Average Error: 0.2 → 0.2
Time: 9.3s
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 r88325 = x;
        double r88326 = 1.0;
        double r88327 = r88325 + r88326;
        double r88328 = sqrt(r88327);
        double r88329 = r88326 + r88328;
        double r88330 = r88325 / r88329;
        return r88330;
}
↓
double f(double x) {
        double r88331 = x;
        double r88332 = 1.0;
        double r88333 = r88331 + r88332;
        double r88334 = sqrt(r88333);
        double r88335 = r88332 + r88334;
        double r88336 = r88331 / r88335;
        return r88336;
}

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 2019305 +o rules:numerics
(FPCore (x)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, B"
  :precision binary64
  (/ x (+ 1 (sqrt (+ x 1)))))