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

Average Error: 0.2 → 0.2

Time: 7.0s

Precision: 64

Math

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

↓

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

C

double f(double x) {
        double r70652 = x;
        double r70653 = 1.0;
        double r70654 = r70652 + r70653;
        double r70655 = sqrt(r70654);
        double r70656 = r70653 + r70655;
        double r70657 = r70652 / r70656;
        return r70657;
}

↓

double f(double x) {
        double r70658 = x;
        double r70659 = 1.0;
        double r70660 = r70658 + r70659;
        double r70661 = sqrt(r70660);
        double r70662 = r70659 + r70661;
        double r70663 = r70658 / r70662;
        return r70663;
}

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 2019199 
(FPCore (x)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, B"
  (/ x (+ 1.0 (sqrt (+ x 1.0)))))