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

Average Error: 0.2 → 0.2

Time: 6.0s

Precision: 64

Math

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

↓

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

C

double f(double x) {
        double r119624 = x;
        double r119625 = 1.0;
        double r119626 = r119624 + r119625;
        double r119627 = sqrt(r119626);
        double r119628 = r119625 + r119627;
        double r119629 = r119624 / r119628;
        return r119629;
}

↓

double f(double x) {
        double r119630 = x;
        double r119631 = 1.0;
        double r119632 = r119630 + r119631;
        double r119633 = sqrt(r119632);
        double r119634 = r119631 + r119633;
        double r119635 = r119630 / r119634;
        return r119635;
}

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 2019308 
(FPCore (x)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, B"
  :precision binary64
  (/ x (+ 1 (sqrt (+ x 1)))))