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 r5900975 = x;
        double r5900976 = 1.0;
        double r5900977 = r5900975 + r5900976;
        double r5900978 = sqrt(r5900977);
        double r5900979 = r5900976 + r5900978;
        double r5900980 = r5900975 / r5900979;
        return r5900980;
}
↓
double f(double x) {
        double r5900981 = x;
        double r5900982 = 1.0;
        double r5900983 = 1.0;
        double r5900984 = r5900981 + r5900983;
        double r5900985 = sqrt(r5900984);
        double r5900986 = r5900983 + r5900985;
        double r5900987 = r5900982 / r5900986;
        double r5900988 = r5900981 * r5900987;
        return r5900988;
}

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 2019163 +o rules:numerics
(FPCore (x)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, B"
  (/ x (+ 1.0 (sqrt (+ x 1.0)))))