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

Percentage Accurate: 43.9% → 56.9%

Time: 14.4s

Alternatives: 4

Speedup: 211.0×

Specification

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{y \cdot 2}\\ \frac{\tan t_0}{\sin t_0} \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ x (* y 2.0)))) (/ (tan t_0) (sin t_0))))

C

double code(double x, double y) {
	double t_0 = x / (y * 2.0);
	return tan(t_0) / sin(t_0);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    t_0 = x / (y * 2.0d0)
    code = tan(t_0) / sin(t_0)
end function

Java

public static double code(double x, double y) {
	double t_0 = x / (y * 2.0);
	return Math.tan(t_0) / Math.sin(t_0);
}

Python

def code(x, y):
	t_0 = x / (y * 2.0)
	return math.tan(t_0) / math.sin(t_0)

Julia

function code(x, y)
	t_0 = Float64(x / Float64(y * 2.0))
	return Float64(tan(t_0) / sin(t_0))
end

MATLAB

function tmp = code(x, y)
	t_0 = x / (y * 2.0);
	tmp = tan(t_0) / sin(t_0);
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(x / N[(y * 2.0), $MachinePrecision]), $MachinePrecision]}, N[(N[Tan[t$95$0], $MachinePrecision] / N[Sin[t$95$0], $MachinePrecision]), $MachinePrecision]]

Initial Program: 43.9% 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, 0.7× speedup

Math

\[\begin{array}{l} x = |x|\\ y = |y|\\ \\ \begin{array}{l} t_0 := \sqrt{\frac{0.5}{y}}\\ \mathbf{if}\;\frac{x}{y \cdot 2} \leq 5 \cdot 10^{+244}:\\ \;\;\;\;\frac{1}{\cos \left(t_0 \cdot \left(x \cdot t_0\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

NOTE: x should be positive before calling this function
NOTE: y should be positive before calling this function
(FPCore (x y)
 :precision binary64
 (let* ((t_0 (sqrt (/ 0.5 y))))
   (if (<= (/ x (* y 2.0)) 5e+244) (/ 1.0 (cos (* t_0 (* x t_0)))) 1.0)))

C

x = abs(x);
y = abs(y);
double code(double x, double y) {
	double t_0 = sqrt((0.5 / y));
	double tmp;
	if ((x / (y * 2.0)) <= 5e+244) {
		tmp = 1.0 / cos((t_0 * (x * t_0)));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

NOTE: x should be positive before calling this function
NOTE: y should be positive before calling this function
real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = sqrt((0.5d0 / y))
    if ((x / (y * 2.0d0)) <= 5d+244) then
        tmp = 1.0d0 / cos((t_0 * (x * t_0)))
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

x = Math.abs(x);
y = Math.abs(y);
public static double code(double x, double y) {
	double t_0 = Math.sqrt((0.5 / y));
	double tmp;
	if ((x / (y * 2.0)) <= 5e+244) {
		tmp = 1.0 / Math.cos((t_0 * (x * t_0)));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

x = abs(x)
y = abs(y)
def code(x, y):
	t_0 = math.sqrt((0.5 / y))
	tmp = 0
	if (x / (y * 2.0)) <= 5e+244:
		tmp = 1.0 / math.cos((t_0 * (x * t_0)))
	else:
		tmp = 1.0
	return tmp

Julia

x = abs(x)
y = abs(y)
function code(x, y)
	t_0 = sqrt(Float64(0.5 / y))
	tmp = 0.0
	if (Float64(x / Float64(y * 2.0)) <= 5e+244)
		tmp = Float64(1.0 / cos(Float64(t_0 * Float64(x * t_0))));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

x = abs(x)
y = abs(y)
function tmp_2 = code(x, y)
	t_0 = sqrt((0.5 / y));
	tmp = 0.0;
	if ((x / (y * 2.0)) <= 5e+244)
		tmp = 1.0 / cos((t_0 * (x * t_0)));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x should be positive before calling this function
NOTE: y should be positive before calling this function
code[x_, y_] := Block[{t$95$0 = N[Sqrt[N[(0.5 / y), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[N[(x / N[(y * 2.0), $MachinePrecision]), $MachinePrecision], 5e+244], N[(1.0 / N[Cos[N[(t$95$0 * N[(x * t$95$0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (*.f64 y 2)) < 5.00000000000000022e244

   1. Initial program 51.3%

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

      1. add-log-exp 51.3%

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

      2. *-un-lft-identity 51.3%

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

      3. log-prod 51.3%

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

      4. metadata-eval 51.3%

         \[\leadsto \color{blue}{0} + \log \left(e^{\frac{\tan \left(\frac{x}{y \cdot 2}\right)}{\sin \left(\frac{x}{y \cdot 2}\right)}}\right) \]

