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

Percentage Accurate: 44.1% → 57.2%

Time: 11.3s

Alternatives: 3

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: 57.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ y_m = \left|y\right| \\ \begin{array}{l} t_0 := \frac{x\_m}{y\_m \cdot 2}\\ \mathbf{if}\;\frac{\tan t\_0}{\sin t\_0} \leq 1.5:\\ \;\;\;\;\frac{1}{\cos \left(e^{\left(0 - 0.5 \cdot \log y\_m\right) - \log \left(\frac{\frac{2}{{y\_m}^{-0.5}}}{x\_m}\right)}\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
y_m = (fabs.f64 y)
(FPCore (x_m y_m)
 :precision binary64
 (let* ((t_0 (/ x_m (* y_m 2.0))))
   (if (<= (/ (tan t_0) (sin t_0)) 1.5)
     (/
      1.0
      (cos
       (exp
        (- (- 0.0 (* 0.5 (log y_m))) (log (/ (/ 2.0 (pow y_m -0.5)) x_m))))))
     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 ((tan(t_0) / sin(t_0)) <= 1.5) {
		tmp = 1.0 / cos(exp(((0.0 - (0.5 * log(y_m))) - log(((2.0 / pow(y_m, -0.5)) / x_m)))));
	} else {
		tmp = 1.0;
	}
	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) :: t_0
    real(8) :: tmp
    t_0 = x_m / (y_m * 2.0d0)
    if ((tan(t_0) / sin(t_0)) <= 1.5d0) then
        tmp = 1.0d0 / cos(exp(((0.0d0 - (0.5d0 * log(y_m))) - log(((2.0d0 / (y_m ** (-0.5d0))) / x_m)))))
    else
        tmp = 1.0d0
    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 t_0 = x_m / (y_m * 2.0);
	double tmp;
	if ((Math.tan(t_0) / Math.sin(t_0)) <= 1.5) {
		tmp = 1.0 / Math.cos(Math.exp(((0.0 - (0.5 * Math.log(y_m))) - Math.log(((2.0 / Math.pow(y_m, -0.5)) / x_m)))));
	} else {
		tmp = 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 (math.tan(t_0) / math.sin(t_0)) <= 1.5:
		tmp = 1.0 / math.cos(math.exp(((0.0 - (0.5 * math.log(y_m))) - math.log(((2.0 / math.pow(y_m, -0.5)) / x_m)))))
	else:
		tmp = 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 (Float64(tan(t_0) / sin(t_0)) <= 1.5)
		tmp = Float64(1.0 / cos(exp(Float64(Float64(0.0 - Float64(0.5 * log(y_m))) - log(Float64(Float64(2.0 / (y_m ^ -0.5)) / x_m))))));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

x_m = abs(x);
y_m = abs(y);
function tmp_2 = code(x_m, y_m)
	t_0 = x_m / (y_m * 2.0);
	tmp = 0.0;
	if ((tan(t_0) / sin(t_0)) <= 1.5)
		tmp = 1.0 / cos(exp(((0.0 - (0.5 * log(y_m))) - log(((2.0 / (y_m ^ -0.5)) / x_m)))));
	else
		tmp = 1.0;
	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_] := Block[{t$95$0 = N[(x$95$m / N[(y$95$m * 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[Tan[t$95$0], $MachinePrecision] / N[Sin[t$95$0], $MachinePrecision]), $MachinePrecision], 1.5], N[(1.0 / N[Cos[N[Exp[N[(N[(0.0 - N[(0.5 * N[Log[y$95$m], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[Log[N[(N[(2.0 / N[Power[y$95$m, -0.5], $MachinePrecision]), $MachinePrecision] / x$95$m), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (tan.f64 (/.f64 x (*.f64 y #s(literal 2 binary64)))) (sin.f64 (/.f64 x (*.f64 y #s(literal 2 binary64))))) < 1.5

   1. Initial program 63.9%

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

   3. Taylor expanded in x around inf

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \color{blue}{\cos \left(\frac{1}{2} \cdot \frac{x}{y}\right)}\right) \]

