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

Average Error: 36.0 → 28.5

Time: 16.4s

Precision: binary64

Cost: 40576

Math

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

↓

\[\begin{array}{l} t_0 := \cos \left(0.5 \cdot \frac{x}{y}\right)\\ \frac{1}{\left|\left(-t_0\right) \cdot \left(t_0 \cdot \frac{\frac{1}{t_0}}{t_0}\right)\right| \cdot t_0} \end{array} \]

FPCore

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

↓

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (cos (* 0.5 (/ x y)))))
   (/ 1.0 (* (fabs (* (- t_0) (* t_0 (/ (/ 1.0 t_0) t_0)))) t_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 = cos((0.5 * (x / y)));
	return 1.0 / (fabs((-t_0 * (t_0 * ((1.0 / t_0) / t_0)))) * t_0);
}

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
    t_0 = cos((0.5d0 * (x / y)))
    code = 1.0d0 / (abs((-t_0 * (t_0 * ((1.0d0 / t_0) / t_0)))) * t_0)
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 = Math.cos((0.5 * (x / y)));
	return 1.0 / (Math.abs((-t_0 * (t_0 * ((1.0 / t_0) / t_0)))) * t_0);
}

Python

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

↓

def code(x, y):
	t_0 = math.cos((0.5 * (x / y)))
	return 1.0 / (math.fabs((-t_0 * (t_0 * ((1.0 / t_0) / t_0)))) * t_0)

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 = cos(Float64(0.5 * Float64(x / y)))
	return Float64(1.0 / Float64(abs(Float64(Float64(-t_0) * Float64(t_0 * Float64(Float64(1.0 / t_0) / t_0)))) * t_0))
end

MATLAB

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

↓

function tmp = code(x, y)
	t_0 = cos((0.5 * (x / y)));
	tmp = 1.0 / (abs((-t_0 * (t_0 * ((1.0 / t_0) / t_0)))) * t_0);
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[Cos[N[(0.5 * N[(x / y), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]}, N[(1.0 / N[(N[Abs[N[((-t$95$0) * N[(t$95$0 * N[(N[(1.0 / t$95$0), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * t$95$0), $MachinePrecision]), $MachinePrecision]]

Target

Original	36.0
Target	28.9
Herbie	28.5

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

Derivation

1. Initial program 36.0

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

2. Simplified 36.0

   \[\leadsto \color{blue}{\frac{\tan \left(\frac{x}{y + y}\right)}{\sin \left(\frac{x}{y + y}\right)}} \]
   Proof

