Average Error: 0.2 → 0.2
Time: 3.1s
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 r90838 = x;
        double r90839 = 1.0;
        double r90840 = r90838 + r90839;
        double r90841 = sqrt(r90840);
        double r90842 = r90839 + r90841;
        double r90843 = r90838 / r90842;
        return r90843;
}
↓
double f(double x) {
        double r90844 = x;
        double r90845 = 1.0;
        double r90846 = 1.0;
        double r90847 = r90844 + r90846;
        double r90848 = sqrt(r90847);
        double r90849 = r90846 + r90848;
        double r90850 = r90845 / r90849;
        double r90851 = r90844 * r90850;
        return r90851;
}

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 2020001 
(FPCore (x)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, B"
  :precision binary64
  (/ x (+ 1 (sqrt (+ x 1)))))