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

Average Error: 0.2 → 0.2

Time: 3.7s

Precision: 64

Math

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

↓

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

C

double f(double x) {
        double r102856 = x;
        double r102857 = 1.0;
        double r102858 = r102856 + r102857;
        double r102859 = sqrt(r102858);
        double r102860 = r102857 + r102859;
        double r102861 = r102856 / r102860;
        return r102861;
}

↓

double f(double x) {
        double r102862 = x;
        double r102863 = 1.0;
        double r102864 = r102862 + r102863;
        double r102865 = sqrt(r102864);
        double r102866 = r102863 + r102865;
        double r102867 = r102862 / r102866;
        return r102867;
}

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 2020100 +o rules:numerics
(FPCore (x)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, B"
  :precision binary64
  (/ x (+ 1 (sqrt (+ x 1)))))