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

Percentage Accurate: 99.3% → 99.3%

Time: 40.2s

Precision: binary64

Cost: 85568

Math

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

↓

\[\frac{2 + \left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\left(\sin y - \frac{\sin x}{16}\right) \cdot \left(\cos x - \cos y\right)\right)}{3 \cdot \left(1 + \mathsf{fma}\left(\cos x, -0.5 + \sqrt{5} \cdot 0.5, \cos y \cdot \frac{1}{\mathsf{fma}\left(0.5, \sqrt{5}, 1.5\right)}\right)\right)} \]

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
    (fma
     (cos x)
     (+ -0.5 (* (sqrt 5.0) 0.5))
     (* (cos y) (/ 1.0 (fma 0.5 (sqrt 5.0) 1.5))))))))

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 + fma(cos(x), (-0.5 + (sqrt(5.0) * 0.5)), (cos(y) * (1.0 / fma(0.5, sqrt(5.0), 1.5))))));
}

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(sqrt(2.0) * Float64(sin(x) - Float64(sin(y) / 16.0))) * Float64(Float64(sin(y) - Float64(sin(x) / 16.0)) * Float64(cos(x) - cos(y))))) / Float64(3.0 * Float64(1.0 + fma(cos(x), Float64(-0.5 + Float64(sqrt(5.0) * 0.5)), Float64(cos(y) * Float64(1.0 / fma(0.5, sqrt(5.0), 1.5)))))))
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[Sqrt[2.0], $MachinePrecision] * N[(N[Sin[x], $MachinePrecision] - N[(N[Sin[y], $MachinePrecision] / 16.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(N[Sin[y], $MachinePrecision] - N[(N[Sin[x], $MachinePrecision] / 16.0), $MachinePrecision]), $MachinePrecision] * N[(N[Cos[x], $MachinePrecision] - N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(3.0 * N[(1.0 + N[(N[Cos[x], $MachinePrecision] * N[(-0.5 + N[(N[Sqrt[5.0], $MachinePrecision] * 0.5), $MachinePrecision]), $MachinePrecision] + N[(N[Cos[y], $MachinePrecision] * N[(1.0 / N[(0.5 * N[Sqrt[5.0], $MachinePrecision] + 1.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.3%

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

2. Simplified 99.3%

   \[\leadsto \color{blue}{\frac{2 + \left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\left(\sin y - \frac{\sin x}{16}\right) \cdot \left(\cos x - \cos y\right)\right)}{3 \cdot \left(1 + \left(\cos x \cdot \left(\frac{\sqrt{5}}{2} - 0.5\right) + \cos y \cdot \left(1.5 - \frac{\sqrt{5}}{2}\right)\right)\right)}} \]
   Step-by-step derivation

   [Start] 99.3%	\[ \frac{2 + \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x - \cos y\right)}{3 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{3 - \sqrt{5}}{2} \cdot \cos y\right)} \]
   associate-*l* [=>] 99.3%	\[ \frac{2 + \color{blue}{\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\left(\sin y - \frac{\sin x}{16}\right) \cdot \left(\cos x - \cos y\right)\right)}}{3 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{3 - \sqrt{5}}{2} \cdot \cos y\right)} \]
   associate-+l+ [=>] 99.3%	\[ \frac{2 + \left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\left(\sin y - \frac{\sin x}{16}\right) \cdot \left(\cos x - \cos y\right)\right)}{3 \cdot \color{blue}{\left(1 + \left(\frac{\sqrt{5} - 1}{2} \cdot \cos x + \frac{3 - \sqrt{5}}{2} \cdot \cos y\right)\right)}} \]
   *-commutative [=>] 99.3%	\[ \frac{2 + \left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\left(\sin y - \frac{\sin x}{16}\right) \cdot \left(\cos x - \cos y\right)\right)}{3 \cdot \left(1 + \left(\color{blue}{\cos x \cdot \frac{\sqrt{5} - 1}{2}} + \frac{3 - \sqrt{5}}{2} \cdot \cos y\right)\right)} \]
   div-sub [=>] 99.3%	\[ \frac{2 + \left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\left(\sin y - \frac{\sin x}{16}\right) \cdot \left(\cos x - \cos y\right)\right)}{3 \cdot \left(1 + \left(\cos x \cdot \color{blue}{\left(\frac{\sqrt{5}}{2} - \frac{1}{2}\right)} + \frac{3 - \sqrt{5}}{2} \cdot \cos y\right)\right)} \]
   metadata-eval [=>] 99.3%	\[ \frac{2 + \left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\left(\sin y - \frac{\sin x}{16}\right) \cdot \left(\cos x - \cos y\right)\right)}{3 \cdot \left(1 + \left(\cos x \cdot \left(\frac{\sqrt{5}}{2} - \color{blue}{0.5}\right) + \frac{3 - \sqrt{5}}{2} \cdot \cos y\right)\right)} \]
   *-commutative [=>] 99.3%	\[ \frac{2 + \left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\left(\sin y - \frac{\sin x}{16}\right) \cdot \left(\cos x - \cos y\right)\right)}{3 \cdot \left(1 + \left(\cos x \cdot \left(\frac{\sqrt{5}}{2} - 0.5\right) + \color{blue}{\cos y \cdot \frac{3 - \sqrt{5}}{2}}\right)\right)} \]
   div-sub [=>] 99.3%	\[ \frac{2 + \left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\left(\sin y - \frac{\sin x}{16}\right) \cdot \left(\cos x - \cos y\right)\right)}{3 \cdot \left(1 + \left(\cos x \cdot \left(\frac{\sqrt{5}}{2} - 0.5\right) + \cos y \cdot \color{blue}{\left(\frac{3}{2} - \frac{\sqrt{5}}{2}\right)}\right)\right)} \]
   metadata-eval [=>] 99.3%	\[ \frac{2 + \left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\left(\sin y - \frac{\sin x}{16}\right) \cdot \left(\cos x - \cos y\right)\right)}{3 \cdot \left(1 + \left(\cos x \cdot \left(\frac{\sqrt{5}}{2} - 0.5\right) + \cos y \cdot \left(\color{blue}{1.5} - \frac{\sqrt{5}}{2}\right)\right)\right)} \]

