(+ (- 2) (* (* 2 x) x))

Average Error: 0.0 → 0.0

Time: 589.0ms

Precision: binary64

Math

\[\left(-2\right) + \left(2 \cdot x\right) \cdot x\]

↓

\[\left(2 \cdot x\right) \cdot x - 2\]

Error

Bits error versus x

Derivation

1. Initial program 0.0

   \[\left(-2\right) + \left(2 \cdot x\right) \cdot x\]

2. Simplified 0.0

   \[\leadsto \color{blue}{\left(2 \cdot x\right) \cdot x - 2}\]

3. Final simplification 0.0

   \[\leadsto \left(2 \cdot x\right) \cdot x - 2\]

Reproduce

herbie shell --seed 2020153 
(FPCore (x)
  :name "(+ (- 2) (* (* 2 x) x))"
  :precision binary64
  (+ (neg 2.0) (* (* 2.0 x) x)))