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

Percentage Accurate: 43.7% → 55.3%

Time: 12.9s

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: 43.7% 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: 55.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \frac{1}{\cos \left(\frac{x}{{\left(\sqrt[3]{2 \cdot y}\right)}^{2}} \cdot \sqrt[3]{\frac{0.5}{y}}\right)} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (/ 1.0 (cos (* (/ x (pow (cbrt (* 2.0 y)) 2.0)) (cbrt (/ 0.5 y))))))

C

double code(double x, double y) {
	return 1.0 / cos(((x / pow(cbrt((2.0 * y)), 2.0)) * cbrt((0.5 / y))));
}

Java

public static double code(double x, double y) {
	return 1.0 / Math.cos(((x / Math.pow(Math.cbrt((2.0 * y)), 2.0)) * Math.cbrt((0.5 / y))));
}

Julia

function code(x, y)
	return Float64(1.0 / cos(Float64(Float64(x / (cbrt(Float64(2.0 * y)) ^ 2.0)) * cbrt(Float64(0.5 / y)))))
end

Wolfram

code[x_, y_] := N[(1.0 / N[Cos[N[(N[(x / N[Power[N[Power[N[(2.0 * y), $MachinePrecision], 1/3], $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] * N[Power[N[(0.5 / y), $MachinePrecision], 1/3], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 44.1%

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

3. Taylor expanded in x around inf 55.5%

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

   1. metadata-eval 55.5%

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

   2. times-frac 55.5%

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

   3. *-un-lft-identity 55.5%

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

   4. *-commutative 55.5%

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

   5. rem-cbrt-cube 46.1%

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

   6. unpow1/3 35.9%

      \[\leadsto \frac{1}{\cos \left(\frac{x}{\color{blue}{{\left({\left(y \cdot 2\right)}^{3}\right)}^{0.3333333333333333}}}\right)} \]

   7. add-cube-cbrt 35.9%

      \[\leadsto \frac{1}{\cos \left(\frac{x}{\color{blue}{\left(\sqrt[3]{{\left({\left(y \cdot 2\right)}^{3}\right)}^{0.3333333333333333}} \cdot \sqrt[3]{{\left({\left(y \cdot 2\right)}^{3}\right)}^{0.3333333333333333}}\right) \cdot \sqrt[3]{{\left({\left(y \cdot 2\right)}^{3}\right)}^{0.3333333333333333}}}}\right)} \]

   8. associate-/r* 36.1%

      \[\leadsto \frac{1}{\cos \color{blue}{\left(\frac{\frac{x}{\sqrt[3]{{\left({\left(y \cdot 2\right)}^{3}\right)}^{0.3333333333333333}} \cdot \sqrt[3]{{\left({\left(y \cdot 2\right)}^{3}\right)}^{0.3333333333333333}}}}{\sqrt[3]{{\left({\left(y \cdot 2\right)}^{3}\right)}^{0.3333333333333333}}}\right)}} \]

   9. pow2 36.1%

      \[\leadsto \frac{1}{\cos \left(\frac{\frac{x}{\color{blue}{{\left(\sqrt[3]{{\left({\left(y \cdot 2\right)}^{3}\right)}^{0.3333333333333333}}\right)}^{2}}}}{\sqrt[3]{{\left({\left(y \cdot 2\right)}^{3}\right)}^{0.3333333333333333}}}\right)} \]

   10. unpow1/3 35.7%

       \[\leadsto \frac{1}{\cos \left(\frac{\frac{x}{{\left(\sqrt[3]{\color{blue}{\sqrt[3]{{\left(y \cdot 2\right)}^{3}}}}\right)}^{2}}}{\sqrt[3]{{\left({\left(y \cdot 2\right)}^{3}\right)}^{0.3333333333333333}}}\right)} \]

   11. rem-cbrt-cube 35.6%

       \[\leadsto \frac{1}{\cos \left(\frac{\frac{x}{{\left(\sqrt[3]{\color{blue}{y \cdot 2}}\right)}^{2}}}{\sqrt[3]{{\left({\left(y \cdot 2\right)}^{3}\right)}^{0.3333333333333333}}}\right)} \]

