Error

Target

Derivation

1. Initial program 0.0

   \[x \cdot \left(x \cdot x\right) + x \cdot x\]
2. Using strategy rm

3. Applied *-un-lft-identity0.0

   \[\leadsto x \cdot \left(x \cdot x\right) + x \cdot \color{blue}{\left(1 \cdot x\right)}\]

4. Applied associate-*r*0.0

   \[\leadsto x \cdot \left(x \cdot x\right) + \color{blue}{\left(x \cdot 1\right) \cdot x}\]

5. Applied *-commutative0.0

   \[\leadsto x \cdot \color{blue}{\left(x \cdot x\right)} + \left(x \cdot 1\right) \cdot x\]

6. Applied associate-*r*0.0

   \[\leadsto \color{blue}{\left(x \cdot x\right) \cdot x} + \left(x \cdot 1\right) \cdot x\]

7. Applied distribute-rgt-out0.0

   \[\leadsto \color{blue}{x \cdot \left(x \cdot x + x \cdot 1\right)}\]

8. Simplified0.0

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

9. Final simplification0.0

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

Reproduce

herbie shell --seed 2019088 
(FPCore (x)
  :name "Expression 3, p15"
  :pre (<= 0 x 2)

  :herbie-target
  (* (* (+ 1.0 x) x) x)

  (+ (* x (* x x)) (* x x)))