Initial program 6.8
\[\left(x.re \cdot x.re - x.im \cdot x.im\right) \cdot x.im + \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.re\]
Applied simplify0.2
\[\leadsto \color{blue}{(\left(x.re - x.im\right) \cdot \left(\left(x.re + x.im\right) \cdot x.im\right) + \left(\left(x.re + x.re\right) \cdot \left(x.re \cdot x.im\right)\right))_*}\]
Taylor expanded around 0 6.7
\[\leadsto \color{blue}{3 \cdot \left({x.re}^{2} \cdot x.im\right) - {x.im}^{3}}\]
- Using strategy
rm Applied add-cube-cbrt7.1
\[\leadsto 3 \cdot \left({x.re}^{2} \cdot x.im\right) - \color{blue}{\left(\sqrt[3]{{x.im}^{3}} \cdot \sqrt[3]{{x.im}^{3}}\right) \cdot \sqrt[3]{{x.im}^{3}}}\]
Applied prod-diff7.1
\[\leadsto \color{blue}{(3 \cdot \left({x.re}^{2} \cdot x.im\right) + \left(-\sqrt[3]{{x.im}^{3}} \cdot \left(\sqrt[3]{{x.im}^{3}} \cdot \sqrt[3]{{x.im}^{3}}\right)\right))_* + (\left(-\sqrt[3]{{x.im}^{3}}\right) \cdot \left(\sqrt[3]{{x.im}^{3}} \cdot \sqrt[3]{{x.im}^{3}}\right) + \left(\sqrt[3]{{x.im}^{3}} \cdot \left(\sqrt[3]{{x.im}^{3}} \cdot \sqrt[3]{{x.im}^{3}}\right)\right))_*}\]
Applied simplify0.2
\[\leadsto \color{blue}{(x.re \cdot \left(\left(x.re \cdot x.im\right) \cdot 3\right) + \left(\left(-x.im\right) \cdot \left(x.im \cdot x.im\right)\right))_*} + (\left(-\sqrt[3]{{x.im}^{3}}\right) \cdot \left(\sqrt[3]{{x.im}^{3}} \cdot \sqrt[3]{{x.im}^{3}}\right) + \left(\sqrt[3]{{x.im}^{3}} \cdot \left(\sqrt[3]{{x.im}^{3}} \cdot \sqrt[3]{{x.im}^{3}}\right)\right))_*\]
Applied simplify0.2
\[\leadsto (x.re \cdot \left(\left(x.re \cdot x.im\right) \cdot 3\right) + \left(\left(-x.im\right) \cdot \left(x.im \cdot x.im\right)\right))_* + \color{blue}{0}\]
