Average Error: 0.2 → 0.2
Time: 14.5s
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 r7127416 = x;
        double r7127417 = 1.0;
        double r7127418 = r7127416 + r7127417;
        double r7127419 = sqrt(r7127418);
        double r7127420 = r7127417 + r7127419;
        double r7127421 = r7127416 / r7127420;
        return r7127421;
}
↓
double f(double x) {
        double r7127422 = x;
        double r7127423 = 1.0;
        double r7127424 = 1.0;
        double r7127425 = r7127422 + r7127424;
        double r7127426 = sqrt(r7127425);
        double r7127427 = r7127424 + r7127426;
        double r7127428 = r7127423 / r7127427;
        double r7127429 = r7127422 * r7127428;
        return r7127429;
}

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)))))