Average Error: 0.2 → 0.2
Time: 14.9s
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 r5817582 = x;
        double r5817583 = 1.0;
        double r5817584 = r5817582 + r5817583;
        double r5817585 = sqrt(r5817584);
        double r5817586 = r5817583 + r5817585;
        double r5817587 = r5817582 / r5817586;
        return r5817587;
}
↓
double f(double x) {
        double r5817588 = x;
        double r5817589 = 1.0;
        double r5817590 = 1.0;
        double r5817591 = r5817588 + r5817590;
        double r5817592 = sqrt(r5817591);
        double r5817593 = r5817590 + r5817592;
        double r5817594 = r5817589 / r5817593;
        double r5817595 = r5817588 * r5817594;
        return r5817595;
}

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. 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)))))