- Started with
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
25.4
- Applied simplify to get
\[\color{red}{\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}} \leadsto \color{blue}{\frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{{a}^{\left(t - 1.0\right)}}}}\]
30.7
- Applied taylor to get
\[\frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{{a}^{\left(t - 1.0\right)}}} \leadsto \frac{\frac{x}{e^{b}}}{\frac{\left(y + \frac{1}{2} \cdot \left({y}^{3} \cdot {\left(\log z\right)}^2\right)\right) - {y}^2 \cdot \log z}{{a}^{\left(t - 1.0\right)}}}\]
30.7
- Taylor expanded around 0 to get
\[\frac{\frac{x}{e^{b}}}{\frac{\color{red}{\left(y + \frac{1}{2} \cdot \left({y}^{3} \cdot {\left(\log z\right)}^2\right)\right) - {y}^2 \cdot \log z}}{{a}^{\left(t - 1.0\right)}}} \leadsto \frac{\frac{x}{e^{b}}}{\frac{\color{blue}{\left(y + \frac{1}{2} \cdot \left({y}^{3} \cdot {\left(\log z\right)}^2\right)\right) - {y}^2 \cdot \log z}}{{a}^{\left(t - 1.0\right)}}}\]
30.7
- Using strategy
rm 30.7
- Applied sub-neg to get
\[\frac{\frac{x}{e^{b}}}{\frac{\left(y + \frac{1}{2} \cdot \left({y}^{3} \cdot {\left(\log z\right)}^2\right)\right) - {y}^2 \cdot \log z}{{a}^{\color{red}{\left(t - 1.0\right)}}}} \leadsto \frac{\frac{x}{e^{b}}}{\frac{\left(y + \frac{1}{2} \cdot \left({y}^{3} \cdot {\left(\log z\right)}^2\right)\right) - {y}^2 \cdot \log z}{{a}^{\color{blue}{\left(t + \left(-1.0\right)\right)}}}}\]
30.7
- Applied unpow-prod-up to get
\[\frac{\frac{x}{e^{b}}}{\frac{\left(y + \frac{1}{2} \cdot \left({y}^{3} \cdot {\left(\log z\right)}^2\right)\right) - {y}^2 \cdot \log z}{\color{red}{{a}^{\left(t + \left(-1.0\right)\right)}}}} \leadsto \frac{\frac{x}{e^{b}}}{\frac{\left(y + \frac{1}{2} \cdot \left({y}^{3} \cdot {\left(\log z\right)}^2\right)\right) - {y}^2 \cdot \log z}{\color{blue}{{a}^{t} \cdot {a}^{\left(-1.0\right)}}}}\]
30.7
- Applied taylor to get
\[\frac{\frac{x}{e^{b}}}{\frac{\left(y + \frac{1}{2} \cdot \left({y}^{3} \cdot {\left(\log z\right)}^2\right)\right) - {y}^2 \cdot \log z}{{a}^{t} \cdot {a}^{\left(-1.0\right)}}} \leadsto 2 \cdot \left(\frac{e^{-1 \cdot \frac{\log a}{t}} \cdot x}{{y}^{3} \cdot \left(e^{\frac{1}{b}} \cdot {\left(\log z\right)}^2\right)} \cdot {\left({a}^{1.0}\right)}^{1.0}\right)\]
6.5
- Taylor expanded around inf to get
\[\color{red}{2 \cdot \left(\frac{e^{-1 \cdot \frac{\log a}{t}} \cdot x}{{y}^{3} \cdot \left(e^{\frac{1}{b}} \cdot {\left(\log z\right)}^2\right)} \cdot {\left({a}^{1.0}\right)}^{1.0}\right)} \leadsto \color{blue}{2 \cdot \left(\frac{e^{-1 \cdot \frac{\log a}{t}} \cdot x}{{y}^{3} \cdot \left(e^{\frac{1}{b}} \cdot {\left(\log z\right)}^2\right)} \cdot {\left({a}^{1.0}\right)}^{1.0}\right)}\]
6.5
- Applied simplify to get
\[\color{red}{2 \cdot \left(\frac{e^{-1 \cdot \frac{\log a}{t}} \cdot x}{{y}^{3} \cdot \left(e^{\frac{1}{b}} \cdot {\left(\log z\right)}^2\right)} \cdot {\left({a}^{1.0}\right)}^{1.0}\right)} \leadsto \color{blue}{\frac{e^{\frac{-1}{t} \cdot \log a}}{\frac{{y}^3}{2}} \cdot \frac{{\left({a}^{1.0}\right)}^{1.0} \cdot x}{e^{\frac{1}{b}} \cdot {\left(\log z\right)}^2}}\]
6.6