\(\left({\left(\sqrt[3]{(\left(1 - a \cdot 3\right) * \left({b}^2\right) + \left((a * a + a)_* \cdot a\right))_*}\right)}^3 \cdot 4 + (\left(\left(b \cdot 2\right) \cdot b\right) * \left(a \cdot a\right) + \left({a}^{4} + {b}^{4}\right))_*\right) - 1\)
- 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
- Applied taylor to get
\[\left({\left({a}^2 + {b}^2\right)}^2 + 4 \cdot \left({a}^2 \cdot \left(1 + a\right) + {b}^2 \cdot \left(1 - 3 \cdot a\right)\right)\right) - 1 \leadsto \left(\left({b}^{4} + \left(2 \cdot \left({b}^2 \cdot {a}^2\right) + {a}^{4}\right)\right) + 4 \cdot \left({a}^2 \cdot \left(1 + a\right) + {b}^2 \cdot \left(1 - 3 \cdot a\right)\right)\right) - 1\]
0.1
- Taylor expanded around inf to get
\[\left(\color{red}{\left({b}^{4} + \left(2 \cdot \left({b}^2 \cdot {a}^2\right) + {a}^{4}\right)\right)} + 4 \cdot \left({a}^2 \cdot \left(1 + a\right) + {b}^2 \cdot \left(1 - 3 \cdot a\right)\right)\right) - 1 \leadsto \left(\color{blue}{\left({b}^{4} + \left(2 \cdot \left({b}^2 \cdot {a}^2\right) + {a}^{4}\right)\right)} + 4 \cdot \left({a}^2 \cdot \left(1 + a\right) + {b}^2 \cdot \left(1 - 3 \cdot a\right)\right)\right) - 1\]
0.1
- Applied simplify to get
\[\color{red}{\left(\left({b}^{4} + \left(2 \cdot \left({b}^2 \cdot {a}^2\right) + {a}^{4}\right)\right) + 4 \cdot \left({a}^2 \cdot \left(1 + a\right) + {b}^2 \cdot \left(1 - 3 \cdot a\right)\right)\right) - 1} \leadsto \color{blue}{(\left((\left(1 - a \cdot 3\right) * \left({b}^2\right) + \left((a * a + a)_* \cdot a\right))_*\right) * 4 + \left((\left(\left(b \cdot 2\right) \cdot b\right) * \left(a \cdot a\right) + \left({a}^{4} + {b}^{4}\right))_*\right))_* - 1}\]
0.1
- Using strategy
rm 0.1
- Applied fma-udef to get
\[\color{red}{(\left((\left(1 - a \cdot 3\right) * \left({b}^2\right) + \left((a * a + a)_* \cdot a\right))_*\right) * 4 + \left((\left(\left(b \cdot 2\right) \cdot b\right) * \left(a \cdot a\right) + \left({a}^{4} + {b}^{4}\right))_*\right))_*} - 1 \leadsto \color{blue}{\left((\left(1 - a \cdot 3\right) * \left({b}^2\right) + \left((a * a + a)_* \cdot a\right))_* \cdot 4 + (\left(\left(b \cdot 2\right) \cdot b\right) * \left(a \cdot a\right) + \left({a}^{4} + {b}^{4}\right))_*\right)} - 1\]
0.1
- Using strategy
rm 0.1
- Applied add-cube-cbrt to get
\[\left(\color{red}{(\left(1 - a \cdot 3\right) * \left({b}^2\right) + \left((a * a + a)_* \cdot a\right))_*} \cdot 4 + (\left(\left(b \cdot 2\right) \cdot b\right) * \left(a \cdot a\right) + \left({a}^{4} + {b}^{4}\right))_*\right) - 1 \leadsto \left(\color{blue}{{\left(\sqrt[3]{(\left(1 - a \cdot 3\right) * \left({b}^2\right) + \left((a * a + a)_* \cdot a\right))_*}\right)}^3} \cdot 4 + (\left(\left(b \cdot 2\right) \cdot b\right) * \left(a \cdot a\right) + \left({a}^{4} + {b}^{4}\right))_*\right) - 1\]
0.2
