Average Error: 0.2 → 0.2
Time: 3.4s
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 r119634 = x;
        double r119635 = 1.0;
        double r119636 = r119634 + r119635;
        double r119637 = sqrt(r119636);
        double r119638 = r119635 + r119637;
        double r119639 = r119634 / r119638;
        return r119639;
}
↓
double f(double x) {
        double r119640 = x;
        double r119641 = 1.0;
        double r119642 = 1.0;
        double r119643 = r119640 + r119642;
        double r119644 = sqrt(r119643);
        double r119645 = r119642 + r119644;
        double r119646 = r119641 / r119645;
        double r119647 = r119640 * r119646;
        return r119647;
}

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 2019353 +o rules:numerics
(FPCore (x)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, B"
  :precision binary64
  (/ x (+ 1 (sqrt (+ x 1)))))