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

Average Error: 0.2 → 0.2

Time: 11.1s

Precision: 64

Math

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

↓

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

C

double f(double x) {
        double r94276 = x;
        double r94277 = 1.0;
        double r94278 = r94276 + r94277;
        double r94279 = sqrt(r94278);
        double r94280 = r94277 + r94279;
        double r94281 = r94276 / r94280;
        return r94281;
}

↓

double f(double x) {
        double r94282 = x;
        double r94283 = 1.0;
        double r94284 = r94282 + r94283;
        double r94285 = sqrt(r94284);
        double r94286 = r94283 + r94285;
        double r94287 = r94282 / r94286;
        return r94287;
}

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)))))