Initial program 3.6
\[\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2\]
- Using strategy
rm Applied add-cube-cbrt3.8
\[\leadsto \color{blue}{\left(\left(\sqrt[3]{a + \left(b + \left(c + d\right)\right)} \cdot \sqrt[3]{a + \left(b + \left(c + d\right)\right)}\right) \cdot \sqrt[3]{a + \left(b + \left(c + d\right)\right)}\right)} \cdot 2\]
- Using strategy
rm Applied *-un-lft-identity3.8
\[\leadsto \left(\left(\sqrt[3]{a + \left(b + \left(c + d\right)\right)} \cdot \color{blue}{\left(1 \cdot \sqrt[3]{a + \left(b + \left(c + d\right)\right)}\right)}\right) \cdot \sqrt[3]{a + \left(b + \left(c + d\right)\right)}\right) \cdot 2\]
Applied associate-*r*3.8
\[\leadsto \left(\color{blue}{\left(\left(\sqrt[3]{a + \left(b + \left(c + d\right)\right)} \cdot 1\right) \cdot \sqrt[3]{a + \left(b + \left(c + d\right)\right)}\right)} \cdot \sqrt[3]{a + \left(b + \left(c + d\right)\right)}\right) \cdot 2\]
Applied simplify3.3
\[\leadsto \left(\left(\color{blue}{\sqrt[3]{\left(b + c\right) + \left(a + d\right)}} \cdot \sqrt[3]{a + \left(b + \left(c + d\right)\right)}\right) \cdot \sqrt[3]{a + \left(b + \left(c + d\right)\right)}\right) \cdot 2\]
- Using strategy
rm Applied flip-+3.4
\[\leadsto \left(\left(\sqrt[3]{\left(b + c\right) + \left(a + d\right)} \cdot \sqrt[3]{\color{blue}{\frac{a \cdot a - \left(b + \left(c + d\right)\right) \cdot \left(b + \left(c + d\right)\right)}{a - \left(b + \left(c + d\right)\right)}}}\right) \cdot \sqrt[3]{a + \left(b + \left(c + d\right)\right)}\right) \cdot 2\]
Applied cbrt-div3.4
\[\leadsto \left(\left(\sqrt[3]{\left(b + c\right) + \left(a + d\right)} \cdot \color{blue}{\frac{\sqrt[3]{a \cdot a - \left(b + \left(c + d\right)\right) \cdot \left(b + \left(c + d\right)\right)}}{\sqrt[3]{a - \left(b + \left(c + d\right)\right)}}}\right) \cdot \sqrt[3]{a + \left(b + \left(c + d\right)\right)}\right) \cdot 2\]
Applied flip3-+3.4
\[\leadsto \left(\left(\sqrt[3]{\left(b + c\right) + \color{blue}{\frac{{a}^{3} + {d}^{3}}{a \cdot a + \left(d \cdot d - a \cdot d\right)}}} \cdot \frac{\sqrt[3]{a \cdot a - \left(b + \left(c + d\right)\right) \cdot \left(b + \left(c + d\right)\right)}}{\sqrt[3]{a - \left(b + \left(c + d\right)\right)}}\right) \cdot \sqrt[3]{a + \left(b + \left(c + d\right)\right)}\right) \cdot 2\]
Applied flip3-+3.4
\[\leadsto \left(\left(\sqrt[3]{\color{blue}{\frac{{b}^{3} + {c}^{3}}{b \cdot b + \left(c \cdot c - b \cdot c\right)}} + \frac{{a}^{3} + {d}^{3}}{a \cdot a + \left(d \cdot d - a \cdot d\right)}} \cdot \frac{\sqrt[3]{a \cdot a - \left(b + \left(c + d\right)\right) \cdot \left(b + \left(c + d\right)\right)}}{\sqrt[3]{a - \left(b + \left(c + d\right)\right)}}\right) \cdot \sqrt[3]{a + \left(b + \left(c + d\right)\right)}\right) \cdot 2\]
Applied frac-add3.4
