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

Average Error: 0.2 → 0.2

Time: 4.5s

Precision: 64

Math

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

↓

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

C

double f(double x) {
        double r85194 = x;
        double r85195 = 1.0;
        double r85196 = r85194 + r85195;
        double r85197 = sqrt(r85196);
        double r85198 = r85195 + r85197;
        double r85199 = r85194 / r85198;
        return r85199;
}

↓

double f(double x) {
        double r85200 = x;
        double r85201 = 1.0;
        double r85202 = r85200 + r85201;
        double r85203 = sqrt(r85202);
        double r85204 = r85201 + r85203;
        double r85205 = r85200 / r85204;
        return r85205;
}

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 1978988140 
(FPCore (x)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, B"
  :precision binary64
  (/ x (+ 1 (sqrt (+ x 1)))))