Average Error: 0.2 → 0.2
Time: 13.5s
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 r4909964 = x;
        double r4909965 = 1.0;
        double r4909966 = r4909964 + r4909965;
        double r4909967 = sqrt(r4909966);
        double r4909968 = r4909965 + r4909967;
        double r4909969 = r4909964 / r4909968;
        return r4909969;
}
↓
double f(double x) {
        double r4909970 = x;
        double r4909971 = 1.0;
        double r4909972 = r4909971 + r4909970;
        double r4909973 = sqrt(r4909972);
        double r4909974 = r4909971 + r4909973;
        double r4909975 = r4909970 / r4909974;
        return r4909975;
}

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)))))