Average Error: 0.2 → 0.2
Time: 4.6s
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 r111306 = x;
        double r111307 = 1.0;
        double r111308 = r111306 + r111307;
        double r111309 = sqrt(r111308);
        double r111310 = r111307 + r111309;
        double r111311 = r111306 / r111310;
        return r111311;
}
↓
double f(double x) {
        double r111312 = x;
        double r111313 = 1.0;
        double r111314 = r111312 + r111313;
        double r111315 = sqrt(r111314);
        double r111316 = r111313 + r111315;
        double r111317 = r111312 / r111316;
        return r111317;
}

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 2020081 +o rules:numerics
(FPCore (x)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, B"
  :precision binary64
  (/ x (+ 1 (sqrt (+ x 1)))))