Average Error: 0.2 → 0.2
Time: 12.6s
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 r5309774 = x;
        double r5309775 = 1.0;
        double r5309776 = r5309774 + r5309775;
        double r5309777 = sqrt(r5309776);
        double r5309778 = r5309775 + r5309777;
        double r5309779 = r5309774 / r5309778;
        return r5309779;
}
↓
double f(double x) {
        double r5309780 = x;
        double r5309781 = 1.0;
        double r5309782 = r5309781 + r5309780;
        double r5309783 = sqrt(r5309782);
        double r5309784 = r5309781 + r5309783;
        double r5309785 = r5309780 / r5309784;
        return r5309785;
}

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 2019172 +o rules:numerics
(FPCore (x)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, B"
  (/ x (+ 1.0 (sqrt (+ x 1.0)))))