Diagrams.TwoD.Path.Metafont.Internal:hobbyF from diagrams-contrib-1.3.0.5

Average Error: 0.5 → 0.4

Time: 47.9s

Precision: binary64

Cost: 92608

Math

\[\frac{2 + \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x - \cos y\right)}{3 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{3 - \sqrt{5}}{2} \cdot \cos y\right)} \]

↓

\[\frac{2 + \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x - \cos y\right)}{3 \cdot \left(\left(1 + \frac{\left(\left(\sqrt{125} + -1\right) \cdot \cos x\right) \cdot \sqrt[3]{0.5}}{\left(6 + \sqrt{5}\right) \cdot \sqrt[3]{4}}\right) + \frac{\frac{4}{3 + \sqrt{5}}}{2} \cdot \cos y\right)} \]

FPCore

(FPCore (x y)
 :precision binary64
 (/
  (+
   2.0
   (*
    (*
     (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
     (- (sin y) (/ (sin x) 16.0)))
    (- (cos x) (cos y))))
  (*
   3.0
   (+
    (+ 1.0 (* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x)))
    (* (/ (- 3.0 (sqrt 5.0)) 2.0) (cos y))))))

↓

(FPCore (x y)
 :precision binary64
 (/
  (+
   2.0
   (*
    (*
     (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
     (- (sin y) (/ (sin x) 16.0)))
    (- (cos x) (cos y))))
  (*
   3.0
   (+
    (+
     1.0
     (/
      (* (* (+ (sqrt 125.0) -1.0) (cos x)) (cbrt 0.5))
      (* (+ 6.0 (sqrt 5.0)) (cbrt 4.0))))
    (* (/ (/ 4.0 (+ 3.0 (sqrt 5.0))) 2.0) (cos y))))))

C

double code(double x, double y) {
	return (2.0 + (((sqrt(2.0) * (sin(x) - (sin(y) / 16.0))) * (sin(y) - (sin(x) / 16.0))) * (cos(x) - cos(y)))) / (3.0 * ((1.0 + (((sqrt(5.0) - 1.0) / 2.0) * cos(x))) + (((3.0 - sqrt(5.0)) / 2.0) * cos(y))));
}

↓

double code(double x, double y) {
	return (2.0 + (((sqrt(2.0) * (sin(x) - (sin(y) / 16.0))) * (sin(y) - (sin(x) / 16.0))) * (cos(x) - cos(y)))) / (3.0 * ((1.0 + ((((sqrt(125.0) + -1.0) * cos(x)) * cbrt(0.5)) / ((6.0 + sqrt(5.0)) * cbrt(4.0)))) + (((4.0 / (3.0 + sqrt(5.0))) / 2.0) * cos(y))));
}

Java

public static double code(double x, double y) {
	return (2.0 + (((Math.sqrt(2.0) * (Math.sin(x) - (Math.sin(y) / 16.0))) * (Math.sin(y) - (Math.sin(x) / 16.0))) * (Math.cos(x) - Math.cos(y)))) / (3.0 * ((1.0 + (((Math.sqrt(5.0) - 1.0) / 2.0) * Math.cos(x))) + (((3.0 - Math.sqrt(5.0)) / 2.0) * Math.cos(y))));
}

↓

public static double code(double x, double y) {
	return (2.0 + (((Math.sqrt(2.0) * (Math.sin(x) - (Math.sin(y) / 16.0))) * (Math.sin(y) - (Math.sin(x) / 16.0))) * (Math.cos(x) - Math.cos(y)))) / (3.0 * ((1.0 + ((((Math.sqrt(125.0) + -1.0) * Math.cos(x)) * Math.cbrt(0.5)) / ((6.0 + Math.sqrt(5.0)) * Math.cbrt(4.0)))) + (((4.0 / (3.0 + Math.sqrt(5.0))) / 2.0) * Math.cos(y))));
}

Julia

function code(x, y)
	return Float64(Float64(2.0 + Float64(Float64(Float64(sqrt(2.0) * Float64(sin(x) - Float64(sin(y) / 16.0))) * Float64(sin(y) - Float64(sin(x) / 16.0))) * Float64(cos(x) - cos(y)))) / Float64(3.0 * Float64(Float64(1.0 + Float64(Float64(Float64(sqrt(5.0) - 1.0) / 2.0) * cos(x))) + Float64(Float64(Float64(3.0 - sqrt(5.0)) / 2.0) * cos(y)))))
end

