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

Average Error: 0.2 → 0.2

Time: 10.0s

Precision: 64

Math

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

↓

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

C

double f(double x) {
        double r66109 = x;
        double r66110 = 1.0;
        double r66111 = r66109 + r66110;
        double r66112 = sqrt(r66111);
        double r66113 = r66110 + r66112;
        double r66114 = r66109 / r66113;
        return r66114;
}

↓

double f(double x) {
        double r66115 = x;
        double r66116 = 1.0;
        double r66117 = r66115 + r66116;
        double r66118 = sqrt(r66117);
        double r66119 = r66116 + r66118;
        double r66120 = r66115 / r66119;
        return r66120;
}

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 2019305 
(FPCore (x)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, B"
  :precision binary64
  (/ x (+ 1 (sqrt (+ x 1)))))