   12. unpow1/3 46.4%

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

   13. rem-cbrt-cube 56.1%

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

5. Applied egg-rr 56.1%

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

   1. div-inv 56.0%

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

   2. add-sqr-sqrt 29.6%

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

   3. associate-*l* 29.9%

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

   4. sqrt-div 27.5%

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

   5. sqrt-pow1 27.5%

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

   6. metadata-eval 27.5%

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

   7. pow1 27.5%

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

   8. sqrt-div 27.7%

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

   9. sqrt-pow1 27.7%

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

   10. metadata-eval 27.7%

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

   11. pow1 27.7%

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

   12. metadata-eval 27.7%

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

   13. metadata-eval 27.7%

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

   14. div-inv 27.7%

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

   15. cbrt-div 27.4%

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

   16. clear-num 27.4%

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

7. Applied egg-rr 27.4%

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

   1. associate-*r* 27.4%

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

   2. times-frac 27.5%

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

   3. rem-square-sqrt 56.4%

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

   4. unpow2 56.4%

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

   5. *-commutative 56.4%

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

9. Simplified 56.4%

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

Alternative 2: 55.4% accurate, 211.0× speedup

Math

\[\begin{array}{l} \\ 1 \end{array} \]

FPCore

(FPCore (x y) :precision binary64 1.0)

C

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

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 1.0d0
end function

Java

public static double code(double x, double y) {
	return 1.0;
}

Python

def code(x, y):
	return 1.0

Julia

function code(x, y)
	return 1.0
end

MATLAB

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

Wolfram

code[x_, y_] := 1.0

Derivation

1. Initial program 44.1%

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

   1. remove-double-neg 44.1%

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

   2. distribute-frac-neg 44.1%

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

   3. tan-neg 44.1%

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

   4. distribute-frac-neg2 44.1%

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

   5. distribute-lft-neg-out 44.1%

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

   6. distribute-frac-neg2 44.1%

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

   7. distribute-lft-neg-out 44.1%

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

   8. distribute-frac-neg2 44.1%

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

   9. distribute-frac-neg 44.1%

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

   10. neg-mul-1 44.1%

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

   11. *-commutative 44.1%

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

   12. associate-/l* 44.0%

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

   13. *-commutative 44.0%

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

   14. associate-/r* 44.0%

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

   15. metadata-eval 44.0%

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

   16. sin-neg 44.0%

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

   17. distribute-frac-neg 44.0%

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

3. Simplified 43.6%

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

5. Taylor expanded in x around 0 56.4%

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

Alternative 3: 6.7% accurate, 211.0× speedup

Math

\[\begin{array}{l} \\ -1 \end{array} \]

FPCore

(FPCore (x y) :precision binary64 -1.0)

C

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

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = -1.0d0
end function

Java

public static double code(double x, double y) {
	return -1.0;
}

Python

def code(x, y):
	return -1.0

Julia

function code(x, y)
	return -1.0
end

MATLAB

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

Wolfram

code[x_, y_] := -1.0

Derivation

1. Initial program 44.1%

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

   1. remove-double-neg 44.1%

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

   2. distribute-frac-neg 44.1%

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

   3. tan-neg 44.1%

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

   4. distribute-frac-neg2 44.1%

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

   5. distribute-lft-neg-out 44.1%

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

   6. distribute-frac-neg2 44.1%

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

   7. distribute-lft-neg-out 44.1%

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

   8. distribute-frac-neg2 44.1%

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

   9. distribute-frac-neg 44.1%

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

   10. neg-mul-1 44.1%

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

   11. *-commutative 44.1%

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

   12. associate-/l* 44.0%

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

   13. *-commutative 44.0%

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

   14. associate-/r* 44.0%

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

   15. metadata-eval 44.0%

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

   16. sin-neg 44.0%

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

   17. distribute-frac-neg 44.0%

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

3. Simplified 43.6%

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

   1. add-sqr-sqrt 23.3%

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

   2. sqrt-unprod 15.8%

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

   3. frac-times 15.6%

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

   4. metadata-eval 15.6%

      \[\leadsto \frac{\tan \left(x \cdot \frac{-0.5}{y}\right)}{\sin \left(x \cdot \sqrt{\frac{\color{blue}{0.25}}{y \cdot y}}\right)} \]

