(- (exp2 x) (* (* (* (sqrt x) (sqrt x)) (sqrt x)) (sqrt x)))

Average Error: 0.0 → 0.0

Time: 1.8s

Precision: binary64

Math

\[2^{x} - \left(\left(\sqrt{x} \cdot \sqrt{x}\right) \cdot \sqrt{x}\right) \cdot \sqrt{x}\]

↓

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

Error

Bits error versus x

Derivation

1. Initial program 0.0

   \[2^{x} - \left(\left(\sqrt{x} \cdot \sqrt{x}\right) \cdot \sqrt{x}\right) \cdot \sqrt{x}\]

2. Simplified 0.0

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

3. Final simplification 0.0

   \[\leadsto 2^{x} + \left(-x \cdot x\right)\]

Reproduce

herbie shell --seed 2020152 
(FPCore (x)
  :name "(- (exp2 x) (* (* (* (sqrt x) (sqrt x)) (sqrt x)) (sqrt x)))"
  :precision binary64
  (- (exp2 x) (* (* (* (sqrt x) (sqrt x)) (sqrt x)) (sqrt x))))