      2. associate-*r/ N/A

         \[\leadsto \mathsf{/.f64}\left(1, \cos \left(\frac{\frac{1}{2} \cdot x}{y}\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(1, \cos \left(\frac{x \cdot \frac{1}{2}}{y}\right)\right) \]

      4. associate-*r/ N/A

         \[\leadsto \mathsf{/.f64}\left(1, \cos \left(x \cdot \frac{\frac{1}{2}}{y}\right)\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(1, \cos \left(x \cdot \frac{\frac{1}{2} \cdot 1}{y}\right)\right) \]

      6. associate-*r/ N/A

         \[\leadsto \mathsf{/.f64}\left(1, \cos \left(x \cdot \left(\frac{1}{2} \cdot \frac{1}{y}\right)\right)\right) \]

      7. cos-lowering-cos.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{cos.f64}\left(\left(x \cdot \left(\frac{1}{2} \cdot \frac{1}{y}\right)\right)\right)\right) \]

      8. associate-*r/ N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{cos.f64}\left(\left(x \cdot \frac{\frac{1}{2} \cdot 1}{y}\right)\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{cos.f64}\left(\left(x \cdot \frac{\frac{1}{2}}{y}\right)\right)\right) \]

      10. associate-*r/ N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{cos.f64}\left(\left(\frac{x \cdot \frac{1}{2}}{y}\right)\right)\right) \]

      11. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{cos.f64}\left(\left(\frac{\frac{1}{2} \cdot x}{y}\right)\right)\right) \]

      12. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{cos.f64}\left(\mathsf{/.f64}\left(\left(\frac{1}{2} \cdot x\right), y\right)\right)\right) \]

      13. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{cos.f64}\left(\mathsf{/.f64}\left(\left(x \cdot \frac{1}{2}\right), y\right)\right)\right) \]

      14. *-lowering-*.f64 63.9%

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{cos.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \frac{1}{2}\right), y\right)\right)\right) \]

   5. Simplified 63.9%

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

      1. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{cos.f64}\left(\left(\frac{x \cdot \frac{1}{2}}{y}\right)\right)\right) \]

      2. div-inv N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{cos.f64}\left(\left(\frac{\frac{x}{2}}{y}\right)\right)\right) \]

      3. clear-num N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{cos.f64}\left(\left(\frac{1}{\frac{y}{\frac{x}{2}}}\right)\right)\right) \]

      4. associate-/r/ N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{cos.f64}\left(\left(\frac{1}{y} \cdot \frac{x}{2}\right)\right)\right) \]

      5. clear-num N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{cos.f64}\left(\left(\frac{1}{y} \cdot \frac{1}{\frac{2}{x}}\right)\right)\right) \]

      6. div-inv N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{cos.f64}\left(\left(\frac{\frac{1}{y}}{\frac{2}{x}}\right)\right)\right) \]

      7. inv-pow N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{cos.f64}\left(\left(\frac{{y}^{-1}}{\frac{2}{x}}\right)\right)\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{cos.f64}\left(\left(\frac{{y}^{\left(\frac{-1}{2} + \frac{-1}{2}\right)}}{\frac{2}{x}}\right)\right)\right) \]

      9. pow-prod-up N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{cos.f64}\left(\left(\frac{{y}^{\frac{-1}{2}} \cdot {y}^{\frac{-1}{2}}}{\frac{2}{x}}\right)\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{cos.f64}\left(\left(\frac{{y}^{\frac{-1}{2}} \cdot {y}^{\frac{-1}{2}}}{\frac{1 \cdot 2}{x}}\right)\right)\right) \]

      11. associate-*l/ N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{cos.f64}\left(\left(\frac{{y}^{\frac{-1}{2}} \cdot {y}^{\frac{-1}{2}}}{\frac{1}{x} \cdot 2}\right)\right)\right) \]

      12. frac-times N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{cos.f64}\left(\left(\frac{{y}^{\frac{-1}{2}}}{\frac{1}{x}} \cdot \frac{{y}^{\frac{-1}{2}}}{2}\right)\right)\right) \]

      13. clear-num N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{cos.f64}\left(\left(\frac{{y}^{\frac{-1}{2}}}{\frac{1}{x}} \cdot \frac{1}{\frac{2}{{y}^{\frac{-1}{2}}}}\right)\right)\right) \]