      5. add-log-exp 51.3%

         \[\leadsto 0 + \color{blue}{\frac{\tan \left(\frac{x}{y \cdot 2}\right)}{\sin \left(\frac{x}{y \cdot 2}\right)}} \]

      6. div-inv 50.8%

         \[\leadsto 0 + \color{blue}{\tan \left(\frac{x}{y \cdot 2}\right) \cdot \frac{1}{\sin \left(\frac{x}{y \cdot 2}\right)}} \]

      7. tan-quot 50.8%

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

      8. associate-*l/ 50.8%

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

      9. pow1 50.8%

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

      10. inv-pow 50.8%

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

      11. pow-prod-up 65.4%

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

      12. metadata-eval 65.4%

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

      13. metadata-eval 65.4%

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

      14. div-inv 65.4%

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

      15. *-commutative 65.4%

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

      16. associate-/r* 65.4%

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

      17. metadata-eval 65.4%

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

   3. Applied egg-rr 65.4%

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

      1. expm1-log1p-u 63.7%

         \[\leadsto 0 + \frac{1}{\cos \color{blue}{\left(\mathsf{expm1}\left(\mathsf{log1p}\left(x \cdot \frac{0.5}{y}\right)\right)\right)}} \]

   5. Applied egg-rr 63.7%

      \[\leadsto 0 + \frac{1}{\cos \color{blue}{\left(\mathsf{expm1}\left(\mathsf{log1p}\left(x \cdot \frac{0.5}{y}\right)\right)\right)}} \]
   6. Step-by-step derivation

      1. expm1-log1p-u 65.4%

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

      2. add-sqr-sqrt 30.2%

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

      3. associate-*r* 30.2%

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

   7. Applied egg-rr 30.2%

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

   if 5.00000000000000022e244 < (/.f64 x (*.f64 y 2))

   1. Initial program 2.5%

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

   2. Taylor expanded in x around 0 12.8%

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

4. Final simplification 28.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y \cdot 2} \leq 5 \cdot 10^{+244}:\\ \;\;\;\;\frac{1}{\cos \left(\sqrt{\frac{0.5}{y}} \cdot \left(x \cdot \sqrt{\frac{0.5}{y}}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 2: 56.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} x = |x|\\ y = |y|\\ \\ \begin{array}{l} t_0 := \frac{x}{y \cdot 2}\\ \mathbf{if}\;\frac{\tan t_0}{\sin t_0} \leq 1.17:\\ \;\;\;\;\frac{1}{\cos \left(\frac{\sqrt[3]{-0.125}}{\frac{y}{x}}\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

NOTE: x should be positive before calling this function
NOTE: y should be positive before calling this function
(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ x (* y 2.0))))
   (if (<= (/ (tan t_0) (sin t_0)) 1.17)
     (/ 1.0 (cos (/ (cbrt -0.125) (/ y x))))
     1.0)))

C

x = abs(x);
y = abs(y);
double code(double x, double y) {
	double t_0 = x / (y * 2.0);
	double tmp;
	if ((tan(t_0) / sin(t_0)) <= 1.17) {
		tmp = 1.0 / cos((cbrt(-0.125) / (y / x)));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Java

x = Math.abs(x);
y = Math.abs(y);
public static double code(double x, double y) {
	double t_0 = x / (y * 2.0);
	double tmp;
	if ((Math.tan(t_0) / Math.sin(t_0)) <= 1.17) {
		tmp = 1.0 / Math.cos((Math.cbrt(-0.125) / (y / x)));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Julia

x = abs(x)
y = abs(y)
function code(x, y)
	t_0 = Float64(x / Float64(y * 2.0))
	tmp = 0.0
	if (Float64(tan(t_0) / sin(t_0)) <= 1.17)
		tmp = Float64(1.0 / cos(Float64(cbrt(-0.125) / Float64(y / x))));
	else
		tmp = 1.0;
	end
	return tmp
end

Wolfram

NOTE: x should be positive before calling this function
NOTE: y should be positive before calling this function
code[x_, y_] := Block[{t$95$0 = N[(x / N[(y * 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[Tan[t$95$0], $MachinePrecision] / N[Sin[t$95$0], $MachinePrecision]), $MachinePrecision], 1.17], N[(1.0 / N[Cos[N[(N[Power[-0.125, 1/3], $MachinePrecision] / N[(y / x), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (tan.f64 (/.f64 x (*.f64 y 2))) (sin.f64 (/.f64 x (*.f64 y 2)))) < 1.1699999999999999

