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

Average Error: 0.2 → 0.2

Time: 3.6s

Precision: 64

Math

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

↓

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

C

double f(double x) {
        double r113084 = x;
        double r113085 = 1.0;
        double r113086 = r113084 + r113085;
        double r113087 = sqrt(r113086);
        double r113088 = r113085 + r113087;
        double r113089 = r113084 / r113088;
        return r113089;
}

↓

double f(double x) {
        double r113090 = x;
        double r113091 = 1.0;
        double r113092 = r113090 + r113091;
        double r113093 = sqrt(r113092);
        double r113094 = r113091 + r113093;
        double r113095 = r113090 / r113094;
        return r113095;
}

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 2020100 
(FPCore (x)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, B"
  :precision binary64
  (/ x (+ 1 (sqrt (+ x 1)))))