Average Error: 0.0 → 0.0
Time: 1.6s
Precision: binary64
\[\left(\sqrt{a - b} + \frac{1}{b} \cdot b\right) - \frac{a}{b}\]
↓
\[\sqrt{a - b} - \left(\frac{a}{b} - 1\right)\]
\left(\sqrt{a - b} + \frac{1}{b} \cdot b\right) - \frac{a}{b}
↓
\sqrt{a - b} - \left(\frac{a}{b} - 1\right)
double code(double a, double b) {
	return ((double) (((double) (((double) sqrt(((double) (a - b)))) + ((double) (((double) (1.0 / b)) * b)))) - ((double) (a / b))));
}
↓
double code(double a, double b) {
	return ((double) (((double) sqrt(((double) (a - b)))) - ((double) (((double) (a / b)) - 1.0))));
}

Error

Bits error versus a

Bits error versus b

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[\left(\sqrt{a - b} + \frac{1}{b} \cdot b\right) - \frac{a}{b}\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\sqrt{a - b} - \left(\frac{a}{b} - 1\right)}\]

  3. Final simplification0.0

    \[\leadsto \sqrt{a - b} - \left(\frac{a}{b} - 1\right)\]

Reproduce

herbie shell --seed 2020152 
(FPCore (a b)
  :name "(- (+ (sqrt (- a b)) (* (/ 1 b) b)) (/ a b))"
  :precision binary64
  (- (+ (sqrt (- a b)) (* (/ 1.0 b) b)) (/ a b)))