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

Average Error: 0.2 → 0.2

Time: 9.4s

Precision: 64

Math

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

↓

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

C

double f(double x) {
        double r92417 = x;
        double r92418 = 1.0;
        double r92419 = r92417 + r92418;
        double r92420 = sqrt(r92419);
        double r92421 = r92418 + r92420;
        double r92422 = r92417 / r92421;
        return r92422;
}

↓

double f(double x) {
        double r92423 = x;
        double r92424 = 1.0;
        double r92425 = r92423 + r92424;
        double r92426 = sqrt(r92425);
        double r92427 = r92424 + r92426;
        double r92428 = r92423 / r92427;
        return r92428;
}

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 2019325 
(FPCore (x)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, B"
  :precision binary64
  (/ x (+ 1 (sqrt (+ x 1)))))