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

Percentage Accurate: 44.7% → 57.3%

Time: 16.9s

Alternatives: 2

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: 44.7% 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: 57.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ y_m = \left|y\right| \\ \begin{array}{l} \mathbf{if}\;\frac{x\_m}{y\_m \cdot 2} \leq 4 \cdot 10^{+89}:\\ \;\;\;\;\frac{1}{\cos \left({e}^{\log \left(x\_m \cdot \frac{0.5}{y\_m}\right)}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{-0.5}{\sqrt[3]{-0.125}}\\ \end{array} \end{array} \]

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)) 4e+89)
   (/ 1.0 (cos (pow E (log (* x_m (/ 0.5 y_m))))))
   (/ -0.5 (cbrt -0.125))))

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)) <= 4e+89) {
		tmp = 1.0 / cos(pow(((double) M_E), log((x_m * (0.5 / y_m)))));
	} else {
		tmp = -0.5 / cbrt(-0.125);
	}
	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)) <= 4e+89) {
		tmp = 1.0 / Math.cos(Math.pow(Math.E, Math.log((x_m * (0.5 / y_m)))));
	} else {
		tmp = -0.5 / Math.cbrt(-0.125);
	}
	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)) <= 4e+89)
		tmp = Float64(1.0 / cos((exp(1) ^ log(Float64(x_m * Float64(0.5 / y_m))))));
	else
		tmp = Float64(-0.5 / cbrt(-0.125));
	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], 4e+89], N[(1.0 / N[Cos[N[Power[E, N[Log[N[(x$95$m * N[(0.5 / y$95$m), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]], $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(-0.5 / N[Power[-0.125, 1/3], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (*.f64 y #s(literal 2 binary64))) < 3.99999999999999998e89

   1. Initial program 46.4%

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

      1. expm1-log1p-u 46.4%

         \[\leadsto \frac{\tan \left(\frac{x}{y \cdot 2}\right)}{\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\sin \left(\frac{x}{y \cdot 2}\right)\right)\right)}} \]

      2. expm1-undefine 5.5%

         \[\leadsto \frac{\tan \left(\frac{x}{y \cdot 2}\right)}{\color{blue}{e^{\mathsf{log1p}\left(\sin \left(\frac{x}{y \cdot 2}\right)\right)} - 1}} \]

      3. *-un-lft-identity 5.5%

         \[\leadsto \frac{\tan \left(\frac{x}{y \cdot 2}\right)}{e^{\mathsf{log1p}\left(\sin \left(\frac{\color{blue}{1 \cdot x}}{y \cdot 2}\right)\right)} - 1} \]

      4. *-commutative 5.5%

         \[\leadsto \frac{\tan \left(\frac{x}{y \cdot 2}\right)}{e^{\mathsf{log1p}\left(\sin \left(\frac{1 \cdot x}{\color{blue}{2 \cdot y}}\right)\right)} - 1} \]

      5. times-frac 5.5%

         \[\leadsto \frac{\tan \left(\frac{x}{y \cdot 2}\right)}{e^{\mathsf{log1p}\left(\sin \color{blue}{\left(\frac{1}{2} \cdot \frac{x}{y}\right)}\right)} - 1} \]

      6. metadata-eval 5.5%

         \[\leadsto \frac{\tan \left(\frac{x}{y \cdot 2}\right)}{e^{\mathsf{log1p}\left(\sin \left(\color{blue}{0.5} \cdot \frac{x}{y}\right)\right)} - 1} \]

   4. Applied egg-rr 5.5%

      \[\leadsto \frac{\tan \left(\frac{x}{y \cdot 2}\right)}{\color{blue}{e^{\mathsf{log1p}\left(\sin \left(0.5 \cdot \frac{x}{y}\right)\right)} - 1}} \]
   5. Step-by-step derivation

      1. expm1-define 46.2%

         \[\leadsto \frac{\tan \left(\frac{x}{y \cdot 2}\right)}{\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\sin \left(0.5 \cdot \frac{x}{y}\right)\right)\right)}} \]

      2. *-commutative 46.2%

         \[\leadsto \frac{\tan \left(\frac{x}{y \cdot 2}\right)}{\mathsf{expm1}\left(\mathsf{log1p}\left(\sin \color{blue}{\left(\frac{x}{y} \cdot 0.5\right)}\right)\right)} \]

      3. associate-*l/ 46.4%

         \[\leadsto \frac{\tan \left(\frac{x}{y \cdot 2}\right)}{\mathsf{expm1}\left(\mathsf{log1p}\left(\sin \color{blue}{\left(\frac{x \cdot 0.5}{y}\right)}\right)\right)} \]

