Average Error: 0.1 → 0.1
Time: 25.5s
Precision: 64
Internal Precision: 576
\[0.954929658551372 \cdot x - 0.12900613773279798 \cdot \left(\left(x \cdot x\right) \cdot x\right)\]
↓
\[x \cdot \left(\left(x \cdot x\right) \cdot \left(-0.12900613773279798\right)\right) + x \cdot 0.954929658551372\]

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

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

  2. Applied simplify0.1

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

  4. Applied fma-udef0.1

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

  6. Applied cube-mult0.1

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

  7. Applied associate-*l*0.1

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

Runtime

Time bar (total: 25.5s)Debug logProfile

herbie shell --seed 2018195 +o rules:numerics
(FPCore (x)
  :name "Rosa's Benchmark"
  (- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x))))