?

Average Accuracy: 99.3% → 99.3%
Time: 40.6s
Precision: binary64
Cost: 91712

?

\[\frac{2 + \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x - \cos y\right)}{3 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{3 - \sqrt{5}}{2} \cdot \cos y\right)} \]
↓
\[\mathsf{fma}\left(\sqrt{2} \cdot \left(\sin x - \sin y \cdot 0.0625\right), \left(\sin y - \sin x \cdot 0.0625\right) \cdot \left(\cos x - \cos y\right), 2\right) \cdot \frac{1}{\mathsf{fma}\left(\mathsf{fma}\left(\frac{4}{3 + \sqrt{5}}, \cos y, \cos x \cdot \left(\sqrt{5} + -1\right)\right), 1.5, 3\right)} \]
(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 x) (* (sin y) 0.0625)))
   (* (- (sin y) (* (sin x) 0.0625)) (- (cos x) (cos y)))
   2.0)
  (/
   1.0
   (fma
    (fma (/ 4.0 (+ 3.0 (sqrt 5.0))) (cos y) (* (cos x) (+ (sqrt 5.0) -1.0)))
    1.5
    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(x) - (sin(y) * 0.0625))), ((sin(y) - (sin(x) * 0.0625)) * (cos(x) - cos(y))), 2.0) * (1.0 / fma(fma((4.0 / (3.0 + sqrt(5.0))), cos(y), (cos(x) * (sqrt(5.0) + -1.0))), 1.5, 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(Float64(sqrt(2.0) * Float64(sin(x) - Float64(sin(y) * 0.0625))), Float64(Float64(sin(y) - Float64(sin(x) * 0.0625)) * Float64(cos(x) - cos(y))), 2.0) * Float64(1.0 / fma(fma(Float64(4.0 / Float64(3.0 + sqrt(5.0))), cos(y), Float64(cos(x) * Float64(sqrt(5.0) + -1.0))), 1.5, 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[(N[Sqrt[2.0], $MachinePrecision] * N[(N[Sin[x], $MachinePrecision] - N[(N[Sin[y], $MachinePrecision] * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(N[Sin[y], $MachinePrecision] - N[(N[Sin[x], $MachinePrecision] * 0.0625), $MachinePrecision]), $MachinePrecision] * N[(N[Cos[x], $MachinePrecision] - N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 2.0), $MachinePrecision] * N[(1.0 / N[(N[(N[(4.0 / N[(3.0 + N[Sqrt[5.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[Cos[y], $MachinePrecision] + N[(N[Cos[x], $MachinePrecision] * N[(N[Sqrt[5.0], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * 1.5 + 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)}
↓
\mathsf{fma}\left(\sqrt{2} \cdot \left(\sin x - \sin y \cdot 0.0625\right), \left(\sin y - \sin x \cdot 0.0625\right) \cdot \left(\cos x - \cos y\right), 2\right) \cdot \frac{1}{\mathsf{fma}\left(\mathsf{fma}\left(\frac{4}{3 + \sqrt{5}}, \cos y, \cos x \cdot \left(\sqrt{5} + -1\right)\right), 1.5, 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%

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

    [Start]99.3

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

    +-commutative [=>]99.3

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

    associate-*l* [=>]99.3

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

    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. Taylor expanded in y around inf 99.3%

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

  4. Simplified99.3%

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

    [Start]99.3

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

    distribute-lft-out [=>]99.3

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

    rem-log-exp [<=]99.3

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

    log-pow [<=]99.3

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

    sub-neg [=>]99.3

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

    metadata-eval [=>]99.3

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

    metadata-eval [<=]99.3

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

    sub-neg [<=]99.3

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

    log-pow [=>]99.3

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

    sub-neg [=>]99.3

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

    metadata-eval [=>]99.3

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

    rem-log-exp [=>]99.3

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

  5. Applied egg-rr99.4%

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

    [Start]99.3

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

    flip-- [=>]99.2

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

    metadata-eval [=>]99.2

    \[ \frac{\mathsf{fma}\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right), \left(\sin y - \frac{\sin x}{16}\right) \cdot \left(\cos x - \cos y\right), 2\right)}{3 + 1.5 \cdot \left(\frac{\color{blue}{9} - \sqrt{5} \cdot \sqrt{5}}{3 + \sqrt{5}} \cdot \cos y + \left(\sqrt{5} + -1\right) \cdot \cos x\right)} \]

