Average Error: 0.2 → 0.2
Time: 3.1s
Precision: binary64
\[\frac{\sin \varepsilon}{\cos x \cdot \cos \varepsilon}\]
↓
\[\frac{\sin \varepsilon}{\cos x \cdot \cos \varepsilon}\]
\frac{\sin \varepsilon}{\cos x \cdot \cos \varepsilon}
↓
\frac{\sin \varepsilon}{\cos x \cdot \cos \varepsilon}
double code(double eps, double x) {
	return ((double) (((double) sin(eps)) / ((double) (((double) cos(x)) * ((double) cos(eps))))));
}
↓
double code(double eps, double x) {
	return ((double) (((double) sin(eps)) / ((double) (((double) cos(x)) * ((double) cos(eps))))));
}

Error

Bits error versus eps

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.2

    \[\frac{\sin \varepsilon}{\cos x \cdot \cos \varepsilon}\]

  2. Final simplification0.2

    \[\leadsto \frac{\sin \varepsilon}{\cos x \cdot \cos \varepsilon}\]

Reproduce

herbie shell --seed 2020152 
(FPCore (eps x)
  :name "(/ (sin eps) (* (cos x) (cos eps)))"
  :precision binary64
  (/ (sin eps) (* (cos x) (cos eps))))