      14. un-div-inv N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{cos.f64}\left(\left(\frac{\frac{{y}^{\frac{-1}{2}}}{\frac{1}{x}}}{\frac{2}{{y}^{\frac{-1}{2}}}}\right)\right)\right) \]

      15. frac-2neg N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{cos.f64}\left(\left(\frac{\mathsf{neg}\left(\frac{{y}^{\frac{-1}{2}}}{\frac{1}{x}}\right)}{\mathsf{neg}\left(\frac{2}{{y}^{\frac{-1}{2}}}\right)}\right)\right)\right) \]

      16. distribute-frac-neg2 N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{cos.f64}\left(\left(\frac{\frac{{y}^{\frac{-1}{2}}}{\mathsf{neg}\left(\frac{1}{x}\right)}}{\mathsf{neg}\left(\frac{2}{{y}^{\frac{-1}{2}}}\right)}\right)\right)\right) \]

      17. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{cos.f64}\left(\mathsf{/.f64}\left(\left(\frac{{y}^{\frac{-1}{2}}}{\mathsf{neg}\left(\frac{1}{x}\right)}\right), \left(\mathsf{neg}\left(\frac{2}{{y}^{\frac{-1}{2}}}\right)\right)\right)\right)\right) \]

      18. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{cos.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(\left({y}^{\frac{-1}{2}}\right), \left(\mathsf{neg}\left(\frac{1}{x}\right)\right)\right), \left(\mathsf{neg}\left(\frac{2}{{y}^{\frac{-1}{2}}}\right)\right)\right)\right)\right) \]

      19. pow-lowering-pow.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{cos.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{pow.f64}\left(y, \frac{-1}{2}\right), \left(\mathsf{neg}\left(\frac{1}{x}\right)\right)\right), \left(\mathsf{neg}\left(\frac{2}{{y}^{\frac{-1}{2}}}\right)\right)\right)\right)\right) \]

      20. distribute-neg-frac N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{cos.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{pow.f64}\left(y, \frac{-1}{2}\right), \left(\frac{\mathsf{neg}\left(1\right)}{x}\right)\right), \left(\mathsf{neg}\left(\frac{2}{{y}^{\frac{-1}{2}}}\right)\right)\right)\right)\right) \]

      21. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{cos.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{pow.f64}\left(y, \frac{-1}{2}\right), \left(\frac{-1}{x}\right)\right), \left(\mathsf{neg}\left(\frac{2}{{y}^{\frac{-1}{2}}}\right)\right)\right)\right)\right) \]

      22. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{cos.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{pow.f64}\left(y, \frac{-1}{2}\right), \mathsf{/.f64}\left(-1, x\right)\right), \left(\mathsf{neg}\left(\frac{2}{{y}^{\frac{-1}{2}}}\right)\right)\right)\right)\right) \]

      23. distribute-neg-frac N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{cos.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{pow.f64}\left(y, \frac{-1}{2}\right), \mathsf{/.f64}\left(-1, x\right)\right), \left(\frac{\mathsf{neg}\left(2\right)}{{y}^{\frac{-1}{2}}}\right)\right)\right)\right) \]

      24. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{cos.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{pow.f64}\left(y, \frac{-1}{2}\right), \mathsf{/.f64}\left(-1, x\right)\right), \mathsf{/.f64}\left(\left(\mathsf{neg}\left(2\right)\right), \left({y}^{\frac{-1}{2}}\right)\right)\right)\right)\right) \]

      25. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{cos.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{pow.f64}\left(y, \frac{-1}{2}\right), \mathsf{/.f64}\left(-1, x\right)\right), \mathsf{/.f64}\left(-2, \left({y}^{\frac{-1}{2}}\right)\right)\right)\right)\right) \]

      26. pow-lowering-pow.f64 35.9%

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{cos.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{pow.f64}\left(y, \frac{-1}{2}\right), \mathsf{/.f64}\left(-1, x\right)\right), \mathsf{/.f64}\left(-2, \mathsf{pow.f64}\left(y, \frac{-1}{2}\right)\right)\right)\right)\right) \]

