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

Percentage Accurate: 44.0% → 57.1%

Time: 17.9s

Alternatives: 6

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: 44.0% 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: 57.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ y_m = \left|y\right| \\ \begin{array}{l} \mathbf{if}\;\frac{x\_m}{y\_m \cdot 2} \leq 2 \cdot 10^{+85}:\\ \;\;\;\;\frac{1}{\cos \left({\left(\sqrt{\frac{x\_m}{y\_m} \cdot 0.5}\right)}^{2}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\mathsf{expm1}\left({\left(\frac{x\_m}{y\_m}\right)}^{2} \cdot -0.0625\right)}\\ \end{array} \end{array} \]

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)) 2e+85)
   (/ 1.0 (cos (pow (sqrt (* (/ x_m y_m) 0.5)) 2.0)))
   (/ 1.0 (expm1 (* (pow (/ x_m y_m) 2.0) -0.0625)))))

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)) <= 2e+85) {
		tmp = 1.0 / cos(pow(sqrt(((x_m / y_m) * 0.5)), 2.0));
	} else {
		tmp = 1.0 / expm1((pow((x_m / y_m), 2.0) * -0.0625));
	}
	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)) <= 2e+85) {
		tmp = 1.0 / Math.cos(Math.pow(Math.sqrt(((x_m / y_m) * 0.5)), 2.0));
	} else {
		tmp = 1.0 / Math.expm1((Math.pow((x_m / y_m), 2.0) * -0.0625));
	}
	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)) <= 2e+85:
		tmp = 1.0 / math.cos(math.pow(math.sqrt(((x_m / y_m) * 0.5)), 2.0))
	else:
		tmp = 1.0 / math.expm1((math.pow((x_m / y_m), 2.0) * -0.0625))
	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)) <= 2e+85)
		tmp = Float64(1.0 / cos((sqrt(Float64(Float64(x_m / y_m) * 0.5)) ^ 2.0)));
	else
		tmp = Float64(1.0 / expm1(Float64((Float64(x_m / y_m) ^ 2.0) * -0.0625)));
	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], 2e+85], N[(1.0 / N[Cos[N[Power[N[Sqrt[N[(N[(x$95$m / y$95$m), $MachinePrecision] * 0.5), $MachinePrecision]], $MachinePrecision], 2.0], $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(1.0 / N[(Exp[N[(N[Power[N[(x$95$m / y$95$m), $MachinePrecision], 2.0], $MachinePrecision] * -0.0625), $MachinePrecision]] - 1), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (*.f64 y #s(literal 2 binary64))) < 2e85

   1. Initial program 48.9%

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

   3. Taylor expanded in x around inf 63.9%

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

      1. *-un-lft-identity 63.9%

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

      2. *-commutative 63.9%

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

      3. clear-num 64.0%

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

      4. un-div-inv 64.0%

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

   5. Applied egg-rr 64.0%

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

      1. *-rgt-identity 64.0%

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

      2. associate-/r/ 63.9%

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

   7. Simplified 63.9%

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

      1. associate-/r/ 64.0%

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

   9. Applied egg-rr 64.0%

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

       1. add-sqr-sqrt 37.7%

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

       2. pow2 37.7%

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

       3. div-inv 37.7%

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

       4. clear-num 37.8%

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

   11. Applied egg-rr 37.8%

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

   if 2e85 < (/.f64 x (*.f64 y #s(literal 2 binary64)))

   1. Initial program 7.2%

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

   3. Taylor expanded in x around inf 7.2%

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

      1. /-rgt-identity 7.2%

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

      2. expm1-log1p-u 7.2%

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

      3. /-rgt-identity 7.2%

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

      4. clear-num 7.7%

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

      5. un-div-inv 7.7%

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

   5. Applied egg-rr 7.7%

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

   6. Taylor expanded in y around inf 13.2%

      \[\leadsto \frac{1}{\mathsf{expm1}\left(\color{blue}{\log 2 + -0.0625 \cdot \frac{{x}^{2}}{{y}^{2}}}\right)} \]
   7. Step-by-step derivation

      1. +-commutative 13.2%

         \[\leadsto \frac{1}{\mathsf{expm1}\left(\color{blue}{-0.0625 \cdot \frac{{x}^{2}}{{y}^{2}} + \log 2}\right)} \]

