Error

Derivation

1. Initial program 0.2

   \[\frac{\left(re \cdot im\right)}{\left(im \cdot re\right)}\]

2. Simplified0.2

   \[\leadsto \color{blue}{\frac{\left(im \cdot re\right)}{\left(im \cdot re\right)}}\]
3. Using strategy rm

4. Applied *-commutative0.2

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

5. Applied *-commutative0.2

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

6. Applied distribute-rgt-out0.1

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

7. Final simplification0.1

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

Reproduce

herbie shell --seed 2019072 
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  (+.p16 (*.p16 re im) (*.p16 im re)))