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

Average Error: 0.5 → 0.4

Time: 45.3s

Precision: binary64

Cost: 72768

Math

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

↓

\[\frac{2 - \sqrt{2} \cdot \left(\left(\cos x - \cos y\right) \cdot \left(\left(\sin y + -0.0625 \cdot \sin x\right) \cdot \left(\sin y \cdot 0.0625 - \sin x\right)\right)\right)}{3 + \left(6 \cdot \frac{\cos y}{3 + \sqrt{5}} + 6 \cdot \frac{\cos x}{\sqrt{5} + 1}\right)} \]

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)
    (*
     (- (cos x) (cos y))
     (* (+ (sin y) (* -0.0625 (sin x))) (- (* (sin y) 0.0625) (sin x))))))
  (+
   3.0
   (+
    (* 6.0 (/ (cos y) (+ 3.0 (sqrt 5.0))))
    (* 6.0 (/ (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) {
	return (2.0 - (sqrt(2.0) * ((cos(x) - cos(y)) * ((sin(y) + (-0.0625 * sin(x))) * ((sin(y) * 0.0625) - sin(x)))))) / (3.0 + ((6.0 * (cos(y) / (3.0 + sqrt(5.0)))) + (6.0 * (cos(x) / (sqrt(5.0) + 1.0)))));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (2.0d0 + (((sqrt(2.0d0) * (sin(x) - (sin(y) / 16.0d0))) * (sin(y) - (sin(x) / 16.0d0))) * (cos(x) - cos(y)))) / (3.0d0 * ((1.0d0 + (((sqrt(5.0d0) - 1.0d0) / 2.0d0) * cos(x))) + (((3.0d0 - sqrt(5.0d0)) / 2.0d0) * cos(y))))
end function

↓

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (2.0d0 - (sqrt(2.0d0) * ((cos(x) - cos(y)) * ((sin(y) + ((-0.0625d0) * sin(x))) * ((sin(y) * 0.0625d0) - sin(x)))))) / (3.0d0 + ((6.0d0 * (cos(y) / (3.0d0 + sqrt(5.0d0)))) + (6.0d0 * (cos(x) / (sqrt(5.0d0) + 1.0d0)))))
end function

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.cos(x) - Math.cos(y)) * ((Math.sin(y) + (-0.0625 * Math.sin(x))) * ((Math.sin(y) * 0.0625) - Math.sin(x)))))) / (3.0 + ((6.0 * (Math.cos(y) / (3.0 + Math.sqrt(5.0)))) + (6.0 * (Math.cos(x) / (Math.sqrt(5.0) + 1.0)))));
}

Python

def code(x, 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))))

↓

def code(x, y):
	return (2.0 - (math.sqrt(2.0) * ((math.cos(x) - math.cos(y)) * ((math.sin(y) + (-0.0625 * math.sin(x))) * ((math.sin(y) * 0.0625) - math.sin(x)))))) / (3.0 + ((6.0 * (math.cos(y) / (3.0 + math.sqrt(5.0)))) + (6.0 * (math.cos(x) / (math.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)
	return Float64(Float64(2.0 - Float64(sqrt(2.0) * Float64(Float64(cos(x) - cos(y)) * Float64(Float64(sin(y) + Float64(-0.0625 * sin(x))) * Float64(Float64(sin(y) * 0.0625) - sin(x)))))) / Float64(3.0 + Float64(Float64(6.0 * Float64(cos(y) / Float64(3.0 + sqrt(5.0)))) + Float64(6.0 * Float64(cos(x) / Float64(sqrt(5.0) + 1.0))))))
end

MATLAB

function tmp = code(x, y)
	tmp = (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))));
end

↓

function tmp = code(x, y)
	tmp = (2.0 - (sqrt(2.0) * ((cos(x) - cos(y)) * ((sin(y) + (-0.0625 * sin(x))) * ((sin(y) * 0.0625) - sin(x)))))) / (3.0 + ((6.0 * (cos(y) / (3.0 + sqrt(5.0)))) + (6.0 * (cos(x) / (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_] := N[(N[(2.0 - N[(N[Sqrt[2.0], $MachinePrecision] * N[(N[(N[Cos[x], $MachinePrecision] - N[Cos[y], $MachinePrecision]), $MachinePrecision] * N[(N[(N[Sin[y], $MachinePrecision] + N[(-0.0625 * N[Sin[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(N[Sin[y], $MachinePrecision] * 0.0625), $MachinePrecision] - N[Sin[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(3.0 + N[(N[(6.0 * N[(N[Cos[y], $MachinePrecision] / N[(3.0 + N[Sqrt[5.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(6.0 * N[(N[Cos[x], $MachinePrecision] / N[(N[Sqrt[5.0], $MachinePrecision] + 1.0), $MachinePrecision]), $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. Simplified 0.4

   \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(\sqrt{2}, \left(\sin y + -0.0625 \cdot \sin x\right) \cdot \left(\left(\sin x + -0.0625 \cdot \sin y\right) \cdot \left(\cos x - \cos y\right)\right), 2\right)}{\mathsf{fma}\left(\cos x, \frac{\sqrt{5} + -1}{0.6666666666666666}, \mathsf{fma}\left(\cos y, 1.5 \cdot \left(3 - \sqrt{5}\right), 3\right)\right)}} \]
   Proof

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

3. Taylor expanded in y around inf 0.4

   \[\leadsto \color{blue}{\frac{\sqrt{2} \cdot \left(\left(\cos x - \cos y\right) \cdot \left(\left(-0.0625 \cdot \sin y + \sin x\right) \cdot \left(-0.0625 \cdot \sin x + \sin y\right)\right)\right) + 2}{3 + \left(1.5 \cdot \left(\left(3 - \sqrt{5}\right) \cdot \cos y\right) + 1.5 \cdot \left(\left(\sqrt{5} - 1\right) \cdot \cos x\right)\right)}} \]

