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

Average Error: 34.2 → 34.2

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 34.2

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

2. Final simplification 34.2

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

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))