $MachinePrecision]}, If[LessEqual[N[(x$95$m / N[(2.0 * y$95$m), $MachinePrecision]), $MachinePrecision], 5e+125], N[(1.0 / N[Cos[N[(N[Power[t$95$0, 2.0], $MachinePrecision] * N[(0.5 * t$95$0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (*.f64 y 2)) < 4.99999999999999962e125

   1. Initial program 53.2%

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

   3. Taylor expanded in x around inf 63.8%

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

      1. associate-*r/ 63.8%

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

   5. Simplified 63.8%

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

      1. expm1-log1p-u 63.8%

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

      2. expm1-udef 63.8%

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

      3. *-commutative 63.8%

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

      4. associate-*r/ 63.9%

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

   7. Applied egg-rr 63.9%

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

      1. expm1-def 63.9%

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

      2. expm1-log1p 63.9%

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

   9. Simplified 63.9%

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

       1. *-commutative 63.9%

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

       2. associate-/r/ 64.0%

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

   11. Applied egg-rr 64.0%

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

       1. div-inv 64.0%

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

       2. clear-num 63.8%

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

       3. *-commutative 63.8%

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

       4. add-cube-cbrt 64.2%

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

       5. associate-*l* 64.2%

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

       6. pow2 64.2%

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

   13. Applied egg-rr 64.2%

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

   if 4.99999999999999962e125 < (/.f64 x (*.f64 y 2))

   1. Initial program 10.9%

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

   3. Taylor expanded in x around 0 11.3%

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

4. Final simplification 56.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{2 \cdot y} \leq 5 \cdot 10^{+125}:\\ \;\;\;\;\frac{1}{\cos \left({\left(\sqrt[3]{\frac{x}{y}}\right)}^{2} \cdot \left(0.5 \cdot \sqrt[3]{\frac{x}{y}}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 55.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ y_m = \left|y\right| \\ \begin{array}{l} t_0 := \sqrt[3]{x\_m \cdot 0.5}\\ \frac{1}{\log \left(e^{\cos \left(\frac{{\left(e^{\log t\_0}\right)}^{2}}{\frac{y\_m}{t\_0}}\right)}\right)} \end{array} \end{array} \]

FPCore

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

C

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

Java

x_m = Math.abs(x);
y_m = Math.abs(y);
public static double code(double x_m, double y_m) {
	double t_0 = Math.cbrt((x_m * 0.5));
	return 1.0 / Math.log(Math.exp(Math.cos((Math.pow(Math.exp(Math.log(t_0)), 2.0) / (y_m / t_0)))));
}

Julia

x_m = abs(x)
y_m = abs(y)
function code(x_m, y_m)
	t_0 = cbrt(Float64(x_m * 0.5))
	return Float64(1.0 / log(exp(cos(Float64((exp(log(t_0)) ^ 2.0) / Float64(y_m / t_0))))))
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[Power[N[(x$95$m * 0.5), $MachinePrecision], 1/3], $MachinePrecision]}, N[(1.0 / N[Log[N[Exp[N[Cos[N[(N[Power[N[Exp[N[Log[t$95$0], $MachinePrecision]], $MachinePrecision], 2.0], $MachinePrecision] / N[(y$95$m / t$95$0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]], $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Initial program 46.9%

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

3. Taylor expanded in x around inf 55.9%

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

   1. associate-*r/ 55.9%

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

5. Simplified 55.9%

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

   1. /-rgt-identity 55.9%

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

   2. add-log-exp 55.9%

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

   3. /-rgt-identity 55.9%

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

   4. *-commutative 55.9%

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

   5. associate-*r/ 55.9%

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

7. Applied egg-rr 55.9%

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

   1. associate-*r/ 55.9%

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

   2. *-commutative 55.9%

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

   3. add-cube-cbrt 56.3%

      \[\leadsto \frac{1}{\log \left(e^{\cos \left(\frac{\color{blue}{\left(\sqrt[3]{0.5 \cdot x} \cdot \sqrt[3]{0.5 \cdot x}\right) \cdot \sqrt[3]{0.5 \cdot x}}}{y}\right)}\right)} \]

