?

Average Accuracy: 99.3% → 99.4%
Time: 35.8s
Precision: binary64
Cost: 85440

?

\[\frac{2 + \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x - \cos y\right)}{3 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{3 - \sqrt{5}}{2} \cdot \cos y\right)} \]
↓
\[\frac{\mathsf{fma}\left(\sqrt{2}, \left(\sin y - \frac{\sin x}{16}\right) \cdot \left(\left(\sin x - \frac{\sin y}{16}\right) \cdot \left(\cos x - \cos y\right)\right), 2\right)}{\frac{\frac{\cos x \cdot 4}{\sqrt{5} + 1}}{0.6666666666666666} + \mathsf{fma}\left(\cos y, \frac{3 - \sqrt{5}}{0.6666666666666666}, 3\right)} \]
(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
 (/
  (fma
   (sqrt 2.0)
   (*
    (- (sin y) (/ (sin x) 16.0))
    (* (- (sin x) (/ (sin y) 16.0)) (- (cos x) (cos y))))
   2.0)
  (+
   (/ (/ (* (cos x) 4.0) (+ (sqrt 5.0) 1.0)) 0.6666666666666666)
   (fma (cos y) (/ (- 3.0 (sqrt 5.0)) 0.6666666666666666) 3.0))))
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 fma(sqrt(2.0), ((sin(y) - (sin(x) / 16.0)) * ((sin(x) - (sin(y) / 16.0)) * (cos(x) - cos(y)))), 2.0) / ((((cos(x) * 4.0) / (sqrt(5.0) + 1.0)) / 0.6666666666666666) + fma(cos(y), ((3.0 - sqrt(5.0)) / 0.6666666666666666), 3.0));
}

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(fma(sqrt(2.0), Float64(Float64(sin(y) - Float64(sin(x) / 16.0)) * Float64(Float64(sin(x) - Float64(sin(y) / 16.0)) * Float64(cos(x) - cos(y)))), 2.0) / Float64(Float64(Float64(Float64(cos(x) * 4.0) / Float64(sqrt(5.0) + 1.0)) / 0.6666666666666666) + fma(cos(y), Float64(Float64(3.0 - sqrt(5.0)) / 0.6666666666666666), 3.0)))
end

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[(N[Sqrt[2.0], $MachinePrecision] * N[(N[(N[Sin[y], $MachinePrecision] - N[(N[Sin[x], $MachinePrecision] / 16.0), $MachinePrecision]), $MachinePrecision] * N[(N[(N[Sin[x], $MachinePrecision] - N[(N[Sin[y], $MachinePrecision] / 16.0), $MachinePrecision]), $MachinePrecision] * N[(N[Cos[x], $MachinePrecision] - N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 2.0), $MachinePrecision] / N[(N[(N[(N[(N[Cos[x], $MachinePrecision] * 4.0), $MachinePrecision] / N[(N[Sqrt[5.0], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] / 0.6666666666666666), $MachinePrecision] + N[(N[Cos[y], $MachinePrecision] * N[(N[(3.0 - N[Sqrt[5.0], $MachinePrecision]), $MachinePrecision] / 0.6666666666666666), $MachinePrecision] + 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

\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{\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)}{\frac{\frac{\cos x \cdot 4}{\sqrt{5} + 1}}{0.6666666666666666} + \mathsf{fma}\left(\cos y, \frac{3 - \sqrt{5}}{0.6666666666666666}, 3\right)}

Error?

