(- (- b) (sqrt (- (pow b 2) (* (* 4 a) c))))

Average Error: 33.3 → 33.3

Time: 2.1s

Precision: binary64

Math

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

↓

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

Error

Bits error versus b

Bits error versus a

Bits error versus c

Derivation

1. Initial program 33.3

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

2. Final simplification 33.3

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

Reproduce

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