   4. associate-/l* 56.3%

      \[\leadsto \frac{1}{\log \left(e^{\cos \color{blue}{\left(\frac{\sqrt[3]{0.5 \cdot x} \cdot \sqrt[3]{0.5 \cdot x}}{\frac{y}{\sqrt[3]{0.5 \cdot x}}}\right)}}\right)} \]

   5. pow2 56.3%

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

   6. *-commutative 56.3%

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

   7. *-commutative 56.3%

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

9. Applied egg-rr 56.3%

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

    1. add-exp-log 30.3%

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

11. Applied egg-rr 30.3%

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

12. Final simplification 30.3%

    \[\leadsto \frac{1}{\log \left(e^{\cos \left(\frac{{\left(e^{\log \left(\sqrt[3]{x \cdot 0.5}\right)}\right)}^{2}}{\frac{y}{\sqrt[3]{x \cdot 0.5}}}\right)}\right)} \]
13. Add Preprocessing

Alternative 3: 55.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ y_m = \left|y\right| \\ \begin{array}{l} t_0 := \sqrt[3]{x\_m \cdot 0.5}\\ t_1 := \sqrt{\frac{y\_m}{t\_0}}\\ \frac{1}{\cos \left(\frac{1}{t\_1} \cdot \frac{{t\_0}^{2}}{t\_1}\right)} \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
y_m = (fabs.f64 y)
(FPCore (x_m y_m)
 :precision binary64
 (let* ((t_0 (cbrt (* x_m 0.5))) (t_1 (sqrt (/ y_m t_0))))
   (/ 1.0 (cos (* (/ 1.0 t_1) (/ (pow t_0 2.0) t_1))))))

C

x_m = fabs(x);
y_m = fabs(y);
double code(double x_m, double y_m) {
	double t_0 = cbrt((x_m * 0.5));
	double t_1 = sqrt((y_m / t_0));
	return 1.0 / cos(((1.0 / t_1) * (pow(t_0, 2.0) / t_1)));
}

Java

x_m = Math.abs(x);
y_m = Math.abs(y);
public static double code(double x_m, double y_m) {
	double t_0 = Math.cbrt((x_m * 0.5));
	double t_1 = Math.sqrt((y_m / t_0));
	return 1.0 / Math.cos(((1.0 / t_1) * (Math.pow(t_0, 2.0) / t_1)));
}

Julia

x_m = abs(x)
y_m = abs(y)
function code(x_m, y_m)
	t_0 = cbrt(Float64(x_m * 0.5))
	t_1 = sqrt(Float64(y_m / t_0))
	return Float64(1.0 / cos(Float64(Float64(1.0 / t_1) * Float64((t_0 ^ 2.0) / t_1))))
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[Power[N[(x$95$m * 0.5), $MachinePrecision], 1/3], $MachinePrecision]}, Block[{t$95$1 = N[Sqrt[N[(y$95$m / t$95$0), $MachinePrecision]], $MachinePrecision]}, N[(1.0 / N[Cos[N[(N[(1.0 / t$95$1), $MachinePrecision] * N[(N[Power[t$95$0, 2.0], $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Initial program 46.9%

