Average Error: 0.2 → 0.2
Time: 7.4s
Precision: 64
\[\frac{x}{1.0 + \sqrt{x + 1.0}}\]
↓
\[\frac{x}{1.0 + \sqrt{1.0 + x}}\]
\frac{x}{1.0 + \sqrt{x + 1.0}}
↓
\frac{x}{1.0 + \sqrt{1.0 + x}}
double f(double x) {
        double r4729597 = x;
        double r4729598 = 1.0;
        double r4729599 = r4729597 + r4729598;
        double r4729600 = sqrt(r4729599);
        double r4729601 = r4729598 + r4729600;
        double r4729602 = r4729597 / r4729601;
        return r4729602;
}
↓
double f(double x) {
        double r4729603 = x;
        double r4729604 = 1.0;
        double r4729605 = r4729604 + r4729603;
        double r4729606 = sqrt(r4729605);
        double r4729607 = r4729604 + r4729606;
        double r4729608 = r4729603 / r4729607;
        return r4729608;
}

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

    \[\frac{x}{1.0 + \sqrt{x + 1.0}}\]

  2. Final simplification0.2

    \[\leadsto \frac{x}{1.0 + \sqrt{1.0 + x}}\]

Reproduce

herbie shell --seed 2019165 
(FPCore (x)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, B"
  (/ x (+ 1.0 (sqrt (+ x 1.0)))))