- Started with
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
13.2
- Applied simplify to get
\[\color{red}{\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}} \leadsto \color{blue}{\left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}}\]
27.9
- Applied taylor to get
\[\left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}} \leadsto \left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \left(\left({\left(\frac{1}{{a}^{1.0}}\right)}^{1.0} + \left(\log a \cdot t\right) \cdot {\left(\frac{1}{{a}^{1.0}}\right)}^{1.0}\right) - b \cdot {\left(\frac{1}{{a}^{1.0}}\right)}^{1.0}\right)\]
13.5
- Taylor expanded around 0 to get
\[\left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \color{red}{\left(\left({\left(\frac{1}{{a}^{1.0}}\right)}^{1.0} + \left(\log a \cdot t\right) \cdot {\left(\frac{1}{{a}^{1.0}}\right)}^{1.0}\right) - b \cdot {\left(\frac{1}{{a}^{1.0}}\right)}^{1.0}\right)} \leadsto \left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \color{blue}{\left(\left({\left(\frac{1}{{a}^{1.0}}\right)}^{1.0} + \left(\log a \cdot t\right) \cdot {\left(\frac{1}{{a}^{1.0}}\right)}^{1.0}\right) - b \cdot {\left(\frac{1}{{a}^{1.0}}\right)}^{1.0}\right)}\]
13.5
- Applied simplify to get
\[\color{red}{\left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \left(\left({\left(\frac{1}{{a}^{1.0}}\right)}^{1.0} + \left(\log a \cdot t\right) \cdot {\left(\frac{1}{{a}^{1.0}}\right)}^{1.0}\right) - b \cdot {\left(\frac{1}{{a}^{1.0}}\right)}^{1.0}\right)} \leadsto \color{blue}{\left({\left(\frac{1}{{a}^{1.0}}\right)}^{1.0} \cdot \left(t \cdot \log a + \left(1 - b\right)\right)\right) \cdot \left({z}^{y} \cdot \frac{x}{y}\right)}\]
13.5
- Applied taylor to get
\[\left({\left(\frac{1}{{a}^{1.0}}\right)}^{1.0} \cdot \left(t \cdot \log a + \left(1 - b\right)\right)\right) \cdot \left({z}^{y} \cdot \frac{x}{y}\right) \leadsto \left({\left(\frac{1}{{a}^{1.0}}\right)}^{1.0} \cdot \left(-1 \cdot \left(\log a \cdot t\right) + \left(1 - b\right)\right)\right) \cdot \left({z}^{y} \cdot \frac{x}{y}\right)\]
13.3
- Taylor expanded around inf to get
\[\left({\left(\frac{1}{{a}^{1.0}}\right)}^{1.0} \cdot \left(\color{red}{-1 \cdot \left(\log a \cdot t\right)} + \left(1 - b\right)\right)\right) \cdot \left({z}^{y} \cdot \frac{x}{y}\right) \leadsto \left({\left(\frac{1}{{a}^{1.0}}\right)}^{1.0} \cdot \left(\color{blue}{-1 \cdot \left(\log a \cdot t\right)} + \left(1 - b\right)\right)\right) \cdot \left({z}^{y} \cdot \frac{x}{y}\right)\]
13.3
- Applied simplify to get
\[\left({\left(\frac{1}{{a}^{1.0}}\right)}^{1.0} \cdot \left(-1 \cdot \left(\log a \cdot t\right) + \left(1 - b\right)\right)\right) \cdot \left({z}^{y} \cdot \frac{x}{y}\right) \leadsto {\left(\frac{1}{{a}^{1.0}}\right)}^{1.0} \cdot \left(\left(\left(1 - b\right) + \log a \cdot \left(-t\right)\right) \cdot \frac{{z}^{y}}{\frac{y}{x}}\right)\]
0.3
- Applied final simplification
- Started with
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
