Average Error: 38.9 → 0.0
Time: 2.8s
Precision: 64
Internal Precision: 1344
\[\left(x + 1\right) \cdot \left(x + 1\right) - 1\]
↓
\[(x \cdot x + x)_* + x\]

Error

Bits error versus x

Derivation

  1. Initial program 38.9

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

  2. Initial simplification0.0

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

  3. Final simplification0.0

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

Runtime

Time bar (total: 2.8s)Debug logProfile

herbie shell --seed 2018227 +o rules:numerics
(FPCore (x)
  :name "Expanding a square"
  (- (* (+ x 1) (+ x 1)) 1))