3. Applied egg-rr 99.4%

   \[\leadsto \frac{2 + \left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\left(\sin y - \frac{\sin x}{16}\right) \cdot \left(\cos x - \cos y\right)\right)}{3 \cdot \left(1 + \color{blue}{\mathsf{fma}\left(\cos x, \sqrt{5} \cdot 0.5 + -0.5, \cos y \cdot \left(1.5 - \sqrt{5} \cdot 0.5\right)\right)}\right)} \]
   Step-by-step derivation

   [Start] 99.3%	\[ \frac{2 + \left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\left(\sin y - \frac{\sin x}{16}\right) \cdot \left(\cos x - \cos y\right)\right)}{3 \cdot \left(1 + \left(\cos x \cdot \left(\frac{\sqrt{5}}{2} - 0.5\right) + \cos y \cdot \left(1.5 - \frac{\sqrt{5}}{2}\right)\right)\right)} \]
   fma-def [=>] 99.4%	\[ \frac{2 + \left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\left(\sin y - \frac{\sin x}{16}\right) \cdot \left(\cos x - \cos y\right)\right)}{3 \cdot \left(1 + \color{blue}{\mathsf{fma}\left(\cos x, \frac{\sqrt{5}}{2} - 0.5, \cos y \cdot \left(1.5 - \frac{\sqrt{5}}{2}\right)\right)}\right)} \]
   sub-neg [=>] 99.4%	\[ \frac{2 + \left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\left(\sin y - \frac{\sin x}{16}\right) \cdot \left(\cos x - \cos y\right)\right)}{3 \cdot \left(1 + \mathsf{fma}\left(\cos x, \color{blue}{\frac{\sqrt{5}}{2} + \left(-0.5\right)}, \cos y \cdot \left(1.5 - \frac{\sqrt{5}}{2}\right)\right)\right)} \]
   metadata-eval [=>] 99.4%	\[ \frac{2 + \left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\left(\sin y - \frac{\sin x}{16}\right) \cdot \left(\cos x - \cos y\right)\right)}{3 \cdot \left(1 + \mathsf{fma}\left(\cos x, \frac{\sqrt{5}}{2} + \color{blue}{-0.5}, \cos y \cdot \left(1.5 - \frac{\sqrt{5}}{2}\right)\right)\right)} \]
   div-inv [=>] 99.4%	\[ \frac{2 + \left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\left(\sin y - \frac{\sin x}{16}\right) \cdot \left(\cos x - \cos y\right)\right)}{3 \cdot \left(1 + \mathsf{fma}\left(\cos x, \color{blue}{\sqrt{5} \cdot \frac{1}{2}} + -0.5, \cos y \cdot \left(1.5 - \frac{\sqrt{5}}{2}\right)\right)\right)} \]
   metadata-eval [=>] 99.4%	\[ \frac{2 + \left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\left(\sin y - \frac{\sin x}{16}\right) \cdot \left(\cos x - \cos y\right)\right)}{3 \cdot \left(1 + \mathsf{fma}\left(\cos x, \sqrt{5} \cdot \color{blue}{0.5} + -0.5, \cos y \cdot \left(1.5 - \frac{\sqrt{5}}{2}\right)\right)\right)} \]
   div-inv [=>] 99.4%	\[ \frac{2 + \left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\left(\sin y - \frac{\sin x}{16}\right) \cdot \left(\cos x - \cos y\right)\right)}{3 \cdot \left(1 + \mathsf{fma}\left(\cos x, \sqrt{5} \cdot 0.5 + -0.5, \cos y \cdot \left(1.5 - \color{blue}{\sqrt{5} \cdot \frac{1}{2}}\right)\right)\right)} \]
   metadata-eval [=>] 99.4%	\[ \frac{2 + \left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\left(\sin y - \frac{\sin x}{16}\right) \cdot \left(\cos x - \cos y\right)\right)}{3 \cdot \left(1 + \mathsf{fma}\left(\cos x, \sqrt{5} \cdot 0.5 + -0.5, \cos y \cdot \left(1.5 - \sqrt{5} \cdot \color{blue}{0.5}\right)\right)\right)} \]

4. Applied egg-rr 99.2%

   \[\leadsto \frac{2 + \left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\left(\sin y - \frac{\sin x}{16}\right) \cdot \left(\cos x - \cos y\right)\right)}{3 \cdot \left(1 + \mathsf{fma}\left(\cos x, \sqrt{5} \cdot 0.5 + -0.5, \cos y \cdot \color{blue}{\frac{2.25 - \left(\sqrt{5} \cdot 0.5\right) \cdot \left(\sqrt{5} \cdot 0.5\right)}{1.5 + \sqrt{5} \cdot 0.5}}\right)\right)} \]
   Step-by-step derivation

