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

Average Error: 0.2 → 0.2

Time: 17.3s

Precision: 64

Math

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

↓

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

C

double f(double x) {
        double r114548 = x;
        double r114549 = 1.0;
        double r114550 = r114548 + r114549;
        double r114551 = sqrt(r114550);
        double r114552 = r114549 + r114551;
        double r114553 = r114548 / r114552;
        return r114553;
}

↓

double f(double x) {
        double r114554 = x;
        double r114555 = 1.0;
        double r114556 = r114554 + r114555;
        double r114557 = sqrt(r114556);
        double r114558 = r114555 + r114557;
        double r114559 = r114554 / r114558;
        return r114559;
}

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 2019303 +o rules:numerics
(FPCore (x)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, B"
  :precision binary64
  (/ x (+ 1 (sqrt (+ x 1)))))