\((\left((a * a + \left({b}^2\right))_*\right) * \left((a * a + \left({b}^2\right))_*\right) + \left(4 \cdot \left((a * \left((a * a + a)_*\right) + \left({b}^2\right))_* - {b}^2 \cdot \left(a \cdot 3\right)\right)\right))_* - 1\)
- Started with
\[\left({\left({a}^2 + {b}^2\right)}^2 + 4 \cdot \left({a}^2 \cdot \left(1 + a\right) + {b}^2 \cdot \left(1 - 3 \cdot a\right)\right)\right) - 1\]
0.2
- Using strategy
rm 0.2
- Applied square-mult to get
\[\left(\color{red}{{\left({a}^2 + {b}^2\right)}^2} + 4 \cdot \left({a}^2 \cdot \left(1 + a\right) + {b}^2 \cdot \left(1 - 3 \cdot a\right)\right)\right) - 1 \leadsto \left(\color{blue}{\left({a}^2 + {b}^2\right) \cdot \left({a}^2 + {b}^2\right)} + 4 \cdot \left({a}^2 \cdot \left(1 + a\right) + {b}^2 \cdot \left(1 - 3 \cdot a\right)\right)\right) - 1\]
0.2
- Applied fma-def to get
\[\color{red}{\left(\left({a}^2 + {b}^2\right) \cdot \left({a}^2 + {b}^2\right) + 4 \cdot \left({a}^2 \cdot \left(1 + a\right) + {b}^2 \cdot \left(1 - 3 \cdot a\right)\right)\right)} - 1 \leadsto \color{blue}{(\left({a}^2 + {b}^2\right) * \left({a}^2 + {b}^2\right) + \left(4 \cdot \left({a}^2 \cdot \left(1 + a\right) + {b}^2 \cdot \left(1 - 3 \cdot a\right)\right)\right))_*} - 1\]
0.2
- Applied taylor to get
\[(\left({a}^2 + {b}^2\right) * \left({a}^2 + {b}^2\right) + \left(4 \cdot \left({a}^2 \cdot \left(1 + a\right) + {b}^2 \cdot \left(1 - 3 \cdot a\right)\right)\right))_* - 1 \leadsto (\left({b}^2 + {a}^2\right) * \left({b}^2 + {a}^2\right) + \left(4 \cdot \left(\left({a}^{3} + \left({b}^2 + {a}^2\right)\right) - 3 \cdot \left({b}^2 \cdot a\right)\right)\right))_* - 1\]
0.2
- Taylor expanded around 0 to get
\[\color{red}{(\left({b}^2 + {a}^2\right) * \left({b}^2 + {a}^2\right) + \left(4 \cdot \left(\left({a}^{3} + \left({b}^2 + {a}^2\right)\right) - 3 \cdot \left({b}^2 \cdot a\right)\right)\right))_*} - 1 \leadsto \color{blue}{(\left({b}^2 + {a}^2\right) * \left({b}^2 + {a}^2\right) + \left(4 \cdot \left(\left({a}^{3} + \left({b}^2 + {a}^2\right)\right) - 3 \cdot \left({b}^2 \cdot a\right)\right)\right))_*} - 1\]
0.2
- Applied simplify to get
\[\color{red}{(\left({b}^2 + {a}^2\right) * \left({b}^2 + {a}^2\right) + \left(4 \cdot \left(\left({a}^{3} + \left({b}^2 + {a}^2\right)\right) - 3 \cdot \left({b}^2 \cdot a\right)\right)\right))_* - 1} \leadsto \color{blue}{(\left((a * a + \left({b}^2\right))_*\right) * \left((a * a + \left({b}^2\right))_*\right) + \left(4 \cdot \left((a * \left((a * a + a)_*\right) + \left({b}^2\right))_* - {b}^2 \cdot \left(a \cdot 3\right)\right)\right))_* - 1}\]
0.2