      2. *-commutative 13.2%

         \[\leadsto \frac{1}{\mathsf{expm1}\left(\color{blue}{\frac{{x}^{2}}{{y}^{2}} \cdot -0.0625} + \log 2\right)} \]

      3. fma-define 13.2%

         \[\leadsto \frac{1}{\mathsf{expm1}\left(\color{blue}{\mathsf{fma}\left(\frac{{x}^{2}}{{y}^{2}}, -0.0625, \log 2\right)}\right)} \]

      4. unpow2 13.2%

         \[\leadsto \frac{1}{\mathsf{expm1}\left(\mathsf{fma}\left(\frac{\color{blue}{x \cdot x}}{{y}^{2}}, -0.0625, \log 2\right)\right)} \]

      5. unpow2 13.2%

         \[\leadsto \frac{1}{\mathsf{expm1}\left(\mathsf{fma}\left(\frac{x \cdot x}{\color{blue}{y \cdot y}}, -0.0625, \log 2\right)\right)} \]

      6. times-frac 13.8%

         \[\leadsto \frac{1}{\mathsf{expm1}\left(\mathsf{fma}\left(\color{blue}{\frac{x}{y} \cdot \frac{x}{y}}, -0.0625, \log 2\right)\right)} \]

      7. unpow2 13.8%

         \[\leadsto \frac{1}{\mathsf{expm1}\left(\mathsf{fma}\left(\color{blue}{{\left(\frac{x}{y}\right)}^{2}}, -0.0625, \log 2\right)\right)} \]

   8. Simplified 13.8%

      \[\leadsto \frac{1}{\mathsf{expm1}\left(\color{blue}{\mathsf{fma}\left({\left(\frac{x}{y}\right)}^{2}, -0.0625, \log 2\right)}\right)} \]

   9. Taylor expanded in x around inf 13.2%

      \[\leadsto \frac{1}{\mathsf{expm1}\left(\color{blue}{-0.0625 \cdot \frac{{x}^{2}}{{y}^{2}}}\right)} \]
   10. Step-by-step derivation

       1. unpow2 13.2%

          \[\leadsto \frac{1}{\mathsf{expm1}\left(-0.0625 \cdot \frac{\color{blue}{x \cdot x}}{{y}^{2}}\right)} \]

       2. unpow2 13.2%

          \[\leadsto \frac{1}{\mathsf{expm1}\left(-0.0625 \cdot \frac{x \cdot x}{\color{blue}{y \cdot y}}\right)} \]

       3. times-frac 13.8%

          \[\leadsto \frac{1}{\mathsf{expm1}\left(-0.0625 \cdot \color{blue}{\left(\frac{x}{y} \cdot \frac{x}{y}\right)}\right)} \]

       4. unpow2 13.8%

          \[\leadsto \frac{1}{\mathsf{expm1}\left(-0.0625 \cdot \color{blue}{{\left(\frac{x}{y}\right)}^{2}}\right)} \]

       5. *-commutative 13.8%

          \[\leadsto \frac{1}{\mathsf{expm1}\left(\color{blue}{{\left(\frac{x}{y}\right)}^{2} \cdot -0.0625}\right)} \]

   11. Simplified 13.8%

       \[\leadsto \frac{1}{\mathsf{expm1}\left(\color{blue}{{\left(\frac{x}{y}\right)}^{2} \cdot -0.0625}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 33.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y \cdot 2} \leq 2 \cdot 10^{+85}:\\ \;\;\;\;\frac{1}{\cos \left({\left(\sqrt{\frac{x}{y} \cdot 0.5}\right)}^{2}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\mathsf{expm1}\left({\left(\frac{x}{y}\right)}^{2} \cdot -0.0625\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 55.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ y_m = \left|y\right| \\ \frac{1}{\mathsf{expm1}\left(\mathsf{fma}\left({\left(\frac{x\_m}{y\_m}\right)}^{2}, -0.0625, \log 2\right)\right)} \end{array} \]

FPCore

x_m = (fabs.f64 x)
y_m = (fabs.f64 y)
(FPCore (x_m y_m)
 :precision binary64
 (/ 1.0 (expm1 (fma (pow (/ x_m y_m) 2.0) -0.0625 (log 2.0)))))

C

x_m = fabs(x);
y_m = fabs(y);
double code(double x_m, double y_m) {
	return 1.0 / expm1(fma(pow((x_m / y_m), 2.0), -0.0625, log(2.0)));
}

