Average Error: 0.2 → 0.2
Time: 14.1s
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 r5948064 = x;
        double r5948065 = 1.0;
        double r5948066 = r5948064 + r5948065;
        double r5948067 = sqrt(r5948066);
        double r5948068 = r5948065 + r5948067;
        double r5948069 = r5948064 / r5948068;
        return r5948069;
}
↓
double f(double x) {
        double r5948070 = x;
        double r5948071 = 1.0;
        double r5948072 = r5948071 + r5948070;
        double r5948073 = sqrt(r5948072);
        double r5948074 = r5948071 + r5948073;
        double r5948075 = r5948070 / r5948074;
        return r5948075;
}

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. Using strategy rm

  3. Applied +-commutative0.2

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

  4. Final simplification0.2

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

Reproduce

herbie shell --seed 2019179 +o rules:numerics
(FPCore (x)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, B"
  (/ x (+ 1.0 (sqrt (+ x 1.0)))))