Average Error: 0.2 → 0.2
Time: 12.8s
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 r106303 = x;
        double r106304 = 1.0;
        double r106305 = r106303 + r106304;
        double r106306 = sqrt(r106305);
        double r106307 = r106304 + r106306;
        double r106308 = r106303 / r106307;
        return r106308;
}
↓
double f(double x) {
        double r106309 = x;
        double r106310 = 1.0;
        double r106311 = r106309 + r106310;
        double r106312 = sqrt(r106311);
        double r106313 = r106310 + r106312;
        double r106314 = r106309 / r106313;
        return r106314;
}

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 2019347 +o rules:numerics
(FPCore (x)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, B"
  :precision binary64
  (/ x (+ 1 (sqrt (+ x 1)))))