    add-sqr-sqrt [<=]99.4

    \[ \frac{\mathsf{fma}\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right), \left(\sin y - \frac{\sin x}{16}\right) \cdot \left(\cos x - \cos y\right), 2\right)}{3 + 1.5 \cdot \left(\frac{9 - \color{blue}{5}}{3 + \sqrt{5}} \cdot \cos y + \left(\sqrt{5} + -1\right) \cdot \cos x\right)} \]

    metadata-eval [=>]99.4

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

    metadata-eval [<=]99.4

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

    div-inv [=>]99.4

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

    metadata-eval [=>]99.4

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

  6. Simplified99.4%

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

    [Start]99.4

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

    associate-*r/ [=>]99.4

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

    metadata-eval [=>]99.4

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

  7. Applied egg-rr99.3%

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

    [Start]99.4

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

    div-inv [=>]99.3

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

    div-inv [=>]99.3

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

    metadata-eval [=>]99.3

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

    div-inv [=>]99.3

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

    metadata-eval [=>]99.3

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

    +-commutative [=>]99.3

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

  8. Final simplification99.3%

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

Alternatives

Alternative 1
Accuracy99.3%
Cost85440
\[\mathsf{fma}\left(\sqrt{2} \cdot \left(\sin x - \sin y \cdot 0.0625\right), \left(\sin y - \sin x \cdot 0.0625\right) \cdot \left(\cos x - \cos y\right), 2\right) \cdot \frac{1}{\mathsf{fma}\left(\cos x \cdot \left(\sqrt{5} + -1\right) + \cos y \cdot \frac{4}{3 + \sqrt{5}}, 1.5, 3\right)} \]
Alternative 2
Accuracy99.4%
Cost85440
\[\frac{\mathsf{fma}\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right), \left(\cos x - \cos y\right) \cdot \left(\sin y - \frac{\sin x}{16}\right), 2\right)}{3 + \mathsf{fma}\left(\cos y, \frac{3 - \sqrt{5}}{0.6666666666666666}, \cos x \cdot \frac{1}{0.16666666666666666 + \sqrt{5} \cdot 0.16666666666666666}\right)} \]
Alternative 3
Accuracy99.4%
Cost79040
\[\frac{\mathsf{fma}\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right), \left(\cos x - \cos y\right) \cdot \left(\sin y - \frac{\sin x}{16}\right), 2\right)}{3 + 1.5 \cdot \left(\cos x \cdot \left(\sqrt{5} + -1\right) + \cos y \cdot \frac{4}{3 + \sqrt{5}}\right)} \]
Alternative 4
Accuracy99.3%
Cost72896
