Average Error: 0.2 → 0.3
Time: 13.9s
Precision: 64
\[\frac{x}{1 + \sqrt{x + 1}}\]
↓
\[\frac{1}{\frac{1 + \sqrt{x + 1}}{x}}\]
\frac{x}{1 + \sqrt{x + 1}}
↓
\frac{1}{\frac{1 + \sqrt{x + 1}}{x}}
double f(double x) {
        double r102413 = x;
        double r102414 = 1.0;
        double r102415 = r102413 + r102414;
        double r102416 = sqrt(r102415);
        double r102417 = r102414 + r102416;
        double r102418 = r102413 / r102417;
        return r102418;
}
↓
double f(double x) {
        double r102419 = 1.0;
        double r102420 = 1.0;
        double r102421 = x;
        double r102422 = r102421 + r102420;
        double r102423 = sqrt(r102422);
        double r102424 = r102420 + r102423;
        double r102425 = r102424 / r102421;
        double r102426 = r102419 / r102425;
        return r102426;
}

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. Using strategy rm

  3. Applied clear-num0.3

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

  4. Final simplification0.3

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

Reproduce

herbie shell --seed 2019291 
(FPCore (x)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, B"
  :precision binary64
  (/ x (+ 1 (sqrt (+ x 1)))))