4. Applied egg-rr 0.4

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

5. Simplified 0.4

   \[\leadsto \frac{\sqrt{2} \cdot \left(\left(\cos x - \cos y\right) \cdot \left(\left(-0.0625 \cdot \sin y + \sin x\right) \cdot \left(-0.0625 \cdot \sin x + \sin y\right)\right)\right) + 2}{3 + \left(1.5 \cdot \left(\left(3 - \sqrt{5}\right) \cdot \cos y\right) + \color{blue}{\frac{6}{\sqrt{5} + 1} \cdot \cos x}\right)} \]
   Proof

   [Start] 0.4	\[ \frac{\sqrt{2} \cdot \left(\left(\cos x - \cos y\right) \cdot \left(\left(-0.0625 \cdot \sin y + \sin x\right) \cdot \left(-0.0625 \cdot \sin x + \sin y\right)\right)\right) + 2}{3 + \left(1.5 \cdot \left(\left(3 - \sqrt{5}\right) \cdot \cos y\right) + \frac{1.5 \cdot \left(\cos x \cdot 4\right)}{\sqrt{5} + 1}\right)} \]
   *-commutative [<=] 0.4	\[ \frac{\sqrt{2} \cdot \left(\left(\cos x - \cos y\right) \cdot \left(\left(-0.0625 \cdot \sin y + \sin x\right) \cdot \left(-0.0625 \cdot \sin x + \sin y\right)\right)\right) + 2}{3 + \left(1.5 \cdot \left(\left(3 - \sqrt{5}\right) \cdot \cos y\right) + \frac{1.5 \cdot \color{blue}{\left(4 \cdot \cos x\right)}}{\sqrt{5} + 1}\right)} \]
   associate-*r* [=>] 0.4	\[ \frac{\sqrt{2} \cdot \left(\left(\cos x - \cos y\right) \cdot \left(\left(-0.0625 \cdot \sin y + \sin x\right) \cdot \left(-0.0625 \cdot \sin x + \sin y\right)\right)\right) + 2}{3 + \left(1.5 \cdot \left(\left(3 - \sqrt{5}\right) \cdot \cos y\right) + \frac{\color{blue}{\left(1.5 \cdot 4\right) \cdot \cos x}}{\sqrt{5} + 1}\right)} \]
   metadata-eval [=>] 0.4	\[ \frac{\sqrt{2} \cdot \left(\left(\cos x - \cos y\right) \cdot \left(\left(-0.0625 \cdot \sin y + \sin x\right) \cdot \left(-0.0625 \cdot \sin x + \sin y\right)\right)\right) + 2}{3 + \left(1.5 \cdot \left(\left(3 - \sqrt{5}\right) \cdot \cos y\right) + \frac{\color{blue}{6} \cdot \cos x}{\sqrt{5} + 1}\right)} \]
   associate-*l/ [<=] 0.4	\[ \frac{\sqrt{2} \cdot \left(\left(\cos x - \cos y\right) \cdot \left(\left(-0.0625 \cdot \sin y + \sin x\right) \cdot \left(-0.0625 \cdot \sin x + \sin y\right)\right)\right) + 2}{3 + \left(1.5 \cdot \left(\left(3 - \sqrt{5}\right) \cdot \cos y\right) + \color{blue}{\frac{6}{\sqrt{5} + 1} \cdot \cos x}\right)} \]

6. Applied egg-rr 0.4

   \[\leadsto \frac{\sqrt{2} \cdot \left(\left(\cos x - \cos y\right) \cdot \left(\left(-0.0625 \cdot \sin y + \sin x\right) \cdot \left(-0.0625 \cdot \sin x + \sin y\right)\right)\right) + 2}{3 + \left(1.5 \cdot \left(\color{blue}{\left(4 \cdot \frac{1}{3 + \sqrt{5}}\right)} \cdot \cos y\right) + \frac{6}{\sqrt{5} + 1} \cdot \cos x\right)} \]

7. Simplified 0.4

   \[\leadsto \frac{\sqrt{2} \cdot \left(\left(\cos x - \cos y\right) \cdot \left(\left(-0.0625 \cdot \sin y + \sin x\right) \cdot \left(-0.0625 \cdot \sin x + \sin y\right)\right)\right) + 2}{3 + \left(1.5 \cdot \left(\color{blue}{\frac{4}{3 + \sqrt{5}}} \cdot \cos y\right) + \frac{6}{\sqrt{5} + 1} \cdot \cos x\right)} \]
   Proof

   [Start] 0.4	\[ \frac{\sqrt{2} \cdot \left(\left(\cos x - \cos y\right) \cdot \left(\left(-0.0625 \cdot \sin y + \sin x\right) \cdot \left(-0.0625 \cdot \sin x + \sin y\right)\right)\right) + 2}{3 + \left(1.5 \cdot \left(\left(4 \cdot \frac{1}{3 + \sqrt{5}}\right) \cdot \cos y\right) + \frac{6}{\sqrt{5} + 1} \cdot \cos x\right)} \]
   associate-*r/ [=>] 0.4	\[ \frac{\sqrt{2} \cdot \left(\left(\cos x - \cos y\right) \cdot \left(\left(-0.0625 \cdot \sin y + \sin x\right) \cdot \left(-0.0625 \cdot \sin x + \sin y\right)\right)\right) + 2}{3 + \left(1.5 \cdot \left(\color{blue}{\frac{4 \cdot 1}{3 + \sqrt{5}}} \cdot \cos y\right) + \frac{6}{\sqrt{5} + 1} \cdot \cos x\right)} \]
   metadata-eval [=>] 0.4	\[ \frac{\sqrt{2} \cdot \left(\left(\cos x - \cos y\right) \cdot \left(\left(-0.0625 \cdot \sin y + \sin x\right) \cdot \left(-0.0625 \cdot \sin x + \sin y\right)\right)\right) + 2}{3 + \left(1.5 \cdot \left(\frac{\color{blue}{4}}{3 + \sqrt{5}} \cdot \cos y\right) + \frac{6}{\sqrt{5} + 1} \cdot \cos x\right)} \]

