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

Average Error: 0.2 → 0.2

Time: 4.2s

Precision: 64

Math

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

↓

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

C

double f(double x) {
        double r103604 = x;
        double r103605 = 1.0;
        double r103606 = r103604 + r103605;
        double r103607 = sqrt(r103606);
        double r103608 = r103605 + r103607;
        double r103609 = r103604 / r103608;
        return r103609;
}

↓

double f(double x) {
        double r103610 = x;
        double r103611 = 1.0;
        double r103612 = r103610 + r103611;
        double r103613 = sqrt(r103612);
        double r103614 = r103611 + r103613;
        double r103615 = r103610 / r103614;
        return r103615;
}

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 2020039 +o rules:numerics
(FPCore (x)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, B"
  :precision binary64
  (/ x (+ 1 (sqrt (+ x 1)))))