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

Average Error: 0.2 → 0.2

Time: 6.7s

Precision: 64

Math

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

↓

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

C

double f(double x) {
        double r125764 = x;
        double r125765 = 1.0;
        double r125766 = r125764 + r125765;
        double r125767 = sqrt(r125766);
        double r125768 = r125765 + r125767;
        double r125769 = r125764 / r125768;
        return r125769;
}

↓

double f(double x) {
        double r125770 = x;
        double r125771 = 1.0;
        double r125772 = r125770 + r125771;
        double r125773 = sqrt(r125772);
        double r125774 = r125771 + r125773;
        double r125775 = r125770 / r125774;
        return r125775;
}

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 2020062 
(FPCore (x)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, B"
  :precision binary64
  (/ x (+ 1 (sqrt (+ x 1)))))