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

Percentage Accurate: 43.8% → 56.6%

Time: 14.9s

Alternatives: 6

Speedup: 211.0×

Specification

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{y \cdot 2}\\ \frac{\tan t\_0}{\sin t\_0} \end{array} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 43.8% 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: 56.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ y_m = \left|y\right| \\ \begin{array}{l} \mathbf{if}\;\frac{x\_m}{y\_m \cdot 2} \leq 10^{+220}:\\ \;\;\;\;\frac{1}{\cos \left(0.5 \cdot \frac{\frac{x\_m}{\sqrt[3]{y\_m}}}{\sqrt{y\_m} \cdot \left(\sqrt[3]{\sqrt[3]{y\_m}} \cdot \sqrt[3]{{y\_m}^{0.16666666666666666}}\right)}\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
y_m = (fabs.f64 y)
(FPCore (x_m y_m)
 :precision binary64
 (if (<= (/ x_m (* y_m 2.0)) 1e+220)
   (/
    1.0
    (cos
     (*
      0.5
      (/
       (/ x_m (cbrt y_m))
       (*
        (sqrt y_m)
        (* (cbrt (cbrt y_m)) (cbrt (pow y_m 0.16666666666666666))))))))
   1.0))

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)) <= 1e+220) {
		tmp = 1.0 / cos((0.5 * ((x_m / cbrt(y_m)) / (sqrt(y_m) * (cbrt(cbrt(y_m)) * cbrt(pow(y_m, 0.16666666666666666)))))));
	} else {
		tmp = 1.0;
	}
	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)) <= 1e+220) {
		tmp = 1.0 / Math.cos((0.5 * ((x_m / Math.cbrt(y_m)) / (Math.sqrt(y_m) * (Math.cbrt(Math.cbrt(y_m)) * Math.cbrt(Math.pow(y_m, 0.16666666666666666)))))));
	} else {
		tmp = 1.0;
	}
	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)) <= 1e+220)
		tmp = Float64(1.0 / cos(Float64(0.5 * Float64(Float64(x_m / cbrt(y_m)) / Float64(sqrt(y_m) * Float64(cbrt(cbrt(y_m)) * cbrt((y_m ^ 0.16666666666666666))))))));
	else
		tmp = 1.0;
	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], 1e+220], N[(1.0 / N[Cos[N[(0.5 * N[(N[(x$95$m / N[Power[y$95$m, 1/3], $MachinePrecision]), $MachinePrecision] / N[(N[Sqrt[y$95$m], $MachinePrecision] * N[(N[Power[N[Power[y$95$m, 1/3], $MachinePrecision], 1/3], $MachinePrecision] * N[Power[N[Power[y$95$m, 0.16666666666666666], $MachinePrecision], 1/3], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 1.0]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (*.f64 y #s(literal 2 binary64))) < 1e220

   1. Initial program 52.2%

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

   3. Taylor expanded in x around inf 65.2%

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

      1. *-un-lft-identity 65.2%

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

      2. add-cube-cbrt 65.4%

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

      3. times-frac 65.2%

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

      4. pow2 65.2%

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

   5. Applied egg-rr 65.2%

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

      1. associate-*l/ 65.6%

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

      2. *-lft-identity 65.6%

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

   7. Simplified 65.6%

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

      1. unpow2 65.6%

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

      2. add-sqr-sqrt 30.9%

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

      3. associate-*r* 31.1%

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

      4. pow1 31.1%

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

      5. metadata-eval 31.1%

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

      6. sqrt-pow1 31.1%

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

      7. sqrt-prod 31.1%

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

      8. unpow2 31.1%

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

      9. add-cube-cbrt 31.0%

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

      10. pow1/3 30.4%

          \[\leadsto \frac{1}{\cos \left(0.5 \cdot \frac{\frac{x}{\sqrt[3]{y}}}{\sqrt{y} \cdot \sqrt{\color{blue}{{y}^{0.3333333333333333}}}}\right)} \]