↓

function code(x, y)
	return Float64(Float64(2.0 + Float64(Float64(Float64(sqrt(2.0) * Float64(sin(x) - Float64(sin(y) / 16.0))) * Float64(sin(y) - Float64(sin(x) / 16.0))) * Float64(cos(x) - cos(y)))) / Float64(3.0 * Float64(Float64(1.0 + Float64(Float64(Float64(Float64(sqrt(125.0) + -1.0) * cos(x)) * cbrt(0.5)) / Float64(Float64(6.0 + sqrt(5.0)) * cbrt(4.0)))) + Float64(Float64(Float64(4.0 / Float64(3.0 + sqrt(5.0))) / 2.0) * cos(y)))))
end

Wolfram

code[x_, y_] := N[(N[(2.0 + N[(N[(N[(N[Sqrt[2.0], $MachinePrecision] * N[(N[Sin[x], $MachinePrecision] - N[(N[Sin[y], $MachinePrecision] / 16.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[Sin[y], $MachinePrecision] - N[(N[Sin[x], $MachinePrecision] / 16.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[Cos[x], $MachinePrecision] - N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(3.0 * N[(N[(1.0 + N[(N[(N[(N[Sqrt[5.0], $MachinePrecision] - 1.0), $MachinePrecision] / 2.0), $MachinePrecision] * N[Cos[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(3.0 - N[Sqrt[5.0], $MachinePrecision]), $MachinePrecision] / 2.0), $MachinePrecision] * N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_] := N[(N[(2.0 + N[(N[(N[(N[Sqrt[2.0], $MachinePrecision] * N[(N[Sin[x], $MachinePrecision] - N[(N[Sin[y], $MachinePrecision] / 16.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[Sin[y], $MachinePrecision] - N[(N[Sin[x], $MachinePrecision] / 16.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[Cos[x], $MachinePrecision] - N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(3.0 * N[(N[(1.0 + N[(N[(N[(N[(N[Sqrt[125.0], $MachinePrecision] + -1.0), $MachinePrecision] * N[Cos[x], $MachinePrecision]), $MachinePrecision] * N[Power[0.5, 1/3], $MachinePrecision]), $MachinePrecision] / N[(N[(6.0 + N[Sqrt[5.0], $MachinePrecision]), $MachinePrecision] * N[Power[4.0, 1/3], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(4.0 / N[(3.0 + N[Sqrt[5.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / 2.0), $MachinePrecision] * N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 0.5

   \[\frac{2 + \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x - \cos y\right)}{3 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{3 - \sqrt{5}}{2} \cdot \cos y\right)} \]

2. Applied egg-rr 0.5

   \[\leadsto \frac{2 + \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x - \cos y\right)}{3 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{\color{blue}{\frac{1}{\sqrt{3 + \sqrt{5}}} \cdot \frac{4}{\sqrt{3 + \sqrt{5}}}}}{2} \cdot \cos y\right)} \]

3. Simplified 0.4

   \[\leadsto \frac{2 + \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x - \cos y\right)}{3 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{\color{blue}{\frac{4}{3 + \sqrt{5}}}}{2} \cdot \cos y\right)} \]
   Proof

4. Applied egg-rr 0.4

   \[\leadsto \frac{2 + \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x - \cos y\right)}{3 \cdot \left(\left(1 + \color{blue}{\frac{\left(\left(\sqrt{125} + -1\right) \cdot \cos x\right) \cdot \sqrt[3]{0.5}}{\left(6 + \sqrt{5}\right) \cdot \sqrt[3]{4}}}\right) + \frac{\frac{4}{3 + \sqrt{5}}}{2} \cdot \cos y\right)} \]

Alternatives

Alternative 1
Error	0.4
Cost	85440

\[\frac{\mathsf{fma}\left(\mathsf{fma}\left(-0.0625, \sin y, \sin x\right) \cdot \left(\sqrt{2} \cdot \left(-0.0625 \cdot \sin x + \sin y\right)\right), \cos x - \cos y, 2\right)}{3 \cdot \left(1 + \frac{\left(\sqrt{5} + -1\right) \cdot \cos x + \frac{4}{3 + \sqrt{5}} \cdot \cos y}{2}\right)} \]

