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

Average Error: 0.2 → 0.2

Time: 3.1s

Precision: 64

Math

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

↓

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

C

double f(double x) {
        double r106938 = x;
        double r106939 = 1.0;
        double r106940 = r106938 + r106939;
        double r106941 = sqrt(r106940);
        double r106942 = r106939 + r106941;
        double r106943 = r106938 / r106942;
        return r106943;
}

↓

double f(double x) {
        double r106944 = x;
        double r106945 = 1.0;
        double r106946 = r106944 + r106945;
        double r106947 = sqrt(r106946);
        double r106948 = r106945 + r106947;
        double r106949 = r106944 / r106948;
        return r106949;
}

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)))))