Error

Derivation

1. Initial program 0.0

   \[re \cdot re - im \cdot im\]
2. Using strategy rm

3. Applied *-commutative0.0

   \[\leadsto re \cdot re - \color{blue}{im \cdot im}\]

4. Applied *-commutative0.0

   \[\leadsto \color{blue}{re \cdot re} - im \cdot im\]

5. Applied difference-of-squares0.0

   \[\leadsto \color{blue}{\left(re + im\right) \cdot \left(re - im\right)}\]

6. Final simplification0.0

   \[\leadsto \left(im + re\right) \cdot \left(re - im\right)\]

Reproduce

herbie shell --seed 2019072 +o rules:numerics
(FPCore (re im)
  :name "math.square on complex, real part"
  (- (* re re) (* im im)))