Average Error: 0.2 → 0.2
Time: 13.2s
Precision: 64
\[\frac{x}{1.0 + \sqrt{x + 1.0}}\]
↓
\[x \cdot \frac{1}{1.0 + \sqrt{x + 1.0}}\]
\frac{x}{1.0 + \sqrt{x + 1.0}}
↓
x \cdot \frac{1}{1.0 + \sqrt{x + 1.0}}
double f(double x) {
        double r5933424 = x;
        double r5933425 = 1.0;
        double r5933426 = r5933424 + r5933425;
        double r5933427 = sqrt(r5933426);
        double r5933428 = r5933425 + r5933427;
        double r5933429 = r5933424 / r5933428;
        return r5933429;
}
↓
double f(double x) {
        double r5933430 = x;
        double r5933431 = 1.0;
        double r5933432 = 1.0;
        double r5933433 = r5933430 + r5933432;
        double r5933434 = sqrt(r5933433);
        double r5933435 = r5933432 + r5933434;
        double r5933436 = r5933431 / r5933435;
        double r5933437 = r5933430 * r5933436;
        return r5933437;
}

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

    \[\frac{x}{1.0 + \sqrt{x + 1.0}}\]
  2. Using strategy rm

  3. Applied div-inv0.2

    \[\leadsto \color{blue}{x \cdot \frac{1}{1.0 + \sqrt{x + 1.0}}}\]

  4. Final simplification0.2

    \[\leadsto x \cdot \frac{1}{1.0 + \sqrt{x + 1.0}}\]

Reproduce

herbie shell --seed 2019164 
(FPCore (x)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, B"
  (/ x (+ 1.0 (sqrt (+ x 1.0)))))