Average Error: 0.2 → 0.2
Time: 7.5s
Precision: 64
\[\frac{x}{1 + \sqrt{x + 1}}\]
↓
\[\frac{x}{1 + \sqrt{1 + x}}\]
\frac{x}{1 + \sqrt{x + 1}}
↓
\frac{x}{1 + \sqrt{1 + x}}
double f(double x) {
        double r92504 = x;
        double r92505 = 1.0;
        double r92506 = r92504 + r92505;
        double r92507 = sqrt(r92506);
        double r92508 = r92505 + r92507;
        double r92509 = r92504 / r92508;
        return r92509;
}
↓
double f(double x) {
        double r92510 = x;
        double r92511 = 1.0;
        double r92512 = r92511 + r92510;
        double r92513 = sqrt(r92512);
        double r92514 = r92511 + r92513;
        double r92515 = r92510 / r92514;
        return r92515;
}

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. Simplified0.2

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

  3. Final simplification0.2

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

Reproduce

herbie shell --seed 2019196 
(FPCore (x)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, B"
  (/ x (+ 1.0 (sqrt (+ x 1.0)))))