Average Error: 0.2 → 0.2
Time: 16.8s
Precision: 64
\[\frac{x}{1.0 + \sqrt{x + 1.0}}\]
↓
\[\frac{x}{1.0 + \sqrt{1.0 + x}}\]
\frac{x}{1.0 + \sqrt{x + 1.0}}
↓
\frac{x}{1.0 + \sqrt{1.0 + x}}
double f(double x) {
        double r7307916 = x;
        double r7307917 = 1.0;
        double r7307918 = r7307916 + r7307917;
        double r7307919 = sqrt(r7307918);
        double r7307920 = r7307917 + r7307919;
        double r7307921 = r7307916 / r7307920;
        return r7307921;
}
↓
double f(double x) {
        double r7307922 = x;
        double r7307923 = 1.0;
        double r7307924 = r7307923 + r7307922;
        double r7307925 = sqrt(r7307924);
        double r7307926 = r7307923 + r7307925;
        double r7307927 = r7307922 / r7307926;
        return r7307927;
}

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. Final simplification0.2

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

Reproduce

herbie shell --seed 2019168 +o rules:numerics
(FPCore (x)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, B"
  (/ x (+ 1.0 (sqrt (+ x 1.0)))))