Julia

x_m = abs(x)
y_m = abs(y)
function code(x_m, y_m)
	return Float64(1.0 / expm1(fma((Float64(x_m / y_m) ^ 2.0), -0.0625, log(2.0))))
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[(Exp[N[(N[Power[N[(x$95$m / y$95$m), $MachinePrecision], 2.0], $MachinePrecision] * -0.0625 + N[Log[2.0], $MachinePrecision]), $MachinePrecision]] - 1), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 40.9%

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

3. Taylor expanded in x around inf 53.0%

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

   1. /-rgt-identity 53.0%

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

   2. expm1-log1p-u 53.1%

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

   3. /-rgt-identity 53.1%

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

   4. clear-num 53.2%

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

   5. un-div-inv 53.2%

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

5. Applied egg-rr 53.2%

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

6. Taylor expanded in y around inf 45.6%

   \[\leadsto \frac{1}{\mathsf{expm1}\left(\color{blue}{\log 2 + -0.0625 \cdot \frac{{x}^{2}}{{y}^{2}}}\right)} \]
7. Step-by-step derivation

   1. +-commutative 45.6%

      \[\leadsto \frac{1}{\mathsf{expm1}\left(\color{blue}{-0.0625 \cdot \frac{{x}^{2}}{{y}^{2}} + \log 2}\right)} \]

   2. *-commutative 45.6%

      \[\leadsto \frac{1}{\mathsf{expm1}\left(\color{blue}{\frac{{x}^{2}}{{y}^{2}} \cdot -0.0625} + \log 2\right)} \]

   3. fma-define 45.6%

      \[\leadsto \frac{1}{\mathsf{expm1}\left(\color{blue}{\mathsf{fma}\left(\frac{{x}^{2}}{{y}^{2}}, -0.0625, \log 2\right)}\right)} \]

   4. unpow2 45.6%

      \[\leadsto \frac{1}{\mathsf{expm1}\left(\mathsf{fma}\left(\frac{\color{blue}{x \cdot x}}{{y}^{2}}, -0.0625, \log 2\right)\right)} \]

   5. unpow2 45.6%

      \[\leadsto \frac{1}{\mathsf{expm1}\left(\mathsf{fma}\left(\frac{x \cdot x}{\color{blue}{y \cdot y}}, -0.0625, \log 2\right)\right)} \]

   6. times-frac 54.5%

      \[\leadsto \frac{1}{\mathsf{expm1}\left(\mathsf{fma}\left(\color{blue}{\frac{x}{y} \cdot \frac{x}{y}}, -0.0625, \log 2\right)\right)} \]

   7. unpow2 54.5%

      \[\leadsto \frac{1}{\mathsf{expm1}\left(\mathsf{fma}\left(\color{blue}{{\left(\frac{x}{y}\right)}^{2}}, -0.0625, \log 2\right)\right)} \]

8. Simplified 54.5%

   \[\leadsto \frac{1}{\mathsf{expm1}\left(\color{blue}{\mathsf{fma}\left({\left(\frac{x}{y}\right)}^{2}, -0.0625, \log 2\right)}\right)} \]
9. Add Preprocessing

Alternative 3: 57.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ y_m = \left|y\right| \\ \begin{array}{l} \mathbf{if}\;\frac{x\_m}{y\_m \cdot 2} \leq 2 \cdot 10^{+85}:\\ \;\;\;\;\frac{1}{\cos \left(\frac{\frac{0.5}{y\_m}}{\frac{1}{x\_m}}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\mathsf{expm1}\left({\left(\frac{x\_m}{y\_m}\right)}^{2} \cdot -0.0625\right)}\\ \end{array} \end{array} \]

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)) 2e+85)
   (/ 1.0 (cos (/ (/ 0.5 y_m) (/ 1.0 x_m))))
   (/ 1.0 (expm1 (* (pow (/ x_m y_m) 2.0) -0.0625)))))

