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

Average Error: 0.2 → 0.2

Time: 4.5s

Precision: 64

Math

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

↓

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

C

double f(double x) {
        double r90650 = x;
        double r90651 = 1.0;
        double r90652 = r90650 + r90651;
        double r90653 = sqrt(r90652);
        double r90654 = r90651 + r90653;
        double r90655 = r90650 / r90654;
        return r90655;
}

↓

double f(double x) {
        double r90656 = x;
        double r90657 = 1.0;
        double r90658 = r90656 + r90657;
        double r90659 = sqrt(r90658);
        double r90660 = r90657 + r90659;
        double r90661 = r90656 / r90660;
        return r90661;
}

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 2020046 
(FPCore (x)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, B"
  :precision binary64
  (/ x (+ 1 (sqrt (+ x 1)))))