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

Average Error: 0.2 → 0.2

Time: 15.5s

Precision: 64

Math

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

↓

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

C

double f(double x) {
        double r8429308 = x;
        double r8429309 = 1.0;
        double r8429310 = r8429308 + r8429309;
        double r8429311 = sqrt(r8429310);
        double r8429312 = r8429309 + r8429311;
        double r8429313 = r8429308 / r8429312;
        return r8429313;
}

↓

double f(double x) {
        double r8429314 = x;
        double r8429315 = 1.0;
        double r8429316 = 1.0;
        double r8429317 = r8429314 + r8429316;
        double r8429318 = sqrt(r8429317);
        double r8429319 = r8429316 + r8429318;
        double r8429320 = r8429315 / r8429319;
        double r8429321 = r8429314 * r8429320;
        return r8429321;
}

Error

Bits error versus x

Derivation

1. Initial program 0.2

   \[\frac{x}{1 + \sqrt{x + 1}}\]
2. Using strategy rm

3. Applied div-inv 0.2

   \[\leadsto \color{blue}{x \cdot \frac{1}{1 + \sqrt{x + 1}}}\]

4. Final simplification 0.2

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

Reproduce

herbie shell --seed 2019174 
(FPCore (x)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, B"
  (/ x (+ 1.0 (sqrt (+ x 1.0)))))