   [Start] 99.4%	\[ \frac{2 + \left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\left(\sin y - \frac{\sin x}{16}\right) \cdot \left(\cos x - \cos y\right)\right)}{3 \cdot \left(1 + \mathsf{fma}\left(\cos x, \sqrt{5} \cdot 0.5 + -0.5, \cos y \cdot \left(1.5 - \sqrt{5} \cdot 0.5\right)\right)\right)} \]
   flip-- [=>] 99.2%	\[ \frac{2 + \left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\left(\sin y - \frac{\sin x}{16}\right) \cdot \left(\cos x - \cos y\right)\right)}{3 \cdot \left(1 + \mathsf{fma}\left(\cos x, \sqrt{5} \cdot 0.5 + -0.5, \cos y \cdot \color{blue}{\frac{1.5 \cdot 1.5 - \left(\sqrt{5} \cdot 0.5\right) \cdot \left(\sqrt{5} \cdot 0.5\right)}{1.5 + \sqrt{5} \cdot 0.5}}\right)\right)} \]
   metadata-eval [=>] 99.2%	\[ \frac{2 + \left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\left(\sin y - \frac{\sin x}{16}\right) \cdot \left(\cos x - \cos y\right)\right)}{3 \cdot \left(1 + \mathsf{fma}\left(\cos x, \sqrt{5} \cdot 0.5 + -0.5, \cos y \cdot \frac{\color{blue}{2.25} - \left(\sqrt{5} \cdot 0.5\right) \cdot \left(\sqrt{5} \cdot 0.5\right)}{1.5 + \sqrt{5} \cdot 0.5}\right)\right)} \]

5. Simplified 99.4%

   \[\leadsto \frac{2 + \left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\left(\sin y - \frac{\sin x}{16}\right) \cdot \left(\cos x - \cos y\right)\right)}{3 \cdot \left(1 + \mathsf{fma}\left(\cos x, \sqrt{5} \cdot 0.5 + -0.5, \cos y \cdot \color{blue}{\frac{1}{\mathsf{fma}\left(0.5, \sqrt{5}, 1.5\right)}}\right)\right)} \]
   Step-by-step derivation

   [Start] 99.2%	\[ \frac{2 + \left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\left(\sin y - \frac{\sin x}{16}\right) \cdot \left(\cos x - \cos y\right)\right)}{3 \cdot \left(1 + \mathsf{fma}\left(\cos x, \sqrt{5} \cdot 0.5 + -0.5, \cos y \cdot \frac{2.25 - \left(\sqrt{5} \cdot 0.5\right) \cdot \left(\sqrt{5} \cdot 0.5\right)}{1.5 + \sqrt{5} \cdot 0.5}\right)\right)} \]
   swap-sqr [=>] 99.2%	\[ \frac{2 + \left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\left(\sin y - \frac{\sin x}{16}\right) \cdot \left(\cos x - \cos y\right)\right)}{3 \cdot \left(1 + \mathsf{fma}\left(\cos x, \sqrt{5} \cdot 0.5 + -0.5, \cos y \cdot \frac{2.25 - \color{blue}{\left(\sqrt{5} \cdot \sqrt{5}\right) \cdot \left(0.5 \cdot 0.5\right)}}{1.5 + \sqrt{5} \cdot 0.5}\right)\right)} \]
   cancel-sign-sub-inv [=>] 99.2%	\[ \frac{2 + \left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\left(\sin y - \frac{\sin x}{16}\right) \cdot \left(\cos x - \cos y\right)\right)}{3 \cdot \left(1 + \mathsf{fma}\left(\cos x, \sqrt{5} \cdot 0.5 + -0.5, \cos y \cdot \frac{\color{blue}{2.25 + \left(-\sqrt{5} \cdot \sqrt{5}\right) \cdot \left(0.5 \cdot 0.5\right)}}{1.5 + \sqrt{5} \cdot 0.5}\right)\right)} \]
   rem-square-sqrt [=>] 99.4%	\[ \frac{2 + \left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\left(\sin y - \frac{\sin x}{16}\right) \cdot \left(\cos x - \cos y\right)\right)}{3 \cdot \left(1 + \mathsf{fma}\left(\cos x, \sqrt{5} \cdot 0.5 + -0.5, \cos y \cdot \frac{2.25 + \left(-\color{blue}{5}\right) \cdot \left(0.5 \cdot 0.5\right)}{1.5 + \sqrt{5} \cdot 0.5}\right)\right)} \]
   metadata-eval [=>] 99.4%	\[ \frac{2 + \left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\left(\sin y - \frac{\sin x}{16}\right) \cdot \left(\cos x - \cos y\right)\right)}{3 \cdot \left(1 + \mathsf{fma}\left(\cos x, \sqrt{5} \cdot 0.5 + -0.5, \cos y \cdot \frac{2.25 + \color{blue}{-5} \cdot \left(0.5 \cdot 0.5\right)}{1.5 + \sqrt{5} \cdot 0.5}\right)\right)} \]
   metadata-eval [=>] 99.4%	\[ \frac{2 + \left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\left(\sin y - \frac{\sin x}{16}\right) \cdot \left(\cos x - \cos y\right)\right)}{3 \cdot \left(1 + \mathsf{fma}\left(\cos x, \sqrt{5} \cdot 0.5 + -0.5, \cos y \cdot \frac{2.25 + -5 \cdot \color{blue}{0.25}}{1.5 + \sqrt{5} \cdot 0.5}\right)\right)} \]
   metadata-eval [=>] 99.4%	\[ \frac{2 + \left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\left(\sin y - \frac{\sin x}{16}\right) \cdot \left(\cos x - \cos y\right)\right)}{3 \cdot \left(1 + \mathsf{fma}\left(\cos x, \sqrt{5} \cdot 0.5 + -0.5, \cos y \cdot \frac{2.25 + \color{blue}{-1.25}}{1.5 + \sqrt{5} \cdot 0.5}\right)\right)} \]
   metadata-eval [=>] 99.4%	\[ \frac{2 + \left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\left(\sin y - \frac{\sin x}{16}\right) \cdot \left(\cos x - \cos y\right)\right)}{3 \cdot \left(1 + \mathsf{fma}\left(\cos x, \sqrt{5} \cdot 0.5 + -0.5, \cos y \cdot \frac{\color{blue}{1}}{1.5 + \sqrt{5} \cdot 0.5}\right)\right)} \]
   +-commutative [=>] 99.4%	\[ \frac{2 + \left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\left(\sin y - \frac{\sin x}{16}\right) \cdot \left(\cos x - \cos y\right)\right)}{3 \cdot \left(1 + \mathsf{fma}\left(\cos x, \sqrt{5} \cdot 0.5 + -0.5, \cos y \cdot \frac{1}{\color{blue}{\sqrt{5} \cdot 0.5 + 1.5}}\right)\right)} \]
   *-commutative [=>] 99.4%	\[ \frac{2 + \left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\left(\sin y - \frac{\sin x}{16}\right) \cdot \left(\cos x - \cos y\right)\right)}{3 \cdot \left(1 + \mathsf{fma}\left(\cos x, \sqrt{5} \cdot 0.5 + -0.5, \cos y \cdot \frac{1}{\color{blue}{0.5 \cdot \sqrt{5}} + 1.5}\right)\right)} \]
   fma-def [=>] 99.4%	\[ \frac{2 + \left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\left(\sin y - \frac{\sin x}{16}\right) \cdot \left(\cos x - \cos y\right)\right)}{3 \cdot \left(1 + \mathsf{fma}\left(\cos x, \sqrt{5} \cdot 0.5 + -0.5, \cos y \cdot \frac{1}{\color{blue}{\mathsf{fma}\left(0.5, \sqrt{5}, 1.5\right)}}\right)\right)} \]

