- Started with
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
12.9
- Applied simplify to get
\[\color{red}{\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}} \leadsto \color{blue}{\frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{{a}^{\left(t - 1.0\right)}}}}\]
9.5
- Using strategy
rm 9.5
- Applied sub-neg to get
\[\frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{{a}^{\color{red}{\left(t - 1.0\right)}}}} \leadsto \frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{{a}^{\color{blue}{\left(t + \left(-1.0\right)\right)}}}}\]
9.5
- Applied unpow-prod-up to get
\[\frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{\color{red}{{a}^{\left(t + \left(-1.0\right)\right)}}}} \leadsto \frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{\color{blue}{{a}^{t} \cdot {a}^{\left(-1.0\right)}}}}\]
9.4
- Applied taylor to get
\[\frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{{a}^{t} \cdot {a}^{\left(-1.0\right)}}} \leadsto \frac{\frac{x}{e^{b}}}{\frac{\left(y + \frac{1}{2} \cdot \left({y}^{3} \cdot {\left(\log z\right)}^2\right)\right) - {y}^2 \cdot \log z}{{a}^{t} \cdot {a}^{\left(-1.0\right)}}}\]
4.9
- Taylor expanded around 0 to get
\[\frac{\frac{x}{e^{b}}}{\frac{\color{red}{\left(y + \frac{1}{2} \cdot \left({y}^{3} \cdot {\left(\log z\right)}^2\right)\right) - {y}^2 \cdot \log z}}{{a}^{t} \cdot {a}^{\left(-1.0\right)}}} \leadsto \frac{\frac{x}{e^{b}}}{\frac{\color{blue}{\left(y + \frac{1}{2} \cdot \left({y}^{3} \cdot {\left(\log z\right)}^2\right)\right) - {y}^2 \cdot \log z}}{{a}^{t} \cdot {a}^{\left(-1.0\right)}}}\]
4.9