Alternative 2
Error	0.4
Cost	79168

\[\frac{\mathsf{fma}\left(\left(\sqrt{2} \cdot \left(\sin x - \sin y \cdot 0.0625\right)\right) \cdot \left(\sin y - \sin x \cdot 0.0625\right), \cos x - \cos y, 2\right)}{3 \cdot \left(1 + \frac{\left(\sqrt{5} + -1\right) \cdot \cos x + \frac{4}{3 + \sqrt{5}} \cdot \cos y}{2}\right)} \]

Alternative 3
Error	12.3
Cost	72904

\[\begin{array}{l} t_0 := 3 - \sqrt{5}\\ t_1 := \cos x - \cos y\\ t_2 := 3 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{t_0}{2} \cdot \cos y\right)\\ t_3 := \sqrt{2} \cdot \sin x\\ t_4 := \sin y - \frac{\sin x}{16}\\ \mathbf{if}\;x \leq -0.04:\\ \;\;\;\;\frac{2 + \left(t_3 \cdot t_4\right) \cdot t_1}{t_2}\\ \mathbf{elif}\;x \leq 0.054:\\ \;\;\;\;\frac{2 + \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot t_4\right) \cdot \left(\left(1 + -0.5 \cdot \left(x \cdot x\right)\right) - \cos y\right)}{t_2}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\frac{\frac{t_3}{3}}{0.3333333333333333} \cdot \left(\sin y - \sin x \cdot 0.0625\right), t_1, 2\right)}{3 \cdot \left(1 + \frac{\left(\sqrt{5} + -1\right) \cdot \cos x + t_0 \cdot \cos y}{2}\right)}\\ \end{array} \]

Alternative 4
Error	0.5
Cost	72896

\[\frac{2 + \left(\sqrt{2} \cdot \left(\left(\sin y - 0.0625 \cdot \sin x\right) \cdot \left(\sin x - 0.0625 \cdot \sin y\right)\right)\right) \cdot \left(\cos x - \cos y\right)}{3 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{3 - \sqrt{5}}{2} \cdot \cos y\right)} \]

Alternative 5
Error	0.4
Cost	72896

\[\frac{2 + \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x - \cos y\right)}{3 \cdot \left(\left(1 + \cos x \cdot \left(\sqrt{1.25} + -0.5\right)\right) + \frac{\frac{4}{3 + \sqrt{5}}}{2} \cdot \cos y\right)} \]

Alternative 6
Error	12.3
Cost	72648

\[\begin{array}{l} t_0 := 3 - \sqrt{5}\\ t_1 := \cos x - \cos y\\ t_2 := 3 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{t_0}{2} \cdot \cos y\right)\\ t_3 := \sqrt{2} \cdot \sin x\\ t_4 := \sin y - \frac{\sin x}{16}\\ \mathbf{if}\;x \leq -0.065:\\ \;\;\;\;\frac{2 + \left(t_3 \cdot t_4\right) \cdot t_1}{t_2}\\ \mathbf{elif}\;x \leq 0.046:\\ \;\;\;\;\frac{2 + \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot t_4\right) \cdot \left(\left(1 + -0.5 \cdot \left(x \cdot x\right)\right) - \cos y\right)}{t_2}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t_3 \cdot \left(\sin y - \sin x \cdot 0.0625\right), t_1, 2\right)}{3 \cdot \left(1 + \frac{\left(\sqrt{5} + -1\right) \cdot \cos x + t_0 \cdot \cos y}{2}\right)}\\ \end{array} \]