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. Simplified99.3%

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

    [Start]99.3

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

  3. Applied egg-rr99.4%

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

    [Start]99.3

    \[ \frac{\mathsf{fma}\left(\sqrt{2}, \left(\sin y - \frac{\sin x}{16}\right) \cdot \left(\left(\sin x - \frac{\sin y}{16}\right) \cdot \left(\cos x - \cos y\right)\right), 2\right)}{\frac{\cos x \cdot \left(\sqrt{5} + -1\right)}{0.6666666666666666} + \mathsf{fma}\left(\cos y, \frac{3 - \sqrt{5}}{0.6666666666666666}, 3\right)} \]

    flip-+ [=>]98.9

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

    associate-*r/ [=>]99.0

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

    add-sqr-sqrt [<=]99.4

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

    metadata-eval [=>]99.4

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

    metadata-eval [=>]99.4

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

    sub-neg [=>]99.4

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

    metadata-eval [=>]99.4

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

  4. Final simplification99.4%

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

Alternatives

Alternative 1
Accuracy99.4%
Cost78912
\[\frac{2 + \sqrt{2} \cdot \left(\left(\cos x - \cos y\right) \cdot \left(\left(\sin y + \sin x \cdot -0.0625\right) \cdot \left(\sin x + \sin y \cdot -0.0625\right)\right)\right)}{3 + \mathsf{fma}\left(\frac{6}{\sqrt{5} + 3}, \cos y, \frac{\cos x}{0.16666666666666666 + \sqrt{0.1388888888888889}}\right)} \]
Alternative 2
Accuracy99.4%
Cost72896
\[\frac{2 + \sqrt{2} \cdot \left(\left(\cos x - \cos y\right) \cdot \left(\left(\sin y + \sin x \cdot -0.0625\right) \cdot \left(\sin x + \sin y \cdot -0.0625\right)\right)\right)}{3 + \left(\frac{\cos x}{0.16666666666666666 + \sqrt{5} \cdot 0.16666666666666666} + 1.5 \cdot \left(\cos y \cdot \frac{4}{\sqrt{5} + 3}\right)\right)} \]
Alternative 3
Accuracy99.4%
Cost72768
\[\frac{2 + \sqrt{2} \cdot \left(\left(\cos x - \cos y\right) \cdot \left(\left(\sin y + \sin x \cdot -0.0625\right) \cdot \left(\sin x + \sin y \cdot -0.0625\right)\right)\right)}{3 + \left(\frac{\cos x}{0.16666666666666666 + \sqrt{5} \cdot 0.16666666666666666} + 1.5 \cdot \left(\cos y \cdot \left(3 - \sqrt{5}\right)\right)\right)} \]
Alternative 4
Accuracy99.4%
Cost72768
\[\frac{2 + \sqrt{2} \cdot \left(\left(\cos x - \cos y\right) \cdot \left(\left(\sin y + \sin x \cdot -0.0625\right) \cdot \left(\sin x + \sin y \cdot -0.0625\right)\right)\right)}{3 + \left(\frac{\cos x}{0.16666666666666666 + \sqrt{5} \cdot 0.16666666666666666} + 6 \cdot \frac{\cos y}{\sqrt{5} + 3}\right)} \]
Alternative 5
Accuracy80.9%
Cost67016
