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

Average Error: 0.2 → 0.2

Time: 4.6s

Precision: 64

Math

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

↓

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

C

double f(double x) {
        double r192242 = x;
        double r192243 = 1.0;
        double r192244 = r192242 + r192243;
        double r192245 = sqrt(r192244);
        double r192246 = r192243 + r192245;
        double r192247 = r192242 / r192246;
        return r192247;
}

↓

double f(double x) {
        double r192248 = x;
        double r192249 = 1.0;
        double r192250 = r192248 + r192249;
        double r192251 = sqrt(r192250);
        double r192252 = r192249 + r192251;
        double r192253 = r192248 / r192252;
        return r192253;
}

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 2020081 
(FPCore (x)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, B"
  :precision binary64
  (/ x (+ 1 (sqrt (+ x 1)))))