Average Error: 0.2 → 0.2
Time: 7.0s
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 r91872 = x;
        double r91873 = 1.0;
        double r91874 = r91872 + r91873;
        double r91875 = sqrt(r91874);
        double r91876 = r91873 + r91875;
        double r91877 = r91872 / r91876;
        return r91877;
}
↓
double f(double x) {
        double r91878 = x;
        double r91879 = 1.0;
        double r91880 = r91878 + r91879;
        double r91881 = sqrt(r91880);
        double r91882 = r91879 + r91881;
        double r91883 = r91878 / r91882;
        return r91883;
}

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 2019199 +o rules:numerics
(FPCore (x)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, B"
  (/ x (+ 1.0 (sqrt (+ x 1.0)))))