Average Error: 0.2 → 0.2
Time: 2.6s
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 r143430 = x;
        double r143431 = 1.0;
        double r143432 = r143430 + r143431;
        double r143433 = sqrt(r143432);
        double r143434 = r143431 + r143433;
        double r143435 = r143430 / r143434;
        return r143435;
}
↓
double f(double x) {
        double r143436 = x;
        double r143437 = 1.0;
        double r143438 = r143436 + r143437;
        double r143439 = sqrt(r143438);
        double r143440 = r143437 + r143439;
        double r143441 = r143436 / r143440;
        return r143441;
}

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 2020065 
(FPCore (x)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, B"
  :precision binary64
  (/ x (+ 1 (sqrt (+ x 1)))))