Average Error: 0.2 → 0.2
Time: 9.2s
Precision: 64
\[\frac{x}{1 + \sqrt{x + 1}}\]
↓
\[\frac{x}{1 + \sqrt{x + 1}}\]
\frac{x}{1 + \sqrt{x + 1}}
↓
\frac{x}{1 + \sqrt{x + 1}}
double f(double x) {
        double r75632 = x;
        double r75633 = 1.0;
        double r75634 = r75632 + r75633;
        double r75635 = sqrt(r75634);
        double r75636 = r75633 + r75635;
        double r75637 = r75632 / r75636;
        return r75637;
}
↓
double f(double x) {
        double r75638 = x;
        double r75639 = 1.0;
        double r75640 = r75638 + r75639;
        double r75641 = sqrt(r75640);
        double r75642 = r75639 + r75641;
        double r75643 = r75638 / r75642;
        return r75643;
}

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. Final simplification0.2

    \[\leadsto \frac{x}{1 + \sqrt{x + 1}}\]

Reproduce

herbie shell --seed 2019325 +o rules:numerics
(FPCore (x)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, B"
  :precision binary64
  (/ x (+ 1 (sqrt (+ x 1)))))