Average Error: 0.2 → 0.2
Time: 3.2s
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 r87225 = x;
        double r87226 = 1.0;
        double r87227 = r87225 + r87226;
        double r87228 = sqrt(r87227);
        double r87229 = r87226 + r87228;
        double r87230 = r87225 / r87229;
        return r87230;
}
↓
double f(double x) {
        double r87231 = x;
        double r87232 = 1.0;
        double r87233 = 1.0;
        double r87234 = r87231 + r87233;
        double r87235 = sqrt(r87234);
        double r87236 = r87233 + r87235;
        double r87237 = r87232 / r87236;
        double r87238 = r87231 * r87237;
        return r87238;
}

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 2019353 
(FPCore (x)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, B"
  :precision binary64
  (/ x (+ 1 (sqrt (+ x 1)))))