   1. Initial program 70.4%

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

      1. add-log-exp 70.4%

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

      2. *-un-lft-identity 70.4%

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

      3. log-prod 70.4%

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

      4. metadata-eval 70.4%

         \[\leadsto \color{blue}{0} + \log \left(e^{\frac{\tan \left(\frac{x}{y \cdot 2}\right)}{\sin \left(\frac{x}{y \cdot 2}\right)}}\right) \]

      5. add-log-exp 70.4%

         \[\leadsto 0 + \color{blue}{\frac{\tan \left(\frac{x}{y \cdot 2}\right)}{\sin \left(\frac{x}{y \cdot 2}\right)}} \]

      6. div-inv 69.7%

         \[\leadsto 0 + \color{blue}{\tan \left(\frac{x}{y \cdot 2}\right) \cdot \frac{1}{\sin \left(\frac{x}{y \cdot 2}\right)}} \]

      7. tan-quot 69.7%

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

      8. associate-*l/ 69.7%

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

      9. pow1 69.7%

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

      10. inv-pow 69.7%

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

      11. pow-prod-up 70.4%

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

      12. metadata-eval 70.4%

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

      13. metadata-eval 70.4%

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

      14. div-inv 70.7%

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

      15. *-commutative 70.7%

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

      16. associate-/r* 70.7%

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

      17. metadata-eval 70.7%

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

   3. Applied egg-rr 70.7%

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

      1. add-cbrt-cube 68.6%

         \[\leadsto 0 + \frac{1}{\cos \color{blue}{\left(\sqrt[3]{\left(\left(x \cdot \frac{0.5}{y}\right) \cdot \left(x \cdot \frac{0.5}{y}\right)\right) \cdot \left(x \cdot \frac{0.5}{y}\right)}\right)}} \]

      2. pow3 68.5%

         \[\leadsto 0 + \frac{1}{\cos \left(\sqrt[3]{\color{blue}{{\left(x \cdot \frac{0.5}{y}\right)}^{3}}}\right)} \]

   5. Applied egg-rr 68.5%

      \[\leadsto 0 + \frac{1}{\cos \color{blue}{\left(\sqrt[3]{{\left(x \cdot \frac{0.5}{y}\right)}^{3}}\right)}} \]

   6. Taylor expanded in x around -inf 71.3%

      \[\leadsto 0 + \frac{1}{\color{blue}{\cos \left(-1 \cdot \frac{\sqrt[3]{-0.125} \cdot x}{y}\right)}} \]
   7. Step-by-step derivation

      1. mul-1-neg 71.3%

         \[\leadsto 0 + \frac{1}{\cos \color{blue}{\left(-\frac{\sqrt[3]{-0.125} \cdot x}{y}\right)}} \]

      2. cos-neg 71.3%

         \[\leadsto 0 + \frac{1}{\color{blue}{\cos \left(\frac{\sqrt[3]{-0.125} \cdot x}{y}\right)}} \]

      3. associate-/l* 71.3%

         \[\leadsto 0 + \frac{1}{\cos \color{blue}{\left(\frac{\sqrt[3]{-0.125}}{\frac{y}{x}}\right)}} \]

   8. Simplified 71.3%

      \[\leadsto 0 + \frac{1}{\color{blue}{\cos \left(\frac{\sqrt[3]{-0.125}}{\frac{y}{x}}\right)}} \]

   if 1.1699999999999999 < (/.f64 (tan.f64 (/.f64 x (*.f64 y 2))) (sin.f64 (/.f64 x (*.f64 y 2))))

   1. Initial program 3.3%

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

   2. Taylor expanded in x around 0 46.5%

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

4. Final simplification 62.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\tan \left(\frac{x}{y \cdot 2}\right)}{\sin \left(\frac{x}{y \cdot 2}\right)} \leq 1.17:\\ \;\;\;\;\frac{1}{\cos \left(\frac{\sqrt[3]{-0.125}}{\frac{y}{x}}\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 3: 56.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} x = |x|\\ y = |y|\\ \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y \cdot 2} \leq 10^{+185}:\\ \;\;\;\;\frac{1}{\cos \left(e^{\log \left(x \cdot \frac{0.5}{y}\right)}\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

NOTE: x should be positive before calling this function
NOTE: y should be positive before calling this function
(FPCore (x y)
 :precision binary64
 (if (<= (/ x (* y 2.0)) 1e+185)
   (/ 1.0 (cos (exp (log (* x (/ 0.5 y))))))
   1.0))

C

x = abs(x);
y = abs(y);
double code(double x, double y) {
	double tmp;
	if ((x / (y * 2.0)) <= 1e+185) {
		tmp = 1.0 / cos(exp(log((x * (0.5 / y)))));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

