Average Error: 0.2 → 0.2
Time: 3.8s
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 r98976 = x;
        double r98977 = 1.0;
        double r98978 = r98976 + r98977;
        double r98979 = sqrt(r98978);
        double r98980 = r98977 + r98979;
        double r98981 = r98976 / r98980;
        return r98981;
}
↓
double f(double x) {
        double r98982 = x;
        double r98983 = 1.0;
        double r98984 = r98982 + r98983;
        double r98985 = sqrt(r98984);
        double r98986 = r98983 + r98985;
        double r98987 = r98982 / r98986;
        return r98987;
}

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 2019347 +o rules:numerics
(FPCore (x)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, B"
  :precision binary64
  (/ x (+ 1 (sqrt (+ x 1)))))