   7. Applied egg-rr 35.9%

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

      1. associate-/l/ N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{cos.f64}\left(\left(\frac{{y}^{\frac{-1}{2}}}{\frac{-2}{{y}^{\frac{-1}{2}}} \cdot \frac{-1}{x}}\right)\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{cos.f64}\left(\left(\frac{{y}^{\frac{-1}{2}}}{\frac{-1}{x} \cdot \frac{-2}{{y}^{\frac{-1}{2}}}}\right)\right)\right) \]

      3. frac-times N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{cos.f64}\left(\left(\frac{{y}^{\frac{-1}{2}}}{\frac{-1 \cdot -2}{x \cdot {y}^{\frac{-1}{2}}}}\right)\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{cos.f64}\left(\left(\frac{{y}^{\frac{-1}{2}}}{\frac{2}{x \cdot {y}^{\frac{-1}{2}}}}\right)\right)\right) \]

      5. associate-/l/ N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{cos.f64}\left(\left(\frac{{y}^{\frac{-1}{2}}}{\frac{\frac{2}{{y}^{\frac{-1}{2}}}}{x}}\right)\right)\right) \]

      6. un-div-inv N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{cos.f64}\left(\left({y}^{\frac{-1}{2}} \cdot \frac{1}{\frac{\frac{2}{{y}^{\frac{-1}{2}}}}{x}}\right)\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{cos.f64}\left(\left(\frac{1}{\frac{\frac{2}{{y}^{\frac{-1}{2}}}}{x}} \cdot {y}^{\frac{-1}{2}}\right)\right)\right) \]

      8. /-rgt-identity N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{cos.f64}\left(\left(\frac{1}{\frac{\frac{2}{{y}^{\frac{-1}{2}}}}{x}} \cdot \frac{{y}^{\frac{-1}{2}}}{1}\right)\right)\right) \]

      9. clear-num N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{cos.f64}\left(\left(\frac{x}{\frac{2}{{y}^{\frac{-1}{2}}}} \cdot \frac{{y}^{\frac{-1}{2}}}{1}\right)\right)\right) \]

      10. clear-num N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{cos.f64}\left(\left(\frac{x}{\frac{2}{{y}^{\frac{-1}{2}}}} \cdot \frac{1}{\frac{1}{{y}^{\frac{-1}{2}}}}\right)\right)\right) \]

      11. div-inv N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{cos.f64}\left(\left(\frac{\frac{x}{\frac{2}{{y}^{\frac{-1}{2}}}}}{\frac{1}{{y}^{\frac{-1}{2}}}}\right)\right)\right) \]

      12. clear-num N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{cos.f64}\left(\left(\frac{\frac{1}{\frac{\frac{2}{{y}^{\frac{-1}{2}}}}{x}}}{\frac{1}{{y}^{\frac{-1}{2}}}}\right)\right)\right) \]

      13. inv-pow N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{cos.f64}\left(\left(\frac{{\left(\frac{\frac{2}{{y}^{\frac{-1}{2}}}}{x}\right)}^{-1}}{\frac{1}{{y}^{\frac{-1}{2}}}}\right)\right)\right) \]

      14. pow-to-exp N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{cos.f64}\left(\left(\frac{e^{\log \left(\frac{\frac{2}{{y}^{\frac{-1}{2}}}}{x}\right) \cdot -1}}{\frac{1}{{y}^{\frac{-1}{2}}}}\right)\right)\right) \]

      15. pow-to-exp N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{cos.f64}\left(\left(\frac{e^{\log \left(\frac{\frac{2}{{y}^{\frac{-1}{2}}}}{x}\right) \cdot -1}}{\frac{1}{e^{\log y \cdot \frac{-1}{2}}}}\right)\right)\right) \]

      16. rec-exp N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{cos.f64}\left(\left(\frac{e^{\log \left(\frac{\frac{2}{{y}^{\frac{-1}{2}}}}{x}\right) \cdot -1}}{e^{\mathsf{neg}\left(\log y \cdot \frac{-1}{2}\right)}}\right)\right)\right) \]

