Average Error: 0.1 → 0.1
Time: 1.6s
Precision: binary64
\[\sqrt{x + 1} - \frac{\sqrt{x}}{4} \cdot \cos 5\]
↓
\[\sqrt{x + 1} - \frac{\sqrt{x}}{4} \cdot \cos 5\]
\sqrt{x + 1} - \frac{\sqrt{x}}{4} \cdot \cos 5
↓
\sqrt{x + 1} - \frac{\sqrt{x}}{4} \cdot \cos 5
double code(double x) {
	return ((double) (((double) sqrt(((double) (x + 1.0)))) - ((double) (((double) (((double) sqrt(x)) / 4.0)) * ((double) cos(5.0))))));
}
↓
double code(double x) {
	return ((double) (((double) sqrt(((double) (x + 1.0)))) - ((double) (((double) (((double) sqrt(x)) / 4.0)) * ((double) cos(5.0))))));
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[\sqrt{x + 1} - \frac{\sqrt{x}}{4} \cdot \cos 5\]

  2. Final simplification0.1

    \[\leadsto \sqrt{x + 1} - \frac{\sqrt{x}}{4} \cdot \cos 5\]

Reproduce

herbie shell --seed 2020152 
(FPCore (x)
  :name "(- (sqrt (+ x 1)) (* (/ (sqrt x) 4) (cos 5)))"
  :precision binary64
  (- (sqrt (+ x 1.0)) (* (/ (sqrt x) 4.0) (cos 5.0))))