(- b (sqrt (- (* b b) c)))

Average Error: 29.3 → 29.3

Time: 4.7s

Precision: binary64

Math

\[b - \sqrt{b \cdot b - c}\]

↓

\[b - \sqrt{b \cdot b - c}\]

C

double code(double b, double c) {
	return ((double) (b - ((double) sqrt(((double) (((double) (b * b)) - c))))));
}

↓

double code(double b, double c) {
	return ((double) (b - ((double) sqrt(((double) (((double) (b * b)) - c))))));
}

Error

Bits error versus b

Bits error versus c

Derivation

1. Initial program 29.3

   \[b - \sqrt{b \cdot b - c}\]

2. Final simplification 29.3

   \[\leadsto b - \sqrt{b \cdot b - c}\]

Reproduce

herbie shell --seed 2020153 
(FPCore (b c)
  :name "(- b (sqrt (- (* b b) c)))"
  :precision binary64
  (- b (sqrt (- (* b b) c))))