Average Error: 0.2 → 0.2
Time: 16.7s
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 r6098562 = x;
        double r6098563 = 1.0;
        double r6098564 = r6098562 + r6098563;
        double r6098565 = sqrt(r6098564);
        double r6098566 = r6098563 + r6098565;
        double r6098567 = r6098562 / r6098566;
        return r6098567;
}
↓
double f(double x) {
        double r6098568 = x;
        double r6098569 = 1.0;
        double r6098570 = 1.0;
        double r6098571 = r6098568 + r6098570;
        double r6098572 = sqrt(r6098571);
        double r6098573 = r6098570 + r6098572;
        double r6098574 = r6098569 / r6098573;
        double r6098575 = r6098568 * r6098574;
        return r6098575;
}

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 2019158 +o rules:numerics
(FPCore (x)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, B"
  (/ x (+ 1.0 (sqrt (+ x 1.0)))))