(- (/ (- b) 2.0) (sqrt (- (/ (* b b) 4.0) c)))

Average Error: 29.6 → 29.6

Time: 1.4s

Precision: binary64

Math

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

↓

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

Error

Bits error versus b

Bits error versus c

Derivation

1. Initial program 29.6

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

2. Final simplification 29.6

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

Reproduce

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