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

Average Error: 0.2 → 0.2

Time: 7.5s

Precision: 64

Math

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

↓

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

C

double f(double x) {
        double r162416 = x;
        double r162417 = 1.0;
        double r162418 = r162416 + r162417;
        double r162419 = sqrt(r162418);
        double r162420 = r162417 + r162419;
        double r162421 = r162416 / r162420;
        return r162421;
}

↓

double f(double x) {
        double r162422 = x;
        double r162423 = 1.0;
        double r162424 = r162422 + r162423;
        double r162425 = sqrt(r162424);
        double r162426 = r162423 + r162425;
        double r162427 = r162422 / r162426;
        return r162427;
}

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