Average Error: 0.2 → 0.1
Time: 49.6s
Precision: 64
Internal Precision: 384
\[0.954929658551372 \cdot x - 0.12900613773279798 \cdot \left(\left(x \cdot x\right) \cdot x\right)\]
↓
\[0.954929658551372 \cdot x - \left(\left(0.12900613773279798 \cdot x\right) \cdot x\right) \cdot x\]

Error

Bits error versus x

Derivation

  1. Initial program 0.2

    \[0.954929658551372 \cdot x - 0.12900613773279798 \cdot \left(\left(x \cdot x\right) \cdot x\right)\]
  2. Using strategy rm

  3. Applied associate-*r*0.1

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

  5. Applied associate-*r*0.1

    \[\leadsto 0.954929658551372 \cdot x - \color{blue}{\left(\left(0.12900613773279798 \cdot x\right) \cdot x\right)} \cdot x\]
  6. Removed slow pow expressions.

Runtime

Time bar (total: 49.6s)Debug log

herbie shell --seed '#(1889797285 268396849 4100589100 2067516092 3019009300 3748763710)' +o rules:numerics
(FPCore (x)
  :name "Rosa's Benchmark"
  (- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x))))