Average Error: 29.8 → 0.2
Time: 12.2s
Precision: 64
\[x \gt 0\]
\[\sqrt{x + 1} - \sqrt{x}\]
\[\frac{1}{\sqrt{1 + x} + \sqrt{x}}\]
\sqrt{x + 1} - \sqrt{x}
\frac{1}{\sqrt{1 + x} + \sqrt{x}}
double f(double x) {
        double r59743046 = x;
        double r59743047 = 1.0;
        double r59743048 = r59743046 + r59743047;
        double r59743049 = sqrt(r59743048);
        double r59743050 = sqrt(r59743046);
        double r59743051 = r59743049 - r59743050;
        return r59743051;
}

double f(double x) {
        double r59743052 = 1.0;
        double r59743053 = x;
        double r59743054 = r59743052 + r59743053;
        double r59743055 = sqrt(r59743054);
        double r59743056 = sqrt(r59743053);
        double r59743057 = r59743055 + r59743056;
        double r59743058 = r59743052 / r59743057;
        return r59743058;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 29.8

    \[\sqrt{x + 1} - \sqrt{x}\]
  2. Using strategy rm
  3. Applied flip--29.6

    \[\leadsto \color{blue}{\frac{\sqrt{x + 1} \cdot \sqrt{x + 1} - \sqrt{x} \cdot \sqrt{x}}{\sqrt{x + 1} + \sqrt{x}}}\]
  4. Simplified0.2

    \[\leadsto \frac{\color{blue}{1}}{\sqrt{x + 1} + \sqrt{x}}\]
  5. Final simplification0.2

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

Reproduce

herbie shell --seed 1 
(FPCore (x)
  :name "sqrt(x + 1) - sqrt(x)"
  :pre (> x 0)
  (- (sqrt (+ x 1)) (sqrt x)))