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

3. Taylor expanded in x around inf 55.9%

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

   1. associate-*r/ 55.9%

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

5. Simplified 55.9%

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

   1. expm1-log1p-u 55.9%

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

   2. expm1-udef 55.9%

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

   3. *-commutative 55.9%

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

   4. associate-*r/ 55.9%

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

7. Applied egg-rr 55.9%

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

   1. expm1-def 55.9%

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

   2. expm1-log1p 55.9%

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

9. Simplified 55.9%

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

    1. *-commutative 55.9%

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

    2. associate-/r/ 56.1%

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

11. Applied egg-rr 56.1%

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

    1. associate-/l* 55.9%

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

    2. *-commutative 55.9%

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

    3. add-cube-cbrt 56.3%

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

    4. unpow2 56.3%

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

    5. associate-/l* 56.3%

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

    6. *-un-lft-identity 56.3%

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

    7. add-sqr-sqrt 28.8%

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

    8. times-frac 29.4%

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

13. Applied egg-rr 29.4%

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

14. Final simplification 29.4%

    \[\leadsto \frac{1}{\cos \left(\frac{1}{\sqrt{\frac{y}{\sqrt[3]{x \cdot 0.5}}}} \cdot \frac{{\left(\sqrt[3]{x \cdot 0.5}\right)}^{2}}{\sqrt{\frac{y}{\sqrt[3]{x \cdot 0.5}}}}\right)} \]
15. Add Preprocessing

Alternative 4: 55.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ y_m = \left|y\right| \\ \begin{array}{l} t_0 := \sqrt[3]{\frac{y\_m}{x\_m}}\\ \frac{1}{\log \left(e^{\cos \left(\frac{\frac{0.5}{{t\_0}^{2}}}{t\_0}\right)}\right)} \end{array} \end{array} \]

FPCore

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

C

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

Java

x_m = Math.abs(x);
y_m = Math.abs(y);
public static double code(double x_m, double y_m) {
	double t_0 = Math.cbrt((y_m / x_m));
	return 1.0 / Math.log(Math.exp(Math.cos(((0.5 / Math.pow(t_0, 2.0)) / t_0))));
}

Julia

x_m = abs(x)
y_m = abs(y)
function code(x_m, y_m)
	t_0 = cbrt(Float64(y_m / x_m))
	return Float64(1.0 / log(exp(cos(Float64(Float64(0.5 / (t_0 ^ 2.0)) / t_0)))))
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[Power[N[(y$95$m / x$95$m), $MachinePrecision], 1/3], $MachinePrecision]}, N[(1.0 / N[Log[N[Exp[N[Cos[N[(N[(0.5 / N[Power[t$95$0, 2.0], $MachinePrecision]), $MachinePrecision] / t$95$0), $MachinePrecision]], $MachinePrecision]], $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Initial program 46.9%

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

3. Taylor expanded in x around inf 55.9%

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

   1. associate-*r/ 55.9%

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

5. Simplified 55.9%

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

   1. /-rgt-identity 55.9%

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

   2. add-log-exp 55.9%

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

   3. /-rgt-identity 55.9%

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

   4. *-commutative 55.9%

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

   5. associate-*r/ 55.9%

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

7. Applied egg-rr 55.9%

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

   1. associate-*r/ 55.9%

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

   2. *-commutative 55.9%

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

   3. add-cbrt-cube 53.4%

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

   4. pow1/3 43.6%

      \[\leadsto \frac{1}{\cos \color{blue}{\left({\left(\left(\frac{0.5 \cdot x}{y} \cdot \frac{0.5 \cdot x}{y}\right) \cdot \frac{0.5 \cdot x}{y}\right)}^{0.3333333333333333}\right)}} \]

   5. pow3 43.5%

      \[\leadsto \frac{1}{\cos \left({\color{blue}{\left({\left(\frac{0.5 \cdot x}{y}\right)}^{3}\right)}}^{0.3333333333333333}\right)} \]

   6. *-un-lft-identity 43.5%

      \[\leadsto \frac{1}{\cos \left({\left({\left(\frac{0.5 \cdot x}{\color{blue}{1 \cdot y}}\right)}^{3}\right)}^{0.3333333333333333}\right)} \]

   7. times-frac 43.5%

      \[\leadsto \frac{1}{\cos \left({\left({\color{blue}{\left(\frac{0.5}{1} \cdot \frac{x}{y}\right)}}^{3}\right)}^{0.3333333333333333}\right)} \]

   8. metadata-eval 43.5%

      \[\leadsto \frac{1}{\cos \left({\left({\left(\color{blue}{0.5} \cdot \frac{x}{y}\right)}^{3}\right)}^{0.3333333333333333}\right)} \]

