Average Error: 0.2 → 0.2
Time: 4.0s
Precision: 64
\[\frac{x}{1 + \sqrt{x + 1}}\]
↓
\[\frac{x}{1 + {\left(\sqrt{x + 1}\right)}^{1}}\]
\frac{x}{1 + \sqrt{x + 1}}
↓
\frac{x}{1 + {\left(\sqrt{x + 1}\right)}^{1}}
double f(double x) {
        double r82245 = x;
        double r82246 = 1.0;
        double r82247 = r82245 + r82246;
        double r82248 = sqrt(r82247);
        double r82249 = r82246 + r82248;
        double r82250 = r82245 / r82249;
        return r82250;
}
↓
double f(double x) {
        double r82251 = x;
        double r82252 = 1.0;
        double r82253 = r82251 + r82252;
        double r82254 = sqrt(r82253);
        double r82255 = 1.0;
        double r82256 = pow(r82254, r82255);
        double r82257 = r82252 + r82256;
        double r82258 = r82251 / r82257;
        return r82258;
}

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 pow10.2

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

  4. Final simplification0.2

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

Reproduce

herbie shell --seed 2020024 
(FPCore (x)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, B"
  :precision binary64
  (/ x (+ 1 (sqrt (+ x 1)))))