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

Average Error: 0.2 → 0.2

Time: 15.1s

Precision: 64

Math

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

↓

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

C

double f(double x) {
        double r117881 = x;
        double r117882 = 1.0;
        double r117883 = r117881 + r117882;
        double r117884 = sqrt(r117883);
        double r117885 = r117882 + r117884;
        double r117886 = r117881 / r117885;
        return r117886;
}

↓

double f(double x) {
        double r117887 = x;
        double r117888 = 1.0;
        double r117889 = r117887 + r117888;
        double r117890 = sqrt(r117889);
        double r117891 = r117888 + r117890;
        double r117892 = r117887 / r117891;
        return r117892;
}

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 2019323 +o rules:numerics
(FPCore (x)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, B"
  :precision binary64
  (/ x (+ 1 (sqrt (+ x 1)))))