Average Error: 0.5 → 0.4
Time: 50.8s
Precision: binary64
\[\frac{2 + \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x - \cos y\right)}{3 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{3 - \sqrt{5}}{2} \cdot \cos y\right)}\]
↓
\[\frac{2 + \left(\cos x \cdot \left(\left(\sin y - \frac{\sin x}{16}\right) \cdot \left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right)\right) + \cos y \cdot \left(\left(\sin y - \frac{\sin x}{16}\right) \cdot \left(\sqrt{2} \cdot \left(\frac{\sin y}{16} - \sin x\right)\right)\right)\right)}{3 \cdot \left(1 + \left(\cos x \cdot \frac{\sqrt{5} - 1}{2} + \cos y \cdot \frac{\frac{3 \cdot 3 - 5}{3 + \sqrt{5}}}{2}\right)\right)}\]
\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(\cos x \cdot \left(\left(\sin y - \frac{\sin x}{16}\right) \cdot \left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right)\right) + \cos y \cdot \left(\left(\sin y - \frac{\sin x}{16}\right) \cdot \left(\sqrt{2} \cdot \left(\frac{\sin y}{16} - \sin x\right)\right)\right)\right)}{3 \cdot \left(1 + \left(\cos x \cdot \frac{\sqrt{5} - 1}{2} + \cos y \cdot \frac{\frac{3 \cdot 3 - 5}{3 + \sqrt{5}}}{2}\right)\right)}
double code(double x, double y) {
	return (((double) (2.0 + ((double) (((double) (((double) (((double) sqrt(2.0)) * ((double) (((double) sin(x)) - (((double) sin(y)) / 16.0))))) * ((double) (((double) sin(y)) - (((double) sin(x)) / 16.0))))) * ((double) (((double) cos(x)) - ((double) cos(y)))))))) / ((double) (3.0 * ((double) (((double) (1.0 + ((double) ((((double) (((double) sqrt(5.0)) - 1.0)) / 2.0) * ((double) cos(x)))))) + ((double) ((((double) (3.0 - ((double) sqrt(5.0)))) / 2.0) * ((double) cos(y)))))))));
}
↓
double code(double x, double y) {
	return (((double) (2.0 + ((double) (((double) (((double) cos(x)) * ((double) (((double) (((double) sin(y)) - (((double) sin(x)) / 16.0))) * ((double) (((double) sqrt(2.0)) * ((double) (((double) sin(x)) - (((double) sin(y)) / 16.0))))))))) + ((double) (((double) cos(y)) * ((double) (((double) (((double) sin(y)) - (((double) sin(x)) / 16.0))) * ((double) (((double) sqrt(2.0)) * ((double) ((((double) sin(y)) / 16.0) - ((double) sin(x)))))))))))))) / ((double) (3.0 * ((double) (1.0 + ((double) (((double) (((double) cos(x)) * (((double) (((double) sqrt(5.0)) - 1.0)) / 2.0))) + ((double) (((double) cos(y)) * ((((double) (((double) (3.0 * 3.0)) - 5.0)) / ((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. Simplified0.5

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

  4. Applied flip--0.5

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

  5. Simplified0.4

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

  7. Applied sub-neg0.4

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

  8. Applied distribute-lft-in0.4

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

  9. Applied distribute-lft-in0.4

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

  10. Applied distribute-lft-in0.4

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

  11. Simplified0.4

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

  12. Simplified0.4

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

  13. Final simplification0.4

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

Reproduce

herbie shell --seed 2020196 
(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))))))