Average Error: 34.7 → 34.7
Time: 1.9s
Precision: binary64
\[\frac{\sqrt{\frac{b \cdot b}{4} - a \cdot c} - \frac{b}{2}}{a}\]
↓
\[\frac{\sqrt{\frac{b \cdot b}{4} - a \cdot c} - \frac{b}{2}}{a}\]
\frac{\sqrt{\frac{b \cdot b}{4} - a \cdot c} - \frac{b}{2}}{a}
↓
\frac{\sqrt{\frac{b \cdot b}{4} - a \cdot c} - \frac{b}{2}}{a}
double code(double b, double a, double c) {
	return ((double) (((double) (((double) sqrt(((double) (((double) (((double) (b * b)) / 4.0)) - ((double) (a * c)))))) - ((double) (b / 2.0)))) / a));
}
↓
double code(double b, double a, double c) {
	return ((double) (((double) (((double) sqrt(((double) (((double) (((double) (b * b)) / 4.0)) - ((double) (a * c)))))) - ((double) (b / 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 34.7

    \[\frac{\sqrt{\frac{b \cdot b}{4} - a \cdot c} - \frac{b}{2}}{a}\]

  2. Final simplification34.7

    \[\leadsto \frac{\sqrt{\frac{b \cdot b}{4} - a \cdot c} - \frac{b}{2}}{a}\]

Reproduce

herbie shell --seed 2020152 
(FPCore (b a c)
  :name "(/ (- (sqrt (- (/ (* b b) 4) (* a c))) (/ b 2)) a)"
  :precision binary64
  (/ (- (sqrt (- (/ (* b b) 4.0) (* a c))) (/ b 2.0)) a))