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

Percentage Accurate: 99.3% → 99.4%

Time: 40.0s

Precision: binary64

Cost: 138048

Math

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

↓

\[\begin{array}{l} t_0 := \left(\cos x - \cos y\right) \cdot \left(\sin y - \sin x \cdot 0.0625\right)\\ \frac{\mathsf{fma}\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right), \sqrt[3]{t_0 \cdot \left(t_0 \cdot t_0\right)}, 2\right)}{3 + \left(\cos y \cdot \left(\frac{4}{3 + \sqrt{5}} \cdot 1.5\right) + 1.5 \cdot \left(\cos x \cdot \left(\sqrt{5} + -1\right)\right)\right)} \end{array} \]

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
 (let* ((t_0 (* (- (cos x) (cos y)) (- (sin y) (* (sin x) 0.0625)))))
   (/
    (fma
     (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
     (cbrt (* t_0 (* t_0 t_0)))
     2.0)
    (+
     3.0
     (+
      (* (cos y) (* (/ 4.0 (+ 3.0 (sqrt 5.0))) 1.5))
      (* 1.5 (* (cos x) (+ (sqrt 5.0) -1.0))))))))

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) {
	double t_0 = (cos(x) - cos(y)) * (sin(y) - (sin(x) * 0.0625));
	return fma((sqrt(2.0) * (sin(x) - (sin(y) / 16.0))), cbrt((t_0 * (t_0 * t_0))), 2.0) / (3.0 + ((cos(y) * ((4.0 / (3.0 + sqrt(5.0))) * 1.5)) + (1.5 * (cos(x) * (sqrt(5.0) + -1.0)))));
}

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)
	t_0 = Float64(Float64(cos(x) - cos(y)) * Float64(sin(y) - Float64(sin(x) * 0.0625)))
	return Float64(fma(Float64(sqrt(2.0) * Float64(sin(x) - Float64(sin(y) / 16.0))), cbrt(Float64(t_0 * Float64(t_0 * t_0))), 2.0) / Float64(3.0 + Float64(Float64(cos(y) * Float64(Float64(4.0 / Float64(3.0 + sqrt(5.0))) * 1.5)) + Float64(1.5 * Float64(cos(x) * Float64(sqrt(5.0) + -1.0))))))
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_] := Block[{t$95$0 = N[(N[(N[Cos[x], $MachinePrecision] - N[Cos[y], $MachinePrecision]), $MachinePrecision] * N[(N[Sin[y], $MachinePrecision] - N[(N[Sin[x], $MachinePrecision] * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(N[(N[(N[Sqrt[2.0], $MachinePrecision] * N[(N[Sin[x], $MachinePrecision] - N[(N[Sin[y], $MachinePrecision] / 16.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[Power[N[(t$95$0 * N[(t$95$0 * t$95$0), $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision] + 2.0), $MachinePrecision] / N[(3.0 + N[(N[(N[Cos[y], $MachinePrecision] * N[(N[(4.0 / N[(3.0 + N[Sqrt[5.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * 1.5), $MachinePrecision]), $MachinePrecision] + N[(1.5 * N[(N[Cos[x], $MachinePrecision] * N[(N[Sqrt[5.0], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Initial program 99.2%

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

2. Simplified 99.3%

   \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right), \left(\sin y - \frac{\sin x}{16}\right) \cdot \left(\cos x - \cos y\right), 2\right)}{3 + \mathsf{fma}\left(\cos y, \frac{3 - \sqrt{5}}{0.6666666666666666}, \frac{\cos x \cdot \left(\sqrt{5} + -1\right)}{0.6666666666666666}\right)}} \]
   Step-by-step derivation

   [Start] 99.2%	\[ \frac{2 + \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x - \cos y\right)}{3 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{3 - \sqrt{5}}{2} \cdot \cos y\right)} \]
   +-commutative [=>] 99.2%	\[ \frac{\color{blue}{\left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x - \cos y\right) + 2}}{3 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{3 - \sqrt{5}}{2} \cdot \cos y\right)} \]
   associate-*l* [=>] 99.2%	\[ \frac{\color{blue}{\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\left(\sin y - \frac{\sin x}{16}\right) \cdot \left(\cos x - \cos y\right)\right)} + 2}{3 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{3 - \sqrt{5}}{2} \cdot \cos y\right)} \]
   fma-def [=>] 99.3%	\[ \frac{\color{blue}{\mathsf{fma}\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right), \left(\sin y - \frac{\sin x}{16}\right) \cdot \left(\cos x - \cos y\right), 2\right)}}{3 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{3 - \sqrt{5}}{2} \cdot \cos y\right)} \]
   associate-+l+ [=>] 99.3%	\[ \frac{\mathsf{fma}\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right), \left(\sin y - \frac{\sin x}{16}\right) \cdot \left(\cos x - \cos y\right), 2\right)}{3 \cdot \color{blue}{\left(1 + \left(\frac{\sqrt{5} - 1}{2} \cdot \cos x + \frac{3 - \sqrt{5}}{2} \cdot \cos y\right)\right)}} \]
   distribute-lft-in [=>] 99.3%	\[ \frac{\mathsf{fma}\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right), \left(\sin y - \frac{\sin x}{16}\right) \cdot \left(\cos x - \cos y\right), 2\right)}{\color{blue}{3 \cdot 1 + 3 \cdot \left(\frac{\sqrt{5} - 1}{2} \cdot \cos x + \frac{3 - \sqrt{5}}{2} \cdot \cos y\right)}} \]
   metadata-eval [=>] 99.3%	\[ \frac{\mathsf{fma}\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right), \left(\sin y - \frac{\sin x}{16}\right) \cdot \left(\cos x - \cos y\right), 2\right)}{\color{blue}{3} + 3 \cdot \left(\frac{\sqrt{5} - 1}{2} \cdot \cos x + \frac{3 - \sqrt{5}}{2} \cdot \cos y\right)} \]