\[\frac{2 + \left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\left(\cos x - \cos y\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right)}{3 \cdot \left(1 + \left(\cos x \cdot \left(\frac{\sqrt{5}}{2} - 0.5\right) + \cos y \cdot \frac{1}{1.5 + \sqrt{1.25}}\right)\right)} \]
Alternative 5
Accuracy99.2%
Cost72768
\[0.3333333333333333 \cdot \frac{2 + \sqrt{2} \cdot \left(\left(\sin y - \sin x \cdot 0.0625\right) \cdot \left(\left(\sin x - \sin y \cdot 0.0625\right) \cdot \left(\cos x - \cos y\right)\right)\right)}{\frac{\cos y}{1.5 + \sqrt{1.25}} + \left(1 + \cos x \cdot \left(\sqrt{5} \cdot 0.5 - 0.5\right)\right)} \]
Alternative 6
Accuracy99.3%
Cost72768
\[\frac{2 + \left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\left(\cos x - \cos y\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right)}{3 \cdot \left(1 + \left(\cos x \cdot \left(\frac{\sqrt{5}}{2} - 0.5\right) + \cos y \cdot \left(1.5 - \sqrt{1.25}\right)\right)\right)} \]
Alternative 7
Accuracy99.3%
Cost72768
\[\frac{2 + \left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\left(\cos x - \cos y\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right)}{3 \cdot \left(1 + \left(\frac{\cos y}{1.5 + \sqrt{1.25}} + \cos x \cdot \left(\sqrt{5} \cdot 0.5 - 0.5\right)\right)\right)} \]
Alternative 8
Accuracy81.5%
Cost72388
\[\begin{array}{l} t_0 := 3 - \sqrt{5}\\ t_1 := \sin y - \frac{\sin x}{16}\\ t_2 := \sqrt{2} \cdot \sin x\\ t_3 := \sqrt{5} + -1\\ t_4 := \left(\cos x - \cos y\right) \cdot t_1\\ \mathbf{if}\;x \leq -0.12:\\ \;\;\;\;\frac{\mathsf{fma}\left(t_2, t_4, 2\right)}{3 + 1.5 \cdot \left(\cos x \cdot t_3 + \cos y \cdot t_0\right)}\\ \mathbf{elif}\;x \leq 0.0165:\\ \;\;\;\;\frac{2 + \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot t_1\right) \cdot \left(1 + \left(-0.5 \cdot \left(x \cdot x\right) - \cos y\right)\right)}{3 \cdot \left(\left(1 + \cos x \cdot \frac{t_3}{2}\right) + \cos y \cdot \frac{t_0}{2}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + t_4 \cdot t_2}{3 \cdot \left(1 + \left(\cos x \cdot \left(\frac{\sqrt{5}}{2} - 0.5\right) + \cos y \cdot \frac{1}{1.5 + \sqrt{1.25}}\right)\right)}\\ \end{array} \]
Alternative 9
Accuracy81.5%
Cost67145
\[\begin{array}{l} t_0 := \sin y - \frac{\sin x}{16}\\ \mathbf{if}\;x \leq -0.061 \lor \neg \left(x \leq 0.0165\right):\\ \;\;\;\;\frac{2 + \left(\left(\cos x - \cos y\right) \cdot t_0\right) \cdot \left(\sqrt{2} \cdot \sin x\right)}{3 \cdot \left(1 + \left(\cos x \cdot \left(\frac{\sqrt{5}}{2} - 0.5\right) + \cos y \cdot \frac{1}{1.5 + \sqrt{1.25}}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot t_0\right) \cdot \left(1 + \left(-0.5 \cdot \left(x \cdot x\right) - \cos y\right)\right)}{3 \cdot \left(\left(1 + \cos x \cdot \frac{\sqrt{5} + -1}{2}\right) + \cos y \cdot \frac{3 - \sqrt{5}}{2}\right)}\\ \end{array} \]
Alternative 10
Accuracy81.5%
Cost66505
