Average Error: 0.2 → 0.2
Time: 11.5s
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 r4096363 = x;
        double r4096364 = 1.0;
        double r4096365 = r4096363 + r4096364;
        double r4096366 = sqrt(r4096365);
        double r4096367 = r4096364 + r4096366;
        double r4096368 = r4096363 / r4096367;
        return r4096368;
}
↓
double f(double x) {
        double r4096369 = x;
        double r4096370 = 1.0;
        double r4096371 = r4096370 + r4096369;
        double r4096372 = sqrt(r4096371);
        double r4096373 = r4096370 + r4096372;
        double r4096374 = r4096369 / r4096373;
        return r4096374;
}

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. Final simplification0.2

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

Reproduce

herbie shell --seed 2019171 +o rules:numerics
(FPCore (x)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, B"
  (/ x (+ 1.0 (sqrt (+ x 1.0)))))