6. Final simplification 99.4%

   \[\leadsto \frac{2 + \left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\left(\sin y - \frac{\sin x}{16}\right) \cdot \left(\cos x - \cos y\right)\right)}{3 \cdot \left(1 + \mathsf{fma}\left(\cos x, -0.5 + \sqrt{5} \cdot 0.5, \cos y \cdot \frac{1}{\mathsf{fma}\left(0.5, \sqrt{5}, 1.5\right)}\right)\right)} \]

Alternatives

Alternative 1
Accuracy	99.3%
Cost	85568

\[\frac{2 + \left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\left(\sin y - \frac{\sin x}{16}\right) \cdot \left(\cos x - \cos y\right)\right)}{3 \cdot \left(1 + \mathsf{fma}\left(\cos x, -0.5 + \sqrt{5} \cdot 0.5, \cos y \cdot \frac{1}{\mathsf{fma}\left(0.5, \sqrt{5}, 1.5\right)}\right)\right)} \]

Alternative 2
Accuracy	99.3%
Cost	78912

\[\frac{2 + \left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\left(\sin y - \frac{\sin x}{16}\right) \cdot \left(\cos x - \cos y\right)\right)}{3 \cdot \left(1 + \mathsf{fma}\left(\cos x, -0.5 + \sqrt{1.25}, \frac{\cos y}{1.5 + \sqrt{1.25}}\right)\right)} \]

Alternative 3
Accuracy	82.2%
Cost	72904

\[\begin{array}{l} t_0 := \sqrt{2} \cdot \sin x\\ t_1 := 1 + \cos x \cdot \frac{\sqrt{5} + -1}{2}\\ t_2 := \cos x - \cos y\\ t_3 := \sin y - \frac{\sin x}{16}\\ \mathbf{if}\;x \leq -0.085:\\ \;\;\;\;\frac{2 + t_2 \cdot \left(t_3 \cdot t_0\right)}{3 \cdot \left(t_1 + \cos y \cdot \frac{\frac{4}{3 + \sqrt{5}}}{2}\right)}\\ \mathbf{elif}\;x \leq 0.022:\\ \;\;\;\;\frac{2 + \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot t_3\right) \cdot \left(1 + \left(-0.5 \cdot \left(x \cdot x\right) - \cos y\right)\right)}{3 \cdot \left(t_1 + \cos y \cdot \frac{3 - \sqrt{5}}{2}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \left(t_3 \cdot t_2\right) \cdot t_0}{3 \cdot \left(1 + \left(\cos y \cdot \frac{1}{\mathsf{fma}\left(0.5, \sqrt{5}, 1.5\right)} + \cos x \cdot \left(\frac{\sqrt{5}}{2} - 0.5\right)\right)\right)}\\ \end{array} \]

Alternative 4
Accuracy	99.3%
Cost	72640

\[\frac{2 + \left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\left(\sin y - \frac{\sin x}{16}\right) \cdot \left(\cos x - \cos y\right)\right)}{3 \cdot \left(1 + \left(\frac{\cos y}{1.5 + \sqrt{1.25}} + \cos x \cdot \left(-0.5 + \sqrt{1.25}\right)\right)\right)} \]

Alternative 5
Accuracy	81.9%
Cost	67145

\[\begin{array}{l} t_0 := \sin y - \frac{\sin x}{16}\\ t_1 := 1 + \cos x \cdot \frac{\sqrt{5} + -1}{2}\\ \mathbf{if}\;x \leq -0.016 \lor \neg \left(x \leq 2.4 \cdot 10^{-11}\right):\\ \;\;\;\;\frac{2 + \left(\cos x - \cos y\right) \cdot \left(t_0 \cdot \left(\sqrt{2} \cdot \sin x\right)\right)}{3 \cdot \left(t_1 + \cos y \cdot \frac{\frac{4}{3 + \sqrt{5}}}{2}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot t_0\right) \cdot \left(1 + \left(-0.5 \cdot \left(x \cdot x\right) - \cos y\right)\right)}{3 \cdot \left(t_1 + \cos y \cdot \frac{3 - \sqrt{5}}{2}\right)}\\ \end{array} \]

