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

Average Error: 0.2 → 0.2

Time: 17.0s

Precision: 64

Math

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

↓

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

C

double f(double x) {
        double r109048 = x;
        double r109049 = 1.0;
        double r109050 = r109048 + r109049;
        double r109051 = sqrt(r109050);
        double r109052 = r109049 + r109051;
        double r109053 = r109048 / r109052;
        return r109053;
}

↓

double f(double x) {
        double r109054 = x;
        double r109055 = 1.0;
        double r109056 = r109054 + r109055;
        double r109057 = sqrt(r109056);
        double r109058 = r109055 + r109057;
        double r109059 = r109054 / r109058;
        return r109059;
}

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 2019303 +o rules:numerics
(FPCore (x)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, B"
  :precision binary64
  (/ x (+ 1 (sqrt (+ x 1)))))