      11. sqrt-pow1 30.4%

          \[\leadsto \frac{1}{\cos \left(0.5 \cdot \frac{\frac{x}{\sqrt[3]{y}}}{\sqrt{y} \cdot \color{blue}{{y}^{\left(\frac{0.3333333333333333}{2}\right)}}}\right)} \]

      12. metadata-eval 30.4%

          \[\leadsto \frac{1}{\cos \left(0.5 \cdot \frac{\frac{x}{\sqrt[3]{y}}}{\sqrt{y} \cdot {y}^{\color{blue}{0.16666666666666666}}}\right)} \]

   9. Applied egg-rr 30.4%

      \[\leadsto \frac{1}{\cos \left(0.5 \cdot \frac{\frac{x}{\sqrt[3]{y}}}{\color{blue}{\sqrt{y} \cdot {y}^{0.16666666666666666}}}\right)} \]
   10. Step-by-step derivation

       1. add-cube-cbrt 31.0%

          \[\leadsto \frac{1}{\cos \left(0.5 \cdot \frac{\frac{x}{\sqrt[3]{y}}}{\sqrt{y} \cdot \color{blue}{\left(\left(\sqrt[3]{{y}^{0.16666666666666666}} \cdot \sqrt[3]{{y}^{0.16666666666666666}}\right) \cdot \sqrt[3]{{y}^{0.16666666666666666}}\right)}}\right)} \]

       2. cbrt-unprod 30.4%

          \[\leadsto \frac{1}{\cos \left(0.5 \cdot \frac{\frac{x}{\sqrt[3]{y}}}{\sqrt{y} \cdot \left(\color{blue}{\sqrt[3]{{y}^{0.16666666666666666} \cdot {y}^{0.16666666666666666}}} \cdot \sqrt[3]{{y}^{0.16666666666666666}}\right)}\right)} \]

       3. pow-prod-up 30.4%

          \[\leadsto \frac{1}{\cos \left(0.5 \cdot \frac{\frac{x}{\sqrt[3]{y}}}{\sqrt{y} \cdot \left(\sqrt[3]{\color{blue}{{y}^{\left(0.16666666666666666 + 0.16666666666666666\right)}}} \cdot \sqrt[3]{{y}^{0.16666666666666666}}\right)}\right)} \]

       4. metadata-eval 30.4%

          \[\leadsto \frac{1}{\cos \left(0.5 \cdot \frac{\frac{x}{\sqrt[3]{y}}}{\sqrt{y} \cdot \left(\sqrt[3]{{y}^{\color{blue}{0.3333333333333333}}} \cdot \sqrt[3]{{y}^{0.16666666666666666}}\right)}\right)} \]

       5. pow1/3 31.0%

          \[\leadsto \frac{1}{\cos \left(0.5 \cdot \frac{\frac{x}{\sqrt[3]{y}}}{\sqrt{y} \cdot \left(\sqrt[3]{\color{blue}{\sqrt[3]{y}}} \cdot \sqrt[3]{{y}^{0.16666666666666666}}\right)}\right)} \]

   11. Applied egg-rr 31.0%

       \[\leadsto \frac{1}{\cos \left(0.5 \cdot \frac{\frac{x}{\sqrt[3]{y}}}{\sqrt{y} \cdot \color{blue}{\left(\sqrt[3]{\sqrt[3]{y}} \cdot \sqrt[3]{{y}^{0.16666666666666666}}\right)}}\right)} \]

   if 1e220 < (/.f64 x (*.f64 y #s(literal 2 binary64)))

