Average Error: 29.7 → 29.7
Time: 1.6s
Precision: binary64
\[\sqrt{\frac{1}{x} + 1} - \sqrt{\frac{1}{x}}\]
↓
\[\sqrt{\frac{1}{x} + 1} - \sqrt{\frac{1}{x}}\]
\sqrt{\frac{1}{x} + 1} - \sqrt{\frac{1}{x}}
↓
\sqrt{\frac{1}{x} + 1} - \sqrt{\frac{1}{x}}
double code(double x) {
	return ((double) (((double) sqrt(((double) (((double) (1.0 / x)) + 1.0)))) - ((double) sqrt(((double) (1.0 / x))))));
}
↓
double code(double x) {
	return ((double) (((double) sqrt(((double) (((double) (1.0 / x)) + 1.0)))) - ((double) sqrt(((double) (1.0 / x))))));
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 29.7

    \[\sqrt{\frac{1}{x} + 1} - \sqrt{\frac{1}{x}}\]

  2. Final simplification29.7

    \[\leadsto \sqrt{\frac{1}{x} + 1} - \sqrt{\frac{1}{x}}\]

Reproduce

herbie shell --seed 2020152 
(FPCore (x)
  :name "(- (sqrt (+ (/ 1 x) 1)) (sqrt (/ 1 x)))"
  :precision binary64
  (- (sqrt (+ (/ 1.0 x) 1.0)) (sqrt (/ 1.0 x))))