Alternative 6
Accuracy	81.9%
Cost	66889

\[\begin{array}{l} t_0 := 3 \cdot \left(\left(1 + \cos x \cdot \frac{\sqrt{5} + -1}{2}\right) + \cos y \cdot \frac{\frac{4}{3 + \sqrt{5}}}{2}\right)\\ \mathbf{if}\;x \leq -0.0027 \lor \neg \left(x \leq 2.4 \cdot 10^{-11}\right):\\ \;\;\;\;\frac{2 + \left(\cos x - \cos y\right) \cdot \left(\left(\sin y - \frac{\sin x}{16}\right) \cdot \left(\sqrt{2} \cdot \sin x\right)\right)}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \left(\left(\sqrt{2} \cdot \left(\sin y + \sin x \cdot -0.0625\right)\right) \cdot \left(\sin x + \sin y \cdot -0.0625\right)\right) \cdot \left(1 - \cos y\right)}{t_0}\\ \end{array} \]

Alternative 7
Accuracy	81.9%
Cost	66761

\[\begin{array}{l} t_0 := \sin y - \frac{\sin x}{16}\\ t_1 := \cos y \cdot \frac{\frac{4}{3 + \sqrt{5}}}{2}\\ \mathbf{if}\;x \leq -0.0022 \lor \neg \left(x \leq 2.4 \cdot 10^{-11}\right):\\ \;\;\;\;\frac{2 + \left(\cos x - \cos y\right) \cdot \left(t_0 \cdot \left(\sqrt{2} \cdot \sin x\right)\right)}{3 \cdot \left(\left(1 + \cos x \cdot \frac{\sqrt{5} + -1}{2}\right) + t_1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot t_0\right) \cdot \left(1 - \cos y\right)}{3 \cdot \left(t_1 + \left(1 + \cos x \cdot \left(-0.5 + \sqrt{1.25}\right)\right)\right)}\\ \end{array} \]

Alternative 8
Accuracy	81.9%
Cost	66761

\[\begin{array}{l} t_0 := \sin y - \frac{\sin x}{16}\\ t_1 := \cos y \cdot \frac{\frac{4}{3 + \sqrt{5}}}{2}\\ \mathbf{if}\;x \leq -0.0095 \lor \neg \left(x \leq 2.4 \cdot 10^{-11}\right):\\ \;\;\;\;\frac{2 + \left(\cos x - \cos y\right) \cdot \left(t_0 \cdot \left(\sqrt{2} \cdot \sin x\right)\right)}{3 \cdot \left(\left(1 + \cos x \cdot \frac{\sqrt{5} + -1}{2}\right) + t_1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot t_0\right) \cdot \left(1 - \cos y\right)}{3 \cdot \left(t_1 + \left(1 + \frac{\cos x}{0.5 + \sqrt{1.25}}\right)\right)}\\ \end{array} \]

Alternative 9
Accuracy	81.9%
Cost	66633

\[\begin{array}{l} t_0 := \sqrt{5} + -1\\ t_1 := \sin y - \frac{\sin x}{16}\\ t_2 := \cos y \cdot \frac{\frac{4}{3 + \sqrt{5}}}{2}\\ \mathbf{if}\;x \leq -0.005 \lor \neg \left(x \leq 2.4 \cdot 10^{-11}\right):\\ \;\;\;\;\frac{2 + \left(\cos x - \cos y\right) \cdot \left(t_1 \cdot \left(\sqrt{2} \cdot \sin x\right)\right)}{3 \cdot \left(\left(1 + \cos x \cdot \frac{t_0}{2}\right) + t_2\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot t_1\right) \cdot \left(1 - \cos y\right)}{3 \cdot \left(t_2 + \left(1 + t_0 \cdot \left(0.5 + \left(x \cdot x\right) \cdot -0.25\right)\right)\right)}\\ \end{array} \]

Alternative 10
Accuracy	81.8%
Cost	66505

\[\begin{array}{l} t_0 := \frac{\sqrt{5}}{2}\\ t_1 := \sin y - \frac{\sin x}{16}\\ \mathbf{if}\;x \leq -0.0027 \lor \neg \left(x \leq 2.4 \cdot 10^{-11}\right):\\ \;\;\;\;\frac{2 + \left(t_1 \cdot \left(\cos x - \cos y\right)\right) \cdot \left(\sqrt{2} \cdot \sin x\right)}{3 \cdot \left(1 + \left(\cos x \cdot \left(t_0 - 0.5\right) + \cos y \cdot \left(1.5 - t_0\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot t_1\right) \cdot \left(1 - \cos y\right)}{3 \cdot \left(\cos y \cdot \frac{\frac{4}{3 + \sqrt{5}}}{2} + \left(1 + \left(\sqrt{5} + -1\right) \cdot \left(0.5 + \left(x \cdot x\right) \cdot -0.25\right)\right)\right)}\\ \end{array} \]

