Average Error: 0.2 → 0.2
Time: 3.0s
Precision: 64
\[\frac{x}{1 + \sqrt{x + 1}}\]
↓
\[\frac{x}{1 + \sqrt{x + 1}}\]
\frac{x}{1 + \sqrt{x + 1}}
↓
\frac{x}{1 + \sqrt{x + 1}}
double f(double x) {
        double r77519 = x;
        double r77520 = 1.0;
        double r77521 = r77519 + r77520;
        double r77522 = sqrt(r77521);
        double r77523 = r77520 + r77522;
        double r77524 = r77519 / r77523;
        return r77524;
}
↓
double f(double x) {
        double r77525 = x;
        double r77526 = 1.0;
        double r77527 = r77525 + r77526;
        double r77528 = sqrt(r77527);
        double r77529 = r77526 + r77528;
        double r77530 = r77525 / r77529;
        return r77530;
}

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

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

Reproduce

herbie shell --seed 2020036 +o rules:numerics
(FPCore (x)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, B"
  :precision binary64
  (/ x (+ 1 (sqrt (+ x 1)))))