Average Error: 0.2 → 0.2
Time: 30.0s
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 r6331434 = x;
        double r6331435 = 1.0;
        double r6331436 = r6331434 + r6331435;
        double r6331437 = sqrt(r6331436);
        double r6331438 = r6331435 + r6331437;
        double r6331439 = r6331434 / r6331438;
        return r6331439;
}
↓
double f(double x) {
        double r6331440 = x;
        double r6331441 = 1.0;
        double r6331442 = r6331441 + r6331440;
        double r6331443 = sqrt(r6331442);
        double r6331444 = r6331441 + r6331443;
        double r6331445 = r6331440 / r6331444;
        return r6331445;
}

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 2019168 
(FPCore (x)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, B"
  (/ x (+ 1.0 (sqrt (+ x 1.0)))))