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

Average Error: 0.2 → 0.2

Time: 6.1s

Precision: 64

Math

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

↓

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

C

double f(double x) {
        double r131020 = x;
        double r131021 = 1.0;
        double r131022 = r131020 + r131021;
        double r131023 = sqrt(r131022);
        double r131024 = r131021 + r131023;
        double r131025 = r131020 / r131024;
        return r131025;
}

↓

double f(double x) {
        double r131026 = x;
        double r131027 = 1.0;
        double r131028 = r131026 + r131027;
        double r131029 = sqrt(r131028);
        double r131030 = r131027 + r131029;
        double r131031 = r131026 / r131030;
        return r131031;
}

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 2020021 
(FPCore (x)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, B"
  :precision binary64
  (/ x (+ 1 (sqrt (+ x 1)))))