   1. Initial program 4.9%

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

      1. remove-double-neg 4.9%

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

      2. distribute-frac-neg 4.9%

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

      3. tan-neg 4.9%

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

      4. distribute-frac-neg2 4.9%

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

      5. distribute-lft-neg-out 4.9%

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

      6. distribute-frac-neg2 4.9%

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

      7. distribute-lft-neg-out 4.9%

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

      8. distribute-frac-neg2 4.9%

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

      9. distribute-frac-neg 4.9%

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

      10. neg-mul-1 4.9%

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

      11. *-commutative 4.9%

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

      12. associate-/l* 4.3%

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

      13. *-commutative 4.3%

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

      14. associate-/r* 4.3%

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

      15. metadata-eval 4.3%

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

      16. sin-neg 4.3%

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

      17. distribute-frac-neg 4.3%

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

   3. Simplified 3.8%

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

   5. Taylor expanded in x around 0 16.6%

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

Alternative 2: 56.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ y_m = \left|y\right| \\ \begin{array}{l} t_0 := \sqrt[3]{x\_m \cdot -0.5}\\ \mathbf{if}\;\frac{x\_m}{y\_m \cdot 2} \leq 5 \cdot 10^{+285}:\\ \;\;\;\;\frac{1}{\cos \left({t\_0}^{2} \cdot \frac{t\_0}{y\_m}\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
y_m = (fabs.f64 y)
(FPCore (x_m y_m)
 :precision binary64
 (let* ((t_0 (cbrt (* x_m -0.5))))
   (if (<= (/ x_m (* y_m 2.0)) 5e+285)
     (/ 1.0 (cos (* (pow t_0 2.0) (/ t_0 y_m))))
     1.0)))

C

x_m = fabs(x);
y_m = fabs(y);
double code(double x_m, double y_m) {
	double t_0 = cbrt((x_m * -0.5));
	double tmp;
	if ((x_m / (y_m * 2.0)) <= 5e+285) {
		tmp = 1.0 / cos((pow(t_0, 2.0) * (t_0 / y_m)));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Java

x_m = Math.abs(x);
y_m = Math.abs(y);
public static double code(double x_m, double y_m) {
	double t_0 = Math.cbrt((x_m * -0.5));
	double tmp;
	if ((x_m / (y_m * 2.0)) <= 5e+285) {
		tmp = 1.0 / Math.cos((Math.pow(t_0, 2.0) * (t_0 / y_m)));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Julia

x_m = abs(x)
y_m = abs(y)
function code(x_m, y_m)
	t_0 = cbrt(Float64(x_m * -0.5))
	tmp = 0.0
	if (Float64(x_m / Float64(y_m * 2.0)) <= 5e+285)
		tmp = Float64(1.0 / cos(Float64((t_0 ^ 2.0) * Float64(t_0 / y_m))));
	else
		tmp = 1.0;
	end
	return 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[Power[N[(x$95$m * -0.5), $MachinePrecision], 1/3], $MachinePrecision]}, If[LessEqual[N[(x$95$m / N[(y$95$m * 2.0), $MachinePrecision]), $MachinePrecision], 5e+285], N[(1.0 / N[Cos[N[(N[Power[t$95$0, 2.0], $MachinePrecision] * N[(t$95$0 / y$95$m), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (*.f64 y #s(literal 2 binary64))) < 5.00000000000000016e285

   1. Initial program 50.3%

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

   3. Taylor expanded in x around inf 62.8%

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

      1. clear-num 62.7%

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

      2. un-div-inv 62.7%

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

   5. Applied egg-rr 62.7%

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

      1. associate-/r/ 62.5%

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

      2. *-commutative 62.5%

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

      3. add-sqr-sqrt 29.3%

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

      4. sqrt-unprod 56.6%

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

      5. frac-times 56.8%

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

      6. metadata-eval 56.8%

         \[\leadsto \frac{1}{\cos \left(x \cdot \sqrt{\frac{\color{blue}{0.25}}{y \cdot y}}\right)} \]

      7. metadata-eval 56.8%

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

      8. frac-times 56.6%

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

      9. sqrt-unprod 32.8%

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

      10. add-sqr-sqrt 62.5%

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

      11. associate-*r/ 62.8%

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

      12. *-un-lft-identity 62.8%

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

      13. add-cube-cbrt 63.1%

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

      14. times-frac 63.3%

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

      15. pow2 63.4%

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

   7. Applied egg-rr 63.4%

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

   if 5.00000000000000016e285 < (/.f64 x (*.f64 y #s(literal 2 binary64)))

