Average Error: 0.2 → 0.2
Time: 13.6s
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 r5264524 = x;
        double r5264525 = 1.0;
        double r5264526 = r5264524 + r5264525;
        double r5264527 = sqrt(r5264526);
        double r5264528 = r5264525 + r5264527;
        double r5264529 = r5264524 / r5264528;
        return r5264529;
}
↓
double f(double x) {
        double r5264530 = x;
        double r5264531 = 1.0;
        double r5264532 = r5264531 + r5264530;
        double r5264533 = sqrt(r5264532);
        double r5264534 = r5264531 + r5264533;
        double r5264535 = r5264530 / r5264534;
        return r5264535;
}

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 2019162 
(FPCore (x)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, B"
  (/ x (+ 1.0 (sqrt (+ x 1.0)))))