8. Taylor expanded in y around inf 0.4

   \[\leadsto \frac{\sqrt{2} \cdot \left(\left(\cos x - \cos y\right) \cdot \left(\left(-0.0625 \cdot \sin y + \sin x\right) \cdot \left(-0.0625 \cdot \sin x + \sin y\right)\right)\right) + 2}{3 + \color{blue}{\left(6 \cdot \frac{\cos y}{\sqrt{5} + 3} + 6 \cdot \frac{\cos x}{\sqrt{5} + 1}\right)}} \]

9. Final simplification 0.4

   \[\leadsto \frac{2 - \sqrt{2} \cdot \left(\left(\cos x - \cos y\right) \cdot \left(\left(\sin y + -0.0625 \cdot \sin x\right) \cdot \left(\sin y \cdot 0.0625 - \sin x\right)\right)\right)}{3 + \left(6 \cdot \frac{\cos y}{3 + \sqrt{5}} + 6 \cdot \frac{\cos x}{\sqrt{5} + 1}\right)} \]

Alternatives

Alternative 1
Error	0.4
Cost	72768

\[\frac{2 - \sqrt{2} \cdot \left(\left(\cos x - \cos y\right) \cdot \left(\left(\sin y + -0.0625 \cdot \sin x\right) \cdot \left(\sin y \cdot 0.0625 - \sin x\right)\right)\right)}{3 - \left(\cos x \cdot \frac{-6}{\sqrt{5} + 1} - -1.5 \cdot \left(\cos y \cdot \left(\sqrt{5} + -3\right)\right)\right)} \]

Alternative 2
Error	0.4
Cost	72640

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

Alternative 3
Error	0.4
Cost	72640

\[\frac{2 - \sqrt{2} \cdot \left(\left(\cos x - \cos y\right) \cdot \left(\left(\sin y + -0.0625 \cdot \sin x\right) \cdot \left(\sin y \cdot 0.0625 - \sin x\right)\right)\right)}{3 + 6 \cdot \left(\frac{\cos y}{3 + \sqrt{5}} + \frac{\cos x}{\sqrt{5} + 1}\right)} \]

Alternative 4
Error	11.6
Cost	67016

\[\begin{array}{l} t_0 := \sin y - \frac{\sin x}{16}\\ t_1 := \sqrt{2} \cdot \sin x\\ t_2 := \cos x - \cos y\\ t_3 := \frac{\sqrt{5}}{2}\\ \mathbf{if}\;x \leq -0.059:\\ \;\;\;\;\frac{2 + t_1 \cdot \left(t_2 \cdot t_0\right)}{3 \cdot \left(1 - \left(\cos x \cdot \left(0.5 - t_3\right) + \cos y \cdot \left(t_3 + -1.5\right)\right)\right)}\\ \mathbf{elif}\;x \leq 0.44:\\ \;\;\;\;\frac{2 + \sqrt{2} \cdot \left(\left(\left(\sin y \cdot 0.0625 - \sin x\right) \cdot \left(\sin x \cdot 0.0625 - \sin y\right)\right) \cdot \left(1 - \left(\cos y + 0.5 \cdot \left(x \cdot x\right)\right)\right)\right)}{3 - \left(\cos x \cdot \frac{-6}{\sqrt{5} + 1} - -1.5 \cdot \left(\cos y \cdot \left(\sqrt{5} + -3\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + t_2 \cdot \left(t_1 \cdot t_0\right)}{3 \cdot \left(\left(1 + \cos x \cdot \frac{\sqrt{5} + -1}{2}\right) + \cos y \cdot \frac{\frac{4}{3 + \sqrt{5}}}{2}\right)}\\ \end{array} \]

Alternative 5
Error	11.7
Cost	66760

\[\begin{array}{l} t_0 := \sqrt{2} \cdot \sin x\\ t_1 := \sin y - \frac{\sin x}{16}\\ t_2 := 1 + \cos x \cdot \frac{\sqrt{5} + -1}{2}\\ t_3 := \cos x - \cos y\\ t_4 := \frac{\sqrt{5}}{2}\\ \mathbf{if}\;x \leq -0.019:\\ \;\;\;\;\frac{2 + t_0 \cdot \left(t_3 \cdot t_1\right)}{3 \cdot \left(1 - \left(\cos x \cdot \left(0.5 - t_4\right) + \cos y \cdot \left(t_4 + -1.5\right)\right)\right)}\\ \mathbf{elif}\;x \leq 0.44:\\ \;\;\;\;\frac{2 - \left(t_1 \cdot \left(\sqrt{2} \cdot \left(x - \sin y \cdot 0.0625\right)\right)\right) \cdot \left(\cos y - \cos x\right)}{3 \cdot \left(t_2 + \cos y \cdot \frac{3 - \sqrt{5}}{2}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + t_3 \cdot \left(t_0 \cdot t_1\right)}{3 \cdot \left(t_2 + \cos y \cdot \frac{\frac{4}{3 + \sqrt{5}}}{2}\right)}\\ \end{array} \]

