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

Average Error: 0.2 → 0.2

Time: 6.9s

Precision: 64

Math

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

↓

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

C

double f(double x) {
        double r113355 = x;
        double r113356 = 1.0;
        double r113357 = r113355 + r113356;
        double r113358 = sqrt(r113357);
        double r113359 = r113356 + r113358;
        double r113360 = r113355 / r113359;
        return r113360;
}

↓

double f(double x) {
        double r113361 = x;
        double r113362 = 1.0;
        double r113363 = r113361 + r113362;
        double r113364 = sqrt(r113363);
        double r113365 = r113362 + r113364;
        double r113366 = r113361 / r113365;
        return r113366;
}

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 2020062 
(FPCore (x)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, B"
  :precision binary64
  (/ x (+ 1 (sqrt (+ x 1)))))