   [Start] 36.0	\[ \frac{\tan \left(\frac{x}{y \cdot 2}\right)}{\sin \left(\frac{x}{y \cdot 2}\right)} \]
   metadata-eval [<=] 36.0	\[ \frac{\tan \left(\frac{x}{y \cdot \color{blue}{\left(1 + 1\right)}}\right)}{\sin \left(\frac{x}{y \cdot 2}\right)} \]
   metadata-eval [<=] 36.0	\[ \frac{\tan \left(\frac{x}{y \cdot \left(\color{blue}{\frac{2}{2}} + 1\right)}\right)}{\sin \left(\frac{x}{y \cdot 2}\right)} \]
   metadata-eval [<=] 36.0	\[ \frac{\tan \left(\frac{x}{y \cdot \left(\frac{2}{2} + \color{blue}{\frac{2}{2}}\right)}\right)}{\sin \left(\frac{x}{y \cdot 2}\right)} \]
   rational_best_oopsla_all_46_json_45_simplify-23 [<=] 36.0	\[ \frac{\tan \left(\frac{x}{\color{blue}{\frac{2}{2} \cdot y + y \cdot \frac{2}{2}}}\right)}{\sin \left(\frac{x}{y \cdot 2}\right)} \]
   rational_best_oopsla_all_46_json_45_simplify-74 [<=] 36.0	\[ \frac{\tan \left(\frac{x}{\color{blue}{y \cdot \frac{2}{2}} + y \cdot \frac{2}{2}}\right)}{\sin \left(\frac{x}{y \cdot 2}\right)} \]
   metadata-eval [=>] 36.0	\[ \frac{\tan \left(\frac{x}{y \cdot \color{blue}{1} + y \cdot \frac{2}{2}}\right)}{\sin \left(\frac{x}{y \cdot 2}\right)} \]
   rational_best_oopsla_all_46_json_45_simplify-52 [=>] 36.0	\[ \frac{\tan \left(\frac{x}{\color{blue}{y} + y \cdot \frac{2}{2}}\right)}{\sin \left(\frac{x}{y \cdot 2}\right)} \]
   metadata-eval [=>] 36.0	\[ \frac{\tan \left(\frac{x}{y + y \cdot \color{blue}{1}}\right)}{\sin \left(\frac{x}{y \cdot 2}\right)} \]
   rational_best_oopsla_all_46_json_45_simplify-52 [=>] 36.0	\[ \frac{\tan \left(\frac{x}{y + \color{blue}{y}}\right)}{\sin \left(\frac{x}{y \cdot 2}\right)} \]
   metadata-eval [<=] 36.0	\[ \frac{\tan \left(\frac{x}{y + y}\right)}{\sin \left(\frac{x}{y \cdot \color{blue}{\left(1 + 1\right)}}\right)} \]
   metadata-eval [<=] 36.0	\[ \frac{\tan \left(\frac{x}{y + y}\right)}{\sin \left(\frac{x}{y \cdot \left(\color{blue}{\frac{2}{2}} + 1\right)}\right)} \]
   metadata-eval [<=] 36.0	\[ \frac{\tan \left(\frac{x}{y + y}\right)}{\sin \left(\frac{x}{y \cdot \left(\frac{2}{2} + \color{blue}{\frac{2}{2}}\right)}\right)} \]
   rational_best_oopsla_all_46_json_45_simplify-23 [<=] 36.0	\[ \frac{\tan \left(\frac{x}{y + y}\right)}{\sin \left(\frac{x}{\color{blue}{\frac{2}{2} \cdot y + y \cdot \frac{2}{2}}}\right)} \]
   rational_best_oopsla_all_46_json_45_simplify-74 [<=] 36.0	\[ \frac{\tan \left(\frac{x}{y + y}\right)}{\sin \left(\frac{x}{\color{blue}{y \cdot \frac{2}{2}} + y \cdot \frac{2}{2}}\right)} \]
   metadata-eval [=>] 36.0	\[ \frac{\tan \left(\frac{x}{y + y}\right)}{\sin \left(\frac{x}{y \cdot \color{blue}{1} + y \cdot \frac{2}{2}}\right)} \]
   rational_best_oopsla_all_46_json_45_simplify-52 [=>] 36.0	\[ \frac{\tan \left(\frac{x}{y + y}\right)}{\sin \left(\frac{x}{\color{blue}{y} + y \cdot \frac{2}{2}}\right)} \]
   metadata-eval [=>] 36.0	\[ \frac{\tan \left(\frac{x}{y + y}\right)}{\sin \left(\frac{x}{y + y \cdot \color{blue}{1}}\right)} \]
   rational_best_oopsla_all_46_json_45_simplify-52 [=>] 36.0	\[ \frac{\tan \left(\frac{x}{y + y}\right)}{\sin \left(\frac{x}{y + \color{blue}{y}}\right)} \]

3. Taylor expanded in x around inf 28.5

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

4. Applied egg-rr 28.5

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

5. Applied egg-rr 28.5

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

6. Final simplification 28.5

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

Alternatives

Alternative 1
Error	28.5
Cost	40256

\[\begin{array}{l} t_0 := \cos \left(0.5 \cdot \frac{x}{y}\right)\\ \frac{1}{\left|\left(-t_0\right) \cdot \left(t_0 \cdot \frac{1}{{t_0}^{2}}\right)\right| \cdot t_0} \end{array} \]

Alternative 2
Error	28.5
Cost	34240

\[\begin{array}{l} t_0 := \cos \left(0.5 \cdot \frac{x}{y}\right)\\ t_1 := \frac{1}{t_0}\\ \frac{1}{\left(\left(\left(t_0 \cdot t_1\right) \cdot t_0\right) \cdot t_1\right) \cdot t_0} \end{array} \]

Alternative 3
Error	28.5
Cost	20544

\[\begin{array}{l} t_0 := \cos \left(0.5 \cdot \frac{x}{y}\right)\\ \frac{1}{\left(t_0 \cdot \frac{1}{t_0}\right) \cdot t_0} \end{array} \]

Alternative 4
Error	28.5
Cost	6848

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

Alternative 5
Error	60.0
Cost	64

\[-2 \]

Alternative 6
Error	28.7
Cost	64

\[1 \]

Reproduce

herbie shell --seed 2023090 
(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)))))