Alternative 6
Error	11.7
Cost	66632

\[\begin{array}{l} t_0 := \sin y - \frac{\sin x}{16}\\ t_1 := \sqrt{2} \cdot \sin x\\ t_2 := \cos x - \cos y\\ t_3 := \frac{\sqrt{5}}{2}\\ \mathbf{if}\;x \leq -0.00385:\\ \;\;\;\;\frac{2 + t_1 \cdot \left(t_2 \cdot t_0\right)}{3 \cdot \left(1 - \left(\cos x \cdot \left(0.5 - t_3\right) + \cos y \cdot \left(t_3 + -1.5\right)\right)\right)}\\ \mathbf{elif}\;x \leq 0.44:\\ \;\;\;\;\frac{2 + \left(\sqrt{2} \cdot \left(\cos y + -1\right)\right) \cdot \left({\sin y}^{2} \cdot 0.0625 + \sin y \cdot \left(x \cdot -1.00390625\right)\right)}{3 - \left(\cos x \cdot \frac{-6}{\sqrt{5} + 1} - -1.5 \cdot \left(\cos y \cdot \left(\sqrt{5} + -3\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + t_2 \cdot \left(t_1 \cdot t_0\right)}{3 \cdot \left(\left(1 + \cos x \cdot \frac{\sqrt{5} + -1}{2}\right) + \cos y \cdot \frac{\frac{4}{3 + \sqrt{5}}}{2}\right)}\\ \end{array} \]

Alternative 7
Error	11.7
Cost	66632

\[\begin{array}{l} t_0 := \sin y - \frac{\sin x}{16}\\ t_1 := \sqrt{2} \cdot \sin x\\ t_2 := \cos x - \cos y\\ t_3 := \frac{\sqrt{5}}{2}\\ \mathbf{if}\;x \leq -0.0037:\\ \;\;\;\;\frac{2 + t_1 \cdot \left(t_2 \cdot t_0\right)}{3 \cdot \left(1 - \left(\cos x \cdot \left(0.5 - t_3\right) + \cos y \cdot \left(t_3 + -1.5\right)\right)\right)}\\ \mathbf{elif}\;x \leq 0.0026:\\ \;\;\;\;\frac{2 + \sqrt{2} \cdot \left(\left(\left(\sin y \cdot 0.0625 - \sin x\right) \cdot \left(\sin x \cdot 0.0625 - \sin y\right)\right) \cdot \left(1 - \cos y\right)\right)}{3 - \left(\cos x \cdot \frac{-6}{\sqrt{5} + 1} - -1.5 \cdot \left(\cos y \cdot \left(\sqrt{5} + -3\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + t_2 \cdot \left(t_1 \cdot t_0\right)}{3 \cdot \left(\left(1 + \cos x \cdot \frac{\sqrt{5} + -1}{2}\right) + \cos y \cdot \frac{\frac{4}{3 + \sqrt{5}}}{2}\right)}\\ \end{array} \]

Alternative 8
Error	11.7
Cost	66505

\[\begin{array}{l} t_0 := \frac{\sqrt{5}}{2}\\ \mathbf{if}\;x \leq -0.00165 \lor \neg \left(x \leq 0.44\right):\\ \;\;\;\;\frac{2 + \left(\sqrt{2} \cdot \sin x\right) \cdot \left(\left(\cos x - \cos y\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right)}{3 \cdot \left(1 - \left(\cos x \cdot \left(0.5 - t_0\right) + \cos y \cdot \left(t_0 + -1.5\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \left(\sqrt{2} \cdot \left(\cos y + -1\right)\right) \cdot \left({\sin y}^{2} \cdot 0.0625 + \sin y \cdot \left(x \cdot -1.00390625\right)\right)}{3 - \left(\cos x \cdot \frac{-6}{\sqrt{5} + 1} - -1.5 \cdot \left(\cos y \cdot \left(\sqrt{5} + -3\right)\right)\right)}\\ \end{array} \]

Alternative 9
Error	11.7
Cost	66504

\[\begin{array}{l} t_0 := \cos x - \cos y\\ t_1 := \frac{\sqrt{5}}{2}\\ \mathbf{if}\;x \leq -0.0028:\\ \;\;\;\;\frac{2 + \left(\sqrt{2} \cdot \sin x\right) \cdot \left(t_0 \cdot \left(\sin y - \frac{\sin x}{16}\right)\right)}{3 \cdot \left(1 - \left(\cos x \cdot \left(0.5 - t_1\right) + \cos y \cdot \left(t_1 + -1.5\right)\right)\right)}\\ \mathbf{elif}\;x \leq 0.44:\\ \;\;\;\;\frac{2 + \left(\sqrt{2} \cdot \left(\cos y + -1\right)\right) \cdot \left({\sin y}^{2} \cdot 0.0625 + \sin y \cdot \left(x \cdot -1.00390625\right)\right)}{3 - \left(\cos x \cdot \frac{-6}{\sqrt{5} + 1} - -1.5 \cdot \left(\cos y \cdot \left(\sqrt{5} + -3\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + t_0 \cdot \left(\sqrt{2} \cdot \left(\sin x \cdot \left(\sin y + -0.0625 \cdot \sin x\right)\right)\right)}{3 \cdot \left(\left(1 + \cos x \cdot \frac{\sqrt{5} + -1}{2}\right) + \cos y \cdot \frac{3 - \sqrt{5}}{2}\right)}\\ \end{array} \]

