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

Average Error: 0.2 → 0.2

Time: 3.6s

Precision: 64

Math

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

↓

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

C

double f(double x) {
        double r95872 = x;
        double r95873 = 1.0;
        double r95874 = r95872 + r95873;
        double r95875 = sqrt(r95874);
        double r95876 = r95873 + r95875;
        double r95877 = r95872 / r95876;
        return r95877;
}

↓

double f(double x) {
        double r95878 = x;
        double r95879 = 1.0;
        double r95880 = r95878 + r95879;
        double r95881 = sqrt(r95880);
        double r95882 = r95879 + r95881;
        double r95883 = r95878 / r95882;
        return r95883;
}

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)))))