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

Average Error: 0.2 → 0.2

Time: 15.8s

Precision: 64

Math

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

↓

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

C

double f(double x) {
        double r139695 = x;
        double r139696 = 1.0;
        double r139697 = r139695 + r139696;
        double r139698 = sqrt(r139697);
        double r139699 = r139696 + r139698;
        double r139700 = r139695 / r139699;
        return r139700;
}

↓

double f(double x) {
        double r139701 = x;
        double r139702 = 1.0;
        double r139703 = r139701 + r139702;
        double r139704 = sqrt(r139703);
        double r139705 = r139702 + r139704;
        double r139706 = r139701 / r139705;
        return r139706;
}

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 2019306 
(FPCore (x)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, B"
  :precision binary64
  (/ x (+ 1 (sqrt (+ x 1)))))