Alternative 10
Error	12.8
Cost	66376

\[\begin{array}{l} t_0 := \sqrt{5} + -3\\ t_1 := \sqrt{5} + -1\\ \mathbf{if}\;x \leq -0.00155:\\ \;\;\;\;\frac{2 + \left(\left(\sqrt{2} \cdot \sin x\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x + -1\right)}{3 \cdot \left(\left(1 + \cos x \cdot \frac{t_1}{2}\right) + \cos y \cdot \frac{3 - \sqrt{5}}{2}\right)}\\ \mathbf{elif}\;x \leq 0.44:\\ \;\;\;\;\frac{2 + \left(\sqrt{2} \cdot \left(\cos y + -1\right)\right) \cdot \left({\sin y}^{2} \cdot 0.0625 + \sin y \cdot \left(x \cdot -1.00390625\right)\right)}{3 - \left(\cos x \cdot \frac{-6}{\sqrt{5} + 1} - -1.5 \cdot \left(\cos y \cdot t_0\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 - \sqrt{2} \cdot \left(\left(\cos x - \cos y\right) \cdot \left(\left(\sin y + -0.0625 \cdot \sin x\right) \cdot \left(\sin y \cdot 0.0625 - \sin x\right)\right)\right)}{3 + -1.5 \cdot \left(t_0 - \cos x \cdot t_1\right)}\\ \end{array} \]

Alternative 11
Error	12.8
Cost	60168

\[\begin{array}{l} t_0 := 3 - \sqrt{5}\\ t_1 := \sqrt{5} + -1\\ \mathbf{if}\;x \leq -0.0122:\\ \;\;\;\;\frac{2 + \left(\left(\sqrt{2} \cdot \sin x\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x + -1\right)}{3 \cdot \left(\left(1 + \cos x \cdot \frac{t_1}{2}\right) + \cos y \cdot \frac{t_0}{2}\right)}\\ \mathbf{elif}\;x \leq 0.44:\\ \;\;\;\;\frac{2 + \left(\sqrt{2} \cdot \left(\cos y + -1\right)\right) \cdot \left({\sin y}^{2} \cdot 0.0625 + \sin y \cdot \left(x \cdot -1.00390625\right)\right)}{3 - \left(\cos x \cdot \frac{-6}{\sqrt{5} + 1} - -1.5 \cdot \left(\cos y \cdot \left(\sqrt{5} + -3\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 - \sqrt{2} \cdot \left(\left(\left(\sin y \cdot 0.0625 - \sin x\right) \cdot \left(\sin x \cdot 0.0625 - \sin y\right)\right) \cdot \left(1 - \cos x\right)\right)}{3 + \left(1.5 \cdot t_0 + 1.5 \cdot \left(\cos x \cdot t_1\right)\right)}\\ \end{array} \]

Alternative 12
Error	12.9
Cost	60104

\[\begin{array}{l} t_0 := \frac{4}{3 + \sqrt{5}}\\ t_1 := 1 + \cos x \cdot \frac{\sqrt{5} + -1}{2}\\ t_2 := \cos x - \cos y\\ \mathbf{if}\;y \leq -0.0042:\\ \;\;\;\;\frac{2 + -0.0625 \cdot \left(\left(1 - \cos y\right) \cdot \frac{1 - \cos \left(y + y\right)}{\frac{2}{\sqrt{2}}}\right)}{3 \cdot \left(t_1 + \cos y \cdot \frac{t_0}{2}\right)}\\ \mathbf{elif}\;y \leq 0.82:\\ \;\;\;\;\frac{2 + t_2 \cdot \left(\left(\sqrt{2} \cdot \sin x\right) \cdot \left(y + -0.0625 \cdot \sin x\right)\right)}{3 \cdot \left(t_1 + \cos y \cdot \frac{3 - \sqrt{5}}{2}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \sqrt{2} \cdot \left(t_2 \cdot \left(-0.0625 \cdot {\sin y}^{2}\right)\right)}{3 - \left(\cos x \cdot \frac{-6}{\sqrt{5} + 1} + -1.5 \cdot \left(\cos y \cdot t_0\right)\right)}\\ \end{array} \]

Alternative 13
Error	12.9
Cost	60104

\[\begin{array}{l} t_0 := \frac{4}{3 + \sqrt{5}}\\ t_1 := 1 + \cos x \cdot \frac{\sqrt{5} + -1}{2}\\ \mathbf{if}\;y \leq -13:\\ \;\;\;\;\frac{2 + -0.0625 \cdot \left(\left(1 - \cos y\right) \cdot \frac{1 - \cos \left(y + y\right)}{\frac{2}{\sqrt{2}}}\right)}{3 \cdot \left(t_1 + \cos y \cdot \frac{t_0}{2}\right)}\\ \mathbf{elif}\;y \leq 0.82:\\ \;\;\;\;\frac{2 + \left(\left(\sqrt{2} \cdot \sin x\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x + -1\right)}{3 \cdot \left(t_1 + \cos y \cdot \frac{3 - \sqrt{5}}{2}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \sqrt{2} \cdot \left(\left(\cos x - \cos y\right) \cdot \left(-0.0625 \cdot {\sin y}^{2}\right)\right)}{3 - \left(\cos x \cdot \frac{-6}{\sqrt{5} + 1} + -1.5 \cdot \left(\cos y \cdot t_0\right)\right)}\\ \end{array} \]

