Average Error: 39.3 → 39.3
Time: 1.2s
Precision: binary64
\[\sqrt{1 + \frac{1}{x}} - 1\]
↓
\[\sqrt{1 + \frac{1}{x}} - 1\]
\sqrt{1 + \frac{1}{x}} - 1
↓
\sqrt{1 + \frac{1}{x}} - 1
double code(double x) {
	return ((double) (((double) sqrt(((double) (1.0 + ((double) (1.0 / x)))))) - 1.0));
}
↓
double code(double x) {
	return ((double) (((double) sqrt(((double) (1.0 + ((double) (1.0 / x)))))) - 1.0));
}

Error

Bits error versus x

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Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 39.3

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

  2. Final simplification39.3

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

Reproduce

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