9. Applied egg-rr 43.5%

   \[\leadsto \frac{1}{\log \left(e^{\cos \color{blue}{\left({\left({\left(0.5 \cdot \frac{x}{y}\right)}^{3}\right)}^{0.3333333333333333}\right)}}\right)} \]
10. Step-by-step derivation

    1. pow1/3 53.4%

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

    2. rem-cbrt-cube 55.9%

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

    3. associate-*r/ 55.9%

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

    4. associate-/l* 56.1%

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

    5. add-cube-cbrt 55.9%

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

    6. associate-/r* 56.4%

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

    7. pow2 56.4%

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

11. Applied egg-rr 56.4%

    \[\leadsto \frac{1}{\log \left(e^{\cos \color{blue}{\left(\frac{\frac{0.5}{{\left(\sqrt[3]{\frac{y}{x}}\right)}^{2}}}{\sqrt[3]{\frac{y}{x}}}\right)}}\right)} \]

12. Final simplification 56.4%

    \[\leadsto \frac{1}{\log \left(e^{\cos \left(\frac{\frac{0.5}{{\left(\sqrt[3]{\frac{y}{x}}\right)}^{2}}}{\sqrt[3]{\frac{y}{x}}}\right)}\right)} \]
13. Add Preprocessing

Alternative 5: 55.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ y_m = \left|y\right| \\ \begin{array}{l} t_0 := \sqrt[3]{\frac{y\_m}{x\_m}}\\ \frac{1}{\cos \left(\frac{\frac{0.5}{{t\_0}^{2}}}{t\_0}\right)} \end{array} \end{array} \]

FPCore

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

C

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

Java

x_m = Math.abs(x);
y_m = Math.abs(y);
public static double code(double x_m, double y_m) {
	double t_0 = Math.cbrt((y_m / x_m));
	return 1.0 / Math.cos(((0.5 / Math.pow(t_0, 2.0)) / t_0));
}

Julia

x_m = abs(x)
y_m = abs(y)
function code(x_m, y_m)
	t_0 = cbrt(Float64(y_m / x_m))
	return Float64(1.0 / cos(Float64(Float64(0.5 / (t_0 ^ 2.0)) / t_0)))
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[Power[N[(y$95$m / x$95$m), $MachinePrecision], 1/3], $MachinePrecision]}, N[(1.0 / N[Cos[N[(N[(0.5 / N[Power[t$95$0, 2.0], $MachinePrecision]), $MachinePrecision] / t$95$0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Initial program 46.9%

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

3. Taylor expanded in x around inf 55.9%

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

   1. associate-*r/ 55.9%

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

5. Simplified 55.9%

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

   1. expm1-log1p-u 55.9%

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

   2. expm1-udef 55.9%

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

   3. *-commutative 55.9%

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

   4. associate-*r/ 55.9%

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

7. Applied egg-rr 55.9%

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

   1. expm1-def 55.9%

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

   2. expm1-log1p 55.9%

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

9. Simplified 55.9%

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

    1. associate-*r/ 55.9%

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

    2. *-commutative 55.9%

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

    3. add-cbrt-cube 53.4%

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

    4. pow1/3 43.6%

       \[\leadsto \frac{1}{\cos \color{blue}{\left({\left(\left(\frac{0.5 \cdot x}{y} \cdot \frac{0.5 \cdot x}{y}\right) \cdot \frac{0.5 \cdot x}{y}\right)}^{0.3333333333333333}\right)}} \]

    5. pow3 43.5%

       \[\leadsto \frac{1}{\cos \left({\color{blue}{\left({\left(\frac{0.5 \cdot x}{y}\right)}^{3}\right)}}^{0.3333333333333333}\right)} \]

    6. *-un-lft-identity 43.5%

       \[\leadsto \frac{1}{\cos \left({\left({\left(\frac{0.5 \cdot x}{\color{blue}{1 \cdot y}}\right)}^{3}\right)}^{0.3333333333333333}\right)} \]

