Average Error: 0.2 → 0.2
Time: 12.3s
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 r4892333 = x;
        double r4892334 = 1.0;
        double r4892335 = r4892333 + r4892334;
        double r4892336 = sqrt(r4892335);
        double r4892337 = r4892334 + r4892336;
        double r4892338 = r4892333 / r4892337;
        return r4892338;
}
↓
double f(double x) {
        double r4892339 = x;
        double r4892340 = 1.0;
        double r4892341 = r4892340 + r4892339;
        double r4892342 = sqrt(r4892341);
        double r4892343 = r4892340 + r4892342;
        double r4892344 = r4892339 / r4892343;
        return r4892344;
}

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)))))