   1. Initial program 0.7%

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

      1. remove-double-neg 0.7%

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

      2. distribute-frac-neg 0.7%

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

      3. tan-neg 0.7%

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

      4. distribute-frac-neg2 0.7%

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

      5. distribute-lft-neg-out 0.7%

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

      6. distribute-frac-neg2 0.7%

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

      7. distribute-lft-neg-out 0.7%

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

      8. distribute-frac-neg2 0.7%

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

      9. distribute-frac-neg 0.7%

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

      10. neg-mul-1 0.7%

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

      11. *-commutative 0.7%

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

      12. associate-/l* 0.7%

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

      13. *-commutative 0.7%

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

      14. associate-/r* 0.7%

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

      15. metadata-eval 0.7%

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

      16. sin-neg 0.7%

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

      17. distribute-frac-neg 0.7%

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

   3. Simplified 0.7%

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

   5. Taylor expanded in x around 0 18.0%

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

4. Final simplification 59.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y \cdot 2} \leq 5 \cdot 10^{+285}:\\ \;\;\;\;\frac{1}{\cos \left({\left(\sqrt[3]{x \cdot -0.5}\right)}^{2} \cdot \frac{\sqrt[3]{x \cdot -0.5}}{y}\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 56.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ y_m = \left|y\right| \\ \begin{array}{l} \mathbf{if}\;\frac{x\_m}{y\_m \cdot 2} \leq 10^{+285}:\\ \;\;\;\;\frac{1}{\cos \left(x\_m \cdot e^{\left(3 \cdot \log \left(\frac{0.5}{y\_m}\right)\right) \cdot 0.3333333333333333}\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
y_m = (fabs.f64 y)
(FPCore (x_m y_m)
 :precision binary64
 (if (<= (/ x_m (* y_m 2.0)) 1e+285)
   (/ 1.0 (cos (* x_m (exp (* (* 3.0 (log (/ 0.5 y_m))) 0.3333333333333333)))))
   1.0))

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)) <= 1e+285) {
		tmp = 1.0 / cos((x_m * exp(((3.0 * log((0.5 / y_m))) * 0.3333333333333333))));
	} 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) :: tmp
    if ((x_m / (y_m * 2.0d0)) <= 1d+285) then
        tmp = 1.0d0 / cos((x_m * exp(((3.0d0 * log((0.5d0 / y_m))) * 0.3333333333333333d0))))
    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 tmp;
	if ((x_m / (y_m * 2.0)) <= 1e+285) {
		tmp = 1.0 / Math.cos((x_m * Math.exp(((3.0 * Math.log((0.5 / y_m))) * 0.3333333333333333))));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

x_m = math.fabs(x)
y_m = math.fabs(y)
def code(x_m, y_m):
	tmp = 0
	if (x_m / (y_m * 2.0)) <= 1e+285:
		tmp = 1.0 / math.cos((x_m * math.exp(((3.0 * math.log((0.5 / y_m))) * 0.3333333333333333))))
	else:
		tmp = 1.0
	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)) <= 1e+285)
		tmp = Float64(1.0 / cos(Float64(x_m * exp(Float64(Float64(3.0 * log(Float64(0.5 / y_m))) * 0.3333333333333333)))));
	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)
	tmp = 0.0;
	if ((x_m / (y_m * 2.0)) <= 1e+285)
		tmp = 1.0 / cos((x_m * exp(((3.0 * log((0.5 / y_m))) * 0.3333333333333333))));
	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_] := If[LessEqual[N[(x$95$m / N[(y$95$m * 2.0), $MachinePrecision]), $MachinePrecision], 1e+285], N[(1.0 / N[Cos[N[(x$95$m * N[Exp[N[(N[(3.0 * N[Log[N[(0.5 / y$95$m), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * 0.3333333333333333), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 1.0]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (*.f64 y #s(literal 2 binary64))) < 9.9999999999999998e284

