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

Average Error: 35.5 → 27.8

Time: 26.6s

Precision: binary64

Cost: 27332

Math

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

↓

\[\begin{array}{l} t_0 := \frac{x}{y \cdot 2}\\ \mathbf{if}\;\frac{\tan t_0}{\sin t_0} \leq 15:\\ \;\;\;\;-1 + \left(1 - \frac{\tan \left(x \cdot \frac{0.5}{y}\right)}{\sin \left(\frac{\frac{x}{y}}{-2}\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

FPCore

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

↓

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ x (* y 2.0))))
   (if (<= (/ (tan t_0) (sin t_0)) 15.0)
     (+ -1.0 (- 1.0 (/ (tan (* x (/ 0.5 y))) (sin (/ (/ 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 = x / (y * 2.0);
	double tmp;
	if ((tan(t_0) / sin(t_0)) <= 15.0) {
		tmp = -1.0 + (1.0 - (tan((x * (0.5 / y))) / sin(((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) :: tmp
    t_0 = x / (y * 2.0d0)
    if ((tan(t_0) / sin(t_0)) <= 15.0d0) then
        tmp = (-1.0d0) + (1.0d0 - (tan((x * (0.5d0 / y))) / sin(((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 = x / (y * 2.0);
	double tmp;
	if ((Math.tan(t_0) / Math.sin(t_0)) <= 15.0) {
		tmp = -1.0 + (1.0 - (Math.tan((x * (0.5 / y))) / Math.sin(((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 = x / (y * 2.0)
	tmp = 0
	if (math.tan(t_0) / math.sin(t_0)) <= 15.0:
		tmp = -1.0 + (1.0 - (math.tan((x * (0.5 / y))) / math.sin(((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(x / Float64(y * 2.0))
	tmp = 0.0
	if (Float64(tan(t_0) / sin(t_0)) <= 15.0)
		tmp = Float64(-1.0 + Float64(1.0 - Float64(tan(Float64(x * Float64(0.5 / y))) / sin(Float64(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 = x / (y * 2.0);
	tmp = 0.0;
	if ((tan(t_0) / sin(t_0)) <= 15.0)
		tmp = -1.0 + (1.0 - (tan((x * (0.5 / y))) / sin(((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[(x / N[(y * 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[Tan[t$95$0], $MachinePrecision] / N[Sin[t$95$0], $MachinePrecision]), $MachinePrecision], 15.0], N[(-1.0 + N[(1.0 - N[(N[Tan[N[(x * N[(0.5 / y), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / N[Sin[N[(N[(x / y), $MachinePrecision] / -2.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]

Target

Original	35.5
Target	29.0
Herbie	27.8

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

Derivation

1. Split input into 2 regimes

2. if (/.f64 (tan.f64 (/.f64 x (*.f64 y 2))) (sin.f64 (/.f64 x (*.f64 y 2)))) < 15

   1. Initial program 26.4

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

   2. Applied egg-rr 26.7

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

   if 15 < (/.f64 (tan.f64 (/.f64 x (*.f64 y 2))) (sin.f64 (/.f64 x (*.f64 y 2))))

   1. Initial program 63.8

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

   2. Taylor expanded in x around 0 31.3

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

4. Final simplification 27.8

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\tan \left(\frac{x}{y \cdot 2}\right)}{\sin \left(\frac{x}{y \cdot 2}\right)} \leq 15:\\ \;\;\;\;-1 + \left(1 - \frac{\tan \left(x \cdot \frac{0.5}{y}\right)}{\sin \left(\frac{\frac{x}{y}}{-2}\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternatives

Alternative 1
Error	27.9
Cost	27076

\[\begin{array}{l} t_0 := \frac{x}{y \cdot 2}\\ \mathbf{if}\;\frac{\tan t_0}{\sin t_0} \leq 15:\\ \;\;\;\;\frac{\tan \left(x \cdot \frac{0.5}{y}\right)}{\sin \left(\frac{\frac{x}{y}}{2}\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 2
Error	28.3
Cost	7108

\[\begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{-21}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\cos \left(\frac{x}{\frac{-2}{\frac{1}{y}}}\right)}\\ \end{array} \]

Alternative 3
Error	28.3
Cost	6980

\[\begin{array}{l} \mathbf{if}\;x \leq -1.35 \cdot 10^{-20}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\cos \left(x \cdot \frac{-0.5}{y}\right)}\\ \end{array} \]

Alternative 4
Error	28.4
Cost	64

\[1 \]

Reproduce

herbie shell --seed 2023075 
(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)))))