Average Error: 0.1 → 0.1
Time: 9.0s
Precision: 64
Internal Precision: 128
\[0.954929658551372 \cdot x - 0.12900613773279798 \cdot \left(\left(x \cdot x\right) \cdot x\right)\]
↓
\[0.954929658551372 \cdot x - \left(x \cdot x\right) \cdot \left(x \cdot 0.12900613773279798\right)\]

Error

Bits error versus x

Derivation

  1. Initial program 0.1

    \[0.954929658551372 \cdot x - 0.12900613773279798 \cdot \left(\left(x \cdot x\right) \cdot x\right)\]

  2. Taylor expanded around -inf 0.1

    \[\leadsto 0.954929658551372 \cdot x - \color{blue}{0.12900613773279798 \cdot {x}^{3}}\]

  3. Simplified0.1

    \[\leadsto 0.954929658551372 \cdot x - \color{blue}{\left(x \cdot x\right) \cdot \left(0.12900613773279798 \cdot x\right)}\]

  4. Final simplification0.1

    \[\leadsto 0.954929658551372 \cdot x - \left(x \cdot x\right) \cdot \left(x \cdot 0.12900613773279798\right)\]

Reproduce

herbie shell --seed 2019068 
(FPCore (x)
  :name "Rosa's Benchmark"
  (- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x))))