Average Error: 0.2 → 0.2
Time: 4.7s
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 r91740 = x;
        double r91741 = 1.0;
        double r91742 = r91740 + r91741;
        double r91743 = sqrt(r91742);
        double r91744 = r91741 + r91743;
        double r91745 = r91740 / r91744;
        return r91745;
}
↓
double f(double x) {
        double r91746 = x;
        double r91747 = 1.0;
        double r91748 = r91746 + r91747;
        double r91749 = sqrt(r91748);
        double r91750 = r91747 + r91749;
        double r91751 = r91746 / r91750;
        return r91751;
}

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 2019354 +o rules:numerics
(FPCore (x)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, B"
  :precision binary64
  (/ x (+ 1 (sqrt (+ x 1)))))