Average Error: 0.2 → 0.2
Time: 2.5s
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 r90611 = x;
        double r90612 = 1.0;
        double r90613 = r90611 + r90612;
        double r90614 = sqrt(r90613);
        double r90615 = r90612 + r90614;
        double r90616 = r90611 / r90615;
        return r90616;
}
↓
double f(double x) {
        double r90617 = x;
        double r90618 = 1.0;
        double r90619 = 1.0;
        double r90620 = r90617 + r90619;
        double r90621 = sqrt(r90620);
        double r90622 = r90619 + r90621;
        double r90623 = r90618 / r90622;
        double r90624 = r90617 * r90623;
        return r90624;
}

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 2020089 +o rules:numerics
(FPCore (x)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, B"
  :precision binary64
  (/ x (+ 1 (sqrt (+ x 1)))))