Average Error: 0.2 → 0.2
Time: 8.2s
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 r89520 = x;
        double r89521 = 1.0;
        double r89522 = r89520 + r89521;
        double r89523 = sqrt(r89522);
        double r89524 = r89521 + r89523;
        double r89525 = r89520 / r89524;
        return r89525;
}
↓
double f(double x) {
        double r89526 = x;
        double r89527 = 1.0;
        double r89528 = r89527 + r89526;
        double r89529 = sqrt(r89528);
        double r89530 = r89527 + r89529;
        double r89531 = r89526 / r89530;
        return r89531;
}

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