Average Error: 0.2 → 0.2
Time: 11.6s
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 r109922 = x;
        double r109923 = 1.0;
        double r109924 = r109922 + r109923;
        double r109925 = sqrt(r109924);
        double r109926 = r109923 + r109925;
        double r109927 = r109922 / r109926;
        return r109927;
}
↓
double f(double x) {
        double r109928 = x;
        double r109929 = 1.0;
        double r109930 = r109928 + r109929;
        double r109931 = sqrt(r109930);
        double r109932 = r109929 + r109931;
        double r109933 = r109928 / r109932;
        return r109933;
}

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 2019198 
(FPCore (x)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, B"
  (/ x (+ 1.0 (sqrt (+ x 1.0)))))