\[\begin{array}{l} t_0 := \frac{\sqrt{5}}{2}\\ t_1 := \sin y - \frac{\sin x}{16}\\ \mathbf{if}\;x \leq -0.0275 \lor \neg \left(x \leq 0.0165\right):\\ \;\;\;\;\frac{2 + \left(\left(\cos x - \cos y\right) \cdot t_1\right) \cdot \left(\sqrt{2} \cdot \sin x\right)}{3 \cdot \left(1 + \left(\cos x \cdot \left(t_0 - 0.5\right) + \cos y \cdot \left(1.5 - t_0\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \left(1 + \left(-0.5 \cdot \left(x \cdot x\right) - \cos y\right)\right) \cdot \left(t_1 \cdot \left(\sqrt{2} \cdot \left(x - \sin y \cdot 0.0625\right)\right)\right)}{3 \cdot \left(\left(1 + \cos x \cdot \frac{\sqrt{5} + -1}{2}\right) + \cos y \cdot \frac{3 - \sqrt{5}}{2}\right)}\\ \end{array} \]
Alternative 11
Accuracy81.5%
Cost66505
\[\begin{array}{l} t_0 := \sin y - \frac{\sin x}{16}\\ \mathbf{if}\;x \leq -0.0295 \lor \neg \left(x \leq 0.015\right):\\ \;\;\;\;\frac{2 + \left(\left(\cos x - \cos y\right) \cdot t_0\right) \cdot \left(\sqrt{2} \cdot \sin x\right)}{3 \cdot \left(1 + \left(\cos x \cdot \left(\frac{\sqrt{5}}{2} - 0.5\right) + \cos y \cdot \frac{1}{1.5 + \sqrt{1.25}}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \left(1 + \left(-0.5 \cdot \left(x \cdot x\right) - \cos y\right)\right) \cdot \left(t_0 \cdot \left(\sqrt{2} \cdot \left(x - \sin y \cdot 0.0625\right)\right)\right)}{3 \cdot \left(\left(1 + \cos x \cdot \frac{\sqrt{5} + -1}{2}\right) + \cos y \cdot \frac{3 - \sqrt{5}}{2}\right)}\\ \end{array} \]
Alternative 12
Accuracy79.7%
Cost60233
\[\begin{array}{l} t_0 := 3 \cdot \left(\left(1 + \cos x \cdot \frac{\sqrt{5} + -1}{2}\right) + \cos y \cdot \frac{3 - \sqrt{5}}{2}\right)\\ t_1 := \cos x - \cos y\\ \mathbf{if}\;y \leq -0.0042 \lor \neg \left(y \leq 0.005\right):\\ \;\;\;\;\frac{2 + t_1 \cdot \left({\sin y}^{2} \cdot \left(\sqrt{2} \cdot -0.0625\right)\right)}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + t_1 \cdot \left(\sqrt{2} \cdot \left(\sin x \cdot \left(y \cdot 1.00390625 - \sin x \cdot 0.0625\right)\right)\right)}{t_0}\\ \end{array} \]
Alternative 13
Accuracy79.4%
Cost59913
\[\begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{-6} \lor \neg \left(y \leq 0.0006\right):\\ \;\;\;\;\frac{2 + \left(\cos x - \cos y\right) \cdot \left({\sin y}^{2} \cdot \left(\sqrt{2} \cdot -0.0625\right)\right)}{3 \cdot \left(\left(1 + \cos x \cdot \frac{\sqrt{5} + -1}{2}\right) + \cos y \cdot \frac{3 - \sqrt{5}}{2}\right)}\\ \mathbf{else}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{2 + -0.0625 \cdot \left(\sqrt{2} \cdot \left({\sin x}^{2} \cdot \left(\cos x + -1\right)\right)\right)}{1 + \left(\cos x \cdot \left(\sqrt{5} \cdot 0.5 - 0.5\right) + \frac{1}{1.5 + \sqrt{1.25}}\right)}\\ \end{array} \]
Alternative 14
Accuracy79.4%
Cost59652
