Average Error: 0.2 → 0.3
Time: 2.7s
Precision: binary64
\[\frac{x}{1 + \sqrt{x + 1}}\]
↓
\[\frac{1}{\frac{1 + \sqrt{1 + x}}{x}}\]
\frac{x}{1 + \sqrt{x + 1}}
↓
\frac{1}{\frac{1 + \sqrt{1 + x}}{x}}
double code(double x) {
	return ((double) (x / ((double) (1.0 + ((double) sqrt(((double) (x + 1.0))))))));
}
↓
double code(double x) {
	return ((double) (1.0 / ((double) (((double) (1.0 + ((double) sqrt(((double) (1.0 + x)))))) / x))));
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.2

    \[\frac{x}{1 + \sqrt{x + 1}}\]
  2. Using strategy rm

  3. Applied clear-num0.3

    \[\leadsto \color{blue}{\frac{1}{\frac{1 + \sqrt{x + 1}}{x}}}\]

  4. Final simplification0.3

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

Reproduce

herbie shell --seed 2020184 
(FPCore (x)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, B"
  :precision binary64
  (/ x (+ 1.0 (sqrt (+ x 1.0)))))