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)) <= 2e+85) {
		tmp = 1.0 / cos(((0.5 / y_m) / (1.0 / x_m)));
	} else {
		tmp = 1.0 / expm1((pow((x_m / y_m), 2.0) * -0.0625));
	}
	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)) <= 2e+85) {
		tmp = 1.0 / Math.cos(((0.5 / y_m) / (1.0 / x_m)));
	} else {
		tmp = 1.0 / Math.expm1((Math.pow((x_m / y_m), 2.0) * -0.0625));
	}
	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)) <= 2e+85:
		tmp = 1.0 / math.cos(((0.5 / y_m) / (1.0 / x_m)))
	else:
		tmp = 1.0 / math.expm1((math.pow((x_m / y_m), 2.0) * -0.0625))
	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)) <= 2e+85)
		tmp = Float64(1.0 / cos(Float64(Float64(0.5 / y_m) / Float64(1.0 / x_m))));
	else
		tmp = Float64(1.0 / expm1(Float64((Float64(x_m / y_m) ^ 2.0) * -0.0625)));
	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], 2e+85], N[(1.0 / N[Cos[N[(N[(0.5 / y$95$m), $MachinePrecision] / N[(1.0 / x$95$m), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(1.0 / N[(Exp[N[(N[Power[N[(x$95$m / y$95$m), $MachinePrecision], 2.0], $MachinePrecision] * -0.0625), $MachinePrecision]] - 1), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (*.f64 y #s(literal 2 binary64))) < 2e85

   1. Initial program 48.9%

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

   3. Taylor expanded in x around inf 63.9%

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

      1. *-un-lft-identity 63.9%

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

      2. *-commutative 63.9%

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

      3. clear-num 64.0%

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

      4. un-div-inv 64.0%

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

   5. Applied egg-rr 64.0%

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

      1. *-rgt-identity 64.0%

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

      2. associate-/r/ 63.9%

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

   7. Simplified 63.9%

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

      1. associate-/r/ 64.0%

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

      2. div-inv 63.8%

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

      3. associate-/r* 63.6%

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

   9. Applied egg-rr 63.6%

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

   if 2e85 < (/.f64 x (*.f64 y #s(literal 2 binary64)))

   1. Initial program 7.2%

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

   3. Taylor expanded in x around inf 7.2%

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

      1. /-rgt-identity 7.2%

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

      2. expm1-log1p-u 7.2%

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

      3. /-rgt-identity 7.2%

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

      4. clear-num 7.7%

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

      5. un-div-inv 7.7%

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

   5. Applied egg-rr 7.7%

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

   6. Taylor expanded in y around inf 13.2%

      \[\leadsto \frac{1}{\mathsf{expm1}\left(\color{blue}{\log 2 + -0.0625 \cdot \frac{{x}^{2}}{{y}^{2}}}\right)} \]
   7. Step-by-step derivation

      1. +-commutative 13.2%

         \[\leadsto \frac{1}{\mathsf{expm1}\left(\color{blue}{-0.0625 \cdot \frac{{x}^{2}}{{y}^{2}} + \log 2}\right)} \]

      2. *-commutative 13.2%

         \[\leadsto \frac{1}{\mathsf{expm1}\left(\color{blue}{\frac{{x}^{2}}{{y}^{2}} \cdot -0.0625} + \log 2\right)} \]

      3. fma-define 13.2%

         \[\leadsto \frac{1}{\mathsf{expm1}\left(\color{blue}{\mathsf{fma}\left(\frac{{x}^{2}}{{y}^{2}}, -0.0625, \log 2\right)}\right)} \]

      4. unpow2 13.2%

         \[\leadsto \frac{1}{\mathsf{expm1}\left(\mathsf{fma}\left(\frac{\color{blue}{x \cdot x}}{{y}^{2}}, -0.0625, \log 2\right)\right)} \]

      5. unpow2 13.2%

         \[\leadsto \frac{1}{\mathsf{expm1}\left(\mathsf{fma}\left(\frac{x \cdot x}{\color{blue}{y \cdot y}}, -0.0625, \log 2\right)\right)} \]

      6. times-frac 13.8%

         \[\leadsto \frac{1}{\mathsf{expm1}\left(\mathsf{fma}\left(\color{blue}{\frac{x}{y} \cdot \frac{x}{y}}, -0.0625, \log 2\right)\right)} \]

      7. unpow2 13.8%

         \[\leadsto \frac{1}{\mathsf{expm1}\left(\mathsf{fma}\left(\color{blue}{{\left(\frac{x}{y}\right)}^{2}}, -0.0625, \log 2\right)\right)} \]

   8. Simplified 13.8%

      \[\leadsto \frac{1}{\mathsf{expm1}\left(\color{blue}{\mathsf{fma}\left({\left(\frac{x}{y}\right)}^{2}, -0.0625, \log 2\right)}\right)} \]