3. Applied egg-rr 99.4%

   \[\leadsto \frac{\mathsf{fma}\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right), \left(\sin y - \frac{\sin x}{16}\right) \cdot \left(\cos x - \cos y\right), 2\right)}{3 + \mathsf{fma}\left(\cos y, \frac{\color{blue}{\frac{4}{3 + \sqrt{5}}}}{0.6666666666666666}, \frac{\cos x \cdot \left(\sqrt{5} + -1\right)}{0.6666666666666666}\right)} \]
   Step-by-step derivation

   [Start] 99.3%	\[ \frac{\mathsf{fma}\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right), \left(\sin y - \frac{\sin x}{16}\right) \cdot \left(\cos x - \cos y\right), 2\right)}{3 + \mathsf{fma}\left(\cos y, \frac{3 - \sqrt{5}}{0.6666666666666666}, \frac{\cos x \cdot \left(\sqrt{5} + -1\right)}{0.6666666666666666}\right)} \]
   flip-- [=>] 99.3%	\[ \frac{\mathsf{fma}\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right), \left(\sin y - \frac{\sin x}{16}\right) \cdot \left(\cos x - \cos y\right), 2\right)}{3 + \mathsf{fma}\left(\cos y, \frac{\color{blue}{\frac{3 \cdot 3 - \sqrt{5} \cdot \sqrt{5}}{3 + \sqrt{5}}}}{0.6666666666666666}, \frac{\cos x \cdot \left(\sqrt{5} + -1\right)}{0.6666666666666666}\right)} \]
   metadata-eval [=>] 99.3%	\[ \frac{\mathsf{fma}\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right), \left(\sin y - \frac{\sin x}{16}\right) \cdot \left(\cos x - \cos y\right), 2\right)}{3 + \mathsf{fma}\left(\cos y, \frac{\frac{\color{blue}{9} - \sqrt{5} \cdot \sqrt{5}}{3 + \sqrt{5}}}{0.6666666666666666}, \frac{\cos x \cdot \left(\sqrt{5} + -1\right)}{0.6666666666666666}\right)} \]
   add-sqr-sqrt [<=] 99.4%	\[ \frac{\mathsf{fma}\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right), \left(\sin y - \frac{\sin x}{16}\right) \cdot \left(\cos x - \cos y\right), 2\right)}{3 + \mathsf{fma}\left(\cos y, \frac{\frac{9 - \color{blue}{5}}{3 + \sqrt{5}}}{0.6666666666666666}, \frac{\cos x \cdot \left(\sqrt{5} + -1\right)}{0.6666666666666666}\right)} \]
   metadata-eval [=>] 99.4%	\[ \frac{\mathsf{fma}\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right), \left(\sin y - \frac{\sin x}{16}\right) \cdot \left(\cos x - \cos y\right), 2\right)}{3 + \mathsf{fma}\left(\cos y, \frac{\frac{\color{blue}{4}}{3 + \sqrt{5}}}{0.6666666666666666}, \frac{\cos x \cdot \left(\sqrt{5} + -1\right)}{0.6666666666666666}\right)} \]

4. Applied egg-rr 99.4%

   \[\leadsto \frac{\mathsf{fma}\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right), \left(\sin y - \frac{\sin x}{16}\right) \cdot \left(\cos x - \cos y\right), 2\right)}{3 + \color{blue}{\left(\cos y \cdot \left(\frac{4}{3 + \sqrt{5}} \cdot 1.5\right) + \left(\cos x \cdot \left(\sqrt{5} + -1\right)\right) \cdot 1.5\right)}} \]
   Step-by-step derivation

