Average Error: 23.6 → 23.6
Time: 822.0ms
Precision: binary64
\[\frac{x + \sqrt{x \cdot x + 4}}{2}\]
↓
\[\frac{x + \sqrt{x \cdot x + 4}}{2}\]
\frac{x + \sqrt{x \cdot x + 4}}{2}
↓
\frac{x + \sqrt{x \cdot x + 4}}{2}
double code(double x) {
	return ((double) (((double) (x + ((double) sqrt(((double) (((double) (x * x)) + 4.0)))))) / 2.0));
}
↓
double code(double x) {
	return ((double) (((double) (x + ((double) sqrt(((double) (((double) (x * x)) + 4.0)))))) / 2.0));
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 23.6

    \[\frac{x + \sqrt{x \cdot x + 4}}{2}\]

  2. Final simplification23.6

    \[\leadsto \frac{x + \sqrt{x \cdot x + 4}}{2}\]

Reproduce

herbie shell --seed 2020153 
(FPCore (x)
  :name "(/ (+ x (sqrt (+ (* x x) 4))) 2)"
  :precision binary64
  (/ (+ x (sqrt (+ (* x x) 4.0))) 2.0))