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

Average Error: 0.2 → 0.2

Time: 3.8s

Precision: 64

Math

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

↓

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

C

double f(double x) {
        double r136889 = x;
        double r136890 = 1.0;
        double r136891 = r136889 + r136890;
        double r136892 = sqrt(r136891);
        double r136893 = r136890 + r136892;
        double r136894 = r136889 / r136893;
        return r136894;
}

↓

double f(double x) {
        double r136895 = x;
        double r136896 = 1.0;
        double r136897 = r136895 + r136896;
        double r136898 = sqrt(r136897);
        double r136899 = r136896 + r136898;
        double r136900 = r136895 / r136899;
        return r136900;
}

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 2020083 +o rules:numerics
(FPCore (x)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, B"
  :precision binary64
  (/ x (+ 1 (sqrt (+ x 1)))))