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

Average Error: 34.7 → 34.7

Time: 1.8s

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 34.7

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

2. Final simplification 34.7

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

Reproduce

herbie shell --seed 2020152 
(FPCore (b2 a c)
  :name "(/ (+ (- b2) (sqrt (- (* b2 b2) (* a c)))) a)"
  :precision binary64
  (/ (+ (neg b2) (sqrt (- (* b2 b2) (* a c)))) a))