    7. times-frac 43.5%

       \[\leadsto \frac{1}{\cos \left({\left({\color{blue}{\left(\frac{0.5}{1} \cdot \frac{x}{y}\right)}}^{3}\right)}^{0.3333333333333333}\right)} \]

    8. metadata-eval 43.5%

       \[\leadsto \frac{1}{\cos \left({\left({\left(\color{blue}{0.5} \cdot \frac{x}{y}\right)}^{3}\right)}^{0.3333333333333333}\right)} \]

11. Applied egg-rr 43.5%

    \[\leadsto \frac{1}{\cos \color{blue}{\left({\left({\left(0.5 \cdot \frac{x}{y}\right)}^{3}\right)}^{0.3333333333333333}\right)}} \]
12. Step-by-step derivation

    1. pow1/3 53.4%

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

    2. rem-cbrt-cube 55.9%

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

    3. associate-*r/ 55.9%

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

    4. associate-/l* 56.1%

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

    5. add-cube-cbrt 55.9%

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

    6. associate-/r* 56.4%

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

    7. pow2 56.4%

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

13. Applied egg-rr 56.4%

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

14. Final simplification 56.4%

    \[\leadsto \frac{1}{\cos \left(\frac{\frac{0.5}{{\left(\sqrt[3]{\frac{y}{x}}\right)}^{2}}}{\sqrt[3]{\frac{y}{x}}}\right)} \]
15. Add Preprocessing

Alternative 6: 57.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ y_m = \left|y\right| \\ \begin{array}{l} \mathbf{if}\;\frac{x\_m}{2 \cdot y\_m} \leq 2 \cdot 10^{+79}:\\ \;\;\;\;\frac{1}{\cos \left({\left(\sqrt[3]{0.5 \cdot \frac{x\_m}{y\_m}}\right)}^{3}\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
y_m = (fabs.f64 y)
(FPCore (x_m y_m)
 :precision binary64
 (if (<= (/ x_m (* 2.0 y_m)) 2e+79)
   (/ 1.0 (cos (pow (cbrt (* 0.5 (/ x_m y_m))) 3.0)))
   1.0))

C

x_m = fabs(x);
y_m = fabs(y);
double code(double x_m, double y_m) {
	double tmp;
	if ((x_m / (2.0 * y_m)) <= 2e+79) {
		tmp = 1.0 / cos(pow(cbrt((0.5 * (x_m / y_m))), 3.0));
	} else {
		tmp = 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 / (2.0 * y_m)) <= 2e+79) {
		tmp = 1.0 / Math.cos(Math.pow(Math.cbrt((0.5 * (x_m / y_m))), 3.0));
	} else {
		tmp = 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(2.0 * y_m)) <= 2e+79)
		tmp = Float64(1.0 / cos((cbrt(Float64(0.5 * Float64(x_m / y_m))) ^ 3.0)));
	else
		tmp = 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[(2.0 * y$95$m), $MachinePrecision]), $MachinePrecision], 2e+79], N[(1.0 / N[Cos[N[Power[N[Power[N[(0.5 * N[(x$95$m / y$95$m), $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision], 3.0], $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 1.0]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (*.f64 y 2)) < 1.99999999999999993e79

   1. Initial program 54.5%

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

   3. Taylor expanded in x around inf 65.3%

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

      1. associate-*r/ 65.3%

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

   5. Simplified 65.3%

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

      1. expm1-log1p-u 65.3%

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

      2. expm1-udef 65.3%

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

      3. *-commutative 65.3%

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

      4. associate-*r/ 65.5%

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

   7. Applied egg-rr 65.5%

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

      1. expm1-def 65.5%

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

      2. expm1-log1p 65.5%

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

   9. Simplified 65.5%

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

       1. associate-*r/ 65.3%

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

       2. *-commutative 65.3%

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

       3. add-cube-cbrt 65.6%

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

       4. pow3 65.5%

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

       5. *-un-lft-identity 65.5%

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

       6. times-frac 65.5%

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

       7. metadata-eval 65.5%

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

   11. Applied egg-rr 65.5%

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

   if 1.99999999999999993e79 < (/.f64 x (*.f64 y 2))