      4. associate-*r/ 46.0%

         \[\leadsto \frac{\tan \left(\frac{x}{y \cdot 2}\right)}{\mathsf{expm1}\left(\mathsf{log1p}\left(\sin \color{blue}{\left(x \cdot \frac{0.5}{y}\right)}\right)\right)} \]

   6. Simplified 46.0%

      \[\leadsto \frac{\tan \left(\frac{x}{y \cdot 2}\right)}{\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\sin \left(x \cdot \frac{0.5}{y}\right)\right)\right)}} \]

   7. Taylor expanded in x around inf 64.8%

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

      1. associate-*r/ 64.8%

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

      2. *-commutative 64.8%

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

      3. associate-*r/ 64.8%

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

   9. Simplified 64.8%

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

       1. frac-2neg 64.8%

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

       2. metadata-eval 64.8%

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

       3. distribute-frac-neg2 64.8%

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

       4. distribute-rgt-neg-in 64.8%

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

       5. add-exp-log 39.1%

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

       6. distribute-rgt-neg-in 39.1%

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

       7. distribute-frac-neg2 39.1%

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

       8. metadata-eval 39.1%

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

       9. frac-2neg 39.1%

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

       10. clear-num 39.1%

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

       11. un-div-inv 39.1%

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

       12. div-inv 39.1%

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

       13. metadata-eval 39.1%

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

   11. Applied egg-rr 39.1%

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

       1. *-un-lft-identity 39.1%

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

       2. exp-prod 39.2%

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

       3. div-inv 39.2%

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

       4. *-commutative 39.2%

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

       5. associate-/r* 39.2%

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

       6. metadata-eval 39.2%

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

   13. Applied egg-rr 39.2%

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

       1. exp-1-e 39.2%

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

   15. Simplified 39.2%

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

   if 3.99999999999999998e89 < (/.f64 x (*.f64 y #s(literal 2 binary64)))

   1. Initial program 8.4%

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

      1. remove-double-neg 8.4%

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

      2. distribute-frac-neg 8.4%

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

      3. tan-neg 8.4%

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

      4. distribute-frac-neg2 8.4%

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

      5. distribute-lft-neg-out 8.4%

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

      6. distribute-frac-neg2 8.4%

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

      7. distribute-lft-neg-out 8.4%

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

      8. distribute-frac-neg2 8.4%

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

      9. distribute-frac-neg 8.4%

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

      10. neg-mul-1 8.4%

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

      11. *-commutative 8.4%

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

      12. associate-/l* 7.6%

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

      13. *-commutative 7.6%

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

      14. associate-/r* 7.6%

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

      15. metadata-eval 7.6%

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

      16. sin-neg 7.6%

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

      17. distribute-frac-neg 7.6%

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

   3. Simplified 7.7%

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

      1. add-cbrt-cube 0.3%

         \[\leadsto \frac{\tan \left(x \cdot \frac{-0.5}{y}\right)}{\sin \color{blue}{\left(\sqrt[3]{\left(\left(x \cdot \frac{-0.5}{y}\right) \cdot \left(x \cdot \frac{-0.5}{y}\right)\right) \cdot \left(x \cdot \frac{-0.5}{y}\right)}\right)}} \]

      2. pow3 0.3%

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

   6. Applied egg-rr 0.3%

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

   7. Taylor expanded in x around 0 14.3%

      \[\leadsto \color{blue}{\frac{-0.5}{\sqrt[3]{-0.125}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 33.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y \cdot 2} \leq 4 \cdot 10^{+89}:\\ \;\;\;\;\frac{1}{\cos \left({e}^{\log \left(x \cdot \frac{0.5}{y}\right)}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{-0.5}{\sqrt[3]{-0.125}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 55.9% 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 38.0%

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

   1. remove-double-neg 38.0%

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

   2. distribute-frac-neg 38.0%

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

   3. tan-neg 38.0%

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

   4. distribute-frac-neg2 38.0%

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

   5. distribute-lft-neg-out 38.0%

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

   6. distribute-frac-neg2 38.0%

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

   7. distribute-lft-neg-out 38.0%

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

   8. distribute-frac-neg2 38.0%

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

   9. distribute-frac-neg 38.0%

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

   10. neg-mul-1 38.0%

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

   11. *-commutative 38.0%

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

   12. associate-/l* 37.9%

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

   13. *-commutative 37.9%

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

   14. associate-/r* 37.9%

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

   15. metadata-eval 37.9%

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

   16. sin-neg 37.9%

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

   17. distribute-frac-neg 37.9%

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

3. Simplified 37.8%

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

5. Taylor expanded in x around 0 53.6%

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

6. Final simplification 53.6%

   \[\leadsto 1 \]
7. Add Preprocessing

Developer target: 55.9% 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 2024079 
(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)))))