Alternative 14
Error	12.9
Cost	60104

\[\begin{array}{l} t_0 := \frac{4}{3 + \sqrt{5}}\\ t_1 := \sqrt{5} + -1\\ \mathbf{if}\;y \leq -13:\\ \;\;\;\;\frac{2 + -0.0625 \cdot \left(\left(1 - \cos y\right) \cdot \frac{1 - \cos \left(y + y\right)}{\frac{2}{\sqrt{2}}}\right)}{3 \cdot \left(\left(1 + \cos x \cdot \frac{t_1}{2}\right) + \cos y \cdot \frac{t_0}{2}\right)}\\ \mathbf{elif}\;y \leq 0.000102:\\ \;\;\;\;\frac{2 - \sqrt{2} \cdot \left(\left(\left(\sin y \cdot 0.0625 - \sin x\right) \cdot \left(\sin x \cdot 0.0625 - \sin y\right)\right) \cdot \left(1 - \cos x\right)\right)}{3 + \left(1.5 \cdot \left(3 - \sqrt{5}\right) + 1.5 \cdot \left(\cos x \cdot t_1\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \sqrt{2} \cdot \left(\left(\cos x - \cos y\right) \cdot \left(-0.0625 \cdot {\sin y}^{2}\right)\right)}{3 - \left(\cos x \cdot \frac{-6}{\sqrt{5} + 1} + -1.5 \cdot \left(\cos y \cdot t_0\right)\right)}\\ \end{array} \]

Alternative 15
Error	12.9
Cost	59912

\[\begin{array}{l} t_0 := \frac{4}{3 + \sqrt{5}}\\ t_1 := 3 - \left(\cos x \cdot \frac{-6}{\sqrt{5} + 1} + -1.5 \cdot \left(\cos y \cdot t_0\right)\right)\\ \mathbf{if}\;y \leq -0.0042:\\ \;\;\;\;\frac{2 + -0.0625 \cdot \left(\left(1 - \cos y\right) \cdot \frac{1 - \cos \left(y + y\right)}{\frac{2}{\sqrt{2}}}\right)}{3 \cdot \left(\left(1 + \cos x \cdot \frac{\sqrt{5} + -1}{2}\right) + \cos y \cdot \frac{t_0}{2}\right)}\\ \mathbf{elif}\;y \leq 0.82:\\ \;\;\;\;\frac{2 + \left(\left(\cos x + -1\right) \cdot {\sin x}^{2}\right) \cdot \left(\sqrt{2} \cdot -0.0625\right)}{t_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \sqrt{2} \cdot \left(\left(\cos x - \cos y\right) \cdot \left(-0.0625 \cdot {\sin y}^{2}\right)\right)}{t_1}\\ \end{array} \]

Alternative 16
Error	13.0
Cost	53512

\[\begin{array}{l} t_0 := \frac{4}{3 + \sqrt{5}}\\ t_1 := \sqrt{5} + 1\\ \mathbf{if}\;y \leq -0.0042:\\ \;\;\;\;\frac{2 + -0.0625 \cdot \left(\left(1 - \cos y\right) \cdot \frac{1 - \cos \left(y + y\right)}{\frac{2}{\sqrt{2}}}\right)}{3 \cdot \left(\left(1 + \cos x \cdot \frac{\sqrt{5} + -1}{2}\right) + \cos y \cdot \frac{t_0}{2}\right)}\\ \mathbf{elif}\;y \leq 0.82:\\ \;\;\;\;\frac{2 + \left(\left(\cos x + -1\right) \cdot {\sin x}^{2}\right) \cdot \left(\sqrt{2} \cdot -0.0625\right)}{3 - \left(\cos x \cdot \frac{-6}{t_1} - -1.5 \cdot \left(\cos y \cdot \left(\sqrt{5} + -3\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 - -0.0625 \cdot \left(\left(\sqrt{2} \cdot {\sin y}^{2}\right) \cdot \left(\cos y + -1\right)\right)}{3 + \left(\cos x \cdot \frac{6}{t_1} + 1.5 \cdot \left(\cos y \cdot t_0\right)\right)}\\ \end{array} \]

Alternative 17
Error	13.0
Cost	53512

\[\begin{array}{l} t_0 := \frac{4}{3 + \sqrt{5}}\\ t_1 := 3 - \left(\cos x \cdot \frac{-6}{\sqrt{5} + 1} + -1.5 \cdot \left(\cos y \cdot t_0\right)\right)\\ \mathbf{if}\;y \leq -0.0042:\\ \;\;\;\;\frac{2 + -0.0625 \cdot \left(\left(1 - \cos y\right) \cdot \frac{1 - \cos \left(y + y\right)}{\frac{2}{\sqrt{2}}}\right)}{3 \cdot \left(\left(1 + \cos x \cdot \frac{\sqrt{5} + -1}{2}\right) + \cos y \cdot \frac{t_0}{2}\right)}\\ \mathbf{elif}\;y \leq 0.82:\\ \;\;\;\;\frac{2 + \left(\left(\cos x + -1\right) \cdot {\sin x}^{2}\right) \cdot \left(\sqrt{2} \cdot -0.0625\right)}{t_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 - -0.0625 \cdot \left(\left(\sqrt{2} \cdot {\sin y}^{2}\right) \cdot \left(\cos y + -1\right)\right)}{t_1}\\ \end{array} \]

