- Started with
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
3.0
- Applied simplify to get
\[\color{red}{\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}} \leadsto \color{blue}{\left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}}\]
16.3
- Using strategy
rm 16.3
- Applied div-inv to get
\[\left(\color{red}{\frac{x}{y}} \cdot {z}^{y}\right) \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}} \leadsto \left(\color{blue}{\left(x \cdot \frac{1}{y}\right)} \cdot {z}^{y}\right) \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}\]
16.3
- Applied associate-*l* to get
\[\color{red}{\left(\left(x \cdot \frac{1}{y}\right) \cdot {z}^{y}\right)} \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}} \leadsto \color{blue}{\left(x \cdot \left(\frac{1}{y} \cdot {z}^{y}\right)\right)} \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}\]
13.4
- Applied simplify to get
\[\left(x \cdot \color{red}{\left(\frac{1}{y} \cdot {z}^{y}\right)}\right) \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}} \leadsto \left(x \cdot \color{blue}{\frac{{z}^{y}}{y}}\right) \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}\]
13.3
- Using strategy
rm 13.3
- Applied pow-to-exp to get
\[\left(x \cdot \frac{{z}^{y}}{y}\right) \cdot \frac{\color{red}{{a}^{\left(t - 1.0\right)}}}{e^{b}} \leadsto \left(x \cdot \frac{{z}^{y}}{y}\right) \cdot \frac{\color{blue}{e^{\log a \cdot \left(t - 1.0\right)}}}{e^{b}}\]
13.3
- Applied div-exp to get
\[\left(x \cdot \frac{{z}^{y}}{y}\right) \cdot \color{red}{\frac{e^{\log a \cdot \left(t - 1.0\right)}}{e^{b}}} \leadsto \left(x \cdot \frac{{z}^{y}}{y}\right) \cdot \color{blue}{e^{\log a \cdot \left(t - 1.0\right) - b}}\]
7.7
- Applied taylor to get
\[\left(x \cdot \frac{{z}^{y}}{y}\right) \cdot e^{\log a \cdot \left(t - 1.0\right) - b} \leadsto \left(\frac{x}{y} + \left(\log z \cdot x + \frac{1}{2} \cdot \left(y \cdot \left({\left(\log z\right)}^2 \cdot x\right)\right)\right)\right) \cdot e^{\log a \cdot \left(t - 1.0\right) - b}\]
3.9
- Taylor expanded around 0 to get
\[\color{red}{\left(\frac{x}{y} + \left(\log z \cdot x + \frac{1}{2} \cdot \left(y \cdot \left({\left(\log z\right)}^2 \cdot x\right)\right)\right)\right)} \cdot e^{\log a \cdot \left(t - 1.0\right) - b} \leadsto \color{blue}{\left(\frac{x}{y} + \left(\log z \cdot x + \frac{1}{2} \cdot \left(y \cdot \left({\left(\log z\right)}^2 \cdot x\right)\right)\right)\right)} \cdot e^{\log a \cdot \left(t - 1.0\right) - b}\]
3.9
- Started with
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
9.7
- Applied simplify to get
\[\color{red}{\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}} \leadsto \color{blue}{\left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}}\]
6.0
- Using strategy
rm 6.0
- Applied div-inv to get
\[\left(\color{red}{\frac{x}{y}} \cdot {z}^{y}\right) \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}} \leadsto \left(\color{blue}{\left(x \cdot \frac{1}{y}\right)} \cdot {z}^{y}\right) \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}\]
6.0
- Applied associate-*l* to get
\[\color{red}{\left(\left(x \cdot \frac{1}{y}\right) \cdot {z}^{y}\right)} \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}} \leadsto \color{blue}{\left(x \cdot \left(\frac{1}{y} \cdot {z}^{y}\right)\right)} \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}\]
4.4
- Applied simplify to get
\[\left(x \cdot \color{red}{\left(\frac{1}{y} \cdot {z}^{y}\right)}\right) \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}} \leadsto \left(x \cdot \color{blue}{\frac{{z}^{y}}{y}}\right) \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}\]
4.3
- Applied taylor to get
\[\left(x \cdot \frac{{z}^{y}}{y}\right) \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}} \leadsto \left(x \cdot \frac{{z}^{y}}{y}\right) \cdot \frac{\left(\log a \cdot t\right) \cdot {\left(\frac{1}{{a}^{1.0}}\right)}^{1.0} + \left({a}^{-1.0} + \frac{1}{2} \cdot \left(\left({\left(\log a\right)}^2 \cdot {t}^2\right) \cdot {\left(\frac{1}{{a}^{1.0}}\right)}^{1.0}\right)\right)}{e^{b}}\]
1.7
- Taylor expanded around 0 to get
\[\left(x \cdot \frac{{z}^{y}}{y}\right) \cdot \frac{\color{red}{\left(\log a \cdot t\right) \cdot {\left(\frac{1}{{a}^{1.0}}\right)}^{1.0} + \left({a}^{-1.0} + \frac{1}{2} \cdot \left(\left({\left(\log a\right)}^2 \cdot {t}^2\right) \cdot {\left(\frac{1}{{a}^{1.0}}\right)}^{1.0}\right)\right)}}{e^{b}} \leadsto \left(x \cdot \frac{{z}^{y}}{y}\right) \cdot \frac{\color{blue}{\left(\log a \cdot t\right) \cdot {\left(\frac{1}{{a}^{1.0}}\right)}^{1.0} + \left({a}^{-1.0} + \frac{1}{2} \cdot \left(\left({\left(\log a\right)}^2 \cdot {t}^2\right) \cdot {\left(\frac{1}{{a}^{1.0}}\right)}^{1.0}\right)\right)}}{e^{b}}\]
1.7