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

Average Error: 0.2 → 0.2

Time: 5.7s

Precision: 64

• Falling back on racket egraph because egg-herbie package not installed

Math

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

↓

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

C

double f(double x) {
        double r128900 = x;
        double r128901 = 1.0;
        double r128902 = r128900 + r128901;
        double r128903 = sqrt(r128902);
        double r128904 = r128901 + r128903;
        double r128905 = r128900 / r128904;
        return r128905;
}

↓

double f(double x) {
        double r128906 = x;
        double r128907 = 1.0;
        double r128908 = r128906 + r128907;
        double r128909 = sqrt(r128908);
        double r128910 = r128907 + r128909;
        double r128911 = r128906 / r128910;
        return r128911;
}

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 2020042 +o rules:numerics
(FPCore (x)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, B"
  :precision binary64
  (/ x (+ 1 (sqrt (+ x 1)))))