Error

Derivation

1. Initial program 6.6

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

2. Applied simplify6.6

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

4. Applied sub-neg6.6

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

5. Applied distribute-lft-in6.6

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

6. Applied associate--l+6.6

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

7. Applied distribute-lft-in6.6

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

8. Applied simplify0.2

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

Runtime

Time bar (total: 2.3m)Debug logProfile

herbie shell --seed '#(1072361757 3390613284 2339397988 1175251238 145061547 3101881848)' 
(FPCore (x.re x.im)
  :name "math.cube on complex, real part"
  (- (* (- (* x.re x.re) (* x.im x.im)) x.re) (* (+ (* x.re x.im) (* x.im x.re)) x.im)))