Average Error: 0.2 → 0.2
Time: 3.2s
Precision: 64
\[\frac{x}{1 + \sqrt{x + 1}}\]
↓
\[x \cdot \frac{1}{1 + \sqrt{x + 1}}\]
\frac{x}{1 + \sqrt{x + 1}}
↓
x \cdot \frac{1}{1 + \sqrt{x + 1}}
double f(double x) {
        double r95496 = x;
        double r95497 = 1.0;
        double r95498 = r95496 + r95497;
        double r95499 = sqrt(r95498);
        double r95500 = r95497 + r95499;
        double r95501 = r95496 / r95500;
        return r95501;
}
↓
double f(double x) {
        double r95502 = x;
        double r95503 = 1.0;
        double r95504 = 1.0;
        double r95505 = r95502 + r95504;
        double r95506 = sqrt(r95505);
        double r95507 = r95504 + r95506;
        double r95508 = r95503 / r95507;
        double r95509 = r95502 * r95508;
        return r95509;
}

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 div-inv0.2

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

  4. Final simplification0.2

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

Reproduce

herbie shell --seed 2019353 
(FPCore (x)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, B"
  :precision binary64
  (/ x (+ 1 (sqrt (+ x 1)))))