Average Error: 0.0 → 0.0
Time: 1.8s
Precision: binary64
\[\frac{\sqrt{x + 1} + \sqrt{x}}{2} + \frac{1}{\left(\sqrt{x + 1} + \sqrt{x}\right) \cdot 2}\]
↓
\[\frac{\sqrt{x + 1} + \sqrt{x}}{2} + \frac{1}{\left(\sqrt{x + 1} + \sqrt{x}\right) \cdot 2}\]
\frac{\sqrt{x + 1} + \sqrt{x}}{2} + \frac{1}{\left(\sqrt{x + 1} + \sqrt{x}\right) \cdot 2}
↓
\frac{\sqrt{x + 1} + \sqrt{x}}{2} + \frac{1}{\left(\sqrt{x + 1} + \sqrt{x}\right) \cdot 2}
double code(double x) {
	return ((double) (((double) (((double) (((double) sqrt(((double) (x + 1.0)))) + ((double) sqrt(x)))) / 2.0)) + ((double) (1.0 / ((double) (((double) (((double) sqrt(((double) (x + 1.0)))) + ((double) sqrt(x)))) * 2.0))))));
}
↓
double code(double x) {
	return ((double) (((double) (((double) (((double) sqrt(((double) (x + 1.0)))) + ((double) sqrt(x)))) / 2.0)) + ((double) (1.0 / ((double) (((double) (((double) sqrt(((double) (x + 1.0)))) + ((double) sqrt(x)))) * 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 0.0

    \[\frac{\sqrt{x + 1} + \sqrt{x}}{2} + \frac{1}{\left(\sqrt{x + 1} + \sqrt{x}\right) \cdot 2}\]

  2. Final simplification0.0

    \[\leadsto \frac{\sqrt{x + 1} + \sqrt{x}}{2} + \frac{1}{\left(\sqrt{x + 1} + \sqrt{x}\right) \cdot 2}\]

Reproduce

herbie shell --seed 2020153 
(FPCore (x)
  :name "(+ (/ (+ (sqrt (+ x 1)) (sqrt x)) 2) (/ 1 (* (+ (sqrt (+ x 1)) (sqrt x)) 2)))"
  :precision binary64
  (+ (/ (+ (sqrt (+ x 1.0)) (sqrt x)) 2.0) (/ 1.0 (* (+ (sqrt (+ x 1.0)) (sqrt x)) 2.0))))