Average Error: 0.2 → 0.2
Time: 23.2s
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 r5543498 = x;
        double r5543499 = 1.0;
        double r5543500 = r5543498 + r5543499;
        double r5543501 = sqrt(r5543500);
        double r5543502 = r5543499 + r5543501;
        double r5543503 = r5543498 / r5543502;
        return r5543503;
}
↓
double f(double x) {
        double r5543504 = x;
        double r5543505 = 1.0;
        double r5543506 = r5543505 + r5543504;
        double r5543507 = sqrt(r5543506);
        double r5543508 = r5543505 + r5543507;
        double r5543509 = r5543504 / r5543508;
        return r5543509;
}

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. Final simplification0.2

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

Reproduce

herbie shell --seed 2019165 
(FPCore (x)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, B"
  (/ x (+ 1.0 (sqrt (+ x 1.0)))))