Average Error: 0.1 → 0.1
Time: 1.2m
Precision: 64
Internal Precision: 128
\[0.954929658551372 \cdot x - 0.12900613773279798 \cdot \left(\left(x \cdot x\right) \cdot x\right)\]
↓
\[x \cdot \left(0.954929658551372 - \left(x \cdot x\right) \cdot 0.12900613773279798\right)\]

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. Simplified0.1

    \[\leadsto \color{blue}{\left(0.954929658551372 - \left(0.12900613773279798 \cdot x\right) \cdot x\right) \cdot x}\]
  3. Using strategy rm

  4. Applied associate-*l*0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2019088 +o rules:numerics
(FPCore (x)
  :name "Rosa's Benchmark"
  (- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x))))