Average Error: 0.5 → 0.5
Time: 10.6s
Precision: binary64
\[\frac{2 + \left(\left(\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\cos x - \cos y\right)}{3 \cdot \left(\left(1 + \frac{\sqrt{5} - 1}{2} \cdot \cos x\right) + \frac{3 - \sqrt{5}}{2} \cdot \cos y\right)}\]
↓
\[\frac{2 + \left(\left(\log \left(\sqrt{e^{\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)}}\right) + \log \left(\sqrt{e^{\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)}}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\sqrt[3]{\cos x - \cos y} \cdot \left(\sqrt[3]{\cos x - \cos y} \cdot \sqrt[3]{\cos x - \cos y}\right)\right)}{3 \cdot \left(\left(1 + \cos x \cdot \frac{\sqrt{5} - 1}{2}\right) + \cos y \cdot \frac{3 - \sqrt{5}}{2}\right)}\]
\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(\log \left(\sqrt{e^{\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)}}\right) + \log \left(\sqrt{e^{\sqrt{2} \cdot \left(\sin x - \frac{\sin y}{16}\right)}}\right)\right) \cdot \left(\sin y - \frac{\sin x}{16}\right)\right) \cdot \left(\sqrt[3]{\cos x - \cos y} \cdot \left(\sqrt[3]{\cos x - \cos y} \cdot \sqrt[3]{\cos x - \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)}
(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
 (/
  (+
   2.0
   (*
    (*
     (+
      (log (sqrt (exp (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))))))
      (log (sqrt (exp (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))))))
     (- (sin y) (/ (sin x) 16.0)))
    (*
     (cbrt (- (cos x) (cos y)))
     (* (cbrt (- (cos x) (cos y))) (cbrt (- (cos x) (cos y)))))))
  (*
   3.0
   (+
    (+ 1.0 (* (cos x) (/ (- (sqrt 5.0) 1.0) 2.0)))
    (* (cos y) (/ (- 3.0 (sqrt 5.0)) 2.0))))))
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) log(((double) sqrt(((double) exp(((double) (((double) sqrt(2.0)) * ((double) (((double) sin(x)) - (((double) sin(y)) / 16.0))))))))))) + ((double) log(((double) sqrt(((double) exp(((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) cbrt(((double) (((double) cos(x)) - ((double) cos(y)))))) * ((double) (((double) cbrt(((double) (((double) cos(x)) - ((double) cos(y)))))) * ((double) cbrt(((double) (((double) cos(x)) - ((double) cos(y)))))))))))))) / ((double) (3.0 * ((double) (((double) (1.0 + ((double) (((double) cos(x)) * (((double) (((double) sqrt(5.0)) - 1.0)) / 2.0))))) + ((double) (((double) cos(y)) * (((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-exp_binary640.5

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

  5. Applied add-sqr-sqrt_binary640.5

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

  6. Applied log-prod_binary640.5

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

  8. Applied add-cube-cbrt_binary640.5

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

  9. Final simplification0.5

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

Reproduce

herbie shell --seed 2020205 
(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))))))