Average Error: 39.0 → 0.0
Time: 3.7s
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

Try it out

  1. Inputs

  2. Original Output:

    Herbie Output:

Derivation

  1. Initial program 39.0

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

  2. Applied simplify0.0

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

  3. Taylor expanded around 0 0.0

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

  4. Applied simplify0.0

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

Runtime

Time bar (total: 3.7s)Debug logProfile

herbie shell --seed '#(1072361757 3390613284 2339397988 1175251238 145061547 3101881848)' 
(FPCore (x)
  :name "Expanding a square"
  (- (* (+ x 1) (+ x 1)) 1))