Average Error: 0.2 → 0.2
Time: 13.6s
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 r7005829 = x;
        double r7005830 = 1.0;
        double r7005831 = r7005829 + r7005830;
        double r7005832 = sqrt(r7005831);
        double r7005833 = r7005830 + r7005832;
        double r7005834 = r7005829 / r7005833;
        return r7005834;
}
↓
double f(double x) {
        double r7005835 = x;
        double r7005836 = 1.0;
        double r7005837 = 1.0;
        double r7005838 = r7005835 + r7005837;
        double r7005839 = sqrt(r7005838);
        double r7005840 = r7005837 + r7005839;
        double r7005841 = r7005836 / r7005840;
        double r7005842 = r7005835 * r7005841;
        return r7005842;
}

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 2019174 
(FPCore (x)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, B"
  (/ x (+ 1.0 (sqrt (+ x 1.0)))))