Average Error: 0.2 → 0.2
Time: 17.0s
Precision: 64
\[\frac{x}{1.0 + \sqrt{x + 1.0}}\]
↓
\[x \cdot \frac{1}{1.0 + \sqrt{x + 1.0}}\]
\frac{x}{1.0 + \sqrt{x + 1.0}}
↓
x \cdot \frac{1}{1.0 + \sqrt{x + 1.0}}
double f(double x) {
        double r4872251 = x;
        double r4872252 = 1.0;
        double r4872253 = r4872251 + r4872252;
        double r4872254 = sqrt(r4872253);
        double r4872255 = r4872252 + r4872254;
        double r4872256 = r4872251 / r4872255;
        return r4872256;
}
↓
double f(double x) {
        double r4872257 = x;
        double r4872258 = 1.0;
        double r4872259 = 1.0;
        double r4872260 = r4872257 + r4872259;
        double r4872261 = sqrt(r4872260);
        double r4872262 = r4872259 + r4872261;
        double r4872263 = r4872258 / r4872262;
        double r4872264 = r4872257 * r4872263;
        return r4872264;
}

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

    \[\frac{x}{1.0 + \sqrt{x + 1.0}}\]
  2. Using strategy rm

  3. Applied div-inv0.2

    \[\leadsto \color{blue}{x \cdot \frac{1}{1.0 + \sqrt{x + 1.0}}}\]

  4. Final simplification0.2

    \[\leadsto x \cdot \frac{1}{1.0 + \sqrt{x + 1.0}}\]

Reproduce

herbie shell --seed 2019164 +o rules:numerics
(FPCore (x)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, B"
  (/ x (+ 1.0 (sqrt (+ x 1.0)))))