Average Error: 0.2 → 0.3
Time: 3.7s
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 r127134 = x;
        double r127135 = 1.0;
        double r127136 = r127134 + r127135;
        double r127137 = sqrt(r127136);
        double r127138 = r127135 + r127137;
        double r127139 = r127134 / r127138;
        return r127139;
}
↓
double f(double x) {
        double r127140 = 1.0;
        double r127141 = 1.0;
        double r127142 = x;
        double r127143 = r127142 + r127141;
        double r127144 = sqrt(r127143);
        double r127145 = r127141 + r127144;
        double r127146 = r127145 / r127142;
        double r127147 = r127140 / r127146;
        return r127147;
}

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