Numeric.Log:$clog1p from log-domain-0.10.2.1, B

Average Error: 0.2 → 0.2

Time: 10.0s

Precision: 64

Math

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

↓

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

C

double f(double x) {
        double r83797 = x;
        double r83798 = 1.0;
        double r83799 = r83797 + r83798;
        double r83800 = sqrt(r83799);
        double r83801 = r83798 + r83800;
        double r83802 = r83797 / r83801;
        return r83802;
}

↓

double f(double x) {
        double r83803 = x;
        double r83804 = 1.0;
        double r83805 = r83803 + r83804;
        double r83806 = sqrt(r83805);
        double r83807 = r83804 + r83806;
        double r83808 = r83803 / r83807;
        return r83808;
}

Error

Bits error versus x

Derivation

1. Initial program 0.2

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

2. Final simplification 0.2

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

Reproduce

herbie shell --seed 2019322 
(FPCore (x)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, B"
  :precision binary64
  (/ x (+ 1 (sqrt (+ x 1)))))