Alternative 7
Error	12.3
Cost	67144

\[\begin{array}{l} t_0 := 1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\\ t_1 := 3 \cdot \left(t_0 + \frac{3 - \sqrt{5}}{2} \cdot \cos y\right)\\ t_2 := \sin y - \frac{\sin x}{16}\\ t_3 := 2 + \left(\left(\sqrt{2} \cdot \sin x\right) \cdot t_2\right) \cdot \left(\cos x - \cos y\right)\\ \mathbf{if}\;x \leq -0.3:\\ \;\;\;\;\frac{t_3}{t_1}\\ \mathbf{elif}\;x \leq 0.057:\\ \;\;\;\;\frac{2 + \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot t_2\right) \cdot \left(\left(1 + -0.5 \cdot \left(x \cdot x\right)\right) - \cos y\right)}{t_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_3}{3 \cdot \left(t_0 + \frac{\frac{4}{3 + \sqrt{5}}}{2} \cdot \cos y\right)}\\ \end{array} \]

Alternative 8
Error	12.5
Cost	66632

\[\begin{array}{l} t_0 := 2 + \left(\left(\sqrt{2} \cdot \sin x\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x - \cos y\right)\\ t_1 := 1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\\ t_2 := 3 \cdot \left(t_1 + \frac{\frac{4}{3 + \sqrt{5}}}{2} \cdot \cos y\right)\\ \mathbf{if}\;x \leq -0.00075:\\ \;\;\;\;\frac{t_0}{3 \cdot \left(t_1 + \frac{3 - \sqrt{5}}{2} \cdot \cos y\right)}\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{-7}:\\ \;\;\;\;\frac{2 + \left(-0.0625 \cdot \left(\sqrt{2} \cdot {\sin y}^{2}\right)\right) \cdot \left(1 - \cos y\right)}{t_2}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_0}{t_2}\\ \end{array} \]

Alternative 9
Error	12.6
Cost	66504

\[\begin{array}{l} t_0 := 1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\\ t_1 := \frac{2 + \left(\left(\sqrt{2} \cdot \sin x\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x - \cos y\right)}{3 \cdot \left(t_0 + \frac{3 - \sqrt{5}}{2} \cdot \cos y\right)}\\ \mathbf{if}\;x \leq -0.00078:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{-7}:\\ \;\;\;\;\frac{2 + \left(-0.0625 \cdot \left(\sqrt{2} \cdot {\sin y}^{2}\right)\right) \cdot \left(1 - \cos y\right)}{3 \cdot \left(t_0 + \frac{\frac{4}{3 + \sqrt{5}}}{2} \cdot \cos y\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 10
Error	13.6
Cost	66248

\[\begin{array}{l} t_0 := 3 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{\frac{4}{3 + \sqrt{5}}}{2} \cdot \cos y\right)\\ t_1 := -0.0625 \cdot \left(\sqrt{2} \cdot {\sin y}^{2}\right)\\ \mathbf{if}\;y \leq -0.0055:\\ \;\;\;\;\frac{2 + t_1 \cdot \left(1 - \cos y\right)}{t_0}\\ \mathbf{elif}\;y \leq 0.00145:\\ \;\;\;\;\frac{\mathsf{fma}\left(\left(\sqrt{2} \cdot \sin x\right) \cdot \left(\sin y - \sin x \cdot 0.0625\right), \cos x - 1, 2\right)}{3 \cdot \left(1 + \frac{\left(\sqrt{5} + -1\right) \cdot \cos x + \left(3 - \sqrt{5}\right) \cdot \cos y}{2}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + t_1 \cdot \left(\cos x - \cos y\right)}{t_0}\\ \end{array} \]

Alternative 11
Error	13.7
Cost	60552

\[\begin{array}{l} t_0 := 1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\\ t_1 := \frac{2 + \left(-0.0625 \cdot \left(\sqrt{2} \cdot {\sin x}^{2}\right)\right) \cdot \left(\left(\sin \left(\left(x + y\right) \cdot 0.5\right) \cdot \sin \left(\left(x - y\right) \cdot 0.5\right)\right) \cdot -2\right)}{3 \cdot \left(t_0 + \frac{3 - \sqrt{5}}{2} \cdot \cos y\right)}\\ \mathbf{if}\;x \leq -0.00074:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{-7}:\\ \;\;\;\;\frac{2 + \left(-0.0625 \cdot \left(\sqrt{2} \cdot {\sin y}^{2}\right)\right) \cdot \left(1 - \cos y\right)}{3 \cdot \left(t_0 + \frac{\frac{4}{3 + \sqrt{5}}}{2} \cdot \cos y\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 12
Error	13.7
Cost	60040

