Average Error: 0.2 → 0.2
Time: 2.9s
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 r86071 = x;
        double r86072 = 1.0;
        double r86073 = r86071 + r86072;
        double r86074 = sqrt(r86073);
        double r86075 = r86072 + r86074;
        double r86076 = r86071 / r86075;
        return r86076;
}
↓
double f(double x) {
        double r86077 = x;
        double r86078 = 1.0;
        double r86079 = 1.0;
        double r86080 = r86077 + r86079;
        double r86081 = sqrt(r86080);
        double r86082 = r86079 + r86081;
        double r86083 = r86078 / r86082;
        double r86084 = r86077 * r86083;
        return r86084;
}

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 2019352 +o rules:numerics
(FPCore (x)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, B"
  :precision binary64
  (/ x (+ 1 (sqrt (+ x 1)))))