Initial program 7.2
\[\left(x.re \cdot x.re - x.im \cdot x.im\right) \cdot x.re - \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.im\]
Applied simplify 7.2
\[\leadsto \color{blue}{x.re \cdot \left(\left({x.re}^2 - {x.im}^2\right) - \left({x.im}^2 + {x.im}^2\right)\right)}\]
- Using strategy
rm
Applied sub-neg 7.2
\[\leadsto x.re \cdot \left(\color{blue}{\left({x.re}^2 + \left(-{x.im}^2\right)\right)} - \left({x.im}^2 + {x.im}^2\right)\right)\]
Applied associate--l+ 7.2
\[\leadsto x.re \cdot \color{blue}{\left({x.re}^2 + \left(\left(-{x.im}^2\right) - \left({x.im}^2 + {x.im}^2\right)\right)\right)}\]
Applied distribute-lft-in 7.2
\[\leadsto \color{blue}{x.re \cdot {x.re}^2 + x.re \cdot \left(\left(-{x.im}^2\right) - \left({x.im}^2 + {x.im}^2\right)\right)}\]
Applied simplify 7.2
\[\leadsto \color{blue}{{x.re}^3} + x.re \cdot \left(\left(-{x.im}^2\right) - \left({x.im}^2 + {x.im}^2\right)\right)\]
Applied simplify 0.2
\[\leadsto {x.re}^3 + \color{blue}{\left(\left(-x.im\right) - \left(x.im + x.im\right)\right) \cdot \left(x.im \cdot x.re\right)}\]
- Using strategy
rm
Applied sum-double 0.2
\[\leadsto {x.re}^3 + \left(\left(-x.im\right) - \color{blue}{2 \cdot x.im}\right) \cdot \left(x.im \cdot x.re\right)\]
Applied neg-mul-1 0.2
\[\leadsto {x.re}^3 + \left(\color{blue}{-1 \cdot x.im} - 2 \cdot x.im\right) \cdot \left(x.im \cdot x.re\right)\]
Applied distribute-rgt-out-- 0.2
\[\leadsto {x.re}^3 + \color{blue}{\left(x.im \cdot \left(-1 - 2\right)\right)} \cdot \left(x.im \cdot x.re\right)\]
Applied associate-*l* 0.2
\[\leadsto {x.re}^3 + \color{blue}{x.im \cdot \left(\left(-1 - 2\right) \cdot \left(x.im \cdot x.re\right)\right)}\]
- Removed slow pow expressions
