Average Error: 38.7 → 38.7
Time: 1.7s
Precision: binary64
\[a - \sqrt{a \cdot a - b \cdot b}\]
↓
\[a - \sqrt{a \cdot a - b \cdot b}\]
a - \sqrt{a \cdot a - b \cdot b}
↓
a - \sqrt{a \cdot a - b \cdot b}
double code(double a, double b) {
	return ((double) (a - ((double) sqrt(((double) (((double) (a * a)) - ((double) (b * b))))))));
}
↓
double code(double a, double b) {
	return ((double) (a - ((double) sqrt(((double) (((double) (a * a)) - ((double) (b * b))))))));
}

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 38.7

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

  2. Final simplification38.7

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

Reproduce

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