      17. div-exp N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{cos.f64}\left(\left(e^{\log \left(\frac{\frac{2}{{y}^{\frac{-1}{2}}}}{x}\right) \cdot -1 - \left(\mathsf{neg}\left(\log y \cdot \frac{-1}{2}\right)\right)}\right)\right)\right) \]

      18. exp-lowering-exp.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{cos.f64}\left(\mathsf{exp.f64}\left(\left(\log \left(\frac{\frac{2}{{y}^{\frac{-1}{2}}}}{x}\right) \cdot -1 - \left(\mathsf{neg}\left(\log y \cdot \frac{-1}{2}\right)\right)\right)\right)\right)\right) \]

      19. --lowering--.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{cos.f64}\left(\mathsf{exp.f64}\left(\mathsf{\_.f64}\left(\left(\log \left(\frac{\frac{2}{{y}^{\frac{-1}{2}}}}{x}\right) \cdot -1\right), \left(\mathsf{neg}\left(\log y \cdot \frac{-1}{2}\right)\right)\right)\right)\right)\right) \]

   9. Applied egg-rr 15.3%

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

   if 1.5 < (/.f64 (tan.f64 (/.f64 x (*.f64 y #s(literal 2 binary64)))) (sin.f64 (/.f64 x (*.f64 y #s(literal 2 binary64)))))

   1. Initial program 2.0%

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

   3. Taylor expanded in x around 0

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

   5. Simplified 43.0%

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

4. Final simplification 24.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\tan \left(\frac{x}{y \cdot 2}\right)}{\sin \left(\frac{x}{y \cdot 2}\right)} \leq 1.5:\\ \;\;\;\;\frac{1}{\cos \left(e^{\left(0 - 0.5 \cdot \log y\right) - \log \left(\frac{\frac{2}{{y}^{-0.5}}}{x}\right)}\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 57.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ y_m = \left|y\right| \\ \begin{array}{l} \mathbf{if}\;y\_m \cdot 2 \leq 10^{-130}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\cos \left({y\_m}^{-0.25} \cdot \frac{{y\_m}^{-0.75}}{\frac{2}{x\_m}}\right)}\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
y_m = (fabs.f64 y)
(FPCore (x_m y_m)
 :precision binary64
 (if (<= (* y_m 2.0) 1e-130)
   1.0
   (/ 1.0 (cos (* (pow y_m -0.25) (/ (pow y_m -0.75) (/ 2.0 x_m)))))))

C

x_m = fabs(x);
y_m = fabs(y);
double code(double x_m, double y_m) {
	double tmp;
	if ((y_m * 2.0) <= 1e-130) {
		tmp = 1.0;
	} else {
		tmp = 1.0 / cos((pow(y_m, -0.25) * (pow(y_m, -0.75) / (2.0 / x_m))));
	}
	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 ((y_m * 2.0d0) <= 1d-130) then
        tmp = 1.0d0
    else
        tmp = 1.0d0 / cos(((y_m ** (-0.25d0)) * ((y_m ** (-0.75d0)) / (2.0d0 / x_m))))
    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 ((y_m * 2.0) <= 1e-130) {
		tmp = 1.0;
	} else {
		tmp = 1.0 / Math.cos((Math.pow(y_m, -0.25) * (Math.pow(y_m, -0.75) / (2.0 / x_m))));
	}
	return tmp;
}

Python

x_m = math.fabs(x)
y_m = math.fabs(y)
def code(x_m, y_m):
	tmp = 0
	if (y_m * 2.0) <= 1e-130:
		tmp = 1.0
	else:
		tmp = 1.0 / math.cos((math.pow(y_m, -0.25) * (math.pow(y_m, -0.75) / (2.0 / x_m))))
	return tmp

