Average Error: 0.2 → 0.2
Time: 20.0s
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 r5710530 = x;
        double r5710531 = 1.0;
        double r5710532 = r5710530 + r5710531;
        double r5710533 = sqrt(r5710532);
        double r5710534 = r5710531 + r5710533;
        double r5710535 = r5710530 / r5710534;
        return r5710535;
}
↓
double f(double x) {
        double r5710536 = x;
        double r5710537 = 1.0;
        double r5710538 = 1.0;
        double r5710539 = r5710536 + r5710538;
        double r5710540 = sqrt(r5710539);
        double r5710541 = r5710538 + r5710540;
        double r5710542 = r5710537 / r5710541;
        double r5710543 = r5710536 * r5710542;
        return r5710543;
}

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