\[\begin{array}{l} t_0 := 3 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{\frac{4}{3 + \sqrt{5}}}{2} \cdot \cos y\right)\\ t_1 := -0.0625 \cdot \left(\sqrt{2} \cdot {\sin y}^{2}\right)\\ t_2 := \cos x - \cos y\\ \mathbf{if}\;y \leq -0.00072:\\ \;\;\;\;\frac{2 + t_1 \cdot \left(1 - \cos y\right)}{t_0}\\ \mathbf{elif}\;y \leq 40:\\ \;\;\;\;\frac{2 + \left(-0.0625 \cdot \left(\sqrt{2} \cdot {\sin x}^{2}\right)\right) \cdot t_2}{3 \cdot \left(\left(1 + \frac{2 \cdot \cos x}{\sqrt{5} + 1}\right) + \frac{3 - \sqrt{5}}{2} \cdot \cos y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + t_1 \cdot t_2}{t_0}\\ \end{array} \]

Alternative 13
Error	13.7
Cost	59912

\[\begin{array}{l} t_0 := \frac{3 - \sqrt{5}}{2} \cdot \cos y\\ t_1 := 1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\\ t_2 := \cos x - \cos y\\ t_3 := {\sin y}^{2}\\ \mathbf{if}\;y \leq -0.00085:\\ \;\;\;\;\frac{2 + \left(-0.0625 \cdot \left(\sqrt{2} \cdot t_3\right)\right) \cdot \left(1 - \cos y\right)}{3 \cdot \left(t_1 + \frac{\frac{4}{3 + \sqrt{5}}}{2} \cdot \cos y\right)}\\ \mathbf{elif}\;y \leq 40:\\ \;\;\;\;\frac{2 + \left(-0.0625 \cdot \left(\sqrt{2} \cdot {\sin x}^{2}\right)\right) \cdot t_2}{3 \cdot \left(\left(1 + \frac{2 \cdot \cos x}{\sqrt{5} + 1}\right) + t_0\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \left(t_3 \cdot \left(-\sqrt{0.0078125}\right)\right) \cdot t_2}{3 \cdot \left(t_1 + t_0\right)}\\ \end{array} \]

Alternative 14
Error	13.7
Cost	59848

\[\begin{array}{l} t_0 := \cos x - \cos y\\ t_1 := 1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\\ t_2 := 3 \cdot \left(t_1 + \frac{3 - \sqrt{5}}{2} \cdot \cos y\right)\\ t_3 := {\sin y}^{2}\\ \mathbf{if}\;y \leq -0.00085:\\ \;\;\;\;\frac{2 + \left(-0.0625 \cdot \left(\sqrt{2} \cdot t_3\right)\right) \cdot \left(1 - \cos y\right)}{3 \cdot \left(t_1 + \frac{\frac{4}{3 + \sqrt{5}}}{2} \cdot \cos y\right)}\\ \mathbf{elif}\;y \leq 40:\\ \;\;\;\;\frac{2 + \left(-0.0625 \cdot \left(\left(\sqrt{2} \cdot \left(1 - \cos \left(x + x\right)\right)\right) \cdot 0.5\right)\right) \cdot t_0}{t_2}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \left(t_3 \cdot \left(-\sqrt{0.0078125}\right)\right) \cdot t_0}{t_2}\\ \end{array} \]

Alternative 15
Error	13.9
Cost	53832

\[\begin{array}{l} t_0 := 1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\\ t_1 := 3 \cdot \left(t_0 + \frac{3 - \sqrt{5}}{2} \cdot \cos y\right)\\ \mathbf{if}\;x \leq -14000000:\\ \;\;\;\;\frac{2 + \left(-0.0625 \cdot \left(\sqrt{2} \cdot {\sin x}^{2}\right)\right) \cdot \left(\cos x - 1\right)}{t_1}\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{-7}:\\ \;\;\;\;\frac{2 + \left(-0.0625 \cdot \left(\sqrt{2} \cdot {\sin y}^{2}\right)\right) \cdot \left(1 - \cos y\right)}{3 \cdot \left(t_0 + \frac{\frac{4}{3 + \sqrt{5}}}{2} \cdot \cos y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \left(-0.0625 \cdot \left(\left(\sqrt{2} \cdot \left(1 - \cos \left(x + x\right)\right)\right) \cdot 0.5\right)\right) \cdot \left(\cos x - \cos y\right)}{t_1}\\ \end{array} \]

