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

Average Error: 0.2 → 0.2

Time: 3.5s

Precision: 64

Math

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

↓

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

C

double f(double x) {
        double r114982 = x;
        double r114983 = 1.0;
        double r114984 = r114982 + r114983;
        double r114985 = sqrt(r114984);
        double r114986 = r114983 + r114985;
        double r114987 = r114982 / r114986;
        return r114987;
}

↓

double f(double x) {
        double r114988 = x;
        double r114989 = 1.0;
        double r114990 = r114988 + r114989;
        double r114991 = sqrt(r114990);
        double r114992 = r114989 + r114991;
        double r114993 = r114988 / r114992;
        return r114993;
}

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