Average Error: 0.2 → 0.2
Time: 13.5s
Precision: 64
\[\frac{x}{1 + \sqrt{x + 1}}\]
↓
\[\frac{x}{1 + \sqrt{1 + x}}\]
\frac{x}{1 + \sqrt{x + 1}}
↓
\frac{x}{1 + \sqrt{1 + x}}
double f(double x) {
        double r4861470 = x;
        double r4861471 = 1.0;
        double r4861472 = r4861470 + r4861471;
        double r4861473 = sqrt(r4861472);
        double r4861474 = r4861471 + r4861473;
        double r4861475 = r4861470 / r4861474;
        return r4861475;
}
↓
double f(double x) {
        double r4861476 = x;
        double r4861477 = 1.0;
        double r4861478 = r4861477 + r4861476;
        double r4861479 = sqrt(r4861478);
        double r4861480 = r4861477 + r4861479;
        double r4861481 = r4861476 / r4861480;
        return r4861481;
}

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 +-commutative0.2

    \[\leadsto \frac{x}{\color{blue}{\sqrt{x + 1} + 1}}\]

  4. Final simplification0.2

    \[\leadsto \frac{x}{1 + \sqrt{1 + x}}\]

Reproduce

herbie shell --seed 2019170 +o rules:numerics
(FPCore (x)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, B"
  (/ x (+ 1.0 (sqrt (+ x 1.0)))))