   [Start] 99.4%	\[ \frac{\mathsf{fma}\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right), \left(\sin y - \frac{\sin x}{16}\right) \cdot \left(\cos x - \cos y\right), 2\right)}{3 + \mathsf{fma}\left(\cos y, \frac{\frac{4}{3 + \sqrt{5}}}{0.6666666666666666}, \frac{\cos x \cdot \left(\sqrt{5} + -1\right)}{0.6666666666666666}\right)} \]
   fma-udef [=>] 99.4%	\[ \frac{\mathsf{fma}\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right), \left(\sin y - \frac{\sin x}{16}\right) \cdot \left(\cos x - \cos y\right), 2\right)}{3 + \color{blue}{\left(\cos y \cdot \frac{\frac{4}{3 + \sqrt{5}}}{0.6666666666666666} + \frac{\cos x \cdot \left(\sqrt{5} + -1\right)}{0.6666666666666666}\right)}} \]
   div-inv [=>] 99.4%	\[ \frac{\mathsf{fma}\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right), \left(\sin y - \frac{\sin x}{16}\right) \cdot \left(\cos x - \cos y\right), 2\right)}{3 + \left(\cos y \cdot \color{blue}{\left(\frac{4}{3 + \sqrt{5}} \cdot \frac{1}{0.6666666666666666}\right)} + \frac{\cos x \cdot \left(\sqrt{5} + -1\right)}{0.6666666666666666}\right)} \]
   metadata-eval [=>] 99.4%	\[ \frac{\mathsf{fma}\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right), \left(\sin y - \frac{\sin x}{16}\right) \cdot \left(\cos x - \cos y\right), 2\right)}{3 + \left(\cos y \cdot \left(\frac{4}{3 + \sqrt{5}} \cdot \color{blue}{1.5}\right) + \frac{\cos x \cdot \left(\sqrt{5} + -1\right)}{0.6666666666666666}\right)} \]
   div-inv [=>] 99.4%	\[ \frac{\mathsf{fma}\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right), \left(\sin y - \frac{\sin x}{16}\right) \cdot \left(\cos x - \cos y\right), 2\right)}{3 + \left(\cos y \cdot \left(\frac{4}{3 + \sqrt{5}} \cdot 1.5\right) + \color{blue}{\left(\cos x \cdot \left(\sqrt{5} + -1\right)\right) \cdot \frac{1}{0.6666666666666666}}\right)} \]
   metadata-eval [=>] 99.4%	\[ \frac{\mathsf{fma}\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right), \left(\sin y - \frac{\sin x}{16}\right) \cdot \left(\cos x - \cos y\right), 2\right)}{3 + \left(\cos y \cdot \left(\frac{4}{3 + \sqrt{5}} \cdot 1.5\right) + \left(\cos x \cdot \left(\sqrt{5} + -1\right)\right) \cdot \color{blue}{1.5}\right)} \]

5. Applied egg-rr 99.4%

   \[\leadsto \frac{\mathsf{fma}\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right), \color{blue}{\sqrt[3]{\left(\left(\left(\cos x - \cos y\right) \cdot \left(\sin y - \sin x \cdot 0.0625\right)\right) \cdot \left(\left(\cos x - \cos y\right) \cdot \left(\sin y - \sin x \cdot 0.0625\right)\right)\right) \cdot \left(\left(\cos x - \cos y\right) \cdot \left(\sin y - \sin x \cdot 0.0625\right)\right)}}, 2\right)}{3 + \left(\cos y \cdot \left(\frac{4}{3 + \sqrt{5}} \cdot 1.5\right) + \left(\cos x \cdot \left(\sqrt{5} + -1\right)\right) \cdot 1.5\right)} \]
   Step-by-step derivation

