Average Error: 0.2 → 0.2
Time: 12.8s
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 r101796 = x;
        double r101797 = 1.0;
        double r101798 = r101796 + r101797;
        double r101799 = sqrt(r101798);
        double r101800 = r101797 + r101799;
        double r101801 = r101796 / r101800;
        return r101801;
}
↓
double f(double x) {
        double r101802 = x;
        double r101803 = 1.0;
        double r101804 = 1.0;
        double r101805 = r101802 + r101804;
        double r101806 = sqrt(r101805);
        double r101807 = r101804 + r101806;
        double r101808 = r101803 / r101807;
        double r101809 = r101802 * r101808;
        return r101809;
}

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 2019212 
(FPCore (x)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, B"
  :precision binary64
  (/ x (+ 1 (sqrt (+ x 1)))))