Average Error: 0.2 → 0.2
Time: 3.3s
Precision: 64
\[\frac{x}{1 + \sqrt{x + 1}}\]
↓
\[x \cdot \frac{1}{1 + \sqrt{x + 1}}\]
\frac{x}{1 + \sqrt{x + 1}}
↓
x \cdot \frac{1}{1 + \sqrt{x + 1}}
double f(double x) {
        double r96876 = x;
        double r96877 = 1.0;
        double r96878 = r96876 + r96877;
        double r96879 = sqrt(r96878);
        double r96880 = r96877 + r96879;
        double r96881 = r96876 / r96880;
        return r96881;
}
↓
double f(double x) {
        double r96882 = x;
        double r96883 = 1.0;
        double r96884 = 1.0;
        double r96885 = r96882 + r96884;
        double r96886 = sqrt(r96885);
        double r96887 = r96884 + r96886;
        double r96888 = r96883 / r96887;
        double r96889 = r96882 * r96888;
        return r96889;
}

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 div-inv0.2

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

  4. Final simplification0.2

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

Reproduce

herbie shell --seed 2020003 
(FPCore (x)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, B"
  :precision binary64
  (/ x (+ 1 (sqrt (+ x 1)))))