\[\begin{array}{l} t_0 := \sin y + \sin x \cdot -0.0625\\ t_1 := \cos x - \cos y\\ t_2 := 3 - \sqrt{5}\\ t_3 := \sqrt{5} + -1\\ t_4 := \frac{\sqrt{5}}{2}\\ \mathbf{if}\;x \leq -0.0075:\\ \;\;\;\;\frac{2 + \left(\sqrt{2} \cdot \sin x\right) \cdot \left(\left(\sin y - \frac{\sin x}{16}\right) \cdot t_1\right)}{3 \cdot \left(1 + \left(\cos x \cdot \left(t_4 + -0.5\right) + \cos y \cdot \left(1.5 - t_4\right)\right)\right)}\\ \mathbf{elif}\;x \leq 0.048:\\ \;\;\;\;\frac{2 + \sqrt{2} \cdot \left(\left(1 + \left(-0.5 \cdot \left(x \cdot x\right) - \cos y\right)\right) \cdot \left(t_0 \cdot \left(\sin x + \sin y \cdot -0.0625\right)\right)\right)}{3 + \left(1.5 \cdot \left(\cos y \cdot t_2\right) + 1.5 \cdot \left(\cos x \cdot t_3\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + t_1 \cdot \left(\sqrt{2} \cdot \left(\sin x \cdot t_0\right)\right)}{3 \cdot \left(\left(1 + \cos x \cdot \frac{t_3}{2}\right) + \cos y \cdot \frac{t_2}{2}\right)}\\ \end{array} \]
Alternative 6
Accuracy80.9%
Cost66888
\[\begin{array}{l} t_0 := \cos x - \cos y\\ t_1 := 3 - \sqrt{5}\\ t_2 := \sqrt{5} + -1\\ t_3 := \sin y + \sin x \cdot -0.0625\\ t_4 := \frac{\sqrt{5}}{2}\\ \mathbf{if}\;x \leq -0.0012:\\ \;\;\;\;\frac{2 + \left(\sqrt{2} \cdot \sin x\right) \cdot \left(\left(\sin y - \frac{\sin x}{16}\right) \cdot t_0\right)}{3 \cdot \left(1 + \left(\cos x \cdot \left(t_4 + -0.5\right) + \cos y \cdot \left(1.5 - t_4\right)\right)\right)}\\ \mathbf{elif}\;x \leq 0.022:\\ \;\;\;\;\frac{2 + \sqrt{2} \cdot \left(t_0 \cdot \left(t_3 \cdot \left(\sin x + \sin y \cdot -0.0625\right)\right)\right)}{3 + \left(1.5 \cdot \left(\cos y \cdot t_1\right) + t_2 \cdot \left(1.5 + \left(x \cdot x\right) \cdot -0.75\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + t_0 \cdot \left(\sqrt{2} \cdot \left(\sin x \cdot t_3\right)\right)}{3 \cdot \left(\left(1 + \cos x \cdot \frac{t_2}{2}\right) + \cos y \cdot \frac{t_1}{2}\right)}\\ \end{array} \]
Alternative 7
Accuracy80.9%
Cost66505
\[\begin{array}{l} t_0 := \frac{\sqrt{5}}{2}\\ \mathbf{if}\;x \leq -0.0012 \lor \neg \left(x \leq 0.0185\right):\\ \;\;\;\;\frac{2 + \left(\sqrt{2} \cdot \sin x\right) \cdot \left(\left(\sin y - \frac{\sin x}{16}\right) \cdot \left(\cos x - \cos y\right)\right)}{3 \cdot \left(1 + \left(\cos x \cdot \left(t_0 + -0.5\right) + \cos y \cdot \left(1.5 - t_0\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \sqrt{2} \cdot \left(\left(1 + \left(-0.5 \cdot \left(x \cdot x\right) - \cos y\right)\right) \cdot \left(\left(\sin y + \sin x \cdot -0.0625\right) \cdot \left(\sin x + \sin y \cdot -0.0625\right)\right)\right)}{3 + \left(1.5 \cdot \left(\cos y \cdot \left(3 - \sqrt{5}\right)\right) + \left(\sqrt{5} + -1\right) \cdot \left(1.5 + \left(x \cdot x\right) \cdot -0.75\right)\right)}\\ \end{array} \]
Alternative 8
Accuracy80.9%
Cost66504