   5. pow2 15.6%

      \[\leadsto \frac{\tan \left(x \cdot \frac{-0.5}{y}\right)}{\sin \left(x \cdot \sqrt{\frac{0.25}{\color{blue}{{y}^{2}}}}\right)} \]

6. Applied egg-rr 15.6%

   \[\leadsto \frac{\tan \left(x \cdot \frac{-0.5}{y}\right)}{\sin \left(x \cdot \color{blue}{\sqrt{\frac{0.25}{{y}^{2}}}}\right)} \]

7. Taylor expanded in x around 0 6.3%

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

Developer Target 1: 54.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{y \cdot 2}\\ t_1 := \sin t\_0\\ \mathbf{if}\;y < -1.2303690911306994 \cdot 10^{+114}:\\ \;\;\;\;1\\ \mathbf{elif}\;y < -9.102852406811914 \cdot 10^{-222}:\\ \;\;\;\;\frac{t\_1}{t\_1 \cdot \log \left(e^{\cos t\_0}\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ x (* y 2.0))) (t_1 (sin t_0)))
   (if (< y -1.2303690911306994e+114)
     1.0
     (if (< y -9.102852406811914e-222)
       (/ t_1 (* t_1 (log (exp (cos t_0)))))
       1.0))))

C

double code(double x, double y) {
	double t_0 = x / (y * 2.0);
	double t_1 = sin(t_0);
	double tmp;
	if (y < -1.2303690911306994e+114) {
		tmp = 1.0;
	} else if (y < -9.102852406811914e-222) {
		tmp = t_1 / (t_1 * log(exp(cos(t_0))));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = x / (y * 2.0d0)
    t_1 = sin(t_0)
    if (y < (-1.2303690911306994d+114)) then
        tmp = 1.0d0
    else if (y < (-9.102852406811914d-222)) then
        tmp = t_1 / (t_1 * log(exp(cos(t_0))))
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = x / (y * 2.0);
	double t_1 = Math.sin(t_0);
	double tmp;
	if (y < -1.2303690911306994e+114) {
		tmp = 1.0;
	} else if (y < -9.102852406811914e-222) {
		tmp = t_1 / (t_1 * Math.log(Math.exp(Math.cos(t_0))));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x / (y * 2.0)
	t_1 = math.sin(t_0)
	tmp = 0
	if y < -1.2303690911306994e+114:
		tmp = 1.0
	elif y < -9.102852406811914e-222:
		tmp = t_1 / (t_1 * math.log(math.exp(math.cos(t_0))))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(x / Float64(y * 2.0))
	t_1 = sin(t_0)
	tmp = 0.0
	if (y < -1.2303690911306994e+114)
		tmp = 1.0;
	elseif (y < -9.102852406811914e-222)
		tmp = Float64(t_1 / Float64(t_1 * log(exp(cos(t_0)))));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = x / (y * 2.0);
	t_1 = sin(t_0);
	tmp = 0.0;
	if (y < -1.2303690911306994e+114)
		tmp = 1.0;
	elseif (y < -9.102852406811914e-222)
		tmp = t_1 / (t_1 * log(exp(cos(t_0))));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(x / N[(y * 2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[Sin[t$95$0], $MachinePrecision]}, If[Less[y, -1.2303690911306994e+114], 1.0, If[Less[y, -9.102852406811914e-222], N[(t$95$1 / N[(t$95$1 * N[Log[N[Exp[N[Cos[t$95$0], $MachinePrecision]], $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]]]

Reproduce

herbie shell --seed 2024137 
(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)))))