Average Error: 0.1 → 0.1
Time: 20.0s
Precision: 64
Internal Precision: 576
\[0.954929658551372 \cdot x - 0.12900613773279798 \cdot \left(\left(x \cdot x\right) \cdot x\right)\]
\[(0.954929658551372 \cdot x + \left(\left(x \cdot x\right) \cdot \left(x \cdot \left(-0.12900613773279798\right)\right)\right))_*\]

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

    \[\leadsto (0.954929658551372 \cdot x + \color{blue}{\left({x}^{3} \cdot \left(-0.12900613773279798\right)\right)})_*\]
  5. Using strategy rm
  6. Applied unpow30.1

    \[\leadsto (0.954929658551372 \cdot x + \left(\color{blue}{\left(\left(x \cdot x\right) \cdot x\right)} \cdot \left(-0.12900613773279798\right)\right))_*\]
  7. Applied associate-*l*0.1

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

Runtime

Time bar (total: 20.0s)Debug logProfile

herbie shell --seed '#(1071215679 2002590028 935158157 1944352234 2656991306 2955288481)' +o rules:numerics
(FPCore (x)
  :name "Rosa's Benchmark"
  (- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x))))