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

Average Error: 0.2 → 0.2

Time: 15.0s

Precision: 64

Math

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

↓

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

C

double f(double x) {
        double r100091 = x;
        double r100092 = 1.0;
        double r100093 = r100091 + r100092;
        double r100094 = sqrt(r100093);
        double r100095 = r100092 + r100094;
        double r100096 = r100091 / r100095;
        return r100096;
}

↓

double f(double x) {
        double r100097 = x;
        double r100098 = 1.0;
        double r100099 = r100097 + r100098;
        double r100100 = sqrt(r100099);
        double r100101 = r100098 + r100100;
        double r100102 = r100097 / r100101;
        return r100102;
}

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 2019323 
(FPCore (x)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, B"
  :precision binary64
  (/ x (+ 1 (sqrt (+ x 1)))))