Julia

x_m = abs(x)
y_m = abs(y)
function code(x_m, y_m)
	tmp = 0.0
	if (Float64(y_m * 2.0) <= 1e-130)
		tmp = 1.0;
	else
		tmp = Float64(1.0 / cos(Float64((y_m ^ -0.25) * Float64((y_m ^ -0.75) / Float64(2.0 / x_m)))));
	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 ((y_m * 2.0) <= 1e-130)
		tmp = 1.0;
	else
		tmp = 1.0 / cos(((y_m ^ -0.25) * ((y_m ^ -0.75) / (2.0 / x_m))));
	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[(y$95$m * 2.0), $MachinePrecision], 1e-130], 1.0, N[(1.0 / N[Cos[N[(N[Power[y$95$m, -0.25], $MachinePrecision] * N[(N[Power[y$95$m, -0.75], $MachinePrecision] / N[(2.0 / x$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y #s(literal 2 binary64)) < 1.0000000000000001e-130

   1. Initial program 32.7%

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

   3. Taylor expanded in x around 0

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

   5. Simplified 44.7%

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

   if 1.0000000000000001e-130 < (*.f64 y #s(literal 2 binary64))

   1. Initial program 65.9%

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

   3. Taylor expanded in x around inf

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \color{blue}{\cos \left(\frac{1}{2} \cdot \frac{x}{y}\right)}\right) \]

      2. associate-*r/ N/A

         \[\leadsto \mathsf{/.f64}\left(1, \cos \left(\frac{\frac{1}{2} \cdot x}{y}\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(1, \cos \left(\frac{x \cdot \frac{1}{2}}{y}\right)\right) \]

      4. associate-*r/ N/A

         \[\leadsto \mathsf{/.f64}\left(1, \cos \left(x \cdot \frac{\frac{1}{2}}{y}\right)\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(1, \cos \left(x \cdot \frac{\frac{1}{2} \cdot 1}{y}\right)\right) \]

      6. associate-*r/ N/A

         \[\leadsto \mathsf{/.f64}\left(1, \cos \left(x \cdot \left(\frac{1}{2} \cdot \frac{1}{y}\right)\right)\right) \]

      7. cos-lowering-cos.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{cos.f64}\left(\left(x \cdot \left(\frac{1}{2} \cdot \frac{1}{y}\right)\right)\right)\right) \]

      8. associate-*r/ N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{cos.f64}\left(\left(x \cdot \frac{\frac{1}{2} \cdot 1}{y}\right)\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{cos.f64}\left(\left(x \cdot \frac{\frac{1}{2}}{y}\right)\right)\right) \]

      10. associate-*r/ N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{cos.f64}\left(\left(\frac{x \cdot \frac{1}{2}}{y}\right)\right)\right) \]

      11. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{cos.f64}\left(\left(\frac{\frac{1}{2} \cdot x}{y}\right)\right)\right) \]

      12. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{cos.f64}\left(\mathsf{/.f64}\left(\left(\frac{1}{2} \cdot x\right), y\right)\right)\right) \]

      13. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{cos.f64}\left(\mathsf{/.f64}\left(\left(x \cdot \frac{1}{2}\right), y\right)\right)\right) \]

      14. *-lowering-*.f64 78.7%

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{cos.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \frac{1}{2}\right), y\right)\right)\right) \]

   5. Simplified 78.7%

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

      1. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{cos.f64}\left(\left(\frac{x \cdot \frac{1}{2}}{y}\right)\right)\right) \]

      2. div-inv N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{cos.f64}\left(\left(\frac{\frac{x}{2}}{y}\right)\right)\right) \]

      3. clear-num N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{cos.f64}\left(\left(\frac{1}{\frac{y}{\frac{x}{2}}}\right)\right)\right) \]

      4. associate-/r/ N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{cos.f64}\left(\left(\frac{1}{y} \cdot \frac{x}{2}\right)\right)\right) \]

      5. clear-num N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{cos.f64}\left(\left(\frac{1}{y} \cdot \frac{1}{\frac{2}{x}}\right)\right)\right) \]

      6. div-inv N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{cos.f64}\left(\left(\frac{\frac{1}{y}}{\frac{2}{x}}\right)\right)\right) \]

      7. inv-pow N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{cos.f64}\left(\left(\frac{{y}^{-1}}{\frac{2}{x}}\right)\right)\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{cos.f64}\left(\left(\frac{{y}^{\left(\frac{-1}{2} + \frac{-1}{2}\right)}}{\frac{2}{x}}\right)\right)\right) \]

