Average Error: 0.2 → 0.2
Time: 13.2s
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 r88066 = x;
        double r88067 = 1.0;
        double r88068 = r88066 + r88067;
        double r88069 = sqrt(r88068);
        double r88070 = r88067 + r88069;
        double r88071 = r88066 / r88070;
        return r88071;
}
↓
double f(double x) {
        double r88072 = x;
        double r88073 = 1.0;
        double r88074 = r88072 + r88073;
        double r88075 = sqrt(r88074);
        double r88076 = r88073 + r88075;
        double r88077 = r88072 / r88076;
        return r88077;
}

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 2019306 +o rules:numerics
(FPCore (x)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, B"
  :precision binary64
  (/ x (+ 1 (sqrt (+ x 1)))))