Average Error: 0.2 → 0.3
Time: 3.0s
Precision: 64
\[\frac{x}{1 + \sqrt{x + 1}}\]
↓
\[\frac{1}{\frac{1 + \sqrt{x + 1}}{x}}\]
\frac{x}{1 + \sqrt{x + 1}}
↓
\frac{1}{\frac{1 + \sqrt{x + 1}}{x}}
double f(double x) {
        double r95746 = x;
        double r95747 = 1.0;
        double r95748 = r95746 + r95747;
        double r95749 = sqrt(r95748);
        double r95750 = r95747 + r95749;
        double r95751 = r95746 / r95750;
        return r95751;
}
↓
double f(double x) {
        double r95752 = 1.0;
        double r95753 = 1.0;
        double r95754 = x;
        double r95755 = r95754 + r95753;
        double r95756 = sqrt(r95755);
        double r95757 = r95753 + r95756;
        double r95758 = r95757 / r95754;
        double r95759 = r95752 / r95758;
        return r95759;
}

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

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

Reproduce

herbie shell --seed 2020018 
(FPCore (x)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, B"
  :precision binary64
  (/ x (+ 1 (sqrt (+ x 1)))))