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

Average Error: 0.2 → 0.2

Time: 14.9s

Precision: 64

Math

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

↓

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

C

double f(double x) {
        double r104238 = x;
        double r104239 = 1.0;
        double r104240 = r104238 + r104239;
        double r104241 = sqrt(r104240);
        double r104242 = r104239 + r104241;
        double r104243 = r104238 / r104242;
        return r104243;
}

↓

double f(double x) {
        double r104244 = x;
        double r104245 = 1.0;
        double r104246 = r104244 + r104245;
        double r104247 = sqrt(r104246);
        double r104248 = r104245 + r104247;
        double r104249 = r104244 / r104248;
        return r104249;
}

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 2019323 +o rules:numerics
(FPCore (x)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, B"
  :precision binary64
  (/ x (+ 1 (sqrt (+ x 1)))))