Average Error: 0.2 → 0.2
Time: 14.6s
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 r116216 = x;
        double r116217 = 1.0;
        double r116218 = r116216 + r116217;
        double r116219 = sqrt(r116218);
        double r116220 = r116217 + r116219;
        double r116221 = r116216 / r116220;
        return r116221;
}
↓
double f(double x) {
        double r116222 = x;
        double r116223 = 1.0;
        double r116224 = 1.0;
        double r116225 = r116222 + r116224;
        double r116226 = sqrt(r116225);
        double r116227 = r116224 + r116226;
        double r116228 = r116223 / r116227;
        double r116229 = r116222 * r116228;
        return r116229;
}

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. Simplified0.2

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

  5. Final simplification0.2

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

Reproduce

herbie shell --seed 2019174 +o rules:numerics
(FPCore (x)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, B"
  (/ x (+ 1.0 (sqrt (+ x 1.0)))))