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

Average Error: 35.7 → 27.7

Time: 32.5s

Precision: binary64

Cost: 41412

Math

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

↓

\[\begin{array}{l} t_0 := \frac{1}{\cos \left(\frac{x}{y} \cdot -0.5\right)}\\ t_1 := \frac{x}{y \cdot 2}\\ \mathbf{if}\;\frac{\tan t_1}{\sin t_1} \leq 1.44:\\ \;\;\;\;\frac{1}{\left(t_0 \cdot t_0\right) \cdot \left(\frac{1}{t_0} \cdot \frac{1 + \cos \left(\frac{x}{y}\right)}{2}\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

FPCore

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

↓

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ 1.0 (cos (* (/ x y) -0.5)))) (t_1 (/ x (* y 2.0))))
   (if (<= (/ (tan t_1) (sin t_1)) 1.44)
     (/ 1.0 (* (* t_0 t_0) (* (/ 1.0 t_0) (/ (+ 1.0 (cos (/ x y))) 2.0))))
     1.0)))

C

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

↓

double code(double x, double y) {
	double t_0 = 1.0 / cos(((x / y) * -0.5));
	double t_1 = x / (y * 2.0);
	double tmp;
	if ((tan(t_1) / sin(t_1)) <= 1.44) {
		tmp = 1.0 / ((t_0 * t_0) * ((1.0 / t_0) * ((1.0 + cos((x / y))) / 2.0)));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

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

↓

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 = 1.0d0 / cos(((x / y) * (-0.5d0)))
    t_1 = x / (y * 2.0d0)
    if ((tan(t_1) / sin(t_1)) <= 1.44d0) then
        tmp = 1.0d0 / ((t_0 * t_0) * ((1.0d0 / t_0) * ((1.0d0 + cos((x / y))) / 2.0d0)))
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

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

↓

public static double code(double x, double y) {
	double t_0 = 1.0 / Math.cos(((x / y) * -0.5));
	double t_1 = x / (y * 2.0);
	double tmp;
	if ((Math.tan(t_1) / Math.sin(t_1)) <= 1.44) {
		tmp = 1.0 / ((t_0 * t_0) * ((1.0 / t_0) * ((1.0 + Math.cos((x / y))) / 2.0)));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

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

↓

def code(x, y):
	t_0 = 1.0 / math.cos(((x / y) * -0.5))
	t_1 = x / (y * 2.0)
	tmp = 0
	if (math.tan(t_1) / math.sin(t_1)) <= 1.44:
		tmp = 1.0 / ((t_0 * t_0) * ((1.0 / t_0) * ((1.0 + math.cos((x / y))) / 2.0)))
	else:
		tmp = 1.0
	return tmp

Julia

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

↓

function code(x, y)
	t_0 = Float64(1.0 / cos(Float64(Float64(x / y) * -0.5)))
	t_1 = Float64(x / Float64(y * 2.0))
	tmp = 0.0
	if (Float64(tan(t_1) / sin(t_1)) <= 1.44)
		tmp = Float64(1.0 / Float64(Float64(t_0 * t_0) * Float64(Float64(1.0 / t_0) * Float64(Float64(1.0 + cos(Float64(x / y))) / 2.0))));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

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

↓

function tmp_2 = code(x, y)
	t_0 = 1.0 / cos(((x / y) * -0.5));
	t_1 = x / (y * 2.0);
	tmp = 0.0;
	if ((tan(t_1) / sin(t_1)) <= 1.44)
		tmp = 1.0 / ((t_0 * t_0) * ((1.0 / t_0) * ((1.0 + cos((x / y))) / 2.0)));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := N[(N[Tan[N[(x / N[(y * 2.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / N[Sin[N[(x / N[(y * 2.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_] := Block[{t$95$0 = N[(1.0 / N[Cos[N[(N[(x / y), $MachinePrecision] * -0.5), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x / N[(y * 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[Tan[t$95$1], $MachinePrecision] / N[Sin[t$95$1], $MachinePrecision]), $MachinePrecision], 1.44], N[(1.0 / N[(N[(t$95$0 * t$95$0), $MachinePrecision] * N[(N[(1.0 / t$95$0), $MachinePrecision] * N[(N[(1.0 + N[Cos[N[(x / y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]]

Target

Original	35.7
Target	28.9
Herbie	27.7

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

Derivation

1. Split input into 2 regimes

2. if (/.f64 (tan.f64 (/.f64 x (*.f64 y 2))) (sin.f64 (/.f64 x (*.f64 y 2)))) < 1.4399999999999999

   1. Initial program 23.0

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

   2. Taylor expanded in x around inf 23.0

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

   3. Applied egg-rr 23.0

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

   if 1.4399999999999999 < (/.f64 (tan.f64 (/.f64 x (*.f64 y 2))) (sin.f64 (/.f64 x (*.f64 y 2))))

   1. Initial program 61.4

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

   2. Taylor expanded in x around 0 37.2

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

4. Final simplification 27.7

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\tan \left(\frac{x}{y \cdot 2}\right)}{\sin \left(\frac{x}{y \cdot 2}\right)} \leq 1.44:\\ \;\;\;\;\frac{1}{\left(\frac{1}{\cos \left(\frac{x}{y} \cdot -0.5\right)} \cdot \frac{1}{\cos \left(\frac{x}{y} \cdot -0.5\right)}\right) \cdot \left(\frac{1}{\frac{1}{\cos \left(\frac{x}{y} \cdot -0.5\right)}} \cdot \frac{1 + \cos \left(\frac{x}{y}\right)}{2}\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternatives

Alternative 1
Error	27.7
Cost	27076

\[\begin{array}{l} t_0 := \frac{x}{y \cdot 2}\\ t_1 := \frac{\tan t_0}{\sin t_0}\\ \mathbf{if}\;t_1 \leq 1.44:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 2
Error	28.5
Cost	64

\[1 \]

Reproduce

herbie shell --seed 2023077 
(FPCore (x y)
  :name "Diagrams.TwoD.Layout.CirclePacking:approxRadius from diagrams-contrib-1.3.0.5"
  :precision binary64

  :herbie-target
  (if (< y -1.2303690911306994e+114) 1.0 (if (< y -9.102852406811914e-222) (/ (sin (/ x (* y 2.0))) (* (sin (/ x (* y 2.0))) (log (exp (cos (/ x (* y 2.0))))))) 1.0))

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