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

Average Error: 33.5 → 33.5

Time: 1.6s

Precision: binary64

Math

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

↓

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

Error

Bits error versus b

Bits error versus a

Bits error versus c

Derivation

1. Initial program 33.5

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

2. Simplified 33.5

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

3. Final simplification 33.5

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

Reproduce

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