Initial program 0.2
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(b \cdot b\right)\right) - 1\]
- Using strategy
rm Applied add-cube-cbrt0.7
\[\leadsto \left({\color{blue}{\left(\left(\sqrt[3]{a \cdot a + b \cdot b} \cdot \sqrt[3]{a \cdot a + b \cdot b}\right) \cdot \sqrt[3]{a \cdot a + b \cdot b}\right)}}^{2} + 4 \cdot \left(b \cdot b\right)\right) - 1\]
Applied unpow-prod-down0.7
\[\leadsto \left(\color{blue}{{\left(\sqrt[3]{a \cdot a + b \cdot b} \cdot \sqrt[3]{a \cdot a + b \cdot b}\right)}^{2} \cdot {\left(\sqrt[3]{a \cdot a + b \cdot b}\right)}^{2}} + 4 \cdot \left(b \cdot b\right)\right) - 1\]
Applied simplify0.5
\[\leadsto \left(\color{blue}{\left(\left(b \cdot b + a \cdot a\right) \cdot \sqrt[3]{b \cdot b + a \cdot a}\right)} \cdot {\left(\sqrt[3]{a \cdot a + b \cdot b}\right)}^{2} + 4 \cdot \left(b \cdot b\right)\right) - 1\]
- Using strategy
rm Applied add-sqr-sqrt0.5
\[\leadsto \left(\left(\left(b \cdot b + a \cdot a\right) \cdot \sqrt[3]{\color{blue}{\sqrt{b \cdot b + a \cdot a} \cdot \sqrt{b \cdot b + a \cdot a}}}\right) \cdot {\left(\sqrt[3]{a \cdot a + b \cdot b}\right)}^{2} + 4 \cdot \left(b \cdot b\right)\right) - 1\]
Applied cbrt-prod0.5
\[\leadsto \left(\left(\left(b \cdot b + a \cdot a\right) \cdot \color{blue}{\left(\sqrt[3]{\sqrt{b \cdot b + a \cdot a}} \cdot \sqrt[3]{\sqrt{b \cdot b + a \cdot a}}\right)}\right) \cdot {\left(\sqrt[3]{a \cdot a + b \cdot b}\right)}^{2} + 4 \cdot \left(b \cdot b\right)\right) - 1\]
Applied associate-*r*0.5
\[\leadsto \left(\color{blue}{\left(\left(\left(b \cdot b + a \cdot a\right) \cdot \sqrt[3]{\sqrt{b \cdot b + a \cdot a}}\right) \cdot \sqrt[3]{\sqrt{b \cdot b + a \cdot a}}\right)} \cdot {\left(\sqrt[3]{a \cdot a + b \cdot b}\right)}^{2} + 4 \cdot \left(b \cdot b\right)\right) - 1\]
