(/ (+ (- (- (- (pow x 3)) (* 9 (pow x 2))) (* 18 x)) 6) 6)

Average Error: 0.1 → 0.1

Time: 1.3s

Precision: binary64

Math

\[\frac{\left(\left(\left(-{x}^{3}\right) - 9 \cdot {x}^{2}\right) - 18 \cdot x\right) + 6}{6}\]

↓

\[\frac{\left(6 - \left({x}^{3} + 9 \cdot {x}^{2}\right)\right) - 18 \cdot x}{6}\]

Error

Bits error versus x

Derivation

1. Initial program 0.1

   \[\frac{\left(\left(\left(-{x}^{3}\right) - 9 \cdot {x}^{2}\right) - 18 \cdot x\right) + 6}{6}\]

2. Simplified 0.1

   \[\leadsto \color{blue}{\frac{\left(6 - \left({x}^{3} + 9 \cdot {x}^{2}\right)\right) - 18 \cdot x}{6}}\]

3. Final simplification 0.1

   \[\leadsto \frac{\left(6 - \left({x}^{3} + 9 \cdot {x}^{2}\right)\right) - 18 \cdot x}{6}\]

Reproduce

herbie shell --seed 2020153 
(FPCore (x)
  :name "(/ (+ (- (- (- (pow x 3)) (* 9 (pow x 2))) (* 18 x)) 6) 6)"
  :precision binary64
  (/ (+ (- (- (neg (pow x 3.0)) (* 9.0 (pow x 2.0))) (* 18.0 x)) 6.0) 6.0))