Average Error: 0.5 → 0.5
Time: 13.0min
Precision: binary64
\[\frac{2 + \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x - \cos y\right)}{3 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{3 - \sqrt{5}}{2} \cdot \cos y\right)}\]
↓
\[\frac{2 + \left(\left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sqrt[3]{\sin y - \frac{\sin x}{16}} \cdot \sqrt[3]{\sin y - \frac{\sin x}{16}}\right)\right) \cdot \sqrt[3]{\sin y - \frac{\sin x}{16}}\right) \cdot \left(\cos x - \cos y\right)}{3 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{3 - \sqrt{5}}{2} \cdot \cos y\right)}\]
\frac{2 + \left(\left(\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(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sqrt[3]{\sin y - \frac{\sin x}{16}} \cdot \sqrt[3]{\sin y - \frac{\sin x}{16}}\right)\right) \cdot \sqrt[3]{\sin y - \frac{\sin x}{16}}\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)}
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) (((double) (((double) sqrt(2.0)) * ((double) (((double) sin(x)) - (((double) sin(y)) / 16.0))))) * ((double) (((double) cbrt(((double) (((double) sin(y)) - (((double) sin(x)) / 16.0))))) * ((double) cbrt(((double) (((double) sin(y)) - (((double) sin(x)) / 16.0))))))))) * ((double) cbrt(((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)))))))));
}

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-cube-cbrt0.5

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

  4. Applied associate-*r*0.5

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

  5. Final simplification0.5

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

Reproduce

herbie shell --seed 2020181 
(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))))))