Average Error: 0.0 → 0.0
Time: 2.1s
Precision: binary64
\[\sqrt{x - 1} + \sqrt{\left(\frac{x}{2} - 1\right) + \frac{x}{2}}\]
↓
\[\sqrt{x - 1} + \sqrt{\left(\frac{x}{2} - 1\right) + \frac{x}{2}}\]
\sqrt{x - 1} + \sqrt{\left(\frac{x}{2} - 1\right) + \frac{x}{2}}
↓
\sqrt{x - 1} + \sqrt{\left(\frac{x}{2} - 1\right) + \frac{x}{2}}
double code(double x) {
	return ((double) (((double) sqrt(((double) (x - 1.0)))) + ((double) sqrt(((double) (((double) (((double) (x / 2.0)) - 1.0)) + ((double) (x / 2.0))))))));
}
↓
double code(double x) {
	return ((double) (((double) sqrt(((double) (x - 1.0)))) + ((double) sqrt(((double) (((double) (((double) (x / 2.0)) - 1.0)) + ((double) (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

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

  2. Final simplification0.0

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

Reproduce

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