\[\leadsto \left(\left(\sqrt[3]{\color{blue}{\frac{\left({b}^{3} + {c}^{3}\right) \cdot \left(a \cdot a + \left(d \cdot d - a \cdot d\right)\right) + \left(b \cdot b + \left(c \cdot c - b \cdot c\right)\right) \cdot \left({a}^{3} + {d}^{3}\right)}{\left(b \cdot b + \left(c \cdot c - b \cdot c\right)\right) \cdot \left(a \cdot a + \left(d \cdot d - a \cdot d\right)\right)}}} \cdot \frac{\sqrt[3]{a \cdot a - \left(b + \left(c + d\right)\right) \cdot \left(b + \left(c + d\right)\right)}}{\sqrt[3]{a - \left(b + \left(c + d\right)\right)}}\right) \cdot \sqrt[3]{a + \left(b + \left(c + d\right)\right)}\right) \cdot 2\]
Applied cbrt-div3.4
\[\leadsto \left(\left(\color{blue}{\frac{\sqrt[3]{\left({b}^{3} + {c}^{3}\right) \cdot \left(a \cdot a + \left(d \cdot d - a \cdot d\right)\right) + \left(b \cdot b + \left(c \cdot c - b \cdot c\right)\right) \cdot \left({a}^{3} + {d}^{3}\right)}}{\sqrt[3]{\left(b \cdot b + \left(c \cdot c - b \cdot c\right)\right) \cdot \left(a \cdot a + \left(d \cdot d - a \cdot d\right)\right)}}} \cdot \frac{\sqrt[3]{a \cdot a - \left(b + \left(c + d\right)\right) \cdot \left(b + \left(c + d\right)\right)}}{\sqrt[3]{a - \left(b + \left(c + d\right)\right)}}\right) \cdot \sqrt[3]{a + \left(b + \left(c + d\right)\right)}\right) \cdot 2\]
Applied frac-times3.4
\[\leadsto \left(\color{blue}{\frac{\sqrt[3]{\left({b}^{3} + {c}^{3}\right) \cdot \left(a \cdot a + \left(d \cdot d - a \cdot d\right)\right) + \left(b \cdot b + \left(c \cdot c - b \cdot c\right)\right) \cdot \left({a}^{3} + {d}^{3}\right)} \cdot \sqrt[3]{a \cdot a - \left(b + \left(c + d\right)\right) \cdot \left(b + \left(c + d\right)\right)}}{\sqrt[3]{\left(b \cdot b + \left(c \cdot c - b \cdot c\right)\right) \cdot \left(a \cdot a + \left(d \cdot d - a \cdot d\right)\right)} \cdot \sqrt[3]{a - \left(b + \left(c + d\right)\right)}}} \cdot \sqrt[3]{a + \left(b + \left(c + d\right)\right)}\right) \cdot 2\]
Applied simplify2.7
\[\leadsto \left(\frac{\color{blue}{\sqrt[3]{\left(\left(a - c\right) - \left(d + b\right)\right) \cdot \left(\left(a + d\right) + \left(b + c\right)\right)} \cdot \sqrt[3]{\left(\left(d - a\right) \cdot d + a \cdot a\right) \cdot \left({c}^{3} + {b}^{3}\right) + \left({d}^{3} + {a}^{3}\right) \cdot \left(c \cdot c - b \cdot \left(c - b\right)\right)}}}{\sqrt[3]{\left(b \cdot b + \left(c \cdot c - b \cdot c\right)\right) \cdot \left(a \cdot a + \left(d \cdot d - a \cdot d\right)\right)} \cdot \sqrt[3]{a - \left(b + \left(c + d\right)\right)}} \cdot \sqrt[3]{a + \left(b + \left(c + d\right)\right)}\right) \cdot 2\]
Applied simplify2.7
\[\leadsto \left(\frac{\sqrt[3]{\left(\left(a - c\right) - \left(d + b\right)\right) \cdot \left(\left(a + d\right) + \left(b + c\right)\right)} \cdot \sqrt[3]{\left(\left(d - a\right) \cdot d + a \cdot a\right) \cdot \left({c}^{3} + {b}^{3}\right) + \left({d}^{3} + {a}^{3}\right) \cdot \left(c \cdot c - b \cdot \left(c - b\right)\right)}}{\color{blue}{\sqrt[3]{\left(a \cdot a + \left(d - a\right) \cdot d\right) \cdot \left(b \cdot b + c \cdot \left(c - b\right)\right)} \cdot \sqrt[3]{\left(a - b\right) - \left(c + d\right)}}} \cdot \sqrt[3]{a + \left(b + \left(c + d\right)\right)}\right) \cdot 2\]
- Removed slow
pow expressions.
