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

Average Error: 16.3 → 16.3

Time: 1.4s

Precision: binary64

Math

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

↓

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

Error

Bits error versus b

Bits error versus ac

Bits error versus a

Derivation

1. Initial program 16.3

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

2. Simplified 16.3

   \[\leadsto \color{blue}{\frac{\sqrt{b \cdot b - 4 \cdot ac}}{2 \cdot a} - b}\]

3. Final simplification 16.3

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

Reproduce

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