Average Error: 22.3 → 22.3
Time: 1.7s
Precision: binary64
\[b + \frac{\frac{\sqrt{{b}^{2} - \left(4 \cdot a\right) \cdot c}}{2}}{a}\]
↓
\[b + \frac{\frac{\sqrt{{b}^{2} - \left(4 \cdot a\right) \cdot c}}{2}}{a}\]
b + \frac{\frac{\sqrt{{b}^{2} - \left(4 \cdot a\right) \cdot c}}{2}}{a}
↓
b + \frac{\frac{\sqrt{{b}^{2} - \left(4 \cdot a\right) \cdot c}}{2}}{a}
double code(double b, double a, double c) {
	return ((double) (b + ((double) (((double) (((double) sqrt(((double) (((double) pow(b, 2.0)) - ((double) (((double) (4.0 * a)) * c)))))) / 2.0)) / a))));
}
↓
double code(double b, double a, double c) {
	return ((double) (b + ((double) (((double) (((double) sqrt(((double) (((double) pow(b, 2.0)) - ((double) (((double) (4.0 * a)) * c)))))) / 2.0)) / a))));
}

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 22.3

    \[b + \frac{\frac{\sqrt{{b}^{2} - \left(4 \cdot a\right) \cdot c}}{2}}{a}\]

  2. Final simplification22.3

    \[\leadsto b + \frac{\frac{\sqrt{{b}^{2} - \left(4 \cdot a\right) \cdot c}}{2}}{a}\]

Reproduce

herbie shell --seed 2020153 
(FPCore (b a c)
  :name "(+ b (/ (/ (sqrt (- (pow b 2) (* (* 4 a) c))) 2) a))"
  :precision binary64
  (+ b (/ (/ (sqrt (- (pow b 2.0) (* (* 4.0 a) c))) 2.0) a)))