Average Error: 0.1 → 0.1
Time: 9.3s
Precision: 64
Internal Precision: 576
\[0.954929658551372 \cdot x - 0.12900613773279798 \cdot \left(\left(x \cdot x\right) \cdot x\right)\]
↓
\[0.954929658551372 \cdot x - 0.12900613773279798 \cdot {x}^{3}\]

Error

Bits error versus x

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Results

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Derivation

  1. Initial program 0.1

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

  2. Initial simplification0.1

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

  3. Taylor expanded around 0 0.1

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

  4. Final simplification0.1

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

Runtime

Time bar (total: 9.3s)Debug logProfile

herbie shell --seed 2018216 
(FPCore (x)
  :name "Rosa's Benchmark"
  (- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x))))