Average Error: 38.7 → 0.0
Time: 27.2s
Precision: 64
Internal Precision: 1344
\[\left(x + 1\right) \cdot \left(x + 1\right) - 1\]
↓
\[x \cdot \left(2 + x\right)\]

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 38.7

    \[\left(x + 1\right) \cdot \left(x + 1\right) - 1\]

  2. Initial simplification0.0

    \[\leadsto x + (x \cdot x + x)_*\]

  3. Taylor expanded around 0 0.0

    \[\leadsto \color{blue}{2 \cdot x + {x}^{2}}\]

  4. Simplified0.0

    \[\leadsto \color{blue}{\left(x + 2\right) \cdot x}\]

  5. Final simplification0.0

    \[\leadsto x \cdot \left(2 + x\right)\]

Runtime

Time bar (total: 27.2s)Debug logProfile

herbie shell --seed 2018230 +o rules:numerics
(FPCore (x)
  :name "Expanding a square"
  (- (* (+ x 1) (+ x 1)) 1))