Average Error: 0.2 → 0.2
Time: 3.1s
Precision: 64
\[\frac{x}{1 + \sqrt{x + 1}}\]
↓
\[x \cdot \frac{1}{1 + \sqrt{x + 1}}\]
\frac{x}{1 + \sqrt{x + 1}}
↓
x \cdot \frac{1}{1 + \sqrt{x + 1}}
double f(double x) {
        double r87139 = x;
        double r87140 = 1.0;
        double r87141 = r87139 + r87140;
        double r87142 = sqrt(r87141);
        double r87143 = r87140 + r87142;
        double r87144 = r87139 / r87143;
        return r87144;
}
↓
double f(double x) {
        double r87145 = x;
        double r87146 = 1.0;
        double r87147 = 1.0;
        double r87148 = r87145 + r87147;
        double r87149 = sqrt(r87148);
        double r87150 = r87147 + r87149;
        double r87151 = r87146 / r87150;
        double r87152 = r87145 * r87151;
        return r87152;
}

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 div-inv0.2

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

  4. Final simplification0.2

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

Reproduce

herbie shell --seed 2020001 +o rules:numerics
(FPCore (x)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, B"
  :precision binary64
  (/ x (+ 1 (sqrt (+ x 1)))))