Average Error: 0.2 → 0.2
Time: 15.7s
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 r6152896 = x;
        double r6152897 = 1.0;
        double r6152898 = r6152896 + r6152897;
        double r6152899 = sqrt(r6152898);
        double r6152900 = r6152897 + r6152899;
        double r6152901 = r6152896 / r6152900;
        return r6152901;
}
↓
double f(double x) {
        double r6152902 = x;
        double r6152903 = 1.0;
        double r6152904 = r6152903 + r6152902;
        double r6152905 = sqrt(r6152904);
        double r6152906 = r6152903 + r6152905;
        double r6152907 = r6152902 / r6152906;
        return r6152907;
}

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