   9. Taylor expanded in x around inf 13.2%

      \[\leadsto \frac{1}{\mathsf{expm1}\left(\color{blue}{-0.0625 \cdot \frac{{x}^{2}}{{y}^{2}}}\right)} \]
   10. Step-by-step derivation

       1. unpow2 13.2%

          \[\leadsto \frac{1}{\mathsf{expm1}\left(-0.0625 \cdot \frac{\color{blue}{x \cdot x}}{{y}^{2}}\right)} \]

       2. unpow2 13.2%

          \[\leadsto \frac{1}{\mathsf{expm1}\left(-0.0625 \cdot \frac{x \cdot x}{\color{blue}{y \cdot y}}\right)} \]

       3. times-frac 13.8%

          \[\leadsto \frac{1}{\mathsf{expm1}\left(-0.0625 \cdot \color{blue}{\left(\frac{x}{y} \cdot \frac{x}{y}\right)}\right)} \]

       4. unpow2 13.8%

          \[\leadsto \frac{1}{\mathsf{expm1}\left(-0.0625 \cdot \color{blue}{{\left(\frac{x}{y}\right)}^{2}}\right)} \]

       5. *-commutative 13.8%

          \[\leadsto \frac{1}{\mathsf{expm1}\left(\color{blue}{{\left(\frac{x}{y}\right)}^{2} \cdot -0.0625}\right)} \]

   11. Simplified 13.8%

       \[\leadsto \frac{1}{\mathsf{expm1}\left(\color{blue}{{\left(\frac{x}{y}\right)}^{2} \cdot -0.0625}\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 55.5% 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 40.9%

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

3. Taylor expanded in x around inf 53.0%

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

   1. *-un-lft-identity 53.0%

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

   2. *-commutative 53.0%

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

   3. clear-num 53.2%

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

   4. un-div-inv 53.2%

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

5. Applied egg-rr 53.2%

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

   1. *-rgt-identity 53.2%

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

   2. associate-/r/ 53.0%

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

7. Simplified 53.0%

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

   1. associate-/r/ 53.2%

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

9. Applied egg-rr 53.2%

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

Alternative 5: 55.5% accurate, 2.0× speedup

Math

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

FPCore

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

C

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

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 / y_m) * 0.5d0))
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 / y_m) * 0.5));
}

Python

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

Julia

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

MATLAB

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

Derivation

1. Initial program 40.9%

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

3. Taylor expanded in x around inf 53.0%

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

4. Final simplification 53.0%

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

Alternative 6: 55.6% 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 40.9%

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

   1. remove-double-neg 40.9%

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

   2. distribute-frac-neg 40.9%

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

   3. tan-neg 40.9%

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

   4. distribute-frac-neg2 40.9%

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

   5. distribute-lft-neg-out 40.9%

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

   6. distribute-frac-neg2 40.9%

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

   7. distribute-lft-neg-out 40.9%

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

   8. distribute-frac-neg2 40.9%

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

   9. distribute-frac-neg 40.9%

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

   10. neg-mul-1 40.9%

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

   11. *-commutative 40.9%

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

   12. associate-/l* 40.5%

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

   13. *-commutative 40.5%

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

   14. associate-/r* 40.5%

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

   15. metadata-eval 40.5%

       \[\leadsto \frac{\tan \left(x \cdot \frac{\color{blue}{-0.5}}{y}\right)}{-\sin \left(\frac{x}{y \cdot 2}\right)} \]

   16. sin-neg 40.5%

       \[\leadsto \frac{\tan \left(x \cdot \frac{-0.5}{y}\right)}{\color{blue}{\sin \left(-\frac{x}{y \cdot 2}\right)}} \]

   17. distribute-frac-neg 40.5%

       \[\leadsto \frac{\tan \left(x \cdot \frac{-0.5}{y}\right)}{\sin \color{blue}{\left(\frac{-x}{y \cdot 2}\right)}} \]

3. Simplified 40.9%

   \[\leadsto \color{blue}{\frac{\tan \left(x \cdot \frac{-0.5}{y}\right)}{\sin \left(x \cdot \frac{-0.5}{y}\right)}} \]
4. Add Preprocessing

5. Taylor expanded in x around 0 51.9%

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

Developer target: 55.6% 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 2024106 
(FPCore (x y)
  :name "Diagrams.TwoD.Layout.CirclePacking:approxRadius from diagrams-contrib-1.3.0.5"
  :precision binary64

  :alt
  (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)))))