Average Error: 29.7 → 29.7
Time: 4.4s
Precision: binary64
\[\frac{\sin \left(\left(x + \varepsilon\right) - x\right)}{\cos x \cdot \cos \varepsilon}\]
↓
\[\frac{\sin \left(\left(x + \varepsilon\right) - x\right)}{\cos x \cdot \cos \varepsilon}\]
\frac{\sin \left(\left(x + \varepsilon\right) - x\right)}{\cos x \cdot \cos \varepsilon}
↓
\frac{\sin \left(\left(x + \varepsilon\right) - x\right)}{\cos x \cdot \cos \varepsilon}
double code(double x, double eps) {
	return ((double) (((double) sin(((double) (((double) (x + eps)) - x)))) / ((double) (((double) cos(x)) * ((double) cos(eps))))));
}
↓
double code(double x, double eps) {
	return ((double) (((double) sin(((double) (((double) (x + eps)) - x)))) / ((double) (((double) cos(x)) * ((double) cos(eps))))));
}

Error

Bits error versus x

Bits error versus eps

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 29.7

    \[\frac{\sin \left(\left(x + \varepsilon\right) - x\right)}{\cos x \cdot \cos \varepsilon}\]

  2. Final simplification29.7

    \[\leadsto \frac{\sin \left(\left(x + \varepsilon\right) - x\right)}{\cos x \cdot \cos \varepsilon}\]

Reproduce

herbie shell --seed 2020153 
(FPCore (x eps)
  :name "(/ (sin (- (+ x eps) x)) (* (cos x) (cos eps)))"
  :precision binary64
  (/ (sin (- (+ x eps) x)) (* (cos x) (cos eps))))