   1. Initial program 50.6%

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

   3. Taylor expanded in x around inf 63.0%

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

      1. *-un-lft-identity 63.0%

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

      2. metadata-eval 63.0%

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

      3. times-frac 63.0%

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

      4. *-un-lft-identity 63.0%

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

      5. *-commutative 63.0%

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

      6. div-inv 62.7%

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

      7. metadata-eval 62.7%

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

      8. div-inv 62.7%

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

      9. clear-num 62.7%

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

   5. Applied egg-rr 62.7%

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

      1. *-lft-identity 62.7%

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

   7. Simplified 62.7%

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

      1. add-cbrt-cube 55.1%

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

      2. pow3 55.3%

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

   9. Applied egg-rr 55.3%

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

       1. pow1/3 43.3%

          \[\leadsto \frac{1}{\cos \left(x \cdot \color{blue}{{\left({\left(\frac{0.5}{y}\right)}^{3}\right)}^{0.3333333333333333}}\right)} \]

       2. pow-to-exp 43.3%

          \[\leadsto \frac{1}{\cos \left(x \cdot \color{blue}{e^{\log \left({\left(\frac{0.5}{y}\right)}^{3}\right) \cdot 0.3333333333333333}}\right)} \]

       3. log-pow 29.8%

          \[\leadsto \frac{1}{\cos \left(x \cdot e^{\color{blue}{\left(3 \cdot \log \left(\frac{0.5}{y}\right)\right)} \cdot 0.3333333333333333}\right)} \]

   11. Applied egg-rr 29.8%

       \[\leadsto \frac{1}{\cos \left(x \cdot \color{blue}{e^{\left(3 \cdot \log \left(\frac{0.5}{y}\right)\right) \cdot 0.3333333333333333}}\right)} \]

   if 9.9999999999999998e284 < (/.f64 x (*.f64 y #s(literal 2 binary64)))

   1. Initial program 0.8%

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

      1. remove-double-neg 0.8%

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

      2. distribute-frac-neg 0.8%

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

      3. tan-neg 0.8%

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

      4. distribute-frac-neg2 0.8%

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

      5. distribute-lft-neg-out 0.8%

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

      6. distribute-frac-neg2 0.8%

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

      7. distribute-lft-neg-out 0.8%

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

      8. distribute-frac-neg2 0.8%

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

      9. distribute-frac-neg 0.8%

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

      10. neg-mul-1 0.8%

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

      11. *-commutative 0.8%

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

      12. associate-/l* 0.8%

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

      13. *-commutative 0.8%

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

      14. associate-/r* 0.8%

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

      15. metadata-eval 0.8%

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

      16. sin-neg 0.8%

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

      17. distribute-frac-neg 0.8%

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

   3. Simplified 0.8%

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

   5. Taylor expanded in x around 0 17.3%

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

Alternative 4: 56.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ y_m = \left|y\right| \\ \begin{array}{l} \mathbf{if}\;\frac{x\_m}{y\_m \cdot 2} \leq 5 \cdot 10^{+285}:\\ \;\;\;\;\frac{1}{\cos \left(x\_m \cdot e^{\log \left(\frac{0.5}{y\_m}\right)}\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
y_m = (fabs.f64 y)
(FPCore (x_m y_m)
 :precision binary64
 (if (<= (/ x_m (* y_m 2.0)) 5e+285)
   (/ 1.0 (cos (* x_m (exp (log (/ 0.5 y_m))))))
   1.0))

