Initial program 0.2
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(b \cdot b\right)\right) - 1\]
Simplified0.2
\[\leadsto \color{blue}{(\left((a \cdot a + \left(b \cdot b\right))_*\right) \cdot \left((a \cdot a + \left(b \cdot b\right))_*\right) + \left((4 \cdot \left(b \cdot b\right) + -1)_*\right))_*}\]
- Using strategy
rm Applied fma-udef0.2
\[\leadsto \color{blue}{(a \cdot a + \left(b \cdot b\right))_* \cdot (a \cdot a + \left(b \cdot b\right))_* + (4 \cdot \left(b \cdot b\right) + -1)_*}\]
Taylor expanded around inf 0.0
\[\leadsto \color{blue}{\left({b}^{4} + \left({a}^{4} + 2 \cdot \left({a}^{2} \cdot {b}^{2}\right)\right)\right)} + (4 \cdot \left(b \cdot b\right) + -1)_*\]
Simplified0.0
\[\leadsto \color{blue}{\left((2 \cdot \left(\left(a \cdot b\right) \cdot \left(a \cdot b\right)\right) + \left({b}^{4}\right))_* + {a}^{4}\right)} + (4 \cdot \left(b \cdot b\right) + -1)_*\]
Final simplification0.0
\[\leadsto (4 \cdot \left(b \cdot b\right) + -1)_* + \left((2 \cdot \left(\left(b \cdot a\right) \cdot \left(b \cdot a\right)\right) + \left({b}^{4}\right))_* + {a}^{4}\right)\]
