Average Error: 0.2 → 0.2
Time: 13.5s
Precision: 64
\[\frac{x}{1 + \sqrt{x + 1}}\]
↓
\[x \cdot \frac{1}{1 + \sqrt{x + 1}}\]
\frac{x}{1 + \sqrt{x + 1}}
↓
x \cdot \frac{1}{1 + \sqrt{x + 1}}
double f(double x) {
        double r117298 = x;
        double r117299 = 1.0;
        double r117300 = r117298 + r117299;
        double r117301 = sqrt(r117300);
        double r117302 = r117299 + r117301;
        double r117303 = r117298 / r117302;
        return r117303;
}
↓
double f(double x) {
        double r117304 = x;
        double r117305 = 1.0;
        double r117306 = 1.0;
        double r117307 = r117304 + r117306;
        double r117308 = sqrt(r117307);
        double r117309 = r117306 + r117308;
        double r117310 = r117305 / r117309;
        double r117311 = r117304 * r117310;
        return r117311;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.2

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

  3. Applied div-inv0.2

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

  4. Final simplification0.2

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

Reproduce

herbie shell --seed 2019212 +o rules:numerics
(FPCore (x)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, B"
  :precision binary64
  (/ x (+ 1 (sqrt (+ x 1)))))