   [Start] 99.4%	\[ \frac{\mathsf{fma}\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right), \left(\sin y - \frac{\sin x}{16}\right) \cdot \left(\cos x - \cos y\right), 2\right)}{3 + \left(\cos y \cdot \left(\frac{4}{3 + \sqrt{5}} \cdot 1.5\right) + \left(\cos x \cdot \left(\sqrt{5} + -1\right)\right) \cdot 1.5\right)} \]
   add-cbrt-cube [=>] 99.4%	\[ \frac{\mathsf{fma}\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right), \color{blue}{\sqrt[3]{\left(\left(\left(\sin y - \frac{\sin x}{16}\right) \cdot \left(\cos x - \cos y\right)\right) \cdot \left(\left(\sin y - \frac{\sin x}{16}\right) \cdot \left(\cos x - \cos y\right)\right)\right) \cdot \left(\left(\sin y - \frac{\sin x}{16}\right) \cdot \left(\cos x - \cos y\right)\right)}}, 2\right)}{3 + \left(\cos y \cdot \left(\frac{4}{3 + \sqrt{5}} \cdot 1.5\right) + \left(\cos x \cdot \left(\sqrt{5} + -1\right)\right) \cdot 1.5\right)} \]
   *-commutative [=>] 99.4%	\[ \frac{\mathsf{fma}\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right), \sqrt[3]{\left(\color{blue}{\left(\left(\cos x - \cos y\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right)} \cdot \left(\left(\sin y - \frac{\sin x}{16}\right) \cdot \left(\cos x - \cos y\right)\right)\right) \cdot \left(\left(\sin y - \frac{\sin x}{16}\right) \cdot \left(\cos x - \cos y\right)\right)}, 2\right)}{3 + \left(\cos y \cdot \left(\frac{4}{3 + \sqrt{5}} \cdot 1.5\right) + \left(\cos x \cdot \left(\sqrt{5} + -1\right)\right) \cdot 1.5\right)} \]
   div-inv [=>] 99.4%	\[ \frac{\mathsf{fma}\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right), \sqrt[3]{\left(\left(\left(\cos x - \cos y\right) \cdot \left(\sin y - \color{blue}{\sin x \cdot \frac{1}{16}}\right)\right) \cdot \left(\left(\sin y - \frac{\sin x}{16}\right) \cdot \left(\cos x - \cos y\right)\right)\right) \cdot \left(\left(\sin y - \frac{\sin x}{16}\right) \cdot \left(\cos x - \cos y\right)\right)}, 2\right)}{3 + \left(\cos y \cdot \left(\frac{4}{3 + \sqrt{5}} \cdot 1.5\right) + \left(\cos x \cdot \left(\sqrt{5} + -1\right)\right) \cdot 1.5\right)} \]
   metadata-eval [=>] 99.4%	\[ \frac{\mathsf{fma}\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right), \sqrt[3]{\left(\left(\left(\cos x - \cos y\right) \cdot \left(\sin y - \sin x \cdot \color{blue}{0.0625}\right)\right) \cdot \left(\left(\sin y - \frac{\sin x}{16}\right) \cdot \left(\cos x - \cos y\right)\right)\right) \cdot \left(\left(\sin y - \frac{\sin x}{16}\right) \cdot \left(\cos x - \cos y\right)\right)}, 2\right)}{3 + \left(\cos y \cdot \left(\frac{4}{3 + \sqrt{5}} \cdot 1.5\right) + \left(\cos x \cdot \left(\sqrt{5} + -1\right)\right) \cdot 1.5\right)} \]
   *-commutative [=>] 99.4%	\[ \frac{\mathsf{fma}\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right), \sqrt[3]{\left(\left(\left(\cos x - \cos y\right) \cdot \left(\sin y - \sin x \cdot 0.0625\right)\right) \cdot \color{blue}{\left(\left(\cos x - \cos y\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right)}\right) \cdot \left(\left(\sin y - \frac{\sin x}{16}\right) \cdot \left(\cos x - \cos y\right)\right)}, 2\right)}{3 + \left(\cos y \cdot \left(\frac{4}{3 + \sqrt{5}} \cdot 1.5\right) + \left(\cos x \cdot \left(\sqrt{5} + -1\right)\right) \cdot 1.5\right)} \]
   div-inv [=>] 99.4%	\[ \frac{\mathsf{fma}\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right), \sqrt[3]{\left(\left(\left(\cos x - \cos y\right) \cdot \left(\sin y - \sin x \cdot 0.0625\right)\right) \cdot \left(\left(\cos x - \cos y\right) \cdot \left(\sin y - \color{blue}{\sin x \cdot \frac{1}{16}}\right)\right)\right) \cdot \left(\left(\sin y - \frac{\sin x}{16}\right) \cdot \left(\cos x - \cos y\right)\right)}, 2\right)}{3 + \left(\cos y \cdot \left(\frac{4}{3 + \sqrt{5}} \cdot 1.5\right) + \left(\cos x \cdot \left(\sqrt{5} + -1\right)\right) \cdot 1.5\right)} \]
   metadata-eval [=>] 99.4%	\[ \frac{\mathsf{fma}\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right), \sqrt[3]{\left(\left(\left(\cos x - \cos y\right) \cdot \left(\sin y - \sin x \cdot 0.0625\right)\right) \cdot \left(\left(\cos x - \cos y\right) \cdot \left(\sin y - \sin x \cdot \color{blue}{0.0625}\right)\right)\right) \cdot \left(\left(\sin y - \frac{\sin x}{16}\right) \cdot \left(\cos x - \cos y\right)\right)}, 2\right)}{3 + \left(\cos y \cdot \left(\frac{4}{3 + \sqrt{5}} \cdot 1.5\right) + \left(\cos x \cdot \left(\sqrt{5} + -1\right)\right) \cdot 1.5\right)} \]

