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

Average Error: 0.2 → 0.2

Time: 20.8s

Precision: 64

Math

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

↓

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

C

double f(double x) {
        double r136335 = x;
        double r136336 = 1.0;
        double r136337 = r136335 + r136336;
        double r136338 = sqrt(r136337);
        double r136339 = r136336 + r136338;
        double r136340 = r136335 / r136339;
        return r136340;
}

↓

double f(double x) {
        double r136341 = x;
        double r136342 = 1.0;
        double r136343 = r136341 + r136342;
        double r136344 = sqrt(r136343);
        double r136345 = r136342 + r136344;
        double r136346 = r136341 / r136345;
        return r136346;
}

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 2019323 
(FPCore (x)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, B"
  :precision binary64
  (/ x (+ 1 (sqrt (+ x 1)))))