\[\begin{array}{l} t_0 := \sin y + \sin x \cdot -0.0625\\ t_1 := \cos x - \cos y\\ t_2 := 3 - \sqrt{5}\\ t_3 := \sqrt{5} + -1\\ t_4 := \frac{\sqrt{5}}{2}\\ \mathbf{if}\;x \leq -0.0012:\\ \;\;\;\;\frac{2 + \left(\sqrt{2} \cdot \sin x\right) \cdot \left(\left(\sin y - \frac{\sin x}{16}\right) \cdot t_1\right)}{3 \cdot \left(1 + \left(\cos x \cdot \left(t_4 + -0.5\right) + \cos y \cdot \left(1.5 - t_4\right)\right)\right)}\\ \mathbf{elif}\;x \leq 0.05:\\ \;\;\;\;\frac{2 + \sqrt{2} \cdot \left(\left(1 + \left(-0.5 \cdot \left(x \cdot x\right) - \cos y\right)\right) \cdot \left(t_0 \cdot \left(\sin x + \sin y \cdot -0.0625\right)\right)\right)}{3 + \left(1.5 \cdot \left(\cos y \cdot t_2\right) + t_3 \cdot \left(1.5 + \left(x \cdot x\right) \cdot -0.75\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + t_1 \cdot \left(\sqrt{2} \cdot \left(\sin x \cdot t_0\right)\right)}{3 \cdot \left(\left(1 + \cos x \cdot \frac{t_3}{2}\right) + \cos y \cdot \frac{t_2}{2}\right)}\\ \end{array} \]
Alternative 9
Accuracy79.1%
Cost60873
\[\begin{array}{l} t_0 := 1.5 \cdot \left(\cos y \cdot \left(3 - \sqrt{5}\right)\right)\\ \mathbf{if}\;x \leq -7.8 \cdot 10^{-7} \lor \neg \left(x \leq 0.0245\right):\\ \;\;\;\;\frac{2 + \sqrt{2} \cdot \left(-0.0625 \cdot \left({\sin x}^{2} \cdot \left(\cos x + -1\right)\right)\right)}{3 + \left(\frac{\cos x}{0.16666666666666666 + \sqrt{5} \cdot 0.16666666666666666} + t_0\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \sqrt{2} \cdot \left(\left(1 + \left(-0.5 \cdot \left(x \cdot x\right) - \cos y\right)\right) \cdot \left(\left(\sin y + \sin x \cdot -0.0625\right) \cdot \left(\sin x + \sin y \cdot -0.0625\right)\right)\right)}{3 + \left(t_0 + \left(\sqrt{5} + -1\right) \cdot \left(1.5 + \left(x \cdot x\right) \cdot -0.75\right)\right)}\\ \end{array} \]
Alternative 10
Accuracy79.0%
Cost60169
\[\begin{array}{l} t_0 := 1.5 \cdot \left(\cos y \cdot \left(3 - \sqrt{5}\right)\right)\\ \mathbf{if}\;x \leq -7.8 \cdot 10^{-7} \lor \neg \left(x \leq 0.0112\right):\\ \;\;\;\;\frac{2 + \sqrt{2} \cdot \left(-0.0625 \cdot \left({\sin x}^{2} \cdot \left(\cos x + -1\right)\right)\right)}{3 + \left(\frac{\cos x}{0.16666666666666666 + \sqrt{5} \cdot 0.16666666666666666} + t_0\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \left(\sqrt{2} \cdot \left(1 - \cos y\right)\right) \cdot \left(-0.0625 \cdot {\sin y}^{2} + x \cdot \left(\sin y \cdot 1.00390625\right)\right)}{3 + \left(t_0 + 1.5 \cdot \left(\cos x \cdot \left(\sqrt{5} + -1\right)\right)\right)}\\ \end{array} \]
Alternative 11
Accuracy79.0%
Cost54025