6. Final simplification 99.4%

   \[\leadsto \frac{\mathsf{fma}\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right), \sqrt[3]{\left(\left(\cos x - \cos y\right) \cdot \left(\sin y - \sin x \cdot 0.0625\right)\right) \cdot \left(\left(\left(\cos x - \cos y\right) \cdot \left(\sin y - \sin x \cdot 0.0625\right)\right) \cdot \left(\left(\cos x - \cos y\right) \cdot \left(\sin y - \sin x \cdot 0.0625\right)\right)\right)}, 2\right)}{3 + \left(\cos y \cdot \left(\frac{4}{3 + \sqrt{5}} \cdot 1.5\right) + 1.5 \cdot \left(\cos x \cdot \left(\sqrt{5} + -1\right)\right)\right)} \]

Alternatives

Alternative 1
Accuracy	99.4%
Cost	138048

\[\begin{array}{l} t_0 := \left(\cos x - \cos y\right) \cdot \left(\sin y - \sin x \cdot 0.0625\right)\\ \frac{\mathsf{fma}\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right), \sqrt[3]{t_0 \cdot \left(t_0 \cdot t_0\right)}, 2\right)}{3 + \left(\cos y \cdot \left(\frac{4}{3 + \sqrt{5}} \cdot 1.5\right) + 1.5 \cdot \left(\cos x \cdot \left(\sqrt{5} + -1\right)\right)\right)} \end{array} \]

Alternative 2
Accuracy	99.4%
Cost	79168

\[\frac{\mathsf{fma}\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right), \left(\cos x - \cos y\right) \cdot \left(\sin y - \frac{\sin x}{16}\right), 2\right)}{3 + \left(\cos y \cdot \left(\frac{4}{3 + \sqrt{5}} \cdot 1.5\right) + 1.5 \cdot \left(\cos x \cdot \left(\sqrt{5} + -1\right)\right)\right)} \]

Alternative 3
Accuracy	99.3%
Cost	79040

\[\frac{\mathsf{fma}\left(\sqrt{2}, \left(\sin y - \frac{\sin x}{16}\right) \cdot \left(\left(\sin x - \frac{\sin y}{16}\right) \cdot \left(\cos x - \cos y\right)\right), 2\right)}{3 + \left(1.5 \cdot \left(\cos x \cdot \left(\sqrt{5} + -1\right)\right) + \cos y \cdot \left(4.5 - \sqrt{5} \cdot 1.5\right)\right)} \]

Alternative 4
Accuracy	99.4%
Cost	79040

\[\frac{\mathsf{fma}\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right), \left(\cos x - \cos y\right) \cdot \left(\sin y - \frac{\sin x}{16}\right), 2\right)}{3 + \left(1.5 \cdot \left(\cos x \cdot \left(\sqrt{5} + -1\right)\right) + 6 \cdot \frac{\cos y}{3 + \sqrt{5}}\right)} \]

Alternative 5
Accuracy	99.3%
Cost	78912

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

Alternative 6
Accuracy	99.3%
Cost	73024

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

Alternative 7
Accuracy	99.3%
Cost	72896

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

Alternative 8
Accuracy	99.3%
Cost	72896

\[\begin{array}{l} t_0 := \frac{\sqrt{5}}{2}\\ \frac{2 + \left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\left(\cos x - \cos y\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right)}{3 \cdot \left(1 + \left(\cos x \cdot \left(t_0 - 0.5\right) + \cos y \cdot \left(1.5 - t_0\right)\right)\right)} \end{array} \]

Alternative 9
Accuracy	81.6%
Cost	72777

\[\begin{array}{l} t_0 := \sin y - \frac{\sin x}{16}\\ t_1 := \sqrt{5} + -1\\ \mathbf{if}\;x \leq -0.0105 \lor \neg \left(x \leq 0.011\right):\\ \;\;\;\;\frac{\mathsf{fma}\left(\sqrt{2} \cdot \sin x, \left(\cos x - \cos y\right) \cdot t_0, 2\right)}{3 + \left(\cos y \cdot \left(\frac{4}{3 + \sqrt{5}} \cdot 1.5\right) + 1.5 \cdot \left(\cos x \cdot t_1\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot t_0\right) \cdot \left(1 + \left(-0.5 \cdot \left(x \cdot x\right) - \cos y\right)\right)}{3 \cdot \left(\cos y \cdot \frac{3 - \sqrt{5}}{2} + \left(1 + t_1 \cdot \left(0.5 + \left(x \cdot x\right) \cdot -0.25\right)\right)\right)}\\ \end{array} \]

