Average Error: 0.2 → 0.2
Time: 12.4s
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 r5114800 = x;
        double r5114801 = 1.0;
        double r5114802 = r5114800 + r5114801;
        double r5114803 = sqrt(r5114802);
        double r5114804 = r5114801 + r5114803;
        double r5114805 = r5114800 / r5114804;
        return r5114805;
}
↓
double f(double x) {
        double r5114806 = x;
        double r5114807 = 1.0;
        double r5114808 = r5114807 + r5114806;
        double r5114809 = sqrt(r5114808);
        double r5114810 = r5114807 + r5114809;
        double r5114811 = r5114806 / r5114810;
        return r5114811;
}

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

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

Reproduce

herbie shell --seed 2019172 
(FPCore (x)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, B"
  (/ x (+ 1.0 (sqrt (+ x 1.0)))))