Average Error: 0.2 → 0.3
Time: 3.5s
Precision: 64
\[\frac{x}{1 + \sqrt{x + 1}}\]
↓
\[\frac{1}{\frac{1 + \sqrt{x + 1}}{x}}\]
\frac{x}{1 + \sqrt{x + 1}}
↓
\frac{1}{\frac{1 + \sqrt{x + 1}}{x}}
double f(double x) {
        double r151162 = x;
        double r151163 = 1.0;
        double r151164 = r151162 + r151163;
        double r151165 = sqrt(r151164);
        double r151166 = r151163 + r151165;
        double r151167 = r151162 / r151166;
        return r151167;
}
↓
double f(double x) {
        double r151168 = 1.0;
        double r151169 = 1.0;
        double r151170 = x;
        double r151171 = r151170 + r151169;
        double r151172 = sqrt(r151171);
        double r151173 = r151169 + r151172;
        double r151174 = r151173 / r151170;
        double r151175 = r151168 / r151174;
        return r151175;
}

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. Using strategy rm

  3. Applied clear-num0.3

    \[\leadsto \color{blue}{\frac{1}{\frac{1 + \sqrt{x + 1}}{x}}}\]

  4. Final simplification0.3

    \[\leadsto \frac{1}{\frac{1 + \sqrt{x + 1}}{x}}\]

Reproduce

herbie shell --seed 2020057 
(FPCore (x)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, B"
  :precision binary64
  (/ x (+ 1 (sqrt (+ x 1)))))