\[\begin{array}{l} t_0 := 1.5 \cdot \left(\cos y \cdot \left(3 - \sqrt{5}\right)\right)\\ \mathbf{if}\;x \leq -7.8 \cdot 10^{-7} \lor \neg \left(x \leq 0.0154\right):\\ \;\;\;\;\frac{2 + \sqrt{2} \cdot \left(-0.0625 \cdot \left({\sin x}^{2} \cdot \left(\cos x + -1\right)\right)\right)}{3 + \left(\frac{\cos x}{0.16666666666666666 + \sqrt{5} \cdot 0.16666666666666666} + t_0\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \left(\sqrt{2} \cdot \left(1 - \cos y\right)\right) \cdot \left(-0.0625 \cdot {\sin y}^{2} + x \cdot \left(\sin y \cdot 1.00390625\right)\right)}{3 + \left(t_0 + \left(\sqrt{5} + -1\right) \cdot \left(1.5 + \left(x \cdot x\right) \cdot -0.75\right)\right)}\\ \end{array} \]
Alternative 12
Accuracy79.0%
Cost53641
\[\begin{array}{l} t_0 := 1.5 \cdot \left(\cos y \cdot \left(3 - \sqrt{5}\right)\right)\\ \mathbf{if}\;x \leq -7.8 \cdot 10^{-7} \lor \neg \left(x \leq 0.00255\right):\\ \;\;\;\;\frac{2 + \sqrt{2} \cdot \left(-0.0625 \cdot \left({\sin x}^{2} \cdot \left(\cos x + -1\right)\right)\right)}{3 + \left(\frac{\cos x}{0.16666666666666666 + \sqrt{5} \cdot 0.16666666666666666} + t_0\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \left(\sqrt{2} \cdot \left(1 - \cos y\right)\right) \cdot \left(-0.0625 \cdot {\sin y}^{2} + x \cdot \left(\sin y \cdot 1.00390625\right)\right)}{3 + \left(t_0 + \left(\sqrt{5} \cdot 1.5 + -1.5\right)\right)}\\ \end{array} \]
Alternative 13
Accuracy78.8%
Cost53385
\[\begin{array}{l} t_0 := 1.5 \cdot \left(\cos y \cdot \left(3 - \sqrt{5}\right)\right)\\ t_1 := 0.16666666666666666 + \sqrt{5} \cdot 0.16666666666666666\\ \mathbf{if}\;x \leq -7.8 \cdot 10^{-7} \lor \neg \left(x \leq 0.00255\right):\\ \;\;\;\;\frac{2 + \sqrt{2} \cdot \left(-0.0625 \cdot \left({\sin x}^{2} \cdot \left(\cos x + -1\right)\right)\right)}{3 + \left(\frac{\cos x}{t_1} + t_0\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + -0.0625 \cdot \left(\left(\sqrt{2} \cdot \left(1 - \cos y\right)\right) \cdot \left(1 - {\cos y}^{2}\right)\right)}{\frac{1}{t_1} + \left(3 + t_0\right)}\\ \end{array} \]
Alternative 14
Accuracy78.9%
Cost53385
\[\begin{array}{l} t_0 := 3 + \left(\frac{\cos x}{0.16666666666666666 + \sqrt{5} \cdot 0.16666666666666666} + 1.5 \cdot \left(\cos y \cdot \left(3 - \sqrt{5}\right)\right)\right)\\ \mathbf{if}\;x \leq -0.00075 \lor \neg \left(x \leq 0.00255\right):\\ \;\;\;\;\frac{2 + \sqrt{2} \cdot \left(-0.0625 \cdot \left({\sin x}^{2} \cdot \left(\cos x + -1\right)\right)\right)}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \left(\sqrt{2} \cdot -0.0625\right) \cdot \left(\left(1 - \cos y\right) \cdot {\sin y}^{2}\right)}{t_0}\\ \end{array} \]
Alternative 15
Accuracy78.2%
Cost47113
\[\begin{array}{l} t_0 := 3 - \sqrt{5}\\ t_1 := 0.16666666666666666 + \sqrt{5} \cdot 0.16666666666666666\\ \mathbf{if}\;x \leq -7.8 \cdot 10^{-7} \lor \neg \left(x \leq 0.00255\right):\\ \;\;\;\;\frac{2 + -0.0625 \cdot \left(\sqrt{2} \cdot \left({\sin x}^{2} \cdot \left(\cos x + -1\right)\right)\right)}{3 + \left(\frac{\cos x}{t_1} + t_0 \cdot 1.5\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + -0.0625 \cdot \left(\left(\sqrt{2} \cdot \left(1 - \cos y\right)\right) \cdot \left(1 - {\cos y}^{2}\right)\right)}{\frac{1}{t_1} + \left(3 + 1.5 \cdot \left(\cos y \cdot t_0\right)\right)}\\ \end{array} \]
