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

Average Error: 0.2 → 0.2

Time: 3.3s

Precision: 64

Math

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

↓

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

C

double f(double x) {
        double r168024 = x;
        double r168025 = 1.0;
        double r168026 = r168024 + r168025;
        double r168027 = sqrt(r168026);
        double r168028 = r168025 + r168027;
        double r168029 = r168024 / r168028;
        return r168029;
}

↓

double f(double x) {
        double r168030 = x;
        double r168031 = 1.0;
        double r168032 = r168030 + r168031;
        double r168033 = sqrt(r168032);
        double r168034 = r168031 + r168033;
        double r168035 = r168030 / r168034;
        return r168035;
}

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 2019356 
(FPCore (x)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, B"
  :precision binary64
  (/ x (+ 1 (sqrt (+ x 1)))))