Alternative 18
Error	13.1
Cost	53384

\[\begin{array}{l} t_0 := \sqrt{5} + -1\\ \mathbf{if}\;y \leq -13:\\ \;\;\;\;\frac{2 + -0.0625 \cdot \left(\left(1 - \cos y\right) \cdot \frac{1 - \cos \left(y + y\right)}{\frac{2}{\sqrt{2}}}\right)}{3 \cdot \left(\left(1 + \cos x \cdot \frac{t_0}{2}\right) + \cos y \cdot \frac{\frac{4}{3 + \sqrt{5}}}{2}\right)}\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-6}:\\ \;\;\;\;\frac{2 + -0.0625 \cdot \left(\sqrt{2} \cdot \left(\left(\cos x + -1\right) \cdot {\sin x}^{2}\right)\right)}{3 + 1.5 \cdot \left(3 + \left(\cos x \cdot t_0 - \sqrt{5}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 - -0.0625 \cdot \left(\left(\sqrt{2} \cdot {\sin y}^{2}\right) \cdot \left(\cos y + -1\right)\right)}{3 - \left(\cos x \cdot \frac{-6}{\sqrt{5} + 1} - -1.5 \cdot \left(\cos y \cdot \left(\sqrt{5} + -3\right)\right)\right)}\\ \end{array} \]

Alternative 19
Error	13.0
Cost	53384

\[\begin{array}{l} t_0 := 3 - \left(\cos x \cdot \frac{-6}{\sqrt{5} + 1} - -1.5 \cdot \left(\cos y \cdot \left(\sqrt{5} + -3\right)\right)\right)\\ \mathbf{if}\;y \leq -0.0042:\\ \;\;\;\;\frac{2 + -0.0625 \cdot \left(\left(1 - \cos y\right) \cdot \frac{1 - \cos \left(y + y\right)}{\frac{2}{\sqrt{2}}}\right)}{3 \cdot \left(\left(1 + \cos x \cdot \frac{\sqrt{5} + -1}{2}\right) + \cos y \cdot \frac{\frac{4}{3 + \sqrt{5}}}{2}\right)}\\ \mathbf{elif}\;y \leq 0.82:\\ \;\;\;\;\frac{2 + \left(\left(\cos x + -1\right) \cdot {\sin x}^{2}\right) \cdot \left(\sqrt{2} \cdot -0.0625\right)}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 - -0.0625 \cdot \left(\left(\sqrt{2} \cdot {\sin y}^{2}\right) \cdot \left(\cos y + -1\right)\right)}{t_0}\\ \end{array} \]

Alternative 20
Error	13.1
Cost	47561

\[\begin{array}{l} t_0 := \sqrt{5} + -1\\ \mathbf{if}\;y \leq -13 \lor \neg \left(y \leq 1.02 \cdot 10^{-5}\right):\\ \;\;\;\;\frac{2 + -0.0625 \cdot \left(\left(1 - \cos y\right) \cdot \frac{1 - \cos \left(y + y\right)}{\frac{2}{\sqrt{2}}}\right)}{3 \cdot \left(\left(1 + \cos x \cdot \frac{t_0}{2}\right) + \cos y \cdot \frac{\frac{4}{3 + \sqrt{5}}}{2}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + -0.0625 \cdot \left(\sqrt{2} \cdot \left(\left(\cos x + -1\right) \cdot {\sin x}^{2}\right)\right)}{3 + 1.5 \cdot \left(3 + \left(\cos x \cdot t_0 - \sqrt{5}\right)\right)}\\ \end{array} \]

Alternative 21
Error	13.3
Cost	47112

\[\begin{array}{l} t_0 := \frac{4}{3 + \sqrt{5}}\\ t_1 := \cos x \cdot \left(\sqrt{5} + -1\right)\\ \mathbf{if}\;x \leq -1.8 \cdot 10^{-5}:\\ \;\;\;\;\frac{2 + -0.0625 \cdot \left(\sqrt{2} \cdot \left(\left(1 - \cos x\right) \cdot \left(-0.5 + \frac{\cos \left(x + x\right)}{2}\right)\right)\right)}{3 + -1.5 \cdot \left(\left(\sqrt{5} + -3\right) - t_1\right)}\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{-5}:\\ \;\;\;\;\frac{2 - -0.0625 \cdot \left(\left(\sqrt{2} \cdot {\sin y}^{2}\right) \cdot \left(\cos y + -1\right)\right)}{3 \cdot \left(\cos y \cdot \frac{t_0}{2} + \left(1 + \left(-0.5 - \sqrt{5} \cdot -0.5\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + -0.0625 \cdot \left(\sqrt{2} \cdot \left(\left(\cos x + -1\right) \cdot {\sin x}^{2}\right)\right)}{3 + 1.5 \cdot \left(t_1 + t_0\right)}\\ \end{array} \]

Alternative 22
Error	13.4
Cost	46856

\[\begin{array}{l} t_0 := \cos x \cdot \left(\sqrt{5} + -1\right)\\ \mathbf{if}\;x \leq -4 \cdot 10^{-5}:\\ \;\;\;\;\frac{2 + -0.0625 \cdot \left(\sqrt{2} \cdot \left(\left(1 - \cos x\right) \cdot \left(-0.5 + \frac{\cos \left(x + x\right)}{2}\right)\right)\right)}{3 + -1.5 \cdot \left(\left(\sqrt{5} + -3\right) - t_0\right)}\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{-5}:\\ \;\;\;\;\frac{0.3333333333333333}{\frac{0.5 + \left(\sqrt{5} \cdot 0.5 + \cos y \cdot \left(1.5 + \sqrt{5} \cdot -0.5\right)\right)}{2 - -0.0625 \cdot \left(\sqrt{2} \cdot \left({\sin y}^{2} \cdot \left(\cos y + -1\right)\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + -0.0625 \cdot \left(\sqrt{2} \cdot \left(\left(\cos x + -1\right) \cdot {\sin x}^{2}\right)\right)}{3 + 1.5 \cdot \left(3 + \left(t_0 - \sqrt{5}\right)\right)}\\ \end{array} \]

