Average Error: 0.1 → 0.1
Time: 19.8s
Precision: 64
Internal Precision: 576
\[0.954929658551372 \cdot x - 0.12900613773279798 \cdot \left(\left(x \cdot x\right) \cdot x\right)\]
↓
\[(0.954929658551372 \cdot x + \left({x}^{3} \cdot \left(-0.12900613773279798\right)\right))_*\]

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. Using strategy rm

  3. Applied fma-neg0.1

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

  4. Applied simplify0.1

    \[\leadsto (0.954929658551372 \cdot x + \color{blue}{\left({x}^{3} \cdot \left(-0.12900613773279798\right)\right)})_*\]

Runtime

Time bar (total: 19.8s)Debug logProfile

herbie shell --seed '#(1072330854 3074818769 591214268 3603999196 3863745332 3332387116)' +o rules:numerics
(FPCore (x)
  :name "Rosa's Benchmark"
  (- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x))))