\[\begin{array}{l} t_0 := 3 - \sqrt{5}\\ t_1 := {\sin x}^{2}\\ t_2 := \sqrt{5} + -1\\ \mathbf{if}\;x \leq -0.0126:\\ \;\;\;\;0.3333333333333333 \cdot \frac{2 + -0.0625 \cdot \left(\sqrt{2} \cdot \left(\left(\cos x - \cos y\right) \cdot t_1\right)\right)}{1 + 0.5 \cdot \left(\cos x \cdot t_2 + \cos y \cdot t_0\right)}\\ \mathbf{elif}\;x \leq 3.15 \cdot 10^{-6}:\\ \;\;\;\;\frac{2 + -0.0625 \cdot \left(\sqrt{2} \cdot \left({\sin y}^{2} \cdot \left(1 - \cos y\right)\right)\right)}{3 + 1.5 \cdot \left(-1 + \left(\sqrt{5} + 4 \cdot \frac{\cos y}{3 + \sqrt{5}}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \left(\cos x + -1\right) \cdot \left(\left(\sqrt{2} \cdot -0.0625\right) \cdot t_1\right)}{3 \cdot \left(\left(1 + \cos x \cdot \frac{t_2}{2}\right) + \cos y \cdot \frac{t_0}{2}\right)}\\ \end{array} \]
Alternative 15
Accuracy79.4%
Cost53513
\[\begin{array}{l} \mathbf{if}\;x \leq -0.0126 \lor \neg \left(x \leq 1.16 \cdot 10^{-5}\right):\\ \;\;\;\;\frac{2 + \left(\cos x + -1\right) \cdot \left(\left(\sqrt{2} \cdot -0.0625\right) \cdot {\sin x}^{2}\right)}{3 \cdot \left(\left(1 + \cos x \cdot \frac{\sqrt{5} + -1}{2}\right) + \cos y \cdot \frac{3 - \sqrt{5}}{2}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + -0.0625 \cdot \left(\sqrt{2} \cdot \left({\sin y}^{2} \cdot \left(1 - \cos y\right)\right)\right)}{3 + 1.5 \cdot \left(-1 + \left(\sqrt{5} + 4 \cdot \frac{\cos y}{3 + \sqrt{5}}\right)\right)}\\ \end{array} \]
Alternative 16
Accuracy78.8%
Cost53128
\[\begin{array}{l} t_0 := 3 + \sqrt{5}\\ t_1 := {\sin x}^{2} \cdot \left(\cos x + -1\right)\\ \mathbf{if}\;x \leq -0.018:\\ \;\;\;\;0.3333333333333333 \cdot \frac{2 + -0.0625 \cdot \left(\sqrt{2} \cdot t_1\right)}{1 + \left(\cos x \cdot \left(\sqrt{5} \cdot 0.5 - 0.5\right) + \frac{1}{1.5 + \sqrt{1.25}}\right)}\\ \mathbf{elif}\;x \leq 1.95 \cdot 10^{-5}:\\ \;\;\;\;\frac{2 + -0.0625 \cdot \left(\sqrt{2} \cdot \left({\sin y}^{2} \cdot \left(1 - \cos y\right)\right)\right)}{3 + 1.5 \cdot \left(-1 + \left(\sqrt{5} + 4 \cdot \frac{\cos y}{t_0}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \left(\sqrt{2} \cdot -0.0625\right) \cdot t_1}{3 + 1.5 \cdot \mathsf{fma}\left(\sqrt{5} + -1, \cos x, \frac{4}{t_0}\right)}\\ \end{array} \]
Alternative 17
Accuracy78.8%
Cost46985
\[\begin{array}{l} \mathbf{if}\;x \leq -0.018 \lor \neg \left(x \leq 6 \cdot 10^{-5}\right):\\ \;\;\;\;0.3333333333333333 \cdot \frac{2 + -0.0625 \cdot \left(\sqrt{2} \cdot \left({\sin x}^{2} \cdot \left(\cos x + -1\right)\right)\right)}{1 + \left(\cos x \cdot \left(\sqrt{5} \cdot 0.5 - 0.5\right) + \frac{1}{1.5 + \sqrt{1.25}}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + -0.0625 \cdot \left(\sqrt{2} \cdot \left({\sin y}^{2} \cdot \left(1 - \cos y\right)\right)\right)}{3 + 1.5 \cdot \left(-1 + \left(\sqrt{5} + 4 \cdot \frac{\cos y}{3 + \sqrt{5}}\right)\right)}\\ \end{array} \]
Alternative 18
Accuracy78.8%
Cost46984
