Average Error: 0.2 → 0.2
Time: 5.5s
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 r481 = x;
        double r482 = 1.0;
        double r483 = r481 + r482;
        double r484 = sqrt(r483);
        double r485 = r482 + r484;
        double r486 = r481 / r485;
        return r486;
}
↓
double f(double x) {
        double r487 = x;
        double r488 = 1.0;
        double r489 = r487 + r488;
        double r490 = sqrt(r489);
        double r491 = r488 + r490;
        double r492 = r487 / r491;
        return r492;
}

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 2020025 +o rules:numerics
(FPCore (x)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, B"
  :precision binary64
  (/ x (+ 1 (sqrt (+ x 1)))))