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)) <= 5e+285) {
		tmp = 1.0 / cos((x_m * exp(log((0.5 / y_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) :: tmp
    if ((x_m / (y_m * 2.0d0)) <= 5d+285) then
        tmp = 1.0d0 / cos((x_m * exp(log((0.5d0 / y_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 tmp;
	if ((x_m / (y_m * 2.0)) <= 5e+285) {
		tmp = 1.0 / Math.cos((x_m * Math.exp(Math.log((0.5 / y_m)))));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

x_m = math.fabs(x)
y_m = math.fabs(y)
def code(x_m, y_m):
	tmp = 0
	if (x_m / (y_m * 2.0)) <= 5e+285:
		tmp = 1.0 / math.cos((x_m * math.exp(math.log((0.5 / y_m)))))
	else:
		tmp = 1.0
	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)) <= 5e+285)
		tmp = Float64(1.0 / cos(Float64(x_m * exp(log(Float64(0.5 / y_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)
	tmp = 0.0;
	if ((x_m / (y_m * 2.0)) <= 5e+285)
		tmp = 1.0 / cos((x_m * exp(log((0.5 / y_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_] := If[LessEqual[N[(x$95$m / N[(y$95$m * 2.0), $MachinePrecision]), $MachinePrecision], 5e+285], N[(1.0 / N[Cos[N[(x$95$m * N[Exp[N[Log[N[(0.5 / y$95$m), $MachinePrecision]], $MachinePrecision]], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 1.0]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (*.f64 y #s(literal 2 binary64))) < 5.00000000000000016e285

   1. Initial program 50.3%

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

   3. Taylor expanded in x around inf 62.8%

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

      1. *-un-lft-identity 62.8%

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

      2. metadata-eval 62.8%

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

      3. times-frac 62.8%

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

      4. *-un-lft-identity 62.8%

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

      5. *-commutative 62.8%

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

      6. div-inv 62.5%

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

      7. metadata-eval 62.5%

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

      8. div-inv 62.5%

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

      9. clear-num 62.5%

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

   5. Applied egg-rr 62.5%

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

      1. *-lft-identity 62.5%

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

   7. Simplified 62.5%

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

      1. add-exp-log 29.6%

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

   9. Applied egg-rr 29.6%

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

   if 5.00000000000000016e285 < (/.f64 x (*.f64 y #s(literal 2 binary64)))

   1. Initial program 0.7%

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

      1. remove-double-neg 0.7%

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

      2. distribute-frac-neg 0.7%

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

      3. tan-neg 0.7%

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

      4. distribute-frac-neg2 0.7%

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

      5. distribute-lft-neg-out 0.7%

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

      6. distribute-frac-neg2 0.7%

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

      7. distribute-lft-neg-out 0.7%

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

      8. distribute-frac-neg2 0.7%

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

      9. distribute-frac-neg 0.7%

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

      10. neg-mul-1 0.7%

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

      11. *-commutative 0.7%

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

      12. associate-/l* 0.7%

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

      13. *-commutative 0.7%

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

      14. associate-/r* 0.7%

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

      15. metadata-eval 0.7%

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

      16. sin-neg 0.7%

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

      17. distribute-frac-neg 0.7%

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

   3. Simplified 0.7%

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

   5. Taylor expanded in x around 0 18.0%

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

Alternative 5: 56.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ y_m = \left|y\right| \\ \begin{array}{l} \mathbf{if}\;\frac{x\_m}{y\_m \cdot 2} \leq 2 \cdot 10^{+214}:\\ \;\;\;\;\frac{1}{\cos \left(\frac{x\_m \cdot \sqrt[3]{-0.125}}{-y\_m}\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
y_m = (fabs.f64 y)
(FPCore (x_m y_m)
 :precision binary64
 (if (<= (/ x_m (* y_m 2.0)) 2e+214)
   (/ 1.0 (cos (/ (* x_m (cbrt -0.125)) (- y_m))))
   1.0))

