Average Error: 0.2 → 0.2
Time: 35.7s
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 r6278685 = x;
        double r6278686 = 1.0;
        double r6278687 = r6278685 + r6278686;
        double r6278688 = sqrt(r6278687);
        double r6278689 = r6278686 + r6278688;
        double r6278690 = r6278685 / r6278689;
        return r6278690;
}
↓
double f(double x) {
        double r6278691 = x;
        double r6278692 = 1.0;
        double r6278693 = r6278692 + r6278691;
        double r6278694 = sqrt(r6278693);
        double r6278695 = r6278692 + r6278694;
        double r6278696 = r6278691 / r6278695;
        return r6278696;
}

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 2019168 +o rules:numerics
(FPCore (x)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, B"
  (/ x (+ 1.0 (sqrt (+ x 1.0)))))