Alternative 11
Accuracy	80.5%
Cost	66504

\[\begin{array}{l} t_0 := \sin y - \frac{\sin x}{16}\\ t_1 := \sqrt{5} + -1\\ t_2 := \cos y \cdot \frac{\frac{4}{3 + \sqrt{5}}}{2}\\ \mathbf{if}\;x \leq -0.0048:\\ \;\;\;\;\frac{2 + \left(\cos x - \cos y\right) \cdot \left({\sin x}^{2} \cdot \left(\sqrt{2} \cdot -0.0625\right)\right)}{3 \cdot \left(\left(1 + \cos x \cdot \frac{t_1}{2}\right) + t_2\right)}\\ \mathbf{elif}\;x \leq 0.008:\\ \;\;\;\;\frac{2 + \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot t_0\right) \cdot \left(1 - \cos y\right)}{3 \cdot \left(t_2 + \left(1 + t_1 \cdot \left(0.5 + \left(x \cdot x\right) \cdot -0.25\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \left(\sqrt{2} \cdot \sin x\right) \cdot \left(t_0 \cdot \left(\cos x + -1\right)\right)}{3 \cdot \left(1 + \left(\cos y \cdot \frac{1}{\mathsf{fma}\left(0.5, \sqrt{5}, 1.5\right)} + \cos x \cdot \left(\frac{\sqrt{5}}{2} - 0.5\right)\right)\right)}\\ \end{array} \]

Alternative 12
Accuracy	81.8%
Cost	66504

\[\begin{array}{l} t_0 := \sqrt{2} \cdot \sin x\\ t_1 := \frac{\sqrt{5}}{2}\\ t_2 := \cos x - \cos y\\ t_3 := \sqrt{5} + -1\\ t_4 := \sin y - \frac{\sin x}{16}\\ \mathbf{if}\;x \leq -0.0052:\\ \;\;\;\;\frac{2 + t_2 \cdot \left(t_4 \cdot t_0\right)}{3 \cdot \left(\left(1 + \cos x \cdot \frac{t_3}{2}\right) + \cos y \cdot \frac{3 - \sqrt{5}}{2}\right)}\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{-11}:\\ \;\;\;\;\frac{2 + \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot t_4\right) \cdot \left(1 - \cos y\right)}{3 \cdot \left(\cos y \cdot \frac{\frac{4}{3 + \sqrt{5}}}{2} + \left(1 + t_3 \cdot \left(0.5 + \left(x \cdot x\right) \cdot -0.25\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \left(t_4 \cdot t_2\right) \cdot t_0}{3 \cdot \left(1 + \left(\cos x \cdot \left(t_1 - 0.5\right) + \cos y \cdot \left(1.5 - t_1\right)\right)\right)}\\ \end{array} \]

Alternative 13
Accuracy	80.2%
Cost	60745

\[\begin{array}{l} t_0 := \cos y \cdot \frac{\frac{4}{3 + \sqrt{5}}}{2}\\ t_1 := \sqrt{5} + -1\\ \mathbf{if}\;x \leq -0.0036 \lor \neg \left(x \leq 2.4 \cdot 10^{-11}\right):\\ \;\;\;\;\frac{2 + \left(\cos x - \cos y\right) \cdot \left({\sin x}^{2} \cdot \left(\sqrt{2} \cdot -0.0625\right)\right)}{3 \cdot \left(\left(1 + \cos x \cdot \frac{t_1}{2}\right) + t_0\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(1 - \cos y\right)}{3 \cdot \left(t_0 + \left(1 + t_1 \cdot \left(0.5 + \left(x \cdot x\right) \cdot -0.25\right)\right)\right)}\\ \end{array} \]

Alternative 14
Accuracy	80.2%
Cost	60361

\[\begin{array}{l} t_0 := \cos y \cdot \frac{\frac{4}{3 + \sqrt{5}}}{2}\\ t_1 := \sqrt{5} + -1\\ \mathbf{if}\;x \leq -0.00029 \lor \neg \left(x \leq 2.4 \cdot 10^{-11}\right):\\ \;\;\;\;\frac{2 + \left(\cos x - \cos y\right) \cdot \left({\sin x}^{2} \cdot \left(\sqrt{2} \cdot -0.0625\right)\right)}{3 \cdot \left(\left(1 + \cos x \cdot \frac{t_1}{2}\right) + t_0\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(1 - \cos y\right)}{3 \cdot \left(t_0 + \left(1 + 0.5 \cdot t_1\right)\right)}\\ \end{array} \]

Alternative 15
Accuracy	80.1%
Cost	60297

\[\begin{array}{l} t_0 := \sqrt{5} \cdot 0.5\\ \mathbf{if}\;x \leq -0.0027 \lor \neg \left(x \leq 2.4 \cdot 10^{-11}\right):\\ \;\;\;\;\frac{2 + \left(\cos x - \cos y\right) \cdot \left({\sin x}^{2} \cdot \left(\sqrt{2} \cdot -0.0625\right)\right)}{3 \cdot \left(\left(1 + \cos x \cdot \frac{\sqrt{5} + -1}{2}\right) + \cos y \cdot \frac{\frac{4}{3 + \sqrt{5}}}{2}\right)}\\ \mathbf{else}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{2 + \sqrt{2} \cdot \left(\left(1 - \cos y\right) \cdot \left(-0.0625 \cdot {\sin y}^{2} + \sin y \cdot \left(x \cdot 1.00390625\right)\right)\right)}{1 + \left(\frac{\cos y}{1.5 + t_0} + \cos x \cdot \left(t_0 - 0.5\right)\right)}\\ \end{array} \]

