Average Error: 1.6 → 0
Time: 3.5s
Precision: 64
\[\sqrt{x + 1} - \sqrt{x}\]
\[\frac{1}{\sqrt{x + 1} + \sqrt{x}}\]
\sqrt{x + 1} - \sqrt{x}
\frac{1}{\sqrt{x + 1} + \sqrt{x}}
double f(double x) {
        double r1596901 = x;
        double r1596902 = 1.0;
        double r1596903 = r1596901 + r1596902;
        double r1596904 = sqrt(r1596903);
        double r1596905 = sqrt(r1596901);
        double r1596906 = r1596904 - r1596905;
        return r1596906;
}

double f(double x) {
        double r1596907 = 1.0;
        double r1596908 = x;
        double r1596909 = r1596908 + r1596907;
        double r1596910 = sqrt(r1596909);
        double r1596911 = sqrt(r1596908);
        double r1596912 = r1596910 + r1596911;
        double r1596913 = r1596907 / r1596912;
        return r1596913;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 1.6

    \[\sqrt{x + 1} - \sqrt{x}\]
  2. Using strategy rm
  3. Applied flip--1.6

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

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

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

Reproduce

herbie shell --seed 1 
(FPCore (x)
  :name "sqrt(x+1)-sqrt(x)"
  :precision binary32
  (- (sqrt (+ x 1)) (sqrt x)))