Average Error: 0.2 → 0.2
Time: 9.5s
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 r116679 = x;
        double r116680 = 1.0;
        double r116681 = r116679 + r116680;
        double r116682 = sqrt(r116681);
        double r116683 = r116680 + r116682;
        double r116684 = r116679 / r116683;
        return r116684;
}
↓
double f(double x) {
        double r116685 = x;
        double r116686 = 1.0;
        double r116687 = r116685 + r116686;
        double r116688 = sqrt(r116687);
        double r116689 = r116686 + r116688;
        double r116690 = r116685 / r116689;
        return r116690;
}

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