Average Error: 0.2 → 0.2
Time: 13.2s
Precision: 64
\[\frac{x}{1.0 + \sqrt{x + 1.0}}\]
↓
\[\frac{x}{1.0 + \sqrt{1.0 + x}}\]
\frac{x}{1.0 + \sqrt{x + 1.0}}
↓
\frac{x}{1.0 + \sqrt{1.0 + x}}
double f(double x) {
        double r6039681 = x;
        double r6039682 = 1.0;
        double r6039683 = r6039681 + r6039682;
        double r6039684 = sqrt(r6039683);
        double r6039685 = r6039682 + r6039684;
        double r6039686 = r6039681 / r6039685;
        return r6039686;
}
↓
double f(double x) {
        double r6039687 = x;
        double r6039688 = 1.0;
        double r6039689 = r6039688 + r6039687;
        double r6039690 = sqrt(r6039689);
        double r6039691 = r6039688 + r6039690;
        double r6039692 = r6039687 / r6039691;
        return r6039692;
}

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 +-commutative0.2

    \[\leadsto \frac{x}{\color{blue}{\sqrt{x + 1.0} + 1.0}}\]

  4. Final simplification0.2

    \[\leadsto \frac{x}{1.0 + \sqrt{1.0 + x}}\]

Reproduce

herbie shell --seed 2019162 +o rules:numerics
(FPCore (x)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, B"
  (/ x (+ 1.0 (sqrt (+ x 1.0)))))