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 r5528426 = x;
        double r5528427 = 1.0;
        double r5528428 = r5528426 + r5528427;
        double r5528429 = sqrt(r5528428);
        double r5528430 = r5528427 + r5528429;
        double r5528431 = r5528426 / r5528430;
        return r5528431;
}
↓
double f(double x) {
        double r5528432 = x;
        double r5528433 = 1.0;
        double r5528434 = 1.0;
        double r5528435 = r5528432 + r5528434;
        double r5528436 = sqrt(r5528435);
        double r5528437 = r5528434 + r5528436;
        double r5528438 = r5528433 / r5528437;
        double r5528439 = r5528432 * r5528438;
        return r5528439;
}

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