NOTE: x should be positive before calling this function
NOTE: y should be positive before calling this function
real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((x / (y * 2.0d0)) <= 1d+185) then
        tmp = 1.0d0 / cos(exp(log((x * (0.5d0 / y)))))
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

x = Math.abs(x);
y = Math.abs(y);
public static double code(double x, double y) {
	double tmp;
	if ((x / (y * 2.0)) <= 1e+185) {
		tmp = 1.0 / Math.cos(Math.exp(Math.log((x * (0.5 / y)))));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

x = abs(x)
y = abs(y)
def code(x, y):
	tmp = 0
	if (x / (y * 2.0)) <= 1e+185:
		tmp = 1.0 / math.cos(math.exp(math.log((x * (0.5 / y)))))
	else:
		tmp = 1.0
	return tmp

Julia

x = abs(x)
y = abs(y)
function code(x, y)
	tmp = 0.0
	if (Float64(x / Float64(y * 2.0)) <= 1e+185)
		tmp = Float64(1.0 / cos(exp(log(Float64(x * Float64(0.5 / y))))));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

x = abs(x)
y = abs(y)
function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x / (y * 2.0)) <= 1e+185)
		tmp = 1.0 / cos(exp(log((x * (0.5 / y)))));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x should be positive before calling this function
NOTE: y should be positive before calling this function
code[x_, y_] := If[LessEqual[N[(x / N[(y * 2.0), $MachinePrecision]), $MachinePrecision], 1e+185], N[(1.0 / N[Cos[N[Exp[N[Log[N[(x * N[(0.5 / y), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]], $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 1.0]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (*.f64 y 2)) < 9.9999999999999998e184

   1. Initial program 54.1%

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

      1. add-log-exp 54.1%

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

      2. *-un-lft-identity 54.1%

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

      3. log-prod 54.1%

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

      4. metadata-eval 54.1%

         \[\leadsto \color{blue}{0} + \log \left(e^{\frac{\tan \left(\frac{x}{y \cdot 2}\right)}{\sin \left(\frac{x}{y \cdot 2}\right)}}\right) \]

      5. add-log-exp 54.1%

         \[\leadsto 0 + \color{blue}{\frac{\tan \left(\frac{x}{y \cdot 2}\right)}{\sin \left(\frac{x}{y \cdot 2}\right)}} \]

      6. div-inv 53.6%

         \[\leadsto 0 + \color{blue}{\tan \left(\frac{x}{y \cdot 2}\right) \cdot \frac{1}{\sin \left(\frac{x}{y \cdot 2}\right)}} \]

      7. tan-quot 53.6%

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

      8. associate-*l/ 53.6%

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

      9. pow1 53.6%

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

      10. inv-pow 53.6%

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

      11. pow-prod-up 69.2%

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

      12. metadata-eval 69.2%

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

      13. metadata-eval 69.2%

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

      14. div-inv 69.2%

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

      15. *-commutative 69.2%

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

      16. associate-/r* 69.2%

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

      17. metadata-eval 69.2%

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

   3. Applied egg-rr 69.2%

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

      1. add-exp-log 37.7%

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

   5. Applied egg-rr 37.7%

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

   if 9.9999999999999998e184 < (/.f64 x (*.f64 y 2))

   1. Initial program 5.4%

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

   2. Taylor expanded in x around 0 12.5%

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

4. Final simplification 34.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y \cdot 2} \leq 10^{+185}:\\ \;\;\;\;\frac{1}{\cos \left(e^{\log \left(x \cdot \frac{0.5}{y}\right)}\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 4: 55.5% accurate, 211.0× speedup

Math

\[\begin{array}{l} x = |x|\\ y = |y|\\ \\ 1 \end{array} \]

FPCore

NOTE: x should be positive before calling this function
NOTE: y should be positive before calling this function
(FPCore (x y) :precision binary64 1.0)

C

x = abs(x);
y = abs(y);
double code(double x, double y) {
	return 1.0;
}

Fortran

NOTE: x should be positive before calling this function
NOTE: y should be positive before calling this function
real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 1.0d0
end function

Java

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

Python

x = abs(x)
y = abs(y)
def code(x, y):
	return 1.0

Julia

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

MATLAB

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

Wolfram

NOTE: x should be positive before calling this function
NOTE: y should be positive before calling this function
code[x_, y_] := 1.0

Derivation

1. Initial program 47.1%

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

2. Taylor expanded in x around 0 61.0%

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

3. Final simplification 61.0%

   \[\leadsto 1 \]

Developer target: 55.5% 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 2023228 
(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)))))