Average Error: 0.2 → 0.2
Time: 15.6s
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 r8306269 = x;
        double r8306270 = 1.0;
        double r8306271 = r8306269 + r8306270;
        double r8306272 = sqrt(r8306271);
        double r8306273 = r8306270 + r8306272;
        double r8306274 = r8306269 / r8306273;
        return r8306274;
}
↓
double f(double x) {
        double r8306275 = x;
        double r8306276 = 1.0;
        double r8306277 = 1.0;
        double r8306278 = r8306275 + r8306277;
        double r8306279 = sqrt(r8306278);
        double r8306280 = r8306277 + r8306279;
        double r8306281 = r8306276 / r8306280;
        double r8306282 = r8306275 * r8306281;
        return r8306282;
}

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 2019163 
(FPCore (x)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, B"
  (/ x (+ 1.0 (sqrt (+ x 1.0)))))