Average Error: 16.3 → 16.3
Time: 935.0ms
Precision: binary64
\[\sqrt{\left|\left(8 \cdot a + b \cdot b\right) - 4 \cdot c\right|}\]
↓
\[\sqrt{\left|\left(8 \cdot a + b \cdot b\right) - 4 \cdot c\right|}\]
\sqrt{\left|\left(8 \cdot a + b \cdot b\right) - 4 \cdot c\right|}
↓
\sqrt{\left|\left(8 \cdot a + b \cdot b\right) - 4 \cdot c\right|}
double code(double a, double b, double c) {
	return ((double) sqrt(((double) fabs(((double) (((double) (((double) (8.0 * a)) + ((double) (b * b)))) - ((double) (4.0 * c))))))));
}
↓
double code(double a, double b, double c) {
	return ((double) sqrt(((double) fabs(((double) (((double) (((double) (8.0 * a)) + ((double) (b * b)))) - ((double) (4.0 * c))))))));
}

Error

Bits error versus a

Bits error versus b

Bits error versus c

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 16.3

    \[\sqrt{\left|\left(8 \cdot a + b \cdot b\right) - 4 \cdot c\right|}\]

  2. Final simplification16.3

    \[\leadsto \sqrt{\left|\left(8 \cdot a + b \cdot b\right) - 4 \cdot c\right|}\]

Reproduce

herbie shell --seed 2020152 
(FPCore (a b c)
  :name "(sqrt (fabs (- (+ (* 8 a) (* b b)) (* 4 c))))"
  :precision binary64
  (sqrt (fabs (- (+ (* 8.0 a) (* b b)) (* 4.0 c)))))