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

Average Error: 22.3 → 22.3

Time: 1.4s

Precision: binary64

Math

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

↓

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

Error

Bits error versus b

Bits error versus a

Bits error versus c

Derivation

1. Initial program 22.3

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

2. Simplified 22.3

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

3. Final simplification 22.3

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

Reproduce

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