(- (+ (* (- 3) (* x x)) (* 2.87 x)) 0.275)

Average Error: 0.1 → 0.1

Time: 797.0ms

Precision: binary64

Math

\[\left(\left(-3\right) \cdot \left(x \cdot x\right) + 2.8700000000000001 \cdot x\right) - 0.27500000000000002\]

↓

\[x \cdot \left(2.8700000000000001 - 3 \cdot x\right) - 0.27500000000000002\]

Error

Bits error versus x

Derivation

1. Initial program 0.1

   \[\left(\left(-3\right) \cdot \left(x \cdot x\right) + 2.8700000000000001 \cdot x\right) - 0.27500000000000002\]

2. Simplified 0.1

   \[\leadsto \color{blue}{x \cdot \left(2.8700000000000001 - 3 \cdot x\right) - 0.27500000000000002}\]

3. Final simplification 0.1

   \[\leadsto x \cdot \left(2.8700000000000001 - 3 \cdot x\right) - 0.27500000000000002\]

Reproduce

herbie shell --seed 2020153 
(FPCore (x)
  :name "(- (+ (* (- 3) (* x x)) (* 2.87 x)) 0.275)"
  :precision binary64
  (- (+ (* (neg 3.0) (* x x)) (* 2.87 x)) 0.275))