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

Average Error: 30.3 → 30.3

Time: 1.6s

Precision: binary64

Math

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

↓

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

Error

Bits error versus b

Bits error versus c

Derivation

1. Initial program 30.3

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

2. Final simplification 30.3

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

Reproduce

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