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

Average Error: 0.2 → 0.2

Time: 6.4s

Precision: 64

Math

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

↓

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

C

double f(double x) {
        double r115815 = x;
        double r115816 = 1.0;
        double r115817 = r115815 + r115816;
        double r115818 = sqrt(r115817);
        double r115819 = r115816 + r115818;
        double r115820 = r115815 / r115819;
        return r115820;
}

↓

double f(double x) {
        double r115821 = x;
        double r115822 = 1.0;
        double r115823 = r115821 + r115822;
        double r115824 = sqrt(r115823);
        double r115825 = r115822 + r115824;
        double r115826 = r115821 / r115825;
        return r115826;
}

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 2019298 
(FPCore (x)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, B"
  :precision binary64
  (/ x (+ 1 (sqrt (+ x 1)))))