Alternative 10
Accuracy	81.6%
Cost	66505

\[\begin{array}{l} t_0 := \frac{\sqrt{5}}{2}\\ t_1 := \sin y - \frac{\sin x}{16}\\ \mathbf{if}\;x \leq -0.005 \lor \neg \left(x \leq 0.031\right):\\ \;\;\;\;\frac{2 + \left(\left(\cos x - \cos y\right) \cdot t_1\right) \cdot \left(\sqrt{2} \cdot \sin x\right)}{3 \cdot \left(1 + \left(\cos x \cdot \left(t_0 - 0.5\right) + \cos y \cdot \left(1.5 - t_0\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot t_1\right) \cdot \left(1 + \left(-0.5 \cdot \left(x \cdot x\right) - \cos y\right)\right)}{3 \cdot \left(\cos y \cdot \frac{3 - \sqrt{5}}{2} + \left(1 + \left(\sqrt{5} + -1\right) \cdot \left(0.5 + \left(x \cdot x\right) \cdot -0.25\right)\right)\right)}\\ \end{array} \]

Alternative 11
Accuracy	81.6%
Cost	66504

\[\begin{array}{l} t_0 := \cos y \cdot \frac{3 - \sqrt{5}}{2}\\ t_1 := \cos x - \cos y\\ t_2 := \sqrt{5} + -1\\ t_3 := \sin y - \frac{\sin x}{16}\\ t_4 := \sqrt{2} \cdot \sin x\\ t_5 := \frac{\sqrt{5}}{2}\\ \mathbf{if}\;x \leq -0.0135:\\ \;\;\;\;\frac{2 + t_1 \cdot \left(t_3 \cdot t_4\right)}{3 \cdot \left(\left(1 + \cos x \cdot \frac{t_2}{2}\right) + t_0\right)}\\ \mathbf{elif}\;x \leq 0.021:\\ \;\;\;\;\frac{2 + \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot t_3\right) \cdot \left(1 + \left(-0.5 \cdot \left(x \cdot x\right) - \cos y\right)\right)}{3 \cdot \left(t_0 + \left(1 + t_2 \cdot \left(0.5 + \left(x \cdot x\right) \cdot -0.25\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \left(t_1 \cdot t_3\right) \cdot t_4}{3 \cdot \left(1 + \left(\cos x \cdot \left(t_5 - 0.5\right) + \cos y \cdot \left(1.5 - t_5\right)\right)\right)}\\ \end{array} \]

Alternative 12
Accuracy	79.8%
Cost	61000

\[\begin{array}{l} t_0 := \sqrt{5} \cdot 0.5\\ t_1 := \sin y - \frac{\sin x}{16}\\ t_2 := t_1 \cdot \left(\cos x + -1\right)\\ t_3 := \frac{\sqrt{5}}{2}\\ t_4 := \sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\\ \mathbf{if}\;x \leq -0.0085:\\ \;\;\;\;\frac{2 + t_4 \cdot t_2}{3 \cdot \left(1 + \left(\left(1.5 + \cos x \cdot \left(t_0 - 0.5\right)\right) - t_0\right)\right)}\\ \mathbf{elif}\;x \leq 0.033:\\ \;\;\;\;\frac{2 + \left(t_4 \cdot t_1\right) \cdot \left(1 + \left(-0.5 \cdot \left(x \cdot x\right) - \cos y\right)\right)}{3 \cdot \left(\cos y \cdot \frac{3 - \sqrt{5}}{2} + \left(1 + \left(\sqrt{5} + -1\right) \cdot \left(0.5 + \left(x \cdot x\right) \cdot -0.25\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \left(\sqrt{2} \cdot \sin x\right) \cdot t_2}{3 \cdot \left(1 + \left(\cos x \cdot \left(t_3 - 0.5\right) + \cos y \cdot \left(1.5 - t_3\right)\right)\right)}\\ \end{array} \]

Alternative 13
Accuracy	79.9%
Cost	60360

\[\begin{array}{l} t_0 := \frac{\sqrt{5}}{2}\\ t_1 := 3 \cdot \left(1 + \left(\cos x \cdot \left(t_0 - 0.5\right) + \cos y \cdot \left(1.5 - t_0\right)\right)\right)\\ t_2 := \sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\\ t_3 := 1 - \cos y\\ \mathbf{if}\;y \leq -0.0068:\\ \;\;\;\;\frac{2 + -0.0625 \cdot \left(t_3 \cdot \left(\sqrt{2} \cdot {\sin y}^{2}\right)\right)}{3 \cdot \left(\left(1 + \cos x \cdot \frac{\sqrt{5} + -1}{2}\right) + \cos y \cdot \frac{3 - \sqrt{5}}{2}\right)}\\ \mathbf{elif}\;y \leq 0.18:\\ \;\;\;\;\frac{2 + t_2 \cdot \left(\left(\cos x + -1\right) \cdot \left(y + \sin x \cdot -0.0625\right)\right)}{t_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + t_2 \cdot \left(\sin y \cdot t_3\right)}{t_1}\\ \end{array} \]

