Average Error: 0.2 → 0.2
Time: 3.3s
Precision: 64
\[\frac{x}{1 + \sqrt{x + 1}}\]
↓
\[\frac{x}{1 + \sqrt{x + 1}}\]
\frac{x}{1 + \sqrt{x + 1}}
↓
\frac{x}{1 + \sqrt{x + 1}}
double f(double x) {
        double r82926 = x;
        double r82927 = 1.0;
        double r82928 = r82926 + r82927;
        double r82929 = sqrt(r82928);
        double r82930 = r82927 + r82929;
        double r82931 = r82926 / r82930;
        return r82931;
}
↓
double f(double x) {
        double r82932 = x;
        double r82933 = 1.0;
        double r82934 = r82932 + r82933;
        double r82935 = sqrt(r82934);
        double r82936 = r82933 + r82935;
        double r82937 = r82932 / r82936;
        return r82937;
}

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. Final simplification0.2

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

Reproduce

herbie shell --seed 2020036 +o rules:numerics
(FPCore (x)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, B"
  :precision binary64
  (/ x (+ 1 (sqrt (+ x 1)))))