      9. pow-prod-up N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{cos.f64}\left(\left(\frac{{y}^{\frac{-1}{2}} \cdot {y}^{\frac{-1}{2}}}{\frac{2}{x}}\right)\right)\right) \]

      10. sqr-pow N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{cos.f64}\left(\left(\frac{\left({y}^{\left(\frac{\frac{-1}{2}}{2}\right)} \cdot {y}^{\left(\frac{\frac{-1}{2}}{2}\right)}\right) \cdot {y}^{\frac{-1}{2}}}{\frac{2}{x}}\right)\right)\right) \]

      11. associate-*l* N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{cos.f64}\left(\left(\frac{{y}^{\left(\frac{\frac{-1}{2}}{2}\right)} \cdot \left({y}^{\left(\frac{\frac{-1}{2}}{2}\right)} \cdot {y}^{\frac{-1}{2}}\right)}{\frac{2}{x}}\right)\right)\right) \]

      12. *-lft-identity N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{cos.f64}\left(\left(\frac{{y}^{\left(\frac{\frac{-1}{2}}{2}\right)} \cdot \left({y}^{\left(\frac{\frac{-1}{2}}{2}\right)} \cdot {y}^{\frac{-1}{2}}\right)}{1 \cdot \frac{2}{x}}\right)\right)\right) \]

      13. times-frac N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{cos.f64}\left(\left(\frac{{y}^{\left(\frac{\frac{-1}{2}}{2}\right)}}{1} \cdot \frac{{y}^{\left(\frac{\frac{-1}{2}}{2}\right)} \cdot {y}^{\frac{-1}{2}}}{\frac{2}{x}}\right)\right)\right) \]

      14. /-rgt-identity N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{cos.f64}\left(\left({y}^{\left(\frac{\frac{-1}{2}}{2}\right)} \cdot \frac{{y}^{\left(\frac{\frac{-1}{2}}{2}\right)} \cdot {y}^{\frac{-1}{2}}}{\frac{2}{x}}\right)\right)\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{cos.f64}\left(\mathsf{*.f64}\left(\left({y}^{\left(\frac{\frac{-1}{2}}{2}\right)}\right), \left(\frac{{y}^{\left(\frac{\frac{-1}{2}}{2}\right)} \cdot {y}^{\frac{-1}{2}}}{\frac{2}{x}}\right)\right)\right)\right) \]

      16. pow-lowering-pow.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{cos.f64}\left(\mathsf{*.f64}\left(\mathsf{pow.f64}\left(y, \left(\frac{\frac{-1}{2}}{2}\right)\right), \left(\frac{{y}^{\left(\frac{\frac{-1}{2}}{2}\right)} \cdot {y}^{\frac{-1}{2}}}{\frac{2}{x}}\right)\right)\right)\right) \]

      17. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{cos.f64}\left(\mathsf{*.f64}\left(\mathsf{pow.f64}\left(y, \frac{-1}{4}\right), \left(\frac{{y}^{\left(\frac{\frac{-1}{2}}{2}\right)} \cdot {y}^{\frac{-1}{2}}}{\frac{2}{x}}\right)\right)\right)\right) \]

      18. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{cos.f64}\left(\mathsf{*.f64}\left(\mathsf{pow.f64}\left(y, \frac{-1}{4}\right), \mathsf{/.f64}\left(\left({y}^{\left(\frac{\frac{-1}{2}}{2}\right)} \cdot {y}^{\frac{-1}{2}}\right), \left(\frac{2}{x}\right)\right)\right)\right)\right) \]

   7. Applied egg-rr 79.6%

      \[\leadsto \frac{1}{\cos \color{blue}{\left({y}^{-0.25} \cdot \frac{{y}^{-0.75}}{\frac{2}{x}}\right)}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 56.3% 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 43.9%

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

3. Taylor expanded in x around 0

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

5. Simplified 56.1%

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

Developer Target 1: 56.3% 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 2024160 
(FPCore (x y)
  :name "Diagrams.TwoD.Layout.CirclePacking:approxRadius from diagrams-contrib-1.3.0.5"
  :precision binary64

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

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