Average Error: 0.1 → 0.1

Time: 33.5s

Precision: 64

Internal Precision: 128

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

↓

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

Error

The X axis uses an exponential scale — Bits error versus `x`

Derivation

Initial program 0.1
\[0.954929658551372 \cdot x - 0.12900613773279798 \cdot \left(\left(x \cdot x\right) \cdot x\right)\]
Simplified0.1
\[\leadsto \color{blue}{\left(0.954929658551372 - \left(0.12900613773279798 \cdot x\right) \cdot x\right) \cdot x}\]
Final simplification0.1
\[\leadsto x \cdot \left(0.954929658551372 - x \cdot \left(x \cdot 0.12900613773279798\right)\right)\]

Reproduce

herbie shell --seed 2019089 +o rules:numerics
(FPCore (x)
  :name "Rosa's Benchmark"
  (- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x))))