Alternative 16
Error	13.7
Cost	53640

\[\begin{array}{l} t_0 := 1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\\ t_1 := \frac{2 + \left(-0.0625 \cdot \left(\sqrt{2} \cdot {\sin y}^{2}\right)\right) \cdot \left(1 - \cos y\right)}{3 \cdot \left(t_0 + \frac{\frac{4}{3 + \sqrt{5}}}{2} \cdot \cos y\right)}\\ \mathbf{if}\;y \leq -0.00072:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 0.0006:\\ \;\;\;\;\frac{2 + \left(-0.0625 \cdot \left(\sqrt{2} \cdot {\sin x}^{2}\right)\right) \cdot \left(\cos x - 1\right)}{3 \cdot \left(t_0 + \frac{3 - \sqrt{5}}{2} \cdot \cos y\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 17
Error	35.0
Cost	53248

\[\frac{2 + \left(-0.0625 \cdot \left(\sqrt{2} \cdot {\sin x}^{2}\right)\right) \cdot \left(1 - \cos y\right)}{3 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{3 - \sqrt{5}}{2} \cdot \cos y\right)} \]

Alternative 18
Error	24.5
Cost	53248

\[\frac{2 + \left(-0.0625 \cdot \left(\sqrt{2} \cdot {\sin x}^{2}\right)\right) \cdot \left(\cos x - 1\right)}{3 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{3 - \sqrt{5}}{2} \cdot \cos y\right)} \]

Alternative 19
Error	38.4
Cost	47304

\[\begin{array}{l} t_0 := 1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\\ t_1 := \frac{2 + \left(-0.0625 \cdot \left(\sqrt{2} \cdot \left(x \cdot x\right)\right)\right) \cdot \left(\cos x - 1\right)}{3 \cdot \left(t_0 + \frac{3 - \sqrt{5}}{2} \cdot \cos y\right)}\\ \mathbf{if}\;y \leq -3.1:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 40:\\ \;\;\;\;\frac{2 + \left(-0.0625 \cdot \left(\sqrt{2} \cdot \left(y \cdot y\right)\right)\right) \cdot \left(\cos x - \cos y\right)}{3 \cdot \left(t_0 + \frac{\frac{4}{3 + \sqrt{5}}}{2} \cdot \cos y\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 20
Error	41.2
Cost	40512

\[\frac{2 + \left(-0.0625 \cdot \left(\sqrt{2} \cdot \left(x \cdot x\right)\right)\right) \cdot \left(1 - \cos y\right)}{3 \cdot \left(\left(1 + \frac{2 \cdot \cos x}{\sqrt{5} + 1}\right) + \frac{3 - \sqrt{5}}{2} \cdot \cos y\right)} \]

Alternative 21
Error	41.2
Cost	40384

\[\frac{2 + \left(-0.0625 \cdot \left(\sqrt{2} \cdot \left(x \cdot x\right)\right)\right) \cdot \left(1 - \cos y\right)}{3 \cdot \left(\left(1 + \cos x \cdot \left(\sqrt{1.25} + -0.5\right)\right) + \frac{3 - \sqrt{5}}{2} \cdot \cos y\right)} \]

Alternative 22
Error	44.7
Cost	34112

\[\frac{2 + -0.03125 \cdot \left(\sqrt{2} \cdot \left(\left(y \cdot y\right) \cdot \left(x \cdot x\right)\right)\right)}{3 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{3 - \sqrt{5}}{2} \cdot \cos y\right)} \]

Reproduce

herbie shell --seed 2023010 
(FPCore (x y)
  :name "Diagrams.TwoD.Path.Metafont.Internal:hobbyF from diagrams-contrib-1.3.0.5"
  :precision binary64
  (/ (+ 2.0 (* (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y)))) (* 3.0 (+ (+ 1.0 (* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))) (* (/ (- 3.0 (sqrt 5.0)) 2.0) (cos y))))))