Average Error: 0.2 → 0.2
Time: 14.0s
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 r123986 = x;
        double r123987 = 1.0;
        double r123988 = r123986 + r123987;
        double r123989 = sqrt(r123988);
        double r123990 = r123987 + r123989;
        double r123991 = r123986 / r123990;
        return r123991;
}
↓
double f(double x) {
        double r123992 = x;
        double r123993 = 1.0;
        double r123994 = r123993 + r123992;
        double r123995 = sqrt(r123994);
        double r123996 = r123993 + r123995;
        double r123997 = r123992 / r123996;
        return r123997;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.2

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

  2. Simplified0.2

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

  3. Final simplification0.2

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

Reproduce

herbie shell --seed 2019195 
(FPCore (x)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, B"
  (/ x (+ 1.0 (sqrt (+ x 1.0)))))