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 r95884 = x;
        double r95885 = 1.0;
        double r95886 = r95884 + r95885;
        double r95887 = sqrt(r95886);
        double r95888 = r95885 + r95887;
        double r95889 = r95884 / r95888;
        return r95889;
}
↓
double f(double x) {
        double r95890 = x;
        double r95891 = 1.0;
        double r95892 = 1.0;
        double r95893 = r95890 + r95892;
        double r95894 = sqrt(r95893);
        double r95895 = r95892 + r95894;
        double r95896 = r95891 / r95895;
        double r95897 = r95890 * r95896;
        return r95897;
}

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