Average Error: 0.2 → 0.2
Time: 2.1s
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 r83497 = x;
        double r83498 = 1.0;
        double r83499 = r83497 + r83498;
        double r83500 = sqrt(r83499);
        double r83501 = r83498 + r83500;
        double r83502 = r83497 / r83501;
        return r83502;
}
↓
double f(double x) {
        double r83503 = x;
        double r83504 = 1.0;
        double r83505 = r83503 + r83504;
        double r83506 = sqrt(r83505);
        double r83507 = r83504 + r83506;
        double r83508 = r83503 / r83507;
        return r83508;
}

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 2020056 +o rules:numerics
(FPCore (x)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, B"
  :precision binary64
  (/ x (+ 1 (sqrt (+ x 1)))))