Average Error: 0.2 → 0.2
Time: 9.7s
Precision: 64
\[\frac{x}{1 + \sqrt{x + 1}}\]
↓
\[\frac{x}{1 + {\left(1 + x\right)}^{\frac{1}{2}}}\]
\frac{x}{1 + \sqrt{x + 1}}
↓
\frac{x}{1 + {\left(1 + x\right)}^{\frac{1}{2}}}
double f(double x) {
        double r89984 = x;
        double r89985 = 1.0;
        double r89986 = r89984 + r89985;
        double r89987 = sqrt(r89986);
        double r89988 = r89985 + r89987;
        double r89989 = r89984 / r89988;
        return r89989;
}
↓
double f(double x) {
        double r89990 = x;
        double r89991 = 1.0;
        double r89992 = r89991 + r89990;
        double r89993 = 0.5;
        double r89994 = pow(r89992, r89993);
        double r89995 = r89991 + r89994;
        double r89996 = r89990 / r89995;
        return r89996;
}

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. Simplified0.2

    \[\leadsto \color{blue}{\frac{x}{1 + \sqrt{1 + x}}}\]
  3. Using strategy rm

  4. Applied pow1/20.2

    \[\leadsto \frac{x}{1 + \color{blue}{{\left(1 + x\right)}^{\frac{1}{2}}}}\]

  5. Final simplification0.2

    \[\leadsto \frac{x}{1 + {\left(1 + x\right)}^{\frac{1}{2}}}\]

Reproduce

herbie shell --seed 2019179 +o rules:numerics
(FPCore (x)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, B"
  (/ x (+ 1.0 (sqrt (+ x 1.0)))))