Average Error: 0.2 → 0.2
Time: 3.8s
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 r124107 = x;
        double r124108 = 1.0;
        double r124109 = r124107 + r124108;
        double r124110 = sqrt(r124109);
        double r124111 = r124108 + r124110;
        double r124112 = r124107 / r124111;
        return r124112;
}
↓
double f(double x) {
        double r124113 = x;
        double r124114 = 1.0;
        double r124115 = 1.0;
        double r124116 = r124113 + r124115;
        double r124117 = sqrt(r124116);
        double r124118 = r124115 + r124117;
        double r124119 = r124114 / r124118;
        double r124120 = r124113 * r124119;
        return r124120;
}

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 2020049 
(FPCore (x)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, B"
  :precision binary64
  (/ x (+ 1 (sqrt (+ x 1)))))