Average Error: 0.2 → 0.3
Time: 14.0s
Precision: 64
\[\frac{x}{1 + \sqrt{x + 1}}\]
↓
\[\frac{1}{\frac{1 + \sqrt{1 + x}}{x}}\]
\frac{x}{1 + \sqrt{x + 1}}
↓
\frac{1}{\frac{1 + \sqrt{1 + x}}{x}}
double f(double x) {
        double r5501929 = x;
        double r5501930 = 1.0;
        double r5501931 = r5501929 + r5501930;
        double r5501932 = sqrt(r5501931);
        double r5501933 = r5501930 + r5501932;
        double r5501934 = r5501929 / r5501933;
        return r5501934;
}
↓
double f(double x) {
        double r5501935 = 1.0;
        double r5501936 = 1.0;
        double r5501937 = x;
        double r5501938 = r5501936 + r5501937;
        double r5501939 = sqrt(r5501938);
        double r5501940 = r5501936 + r5501939;
        double r5501941 = r5501940 / r5501937;
        double r5501942 = r5501935 / r5501941;
        return r5501942;
}

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

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

Reproduce

herbie shell --seed 2019170 
(FPCore (x)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, B"
  (/ x (+ 1.0 (sqrt (+ x 1.0)))))