Average Error: 40.4 → 40.4
Time: 3.4s
Precision: binary64
\[\sqrt{x + \frac{1}{x}} - \sqrt{x - \frac{1}{x}}\]
↓
\[\sqrt{x + \frac{1}{x}} - \sqrt{x - \frac{1}{x}}\]
\sqrt{x + \frac{1}{x}} - \sqrt{x - \frac{1}{x}}
↓
\sqrt{x + \frac{1}{x}} - \sqrt{x - \frac{1}{x}}
double code(double x) {
	return ((double) (((double) sqrt(((double) (x + ((double) (1.0 / x)))))) - ((double) sqrt(((double) (x - ((double) (1.0 / x))))))));
}
↓
double code(double x) {
	return ((double) (((double) sqrt(((double) (x + ((double) (1.0 / x)))))) - ((double) sqrt(((double) (x - ((double) (1.0 / x))))))));
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 40.4

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

  2. Final simplification40.4

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

Reproduce

herbie shell --seed 2020153 
(FPCore (x)
  :name "(- (sqrt (+ x (/ 1 x))) (sqrt (- x (/ 1 x))))"
  :precision binary64
  (- (sqrt (+ x (/ 1.0 x))) (sqrt (- x (/ 1.0 x)))))