   1. Initial program 10.5%

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

   3. Taylor expanded in x around 0 11.5%

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

4. Final simplification 56.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{2 \cdot y} \leq 2 \cdot 10^{+79}:\\ \;\;\;\;\frac{1}{\cos \left({\left(\sqrt[3]{0.5 \cdot \frac{x}{y}}\right)}^{3}\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 55.4% accurate, 0.7× speedup

Math

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

FPCore

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

C

x_m = fabs(x);
y_m = fabs(y);
double code(double x_m, double y_m) {
	return 1.0 / log(exp(cos((0.5 / (y_m / x_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 / log(exp(cos((0.5d0 / (y_m / x_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.log(Math.exp(Math.cos((0.5 / (y_m / x_m)))));
}

Python

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

Julia

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

MATLAB

x_m = abs(x);
y_m = abs(y);
function tmp = code(x_m, y_m)
	tmp = 1.0 / log(exp(cos((0.5 / (y_m / x_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[Log[N[Exp[N[Cos[N[(0.5 / N[(y$95$m / x$95$m), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]], $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 46.9%

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

3. Taylor expanded in x around inf 55.9%

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

   1. associate-*r/ 55.9%

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

5. Simplified 55.9%

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

   1. /-rgt-identity 55.9%

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

   2. add-log-exp 55.9%

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

   3. /-rgt-identity 55.9%

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

   4. *-commutative 55.9%

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

   5. associate-*r/ 55.9%

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

7. Applied egg-rr 55.9%

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

   1. *-commutative 55.9%

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

   2. associate-/r/ 56.1%

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

9. Applied egg-rr 56.1%

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

10. Final simplification 56.1%

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

Alternative 8: 55.4% 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 46.9%

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

3. Taylor expanded in x around inf 55.9%

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

   1. associate-*r/ 55.9%

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

5. Simplified 55.9%

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

   1. expm1-log1p-u 55.9%

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

   2. expm1-udef 55.9%

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

   3. *-commutative 55.9%

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

   4. associate-*r/ 55.9%

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

7. Applied egg-rr 55.9%

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

   1. expm1-def 55.9%

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

   2. expm1-log1p 55.9%

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

9. Simplified 55.9%

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

10. Final simplification 55.9%

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

Alternative 9: 55.4% accurate, 2.0× speedup

Math

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

FPCore

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

C

x_m = fabs(x);
y_m = fabs(y);
double code(double x_m, double y_m) {
	return 1.0 / cos((0.5 / (y_m / x_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((0.5d0 / (y_m / x_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((0.5 / (y_m / x_m)));
}

Python

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

Julia

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

MATLAB

x_m = abs(x);
y_m = abs(y);
function tmp = code(x_m, y_m)
	tmp = 1.0 / cos((0.5 / (y_m / x_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[(0.5 / N[(y$95$m / x$95$m), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 46.9%

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

3. Taylor expanded in x around inf 55.9%

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

   1. associate-*r/ 55.9%

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

5. Simplified 55.9%

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

   1. expm1-log1p-u 55.9%

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

   2. expm1-udef 55.9%

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

   3. *-commutative 55.9%

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

   4. associate-*r/ 55.9%

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

7. Applied egg-rr 55.9%

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

   1. expm1-def 55.9%

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

   2. expm1-log1p 55.9%

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

9. Simplified 55.9%

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

    1. *-commutative 55.9%

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

    2. associate-/r/ 56.1%

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

11. Applied egg-rr 56.1%

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

12. Final simplification 56.1%

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

Alternative 10: 55.3% 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 46.9%

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

3. Taylor expanded in x around 0 55.4%

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

4. Final simplification 55.4%

   \[\leadsto 1 \]
5. Add Preprocessing

Developer target: 55.3% 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 2024031 
(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)))))