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

Average Error: 0.2 → 0.2

Time: 2.7s

Precision: 64

Math

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

↓

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

C

double f(double x) {
        double r114887 = x;
        double r114888 = 1.0;
        double r114889 = r114887 + r114888;
        double r114890 = sqrt(r114889);
        double r114891 = r114888 + r114890;
        double r114892 = r114887 / r114891;
        return r114892;
}

↓

double f(double x) {
        double r114893 = x;
        double r114894 = 1.0;
        double r114895 = r114893 + r114894;
        double r114896 = sqrt(r114895);
        double r114897 = r114894 + r114896;
        double r114898 = r114893 / r114897;
        return r114898;
}

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 2020065 +o rules:numerics
(FPCore (x)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, B"
  :precision binary64
  (/ x (+ 1 (sqrt (+ x 1)))))