Alternative 16
Accuracy	80.1%
Cost	60041

\[\begin{array}{l} t_0 := 3 \cdot \left(\left(1 + \cos x \cdot \frac{\sqrt{5} + -1}{2}\right) + \cos y \cdot \frac{\frac{4}{3 + \sqrt{5}}}{2}\right)\\ \mathbf{if}\;x \leq -0.0008 \lor \neg \left(x \leq 2.4 \cdot 10^{-11}\right):\\ \;\;\;\;\frac{2 + \left(\cos x - \cos y\right) \cdot \left({\sin x}^{2} \cdot \left(\sqrt{2} \cdot -0.0625\right)\right)}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \left(1 - \cos y\right) \cdot \left(\sqrt{2} \cdot \left(-0.0625 \cdot {\sin y}^{2}\right)\right)}{t_0}\\ \end{array} \]

Alternative 17
Accuracy	80.0%
Cost	59913

\[\begin{array}{l} t_0 := 1 + \cos x \cdot \frac{\sqrt{5} + -1}{2}\\ \mathbf{if}\;x \leq -0.00175 \lor \neg \left(x \leq 2.4 \cdot 10^{-11}\right):\\ \;\;\;\;\frac{2 + \left(\cos x - \cos y\right) \cdot \left({\sin x}^{2} \cdot \left(\sqrt{2} \cdot -0.0625\right)\right)}{3 \cdot \left(t_0 + \cos y \cdot \frac{3 - \sqrt{5}}{2}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \left(1 - \cos y\right) \cdot \left(\sqrt{2} \cdot \left(-0.0625 \cdot {\sin y}^{2}\right)\right)}{3 \cdot \left(t_0 + \cos y \cdot \frac{\frac{4}{3 + \sqrt{5}}}{2}\right)}\\ \end{array} \]

Alternative 18
Accuracy	79.1%
Cost	59908

\[\begin{array}{l} t_0 := 3 \cdot \left(\left(1 + \cos x \cdot \frac{\sqrt{5} + -1}{2}\right) + \cos y \cdot \frac{\frac{4}{3 + \sqrt{5}}}{2}\right)\\ t_1 := \sqrt{2} \cdot \left(-0.0625 \cdot {\sin y}^{2}\right)\\ \mathbf{if}\;y \leq -1.2 \cdot 10^{+15}:\\ \;\;\;\;\frac{2 + \left(\cos x - \cos y\right) \cdot t_1}{t_0}\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-26}:\\ \;\;\;\;\frac{2 + \left(\sqrt{2} \cdot \sin x\right) \cdot \left(\left(\sin y - \frac{\sin x}{16}\right) \cdot \left(\cos x + -1\right)\right)}{3 \cdot \left(1 + \left(1.5 + \left(\cos x \cdot \mathsf{fma}\left(0.5, \sqrt{5}, -0.5\right) - \sqrt{5} \cdot 0.5\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \left(1 - \cos y\right) \cdot t_1}{t_0}\\ \end{array} \]

Alternative 19
Accuracy	79.1%
Cost	59849

\[\begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{+15} \lor \neg \left(y \leq 1.45 \cdot 10^{-26}\right):\\ \;\;\;\;\frac{2 + \left(1 - \cos y\right) \cdot \left(\sqrt{2} \cdot \left(-0.0625 \cdot {\sin y}^{2}\right)\right)}{3 \cdot \left(\left(1 + \cos x \cdot \frac{\sqrt{5} + -1}{2}\right) + \cos y \cdot \frac{\frac{4}{3 + \sqrt{5}}}{2}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \left(\sqrt{2} \cdot \sin x\right) \cdot \left(\left(\sin y - \frac{\sin x}{16}\right) \cdot \left(\cos x + -1\right)\right)}{3 \cdot \left(1 + \left(1.5 + \left(\cos x \cdot \mathsf{fma}\left(0.5, \sqrt{5}, -0.5\right) - \sqrt{5} \cdot 0.5\right)\right)\right)}\\ \end{array} \]

Alternative 20
Accuracy	79.1%
Cost	59848

\[\begin{array}{l} t_0 := 1 + \cos x \cdot \frac{\sqrt{5} + -1}{2}\\ t_1 := \sqrt{2} \cdot \left(-0.0625 \cdot {\sin y}^{2}\right)\\ \mathbf{if}\;y \leq -1.2 \cdot 10^{+15}:\\ \;\;\;\;\frac{2 + \left(\cos x - \cos y\right) \cdot t_1}{3 \cdot \left(t_0 + \cos y \cdot \frac{3 - \sqrt{5}}{2}\right)}\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-26}:\\ \;\;\;\;\frac{2 + \left(\sqrt{2} \cdot \sin x\right) \cdot \left(\left(\sin y - \frac{\sin x}{16}\right) \cdot \left(\cos x + -1\right)\right)}{3 \cdot \left(1 + \left(1.5 + \left(\cos x \cdot \mathsf{fma}\left(0.5, \sqrt{5}, -0.5\right) - \sqrt{5} \cdot 0.5\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \left(1 - \cos y\right) \cdot t_1}{3 \cdot \left(t_0 + \cos y \cdot \frac{\frac{4}{3 + \sqrt{5}}}{2}\right)}\\ \end{array} \]

Alternative 21
Accuracy	79.0%
Cost	53641

\[\begin{array}{l} t_0 := \sqrt{5} \cdot 0.5\\ \mathbf{if}\;y \leq -1.2 \cdot 10^{+15} \lor \neg \left(y \leq 1.45 \cdot 10^{-26}\right):\\ \;\;\;\;\frac{2 + \left(1 - \cos y\right) \cdot \left(\sqrt{2} \cdot \left(-0.0625 \cdot {\sin y}^{2}\right)\right)}{3 \cdot \left(\left(1 + \cos x \cdot \frac{\sqrt{5} + -1}{2}\right) + \cos y \cdot \frac{\frac{4}{3 + \sqrt{5}}}{2}\right)}\\ \mathbf{else}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{2 + -0.0625 \cdot \left(\sqrt{2} \cdot \left({\sin x}^{2} \cdot \left(\cos x + -1\right)\right)\right)}{1 + \left(\cos x \cdot \left(t_0 - 0.5\right) + \frac{1}{1.5 + t_0}\right)}\\ \end{array} \]

