Average Error: 0.0 → 0.0
Time: 12.6s
Precision: 64
\[\sqrt{\frac{x}{x - 1}} - \sqrt{x}\]
\[\sqrt{\frac{x}{x - 1}} - \sqrt{x}\]
\sqrt{\frac{x}{x - 1}} - \sqrt{x}
\sqrt{\frac{x}{x - 1}} - \sqrt{x}
double f(double x) {
        double r2455077 = x;
        double r2455078 = 1.0;
        double r2455079 = r2455077 - r2455078;
        double r2455080 = r2455077 / r2455079;
        double r2455081 = sqrt(r2455080);
        double r2455082 = sqrt(r2455077);
        double r2455083 = r2455081 - r2455082;
        return r2455083;
}

double f(double x) {
        double r2455084 = x;
        double r2455085 = 1.0;
        double r2455086 = r2455084 - r2455085;
        double r2455087 = r2455084 / r2455086;
        double r2455088 = sqrt(r2455087);
        double r2455089 = sqrt(r2455084);
        double r2455090 = r2455088 - r2455089;
        return r2455090;
}

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

    \[\sqrt{\frac{x}{x - 1}} - \sqrt{x}\]
  2. Final simplification0.0

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

Reproduce

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