Alternative 16
Accuracy78.2%
Cost46857
\[\begin{array}{l} t_0 := 3 - \sqrt{5}\\ t_1 := 0.16666666666666666 + \sqrt{5} \cdot 0.16666666666666666\\ \mathbf{if}\;x \leq -7.8 \cdot 10^{-7} \lor \neg \left(x \leq 0.00255\right):\\ \;\;\;\;\frac{2 + -0.0625 \cdot \left(\sqrt{2} \cdot \left({\sin x}^{2} \cdot \left(\cos x + -1\right)\right)\right)}{3 + \left(\frac{\cos x}{t_1} + t_0 \cdot 1.5\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + -0.0625 \cdot \left(\sqrt{2} \cdot \left(\left(1 - \cos y\right) \cdot \left(0.5 - \frac{\cos \left(y + y\right)}{2}\right)\right)\right)}{\frac{1}{t_1} + \left(3 + 1.5 \cdot \left(\cos y \cdot t_0\right)\right)}\\ \end{array} \]
Alternative 17
Accuracy78.1%
Cost46729
\[\begin{array}{l} t_0 := 3 - \sqrt{5}\\ \mathbf{if}\;x \leq -7.8 \cdot 10^{-7} \lor \neg \left(x \leq 0.00255\right):\\ \;\;\;\;\frac{2 + \left(\sqrt{2} \cdot -0.0625\right) \cdot \left({\sin x}^{2} \cdot \left(\cos x + -1\right)\right)}{3 + 1.5 \cdot \left(t_0 + \cos x \cdot \left(\sqrt{5} + -1\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + -0.0625 \cdot \left(\sqrt{2} \cdot \left(\left(1 - \cos y\right) \cdot \left(0.5 - \frac{\cos \left(y + y\right)}{2}\right)\right)\right)}{\frac{1}{0.16666666666666666 + \sqrt{5} \cdot 0.16666666666666666} + \left(3 + 1.5 \cdot \left(\cos y \cdot t_0\right)\right)}\\ \end{array} \]
Alternative 18
Accuracy60.9%
Cost46601
\[\begin{array}{l} t_0 := 3 - \sqrt{5}\\ \mathbf{if}\;y \leq -1.6 \cdot 10^{-7} \lor \neg \left(y \leq 9.6 \cdot 10^{-9}\right):\\ \;\;\;\;\frac{2 + -0.0625 \cdot \left(\sqrt{2} \cdot \left(\left(1 - \cos y\right) \cdot \left(0.5 - \frac{\cos \left(y + y\right)}{2}\right)\right)\right)}{\frac{1}{0.16666666666666666 + \sqrt{5} \cdot 0.16666666666666666} + \left(3 + 1.5 \cdot \left(\cos y \cdot t_0\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + {\sin x}^{2} \cdot \left(\left(\cos x + -1\right) \cdot \sqrt{0.0078125}\right)}{3 + 1.5 \cdot \left(t_0 + \cos x \cdot \left(\sqrt{5} + -1\right)\right)}\\ \end{array} \]
Alternative 19
Accuracy59.2%
Cost40640
\[\frac{2 + -0.0625 \cdot \left(\sqrt{2} \cdot \left(\left(1 - \cos y\right) \cdot \left(0.5 - \frac{\cos \left(y + y\right)}{2}\right)\right)\right)}{\frac{1}{0.16666666666666666 + \sqrt{5} \cdot 0.16666666666666666} + \left(3 + 1.5 \cdot \left(\cos y \cdot \left(3 - \sqrt{5}\right)\right)\right)} \]
Alternative 20
Accuracy40.4%
Cost20416
\[\frac{2 + \left(\sqrt{2} \cdot -0.0625\right) \cdot \frac{\cos x + -1}{\frac{2}{1 - \cos \left(x + x\right)}}}{6} \]
Alternative 21
Accuracy40.4%
Cost64
\[0.3333333333333333 \]

Error

Reproduce?

herbie shell --seed 2023138 
(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))))))