- Started with
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
3.3
- Using strategy
rm 3.3
- Applied add-cbrt-cube to get
\[\color{red}{\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}} \leadsto \color{blue}{\sqrt[3]{{\left(\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\right)}^3}}\]
15.7
- Applied taylor to get
\[\sqrt[3]{{\left(\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\right)}^3} \leadsto \sqrt[3]{{\left(\frac{230661.510616 \cdot y + \left({y}^{3} \cdot z + \left(t + \left({y}^{4} \cdot x + 27464.7644705 \cdot {y}^2\right)\right)\right)}{{y}^{3} \cdot a + \left(y \cdot c + \left({y}^{4} + \left(i + {y}^2 \cdot b\right)\right)\right)}\right)}^3}\]
15.0
- Taylor expanded around 0 to get
\[\sqrt[3]{\color{red}{{\left(\frac{230661.510616 \cdot y + \left({y}^{3} \cdot z + \left(t + \left({y}^{4} \cdot x + 27464.7644705 \cdot {y}^2\right)\right)\right)}{{y}^{3} \cdot a + \left(y \cdot c + \left({y}^{4} + \left(i + {y}^2 \cdot b\right)\right)\right)}\right)}^3}} \leadsto \sqrt[3]{\color{blue}{{\left(\frac{230661.510616 \cdot y + \left({y}^{3} \cdot z + \left(t + \left({y}^{4} \cdot x + 27464.7644705 \cdot {y}^2\right)\right)\right)}{{y}^{3} \cdot a + \left(y \cdot c + \left({y}^{4} + \left(i + {y}^2 \cdot b\right)\right)\right)}\right)}^3}}\]
15.0
- Applied simplify to get
\[\sqrt[3]{{\left(\frac{230661.510616 \cdot y + \left({y}^{3} \cdot z + \left(t + \left({y}^{4} \cdot x + 27464.7644705 \cdot {y}^2\right)\right)\right)}{{y}^{3} \cdot a + \left(y \cdot c + \left({y}^{4} + \left(i + {y}^2 \cdot b\right)\right)\right)}\right)}^3} \leadsto \frac{\left(\left(27464.7644705 \cdot y\right) \cdot y + \left({y}^{4} \cdot x + t\right)\right) + \left(y \cdot 230661.510616 + {y}^3 \cdot z\right)}{\left(c \cdot y + {y}^3 \cdot a\right) + \left(b \cdot \left(y \cdot y\right) + \left({y}^{4} + i\right)\right)}\]
2.8
- Applied final simplification
- Applied simplify to get
\[\color{red}{\frac{\left(\left(27464.7644705 \cdot y\right) \cdot y + \left({y}^{4} \cdot x + t\right)\right) + \left(y \cdot 230661.510616 + {y}^3 \cdot z\right)}{\left(c \cdot y + {y}^3 \cdot a\right) + \left(b \cdot \left(y \cdot y\right) + \left({y}^{4} + i\right)\right)}} \leadsto \color{blue}{\frac{\left(27464.7644705 + z \cdot y\right) \cdot \left(y \cdot y\right) + \left(x \cdot {y}^{4} + \left(t + y \cdot 230661.510616\right)\right)}{\left(a \cdot y + b\right) \cdot \left(y \cdot y\right) + \left(i + \left({y}^{4} + y \cdot c\right)\right)}}\]
2.7