Average Error: 5.4 → 5.4
Time: 1.6s
Precision: binary64
\[b + \left|b\right| \cdot \sqrt{b \cdot b - a \cdot c}\]
↓
\[b + \left|b\right| \cdot \sqrt{b \cdot b - a \cdot c}\]
b + \left|b\right| \cdot \sqrt{b \cdot b - a \cdot c}
↓
b + \left|b\right| \cdot \sqrt{b \cdot b - a \cdot c}
double code(double b, double a, double c) {
	return ((double) (b + ((double) (((double) fabs(b)) * ((double) sqrt(((double) (((double) (b * b)) - ((double) (a * c))))))))));
}
↓
double code(double b, double a, double c) {
	return ((double) (b + ((double) (((double) fabs(b)) * ((double) sqrt(((double) (((double) (b * b)) - ((double) (a * c))))))))));
}

Error

Bits error versus b

Bits error versus a

Bits error versus c

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 5.4

    \[b + \left|b\right| \cdot \sqrt{b \cdot b - a \cdot c}\]

  2. Final simplification5.4

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

Reproduce

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