Alternative 14
Accuracy	79.8%
Cost	60360

\[\begin{array}{l} t_0 := \left(\sin y - \frac{\sin x}{16}\right) \cdot \left(\cos x + -1\right)\\ t_1 := \frac{\sqrt{5}}{2}\\ t_2 := \sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\\ t_3 := \sqrt{5} \cdot 0.5\\ t_4 := 3 \cdot \left(1 + \left(\cos x \cdot \left(t_1 - 0.5\right) + \cos y \cdot \left(1.5 - t_1\right)\right)\right)\\ \mathbf{if}\;x \leq -0.004:\\ \;\;\;\;\frac{2 + t_2 \cdot t_0}{3 \cdot \left(1 + \left(\left(1.5 + \cos x \cdot \left(t_3 - 0.5\right)\right) - t_3\right)\right)}\\ \mathbf{elif}\;x \leq 0.005:\\ \;\;\;\;\frac{2 + t_2 \cdot \left(\left(1 - \cos y\right) \cdot \left(\sin y + x \cdot -0.0625\right)\right)}{t_4}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \left(\sqrt{2} \cdot \sin x\right) \cdot t_0}{t_4}\\ \end{array} \]

Alternative 15
Accuracy	79.3%
Cost	60232

\[\begin{array}{l} t_0 := \frac{\sqrt{5}}{2}\\ t_1 := 1 - \cos y\\ t_2 := \sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\\ t_3 := \sqrt{5} \cdot 0.5\\ \mathbf{if}\;y \leq -1000:\\ \;\;\;\;\frac{2 + -0.0625 \cdot \left(t_1 \cdot \left(\sqrt{2} \cdot {\sin y}^{2}\right)\right)}{3 \cdot \left(\left(1 + \cos x \cdot \frac{\sqrt{5} + -1}{2}\right) + \cos y \cdot \frac{3 - \sqrt{5}}{2}\right)}\\ \mathbf{elif}\;y \leq 235000000000:\\ \;\;\;\;\frac{2 + t_2 \cdot \left(\left(\sin y - \frac{\sin x}{16}\right) \cdot \left(\cos x + -1\right)\right)}{3 \cdot \left(1 + \left(\left(1.5 + \cos x \cdot \left(t_3 - 0.5\right)\right) - t_3\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + t_2 \cdot \left(\sin y \cdot t_1\right)}{3 \cdot \left(1 + \left(\cos x \cdot \left(t_0 - 0.5\right) + \cos y \cdot \left(1.5 - t_0\right)\right)\right)}\\ \end{array} \]

Alternative 16
Accuracy	79.3%
Cost	60104

\[\begin{array}{l} t_0 := {\sin y}^{2}\\ t_1 := 3 \cdot \left(\left(1 + \cos x \cdot \frac{\sqrt{5} + -1}{2}\right) + \cos y \cdot \frac{3 - \sqrt{5}}{2}\right)\\ t_2 := \frac{\sqrt{5}}{2}\\ \mathbf{if}\;y \leq -1000:\\ \;\;\;\;\frac{2 + -0.0625 \cdot \left(\left(1 - \cos y\right) \cdot \left(\sqrt{2} \cdot t_0\right)\right)}{t_1}\\ \mathbf{elif}\;y \leq 235000000000:\\ \;\;\;\;\frac{2 + \left(\sqrt{2} \cdot \sin x\right) \cdot \left(\left(\sin y - \frac{\sin x}{16}\right) \cdot \left(\cos x + -1\right)\right)}{3 \cdot \left(1 + \left(\cos x \cdot \left(t_2 - 0.5\right) + \cos y \cdot \left(1.5 - t_2\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + -0.0625 \cdot \left(\sqrt{2} \cdot \left(t_0 \cdot \left(\sin y \cdot \tan \left(\frac{y}{2}\right)\right)\right)\right)}{t_1}\\ \end{array} \]

Alternative 17
Accuracy	79.4%
Cost	60104

\[\begin{array}{l} t_0 := \frac{\sqrt{5}}{2}\\ t_1 := 1 - \cos y\\ t_2 := 3 \cdot \left(1 + \left(\cos x \cdot \left(t_0 - 0.5\right) + \cos y \cdot \left(1.5 - t_0\right)\right)\right)\\ \mathbf{if}\;y \leq -1000:\\ \;\;\;\;\frac{2 + -0.0625 \cdot \left(t_1 \cdot \left(\sqrt{2} \cdot {\sin y}^{2}\right)\right)}{3 \cdot \left(\left(1 + \cos x \cdot \frac{\sqrt{5} + -1}{2}\right) + \cos y \cdot \frac{3 - \sqrt{5}}{2}\right)}\\ \mathbf{elif}\;y \leq 235000000000:\\ \;\;\;\;\frac{2 + \left(\sqrt{2} \cdot \sin x\right) \cdot \left(\left(\sin y - \frac{\sin x}{16}\right) \cdot \left(\cos x + -1\right)\right)}{t_2}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y \cdot t_1\right)}{t_2}\\ \end{array} \]

