Average Error: 0.2 → 0.2
Time: 3.2s
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 r95779 = x;
        double r95780 = 1.0;
        double r95781 = r95779 + r95780;
        double r95782 = sqrt(r95781);
        double r95783 = r95780 + r95782;
        double r95784 = r95779 / r95783;
        return r95784;
}
↓
double f(double x) {
        double r95785 = x;
        double r95786 = 1.0;
        double r95787 = 1.0;
        double r95788 = r95785 + r95787;
        double r95789 = sqrt(r95788);
        double r95790 = r95787 + r95789;
        double r95791 = r95786 / r95790;
        double r95792 = r95785 * r95791;
        return r95792;
}

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)))))