(- (- (+ (- 0.00225844) (* 0.0179275 x)) (* 2.1306e-05 (pow x 2))) (* 6.05391e-07 (pow x 3)))

Average Error: 0.4 → 0.4

Time: 1.4s

Precision: binary64

Math

\[\left(\left(\left(-0.00225844000000000001\right) + 0.017927499999999999 \cdot x\right) - 2.1305999999999999 \cdot 10^{-5} \cdot {x}^{2}\right) - 6.05391000000000024 \cdot 10^{-7} \cdot {x}^{3}\]

↓

\[\left(\left(\left(-0.00225844000000000001\right) + 0.017927499999999999 \cdot x\right) - 2.1305999999999999 \cdot 10^{-5} \cdot {x}^{2}\right) - 6.05391000000000024 \cdot 10^{-7} \cdot {x}^{3}\]

Error

Bits error versus x

Derivation

1. Initial program 0.4

   \[\left(\left(\left(-0.00225844000000000001\right) + 0.017927499999999999 \cdot x\right) - 2.1305999999999999 \cdot 10^{-5} \cdot {x}^{2}\right) - 6.05391000000000024 \cdot 10^{-7} \cdot {x}^{3}\]

2. Final simplification 0.4

   \[\leadsto \left(\left(\left(-0.00225844000000000001\right) + 0.017927499999999999 \cdot x\right) - 2.1305999999999999 \cdot 10^{-5} \cdot {x}^{2}\right) - 6.05391000000000024 \cdot 10^{-7} \cdot {x}^{3}\]

Reproduce

herbie shell --seed 2020152 
(FPCore (x)
  :name "(- (- (+ (- 0.00225844) (* 0.0179275 x)) (* 2.1306e-05 (pow x 2))) (* 6.05391e-07 (pow x 3)))"
  :precision binary64
  (- (- (+ (neg 0.00225844) (* 0.0179275 x)) (* 2.1306e-05 (pow x 2.0))) (* 6.05391e-07 (pow x 3.0))))