C

x_m = fabs(x);
y_m = fabs(y);
double code(double x_m, double y_m) {
	double tmp;
	if ((x_m / (y_m * 2.0)) <= 2e+214) {
		tmp = 1.0 / cos(((x_m * cbrt(-0.125)) / -y_m));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Java

x_m = Math.abs(x);
y_m = Math.abs(y);
public static double code(double x_m, double y_m) {
	double tmp;
	if ((x_m / (y_m * 2.0)) <= 2e+214) {
		tmp = 1.0 / Math.cos(((x_m * Math.cbrt(-0.125)) / -y_m));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Julia

x_m = abs(x)
y_m = abs(y)
function code(x_m, y_m)
	tmp = 0.0
	if (Float64(x_m / Float64(y_m * 2.0)) <= 2e+214)
		tmp = Float64(1.0 / cos(Float64(Float64(x_m * cbrt(-0.125)) / Float64(-y_m))));
	else
		tmp = 1.0;
	end
	return tmp
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
y_m = N[Abs[y], $MachinePrecision]
code[x$95$m_, y$95$m_] := If[LessEqual[N[(x$95$m / N[(y$95$m * 2.0), $MachinePrecision]), $MachinePrecision], 2e+214], N[(1.0 / N[Cos[N[(N[(x$95$m * N[Power[-0.125, 1/3], $MachinePrecision]), $MachinePrecision] / (-y$95$m)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 1.0]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (*.f64 y #s(literal 2 binary64))) < 1.9999999999999999e214

   1. Initial program 52.4%

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

   3. Taylor expanded in x around inf 65.5%

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

      1. *-un-lft-identity 65.5%

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

      2. metadata-eval 65.5%

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

      3. times-frac 65.5%

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

      4. *-un-lft-identity 65.5%

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

      5. *-commutative 65.5%

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

      6. div-inv 65.4%

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

      7. metadata-eval 65.4%

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

      8. div-inv 65.4%

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

      9. clear-num 65.4%

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

   5. Applied egg-rr 65.4%

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

      1. *-lft-identity 65.4%

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

   7. Simplified 65.4%

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

      1. add-cbrt-cube 57.6%

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

      2. pow3 57.8%

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

   9. Applied egg-rr 57.8%

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

   10. Taylor expanded in y around -inf 65.5%

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

   if 1.9999999999999999e214 < (/.f64 x (*.f64 y #s(literal 2 binary64)))

   1. Initial program 4.8%

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

      1. remove-double-neg 4.8%

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

      2. distribute-frac-neg 4.8%

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

      3. tan-neg 4.8%

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

      4. distribute-frac-neg2 4.8%

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

      5. distribute-lft-neg-out 4.8%

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

      6. distribute-frac-neg2 4.8%

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

      7. distribute-lft-neg-out 4.8%

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

      8. distribute-frac-neg2 4.8%

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

      9. distribute-frac-neg 4.8%

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

      10. neg-mul-1 4.8%

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

      11. *-commutative 4.8%

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

      12. associate-/l* 4.2%

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

      13. *-commutative 4.2%

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

      14. associate-/r* 4.2%

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

      15. metadata-eval 4.2%

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

      16. sin-neg 4.2%

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

      17. distribute-frac-neg 4.2%

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

   3. Simplified 3.8%

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

   5. Taylor expanded in x around 0 16.7%

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

4. Final simplification 59.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y \cdot 2} \leq 2 \cdot 10^{+214}:\\ \;\;\;\;\frac{1}{\cos \left(\frac{x \cdot \sqrt[3]{-0.125}}{-y}\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 55.2% 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 46.1%

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

   1. remove-double-neg 46.1%

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

   2. distribute-frac-neg 46.1%

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

   3. tan-neg 46.1%

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

   4. distribute-frac-neg2 46.1%

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

   5. distribute-lft-neg-out 46.1%

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

   6. distribute-frac-neg2 46.1%

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

   7. distribute-lft-neg-out 46.1%

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

   8. distribute-frac-neg2 46.1%

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

   9. distribute-frac-neg 46.1%

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

   10. neg-mul-1 46.1%

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

   11. *-commutative 46.1%

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

   12. associate-/l* 45.6%

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

   13. *-commutative 45.6%

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

   14. associate-/r* 45.6%

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

   15. metadata-eval 45.6%

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

   16. sin-neg 45.6%

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

   17. distribute-frac-neg 45.6%

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

3. Simplified 45.8%

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

5. Taylor expanded in x around 0 58.2%

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

Developer Target 1: 55.2% 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 2024157 
(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)))))