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

Average Error: 0.2 → 0.2

Time: 3.6s

Precision: 64

Math

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

↓

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

C

double f(double x) {
        double r121295 = x;
        double r121296 = 1.0;
        double r121297 = r121295 + r121296;
        double r121298 = sqrt(r121297);
        double r121299 = r121296 + r121298;
        double r121300 = r121295 / r121299;
        return r121300;
}

↓

double f(double x) {
        double r121301 = x;
        double r121302 = 1.0;
        double r121303 = r121301 + r121302;
        double r121304 = sqrt(r121303);
        double r121305 = r121302 + r121304;
        double r121306 = r121301 / r121305;
        return r121306;
}

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 2019347 
(FPCore (x)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, B"
  :precision binary64
  (/ x (+ 1 (sqrt (+ x 1)))))