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

Average Error: 0.2 → 0.2

Time: 3.6s

Precision: 64

Math

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

↓

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

C

double f(double x) {
        double r89450 = x;
        double r89451 = 1.0;
        double r89452 = r89450 + r89451;
        double r89453 = sqrt(r89452);
        double r89454 = r89451 + r89453;
        double r89455 = r89450 / r89454;
        return r89455;
}

↓

double f(double x) {
        double r89456 = x;
        double r89457 = 1.0;
        double r89458 = r89456 + r89457;
        double r89459 = sqrt(r89458);
        double r89460 = r89457 + r89459;
        double r89461 = r89456 / r89460;
        return r89461;
}

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 2020025 
(FPCore (x)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, B"
  :precision binary64
  (/ x (+ 1 (sqrt (+ x 1)))))