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

Average Error: 0.2 → 0.2

Time: 2.8s

Precision: 64

Math

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

↓

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

C

double f(double x) {
        double r75185 = x;
        double r75186 = 1.0;
        double r75187 = r75185 + r75186;
        double r75188 = sqrt(r75187);
        double r75189 = r75186 + r75188;
        double r75190 = r75185 / r75189;
        return r75190;
}

↓

double f(double x) {
        double r75191 = x;
        double r75192 = 1.0;
        double r75193 = r75191 + r75192;
        double r75194 = sqrt(r75193);
        double r75195 = r75192 + r75194;
        double r75196 = r75191 / r75195;
        return r75196;
}

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 2020036 
(FPCore (x)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, B"
  :precision binary64
  (/ x (+ 1 (sqrt (+ x 1)))))