Alternative 18
Accuracy	79.6%
Cost	59721

\[\begin{array}{l} t_0 := \sqrt{5} \cdot 0.5\\ \mathbf{if}\;x \leq -0.00022 \lor \neg \left(x \leq 0.000175\right):\\ \;\;\;\;\frac{2 + \left(\left(\cos x + -1\right) \cdot {\sin x}^{2}\right) \cdot \left(\sqrt{2} \cdot -0.0625\right)}{3 \cdot \left(\left(1 + \cos x \cdot \frac{\sqrt{5} + -1}{2}\right) + \cos y \cdot \frac{3 - \sqrt{5}}{2}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right), \sin y \cdot \left(1 - \cos y\right), 2\right)}{3 \cdot \left(0.5 + \left(t_0 + \cos y \cdot \left(1.5 - t_0\right)\right)\right)}\\ \end{array} \]

Alternative 19
Accuracy	79.6%
Cost	59721

\[\begin{array}{l} t_0 := \sqrt{5} + -1\\ \mathbf{if}\;x \leq -9.8 \cdot 10^{-5} \lor \neg \left(x \leq 5.7 \cdot 10^{-5}\right):\\ \;\;\;\;\frac{2 + \left(\left(\cos x + -1\right) \cdot {\sin x}^{2}\right) \cdot \left(\sqrt{2} \cdot -0.0625\right)}{3 \cdot \left(\left(1 + \cos x \cdot \frac{t_0}{2}\right) + \cos y \cdot \frac{3 - \sqrt{5}}{2}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right), \sin y \cdot \left(1 - \cos y\right), 2\right)}{3 + \left(6 \cdot \frac{\cos y}{3 + \sqrt{5}} + 1.5 \cdot t_0\right)}\\ \end{array} \]

Alternative 20
Accuracy	79.6%
Cost	53513

\[\begin{array}{l} t_0 := 3 \cdot \left(\left(1 + \cos x \cdot \frac{\sqrt{5} + -1}{2}\right) + \cos y \cdot \frac{3 - \sqrt{5}}{2}\right)\\ \mathbf{if}\;y \leq -0.00065 \lor \neg \left(y \leq 0.00074\right):\\ \;\;\;\;\frac{2 + -0.0625 \cdot \left(\left(1 - \cos y\right) \cdot \left(\sqrt{2} \cdot {\sin y}^{2}\right)\right)}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \left(\left(\cos x + -1\right) \cdot {\sin x}^{2}\right) \cdot \left(\sqrt{2} \cdot -0.0625\right)}{t_0}\\ \end{array} \]

Alternative 21
Accuracy	62.6%
Cost	53248

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

Alternative 22
Accuracy	62.6%
Cost	53248

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

Alternative 23
Accuracy	59.8%
Cost	46720

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

Alternative 24
Accuracy	33.3%
Cost	40448

\[\frac{2 + -0.0625 \cdot \left({y}^{4} \cdot \left(\sqrt{2} \cdot 0.5\right)\right)}{3 \cdot \left(1 + \mathsf{fma}\left(\cos x \cdot \left(\sqrt{5} + -1\right), 0.5, \left(3 - \sqrt{5}\right) \cdot \left(0.5 + -0.25 \cdot \left(y \cdot y\right)\right)\right)\right)} \]

Alternative 25
Accuracy	32.3%
Cost	33664

\[\frac{2 + -0.0625 \cdot \left({y}^{4} \cdot \left(\sqrt{2} \cdot 0.5\right)\right)}{3 \cdot \left(1 + 0.5 \cdot \left(\cos x \cdot \left(\sqrt{5} + -1\right) + \left(3 - \sqrt{5}\right)\right)\right)} \]

Alternative 26
Accuracy	32.3%
Cost	33664

\[\frac{2 + -0.0625 \cdot \left({y}^{4} \cdot \left(\sqrt{2} \cdot 0.5\right)\right)}{3 \cdot \left(1 + 0.5 \cdot \left(\left(3 + \cos x \cdot \left(\sqrt{5} + -1\right)\right) - \sqrt{5}\right)\right)} \]

Alternative 27
Accuracy	32.3%
Cost	33664

\[\frac{2 + -0.0625 \cdot \left({y}^{4} \cdot \left(\sqrt{2} \cdot 0.5\right)\right)}{3 + 3 \cdot \left(0.5 \cdot \left(\cos x \cdot \left(\sqrt{5} + -1\right) + \left(3 - \sqrt{5}\right)\right)\right)} \]

Alternative 28
Accuracy	30.2%
Cost	13568

\[\frac{2 + -0.0625 \cdot \left({y}^{4} \cdot \left(\sqrt{2} \cdot 0.5\right)\right)}{6} \]

Reproduce

herbie shell --seed 2023271 
(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))))))