Average Error: 0.5 → 0.5
Time: 13.2s
Precision: binary64
\[\frac{2 + \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x - \cos y\right)}{3 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{3 - \sqrt{5}}{2} \cdot \cos y\right)}\]
↓
\[\frac{2 + \left(\left(\sin y - \frac{\sin x}{16}\right) \cdot \log \left(\sqrt{{\left(e^{\sqrt{2}}\right)}^{\left(\sin x - \frac{\sin y}{16}\right)}}\right) + \left(\sin y - \frac{\sin x}{16}\right) \cdot \log \left(\sqrt{{\left(e^{\sqrt{2}}\right)}^{\left(\sin x - \frac{\sin y}{16}\right)}}\right)\right) \cdot \left(\cos x - \cos y\right)}{3 \cdot \left(\left(1 + \cos x \cdot \frac{\sqrt{5} - 1}{2}\right) + \cos y \cdot \frac{3 - \sqrt{5}}{2}\right)}\]
\frac{2 + \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x - \cos y\right)}{3 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{3 - \sqrt{5}}{2} \cdot \cos y\right)}
↓
\frac{2 + \left(\left(\sin y - \frac{\sin x}{16}\right) \cdot \log \left(\sqrt{{\left(e^{\sqrt{2}}\right)}^{\left(\sin x - \frac{\sin y}{16}\right)}}\right) + \left(\sin y - \frac{\sin x}{16}\right) \cdot \log \left(\sqrt{{\left(e^{\sqrt{2}}\right)}^{\left(\sin x - \frac{\sin y}{16}\right)}}\right)\right) \cdot \left(\cos x - \cos y\right)}{3 \cdot \left(\left(1 + \cos x \cdot \frac{\sqrt{5} - 1}{2}\right) + \cos y \cdot \frac{3 - \sqrt{5}}{2}\right)}
double code(double x, double y) {
	return ((double) (((double) (2.0 + ((double) (((double) (((double) (((double) sqrt(2.0)) * ((double) (((double) sin(x)) - ((double) (((double) sin(y)) / 16.0)))))) * ((double) (((double) sin(y)) - ((double) (((double) sin(x)) / 16.0)))))) * ((double) (((double) cos(x)) - ((double) cos(y)))))))) / ((double) (3.0 * ((double) (((double) (1.0 + ((double) (((double) (((double) (((double) sqrt(5.0)) - 1.0)) / 2.0)) * ((double) cos(x)))))) + ((double) (((double) (((double) (3.0 - ((double) sqrt(5.0)))) / 2.0)) * ((double) cos(y))))))))));
}
↓
double code(double x, double y) {
	return ((double) (((double) (2.0 + ((double) (((double) (((double) (((double) (((double) sin(y)) - ((double) (((double) sin(x)) / 16.0)))) * ((double) log(((double) sqrt(((double) pow(((double) exp(((double) sqrt(2.0)))), ((double) (((double) sin(x)) - ((double) (((double) sin(y)) / 16.0)))))))))))) + ((double) (((double) (((double) sin(y)) - ((double) (((double) sin(x)) / 16.0)))) * ((double) log(((double) sqrt(((double) pow(((double) exp(((double) sqrt(2.0)))), ((double) (((double) sin(x)) - ((double) (((double) sin(y)) / 16.0)))))))))))))) * ((double) (((double) cos(x)) - ((double) cos(y)))))))) / ((double) (3.0 * ((double) (((double) (1.0 + ((double) (((double) cos(x)) * ((double) (((double) (((double) sqrt(5.0)) - 1.0)) / 2.0)))))) + ((double) (((double) cos(y)) * ((double) (((double) (3.0 - ((double) sqrt(5.0)))) / 2.0))))))))));
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

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. Using strategy rm

  3. Applied add-log-exp0.5

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

  4. Simplified0.5

    \[\leadsto \frac{2 + \log \color{blue}{\left({\left({\left(e^{\sqrt{2}}\right)}^{\left(\sin x - \frac{\sin y}{16}\right)}\right)}^{\left(\sin y - \frac{\sin x}{16}\right)}\right)} \cdot \left(\cos x - \cos y\right)}{3 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{3 - \sqrt{5}}{2} \cdot \cos y\right)}\]
  5. Using strategy rm

  6. Applied add-sqr-sqrt0.5

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

  7. Applied unpow-prod-down0.5

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

  8. Applied log-prod0.5

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

  9. Simplified0.5

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

  10. Simplified0.5

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

  11. Final simplification0.5

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

Reproduce

herbie shell --seed 2020184 
(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))))))