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

Average Error: 33.8 → 33.8

Time: 1.9s

Precision: binary64

Math

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

↓

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

Error

Bits error versus b

Bits error versus a

Bits error versus c

Derivation

1. Initial program 33.8

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

2. Final simplification 33.8

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

Reproduce

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