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

Average Error: 0.2 → 0.2

Time: 11.4s

Precision: 64

Math

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

↓

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

C

double f(double x) {
        double r88191 = x;
        double r88192 = 1.0;
        double r88193 = r88191 + r88192;
        double r88194 = sqrt(r88193);
        double r88195 = r88192 + r88194;
        double r88196 = r88191 / r88195;
        return r88196;
}

↓

double f(double x) {
        double r88197 = x;
        double r88198 = 1.0;
        double r88199 = r88197 + r88198;
        double r88200 = sqrt(r88199);
        double r88201 = r88198 + r88200;
        double r88202 = r88197 / r88201;
        return r88202;
}

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 2019294 
(FPCore (x)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, B"
  :precision binary64
  (/ x (+ 1 (sqrt (+ x 1)))))