Average Error: 0.2 → 0.2
Time: 12.2s
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 r5113533 = x;
        double r5113534 = 1.0;
        double r5113535 = r5113533 + r5113534;
        double r5113536 = sqrt(r5113535);
        double r5113537 = r5113534 + r5113536;
        double r5113538 = r5113533 / r5113537;
        return r5113538;
}
↓
double f(double x) {
        double r5113539 = x;
        double r5113540 = 1.0;
        double r5113541 = 1.0;
        double r5113542 = r5113539 + r5113541;
        double r5113543 = sqrt(r5113542);
        double r5113544 = r5113541 + r5113543;
        double r5113545 = r5113540 / r5113544;
        double r5113546 = r5113539 * r5113545;
        return r5113546;
}

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)))))