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

Average Error: 0.2 → 0.2

Time: 7.2s

Precision: 64

Math

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

↓

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

C

double f(double x) {
        double r116772 = x;
        double r116773 = 1.0;
        double r116774 = r116772 + r116773;
        double r116775 = sqrt(r116774);
        double r116776 = r116773 + r116775;
        double r116777 = r116772 / r116776;
        return r116777;
}

↓

double f(double x) {
        double r116778 = x;
        double r116779 = 1.0;
        double r116780 = r116778 + r116779;
        double r116781 = sqrt(r116780);
        double r116782 = r116779 + r116781;
        double r116783 = r116778 / r116782;
        return r116783;
}

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)))))