Alternative 22
Accuracy	78.9%
Cost	53513

\[\begin{array}{l} t_0 := \sqrt{5} \cdot 0.5\\ t_1 := \cos x \cdot \left(t_0 - 0.5\right)\\ t_2 := 1.5 + t_0\\ \mathbf{if}\;y \leq -1.2 \cdot 10^{+15} \lor \neg \left(y \leq 1.45 \cdot 10^{-26}\right):\\ \;\;\;\;0.3333333333333333 \cdot \frac{2 + \left(\sqrt{2} \cdot -0.0625\right) \cdot \left(\left(1 - \cos y\right) \cdot {\sin y}^{2}\right)}{1 + \left(\frac{\cos y}{t_2} + t_1\right)}\\ \mathbf{else}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{2 + -0.0625 \cdot \left(\sqrt{2} \cdot \left({\sin x}^{2} \cdot \left(\cos x + -1\right)\right)\right)}{1 + \left(t_1 + \frac{1}{t_2}\right)}\\ \end{array} \]

Alternative 23
Accuracy	79.4%
Cost	47113

\[\begin{array}{l} t_0 := \sqrt{5} \cdot 0.5\\ \mathbf{if}\;x \leq -0.000135 \lor \neg \left(x \leq 2.4 \cdot 10^{-11}\right):\\ \;\;\;\;0.3333333333333333 \cdot \frac{2 + -0.0625 \cdot \left(\sqrt{2} \cdot \left({\sin x}^{2} \cdot \left(\cos x + -1\right)\right)\right)}{1 + \left(\cos x \cdot \left(t_0 - 0.5\right) + \frac{1}{1.5 + t_0}\right)}\\ \mathbf{else}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{2 + -0.0625 \cdot \left(\sqrt{2} \cdot \left(\left(1 - \cos y\right) \cdot {\sin y}^{2}\right)\right)}{0.5 + \left(t_0 + \cos y \cdot \left(1.5 - t_0\right)\right)}\\ \end{array} \]

Alternative 24
Accuracy	79.3%
Cost	46857

\[\begin{array}{l} t_0 := \sqrt{5} \cdot 0.5\\ \mathbf{if}\;x \leq -0.00019 \lor \neg \left(x \leq 2.4 \cdot 10^{-11}\right):\\ \;\;\;\;0.3333333333333333 \cdot \frac{2 + -0.0625 \cdot \left(\sqrt{2} \cdot \left({\sin x}^{2} \cdot \left(\cos x + -1\right)\right)\right)}{\left(\cos x \cdot \left(t_0 - 0.5\right) + 2.5\right) - t_0}\\ \mathbf{else}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{2 + -0.0625 \cdot \left(\sqrt{2} \cdot \left(\left(1 - \cos y\right) \cdot {\sin y}^{2}\right)\right)}{0.5 + \left(t_0 + \cos y \cdot \left(1.5 - t_0\right)\right)}\\ \end{array} \]

Alternative 25
Accuracy	79.3%
Cost	46856

\[\begin{array}{l} t_0 := {\sin x}^{2}\\ t_1 := \sqrt{5} \cdot 0.5\\ t_2 := \cos x \cdot \left(t_1 - 0.5\right)\\ \mathbf{if}\;x \leq -0.000135:\\ \;\;\;\;\frac{2 + \left(\sqrt{2} \cdot t_0\right) \cdot \left(0.0625 + \cos x \cdot -0.0625\right)}{3 \cdot \left(1 + \left(\left(1.5 + t_2\right) - t_1\right)\right)}\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{-11}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{2 + -0.0625 \cdot \left(\sqrt{2} \cdot \left(\left(1 - \cos y\right) \cdot {\sin y}^{2}\right)\right)}{0.5 + \left(t_1 + \cos y \cdot \left(1.5 - t_1\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{2 + -0.0625 \cdot \left(\sqrt{2} \cdot \left(t_0 \cdot \left(\cos x + -1\right)\right)\right)}{\left(t_2 + 2.5\right) - t_1}\\ \end{array} \]

Alternative 26
Accuracy	61.1%
Cost	46592

\[\begin{array}{l} t_0 := \sqrt{5} \cdot 0.5\\ 0.3333333333333333 \cdot \frac{2 + -0.0625 \cdot \left(\sqrt{2} \cdot \left({\sin x}^{2} \cdot \left(\cos x + -1\right)\right)\right)}{\left(\cos x \cdot \left(t_0 - 0.5\right) + 2.5\right) - t_0} \end{array} \]

Alternative 27
Accuracy	41.0%
Cost	39424

\[\log \left(e^{0.3333333333333333 \cdot \left(0.5 \cdot \left(2 + -0.0625 \cdot \left(\sqrt{2} \cdot \left({\sin x}^{2} \cdot \left(\cos x + -1\right)\right)\right)\right)\right)}\right) \]

Alternative 28
Accuracy	41.0%
Cost	26368

\[0.3333333333333333 + \left(\left(\sqrt{2} \cdot {\sin x}^{2}\right) \cdot \left(\cos x + -1\right)\right) \cdot -0.010416666666666666 \]

Alternative 29
Accuracy	41.0%
Cost	64

\[0.3333333333333333 \]

Reproduce

herbie shell --seed 2023272 
(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))))))