31.5
- Applied simplify to get
\[\color{red}{\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}} \leadsto \color{blue}{\left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}}\]
45.9
- Using strategy
rm 45.9
- Applied pow-to-exp to get
\[\left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{\color{red}{{a}^{\left(t - 1.0\right)}}}{e^{b}} \leadsto \left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{\color{blue}{e^{\log a \cdot \left(t - 1.0\right)}}}{e^{b}}\]
45.9
- Applied div-exp to get
\[\left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \color{red}{\frac{e^{\log a \cdot \left(t - 1.0\right)}}{e^{b}}} \leadsto \left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \color{blue}{e^{\log a \cdot \left(t - 1.0\right) - b}}\]
45.2
- Applied taylor to get
\[\left(\frac{x}{y} \cdot {z}^{y}\right) \cdot e^{\log a \cdot \left(t - 1.0\right) - b} \leadsto \frac{e^{-1 \cdot \frac{\log z}{y}} \cdot x}{y} \cdot e^{\log a \cdot \left(t - 1.0\right) - b}\]
18.2
- Taylor expanded around inf to get
\[\color{red}{\frac{e^{-1 \cdot \frac{\log z}{y}} \cdot x}{y}} \cdot e^{\log a \cdot \left(t - 1.0\right) - b} \leadsto \color{blue}{\frac{e^{-1 \cdot \frac{\log z}{y}} \cdot x}{y}} \cdot e^{\log a \cdot \left(t - 1.0\right) - b}\]
18.2
- Applied simplify to get
\[\color{red}{\frac{e^{-1 \cdot \frac{\log z}{y}} \cdot x}{y} \cdot e^{\log a \cdot \left(t - 1.0\right) - b}} \leadsto \color{blue}{\frac{{z}^{\left(\frac{-1}{y}\right)}}{y} \cdot \left(\frac{x}{e^{b}} \cdot {a}^{\left(t - 1.0\right)}\right)}\]
21.8
- Applied taylor to get
\[\frac{{z}^{\left(\frac{-1}{y}\right)}}{y} \cdot \left(\frac{x}{e^{b}} \cdot {a}^{\left(t - 1.0\right)}\right) \leadsto \frac{{z}^{\left(\frac{-1}{y}\right)}}{y} \cdot \left(\frac{x}{e^{b}} \cdot e^{-1 \cdot \left(\log a \cdot \left(\frac{1}{t} - 1.0\right)\right)}\right)\]
3.9
- Taylor expanded around inf to get
\[\frac{{z}^{\left(\frac{-1}{y}\right)}}{y} \cdot \left(\frac{x}{e^{b}} \cdot \color{red}{e^{-1 \cdot \left(\log a \cdot \left(\frac{1}{t} - 1.0\right)\right)}}\right) \leadsto \frac{{z}^{\left(\frac{-1}{y}\right)}}{y} \cdot \left(\frac{x}{e^{b}} \cdot \color{blue}{e^{-1 \cdot \left(\log a \cdot \left(\frac{1}{t} - 1.0\right)\right)}}\right)\]
3.9
- Applied simplify to get
\[\frac{{z}^{\left(\frac{-1}{y}\right)}}{y} \cdot \left(\frac{x}{e^{b}} \cdot e^{-1 \cdot \left(\log a \cdot \left(\frac{1}{t} - 1.0\right)\right)}\right) \leadsto \left(\frac{{z}^{\left(\frac{-1}{y}\right)}}{y} \cdot \frac{x}{e^{b}}\right) \cdot e^{\left(-\log a\right) \cdot \left(\frac{1}{t} - 1.0\right)}\]
1.0
- Applied final simplification
- Applied simplify to get
\[\color{red}{\left(\frac{{z}^{\left(\frac{-1}{y}\right)}}{y} \cdot \frac{x}{e^{b}}\right) \cdot e^{\left(-\log a\right) \cdot \left(\frac{1}{t} - 1.0\right)}} \leadsto \color{blue}{\frac{x}{e^{b}} \cdot \frac{\frac{{z}^{\left(\frac{-1}{y}\right)}}{y}}{{a}^{\left(\frac{1}{t} - 1.0\right)}}}\]
1.0