\[\begin{array}{l} t_0 := 3 + \sqrt{5}\\ t_1 := 2 + -0.0625 \cdot \left(\sqrt{2} \cdot \left({\sin x}^{2} \cdot \left(\cos x + -1\right)\right)\right)\\ \mathbf{if}\;x \leq -0.018:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t_1}{1 + \left(\cos x \cdot \left(\sqrt{5} \cdot 0.5 - 0.5\right) + \frac{1}{1.5 + \sqrt{1.25}}\right)}\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{-5}:\\ \;\;\;\;\frac{2 + -0.0625 \cdot \left(\sqrt{2} \cdot \left({\sin y}^{2} \cdot \left(1 - \cos y\right)\right)\right)}{3 + 1.5 \cdot \left(-1 + \left(\sqrt{5} + 4 \cdot \frac{\cos y}{t_0}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_1}{3 + 1.5 \cdot \left(\cos x \cdot \left(\sqrt{5} + -1\right) + 4 \cdot \frac{1}{t_0}\right)}\\ \end{array} \]
Alternative 19
Accuracy78.8%
Cost46857
\[\begin{array}{l} \mathbf{if}\;x \leq -0.018 \lor \neg \left(x \leq 6.5 \cdot 10^{-5}\right):\\ \;\;\;\;0.3333333333333333 \cdot \frac{2 + -0.0625 \cdot \left(\sqrt{2} \cdot \left({\sin x}^{2} \cdot \left(\cos x + -1\right)\right)\right)}{1 + 0.5 \cdot \left(\cos x \cdot \left(\sqrt{5} + -1\right) + \left(3 - \sqrt{5}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{2 + -0.0625 \cdot \left(\sqrt{2} \cdot \left({\sin y}^{2} \cdot \left(1 - \cos y\right)\right)\right)}{\frac{\cos y}{1.5 + \sqrt{1.25}} + \left(0.5 + \sqrt{5} \cdot 0.5\right)}\\ \end{array} \]
Alternative 20
Accuracy78.8%
Cost46857
\[\begin{array}{l} \mathbf{if}\;x \leq -0.018 \lor \neg \left(x \leq 9.8 \cdot 10^{-6}\right):\\ \;\;\;\;0.3333333333333333 \cdot \frac{2 + -0.0625 \cdot \left(\sqrt{2} \cdot \left({\sin x}^{2} \cdot \left(\cos x + -1\right)\right)\right)}{1 + 0.5 \cdot \left(\cos x \cdot \left(\sqrt{5} + -1\right) + \left(3 - \sqrt{5}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + -0.0625 \cdot \left(\sqrt{2} \cdot \left({\sin y}^{2} \cdot \left(1 - \cos y\right)\right)\right)}{3 + 1.5 \cdot \left(-1 + \left(\sqrt{5} + 4 \cdot \frac{\cos y}{3 + \sqrt{5}}\right)\right)}\\ \end{array} \]
Alternative 21
Accuracy59.3%
Cost46464
\[0.3333333333333333 \cdot \frac{2 + -0.0625 \cdot \left(\sqrt{2} \cdot \left({\sin y}^{2} \cdot \left(1 - \cos y\right)\right)\right)}{\frac{\cos y}{1.5 + \sqrt{1.25}} + \left(0.5 + \sqrt{5} \cdot 0.5\right)} \]
Alternative 22
Accuracy42.3%
Cost45504
\[\log \left(e^{\frac{0.6666666666666666}{\mathsf{fma}\left(-1 + \mathsf{fma}\left(3 - \sqrt{5}, \cos y, \sqrt{5}\right), 0.5, 1\right)}}\right) \]
Alternative 23
Accuracy42.3%
Cost33088
\[\frac{0.6666666666666666}{1 + 0.5 \cdot \left(\left(\sqrt{5} + -1\right) + \cos y \cdot \left(3 - \sqrt[3]{5} \cdot \sqrt[3]{\sqrt{5}}\right)\right)} \]
Alternative 24
Accuracy42.3%
Cost20160
\[\frac{0.6666666666666666}{1 + 0.5 \cdot \left(\left(\sqrt{5} + -1\right) + \cos y \cdot \left(3 - \sqrt{5}\right)\right)} \]
Alternative 25
Accuracy40.4%
Cost64
\[0.3333333333333333 \]

Error

Reproduce?

herbie shell --seed 2023147 
(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))))))