Average Error: 59.6 → 0.3
Time: 13.4s
Precision: 64
\[\sqrt{x + 1} - \sqrt{x - 1}\]
\[\frac{1 + 1}{\sqrt{x + 1} + \sqrt{x - 1}}\]
\sqrt{x + 1} - \sqrt{x - 1}
\frac{1 + 1}{\sqrt{x + 1} + \sqrt{x - 1}}
double f(double x) {
        double r2087755 = x;
        double r2087756 = 1.0;
        double r2087757 = r2087755 + r2087756;
        double r2087758 = sqrt(r2087757);
        double r2087759 = r2087755 - r2087756;
        double r2087760 = sqrt(r2087759);
        double r2087761 = r2087758 - r2087760;
        return r2087761;
}

double f(double x) {
        double r2087762 = 1.0;
        double r2087763 = r2087762 + r2087762;
        double r2087764 = x;
        double r2087765 = r2087764 + r2087762;
        double r2087766 = sqrt(r2087765);
        double r2087767 = r2087764 - r2087762;
        double r2087768 = sqrt(r2087767);
        double r2087769 = r2087766 + r2087768;
        double r2087770 = r2087763 / r2087769;
        return r2087770;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 59.6

    \[\sqrt{x + 1} - \sqrt{x - 1}\]
  2. Using strategy rm
  3. Applied flip--59.0

    \[\leadsto \color{blue}{\frac{\sqrt{x + 1} \cdot \sqrt{x + 1} - \sqrt{x - 1} \cdot \sqrt{x - 1}}{\sqrt{x + 1} + \sqrt{x - 1}}}\]
  4. Simplified0.3

    \[\leadsto \frac{\color{blue}{1 + \left(0 + 1\right)}}{\sqrt{x + 1} + \sqrt{x - 1}}\]
  5. Final simplification0.3

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

Reproduce

herbie shell --seed 1 
(FPCore (x)
  :name "sqrt(x + 1) - sqrt(x - 1)"
  :precision binary64
  (- (sqrt (+ x 1)) (sqrt (- x 1))))