Average Error: 0.0 → 0.0
Time: 4.3s
Precision: 64
\[\sqrt{\frac{x}{x + 1}}\]
\[\left|\sqrt{\frac{x}{x + 1}}\right|\]
\sqrt{\frac{x}{x + 1}}
\left|\sqrt{\frac{x}{x + 1}}\right|
double f(double x) {
        double r2441091 = x;
        double r2441092 = 1.0;
        double r2441093 = r2441091 + r2441092;
        double r2441094 = r2441091 / r2441093;
        double r2441095 = sqrt(r2441094);
        return r2441095;
}

double f(double x) {
        double r2441096 = x;
        double r2441097 = 1.0;
        double r2441098 = r2441096 + r2441097;
        double r2441099 = r2441096 / r2441098;
        double r2441100 = sqrt(r2441099);
        double r2441101 = fabs(r2441100);
        return r2441101;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[\sqrt{\frac{x}{x + 1}}\]
  2. Using strategy rm
  3. Applied add-sqr-sqrt0.0

    \[\leadsto \sqrt{\color{blue}{\sqrt{\frac{x}{x + 1}} \cdot \sqrt{\frac{x}{x + 1}}}}\]
  4. Applied rem-sqrt-square0.0

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

    \[\leadsto \left|\sqrt{\frac{x}{x + 1}}\right|\]

Reproduce

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