Alternative 23
Error	13.3
Cost	46856

\[\begin{array}{l} t_0 := \sqrt{5} + -1\\ t_1 := \sqrt{5} + -3\\ t_2 := \cos x \cdot t_0\\ \mathbf{if}\;x \leq -5.2 \cdot 10^{-6}:\\ \;\;\;\;\frac{2 + -0.0625 \cdot \left(\sqrt{2} \cdot \left(\left(1 - \cos x\right) \cdot \left(-0.5 + \frac{\cos \left(x + x\right)}{2}\right)\right)\right)}{3 + -1.5 \cdot \left(t_1 - t_2\right)}\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{-5}:\\ \;\;\;\;\frac{2 - -0.0625 \cdot \left(\sqrt{2} \cdot \left({\sin y}^{2} \cdot \left(\cos y + -1\right)\right)\right)}{1.5 \cdot t_0 + \left(3 + -1.5 \cdot \left(\cos y \cdot t_1\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + -0.0625 \cdot \left(\sqrt{2} \cdot \left(\left(\cos x + -1\right) \cdot {\sin x}^{2}\right)\right)}{3 + 1.5 \cdot \left(3 + \left(t_2 - \sqrt{5}\right)\right)}\\ \end{array} \]

Alternative 24
Error	13.3
Cost	46856

\[\begin{array}{l} t_0 := \sqrt{5} + -1\\ t_1 := \sqrt{5} + -3\\ t_2 := \cos x \cdot t_0\\ \mathbf{if}\;x \leq -3.3 \cdot 10^{-6}:\\ \;\;\;\;\frac{2 + -0.0625 \cdot \left(\sqrt{2} \cdot \left(\left(1 - \cos x\right) \cdot \left(-0.5 + \frac{\cos \left(x + x\right)}{2}\right)\right)\right)}{3 + -1.5 \cdot \left(t_1 - t_2\right)}\\ \mathbf{elif}\;x \leq 1.32 \cdot 10^{-5}:\\ \;\;\;\;\frac{2 - -0.0625 \cdot \left(\sqrt{2} \cdot \left({\sin y}^{2} \cdot \left(\cos y + -1\right)\right)\right)}{1.5 \cdot t_0 + \left(3 + -1.5 \cdot \left(\cos y \cdot t_1\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + -0.0625 \cdot \left(\sqrt{2} \cdot \left(\left(\cos x + -1\right) \cdot {\sin x}^{2}\right)\right)}{3 + 1.5 \cdot \left(t_2 + \frac{4}{3 + \sqrt{5}}\right)}\\ \end{array} \]

Alternative 25
Error	13.4
Cost	46728

\[\begin{array}{l} t_0 := \cos x \cdot \left(\sqrt{5} + -1\right)\\ \mathbf{if}\;x \leq -9 \cdot 10^{-6}:\\ \;\;\;\;\frac{2 + -0.0625 \cdot \left(\sqrt{2} \cdot \left(\left(1 - \cos x\right) \cdot \left(-0.5 + \frac{\cos \left(x + x\right)}{2}\right)\right)\right)}{3 + -1.5 \cdot \left(\left(\sqrt{5} + -3\right) - t_0\right)}\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{-5}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{2 + 0.0625 \cdot \left(\sqrt{2} \cdot \left(\left(0.5 - \frac{\cos \left(y + y\right)}{2}\right) \cdot \left(\cos y + -1\right)\right)\right)}{0.5 + \left(\sqrt{5} \cdot 0.5 + \cos y \cdot \left(1.5 + \sqrt{5} \cdot -0.5\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + -0.0625 \cdot \left(\sqrt{2} \cdot \left(\left(\cos x + -1\right) \cdot {\sin x}^{2}\right)\right)}{3 + 1.5 \cdot \left(3 + \left(t_0 - \sqrt{5}\right)\right)}\\ \end{array} \]

Alternative 26
Error	13.4
Cost	40777

\[\begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{-6} \lor \neg \left(x \leq 1.25 \cdot 10^{-5}\right):\\ \;\;\;\;\frac{2 + -0.0625 \cdot \left(\sqrt{2} \cdot \left(\left(1 - \cos x\right) \cdot \left(-0.5 + \frac{\cos \left(x + x\right)}{2}\right)\right)\right)}{3 + -1.5 \cdot \left(\left(\sqrt{5} + -3\right) - \cos x \cdot \left(\sqrt{5} + -1\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{2 + 0.0625 \cdot \left(\sqrt{2} \cdot \left(\left(0.5 - \frac{\cos \left(y + y\right)}{2}\right) \cdot \left(\cos y + -1\right)\right)\right)}{0.5 + \left(\sqrt{5} \cdot 0.5 + \cos y \cdot \left(1.5 + \sqrt{5} \cdot -0.5\right)\right)}\\ \end{array} \]

Alternative 27
Error	25.4
Cost	40384

\[\frac{2 + -0.0625 \cdot \left(\sqrt{2} \cdot \left(\left(1 - \cos x\right) \cdot \left(-0.5 + \frac{\cos \left(x + x\right)}{2}\right)\right)\right)}{3 + -1.5 \cdot \left(\left(\sqrt{5} + -3\right) - \cos x \cdot \left(\sqrt{5} + -1\right)\right)} \]

Alternative 28
Error	37.6
Cost	20416

\[\frac{2 + -0.0625 \cdot \left(\sqrt{2} \cdot \left(\left(1 - \cos x\right) \cdot \left(-0.5 + \frac{\cos \left(x + x\right)}{2}\right)\right)\right)}{6} \]

Alternative 29
Error	37.6
Cost	64

\[0.3333333333333333 \]

Reproduce

herbie shell --seed 2023031 
(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))))))