(/ (- (- b2) (sqrt (- (* b2 b2) (* a c)))) a)

Average Error: 33.8 → 33.8

Time: 1.7s

Precision: binary64

Math

\[\frac{\left(-b2\right) - \sqrt{b2 \cdot b2 - a \cdot c}}{a}\]

↓

\[\frac{\left(-b2\right) - \sqrt{b2 \cdot b2 - a \cdot c}}{a}\]

Error

Bits error versus b2

Bits error versus a

Bits error versus c

Derivation

1. Initial program 33.8

   \[\frac{\left(-b2\right) - \sqrt{b2 \cdot b2 - a \cdot c}}{a}\]

2. Final simplification 33.8

   \[\leadsto \frac{\left(-b2\right) - \sqrt{b2 \cdot b2 - a \cdot c}}{a}\]

Reproduce

herbie shell --seed 2020153 
(FPCore (b2 a c)
  :name "(/ (- (- b2) (sqrt (- (* b2 b2) (* a c)))) a)"
  :precision binary64
  (/ (- (neg b2) (sqrt (- (* b2 b2) (* a c)))) a))