- Started with
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
37.8
- Applied simplify to get
\[\color{red}{\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}} \leadsto \color{blue}{\frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{{a}^{\left(t - 1.0\right)}}}}\]
27.3
- Using strategy
rm 27.3
- Applied *-un-lft-identity to get
\[\frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{\color{red}{{a}^{\left(t - 1.0\right)}}}} \leadsto \frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{\color{blue}{1 \cdot {a}^{\left(t - 1.0\right)}}}}\]
27.3
- Applied *-un-lft-identity to get
\[\frac{\frac{x}{e^{b}}}{\frac{\color{red}{\frac{y}{{z}^{y}}}}{1 \cdot {a}^{\left(t - 1.0\right)}}} \leadsto \frac{\frac{x}{e^{b}}}{\frac{\color{blue}{1 \cdot \frac{y}{{z}^{y}}}}{1 \cdot {a}^{\left(t - 1.0\right)}}}\]
27.3
- Applied times-frac to get
\[\frac{\frac{x}{e^{b}}}{\color{red}{\frac{1 \cdot \frac{y}{{z}^{y}}}{1 \cdot {a}^{\left(t - 1.0\right)}}}} \leadsto \frac{\frac{x}{e^{b}}}{\color{blue}{\frac{1}{1} \cdot \frac{\frac{y}{{z}^{y}}}{{a}^{\left(t - 1.0\right)}}}}\]
27.3
- Applied div-inv to get
\[\frac{\color{red}{\frac{x}{e^{b}}}}{\frac{1}{1} \cdot \frac{\frac{y}{{z}^{y}}}{{a}^{\left(t - 1.0\right)}}} \leadsto \frac{\color{blue}{x \cdot \frac{1}{e^{b}}}}{\frac{1}{1} \cdot \frac{\frac{y}{{z}^{y}}}{{a}^{\left(t - 1.0\right)}}}\]
27.3
- Applied times-frac to get
\[\color{red}{\frac{x \cdot \frac{1}{e^{b}}}{\frac{1}{1} \cdot \frac{\frac{y}{{z}^{y}}}{{a}^{\left(t - 1.0\right)}}}} \leadsto \color{blue}{\frac{x}{\frac{1}{1}} \cdot \frac{\frac{1}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{{a}^{\left(t - 1.0\right)}}}}\]
27.3
- Applied simplify to get
\[\color{red}{\frac{x}{\frac{1}{1}}} \cdot \frac{\frac{1}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{{a}^{\left(t - 1.0\right)}}} \leadsto \color{blue}{\frac{x}{1}} \cdot \frac{\frac{1}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{{a}^{\left(t - 1.0\right)}}}\]
27.3
- Applied simplify to get
\[\frac{x}{1} \cdot \color{red}{\frac{\frac{1}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{{a}^{\left(t - 1.0\right)}}}} \leadsto \frac{x}{1} \cdot \color{blue}{\left(\frac{{a}^{\left(t - 1.0\right)}}{e^{b}} \cdot \frac{{z}^{y}}{y}\right)}\]
27.3
- Applied taylor to get
\[\frac{x}{1} \cdot \left(\frac{{a}^{\left(t - 1.0\right)}}{e^{b}} \cdot \frac{{z}^{y}}{y}\right) \leadsto \frac{x}{1} \cdot \left(\left(\left({\left(\frac{1}{{a}^{1.0}}\right)}^{1.0} + \left(\log a \cdot t\right) \cdot {\left(\frac{1}{{a}^{1.0}}\right)}^{1.0}\right) - b \cdot {\left(\frac{1}{{a}^{1.0}}\right)}^{1.0}\right) \cdot \frac{{z}^{y}}{y}\right)\]
13.4
- Taylor expanded around 0 to get
\[\frac{x}{1} \cdot \left(\color{red}{\left(\left({\left(\frac{1}{{a}^{1.0}}\right)}^{1.0} + \left(\log a \cdot t\right) \cdot {\left(\frac{1}{{a}^{1.0}}\right)}^{1.0}\right) - b \cdot {\left(\frac{1}{{a}^{1.0}}\right)}^{1.0}\right)} \cdot \frac{{z}^{y}}{y}\right) \leadsto \frac{x}{1} \cdot \left(\color{blue}{\left(\left({\left(\frac{1}{{a}^{1.0}}\right)}^{1.0} + \left(\log a \cdot t\right) \cdot {\left(\frac{1}{{a}^{1.0}}\right)}^{1.0}\right) - b \cdot {\left(\frac{1}{{a}^{1.0}}\right)}^{1.0}\right)} \cdot \frac{{z}^{y}}{y}\right)\]
13.4
- Applied simplify to get
\[\color{red}{\frac{x}{1} \cdot \left(\left(\left({\left(\frac{1}{{a}^{1.0}}\right)}^{1.0} + \left(\log a \cdot t\right) \cdot {\left(\frac{1}{{a}^{1.0}}\right)}^{1.0}\right) - b \cdot {\left(\frac{1}{{a}^{1.0}}\right)}^{1.0}\right) \cdot \frac{{z}^{y}}{y}\right)} \leadsto \color{blue}{\left(\frac{\frac{{z}^{y}}{\frac{y}{x}}}{1} \cdot {\left(\frac{1}{{a}^{1.0}}\right)}^{1.0}\right) \cdot (t * \left(\log a\right) + \left(1 - b\right))_*}\]
0.3
- Applied simplify to get
\[\color{red}{\left(\frac{\frac{{z}^{y}}{\frac{y}{x}}}{1} \cdot {\left(\frac{1}{{a}^{1.0}}\right)}^{1.0}\right)} \cdot (t * \left(\log a\right) + \left(1 - b\right))_* \leadsto \color{blue}{\left({\left(\frac{1}{{a}^{1.0}}\right)}^{1.0} \cdot \frac{{z}^{y}}{\frac{y}{x}}\right)} \cdot (t * \left(\log a\right) + \left(1 - b\right))_*\]
0.3
- Started with
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
3.5
- Applied simplify to get
\[\color{red}{\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}} \leadsto \color{blue}{\frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{{a}^{\left(t - 1.0\right)}}}}\]
12.7
- Using strategy
rm 12.7
- Applied *-un-lft-identity to get
\[\frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{\color{red}{{a}^{\left(t - 1.0\right)}}}} \leadsto \frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{\color{blue}{1 \cdot {a}^{\left(t - 1.0\right)}}}}\]
12.7
- Applied *-un-lft-identity to get
\[\frac{\frac{x}{e^{b}}}{\frac{\color{red}{\frac{y}{{z}^{y}}}}{1 \cdot {a}^{\left(t - 1.0\right)}}} \leadsto \frac{\frac{x}{e^{b}}}{\frac{\color{blue}{1 \cdot \frac{y}{{z}^{y}}}}{1 \cdot {a}^{\left(t - 1.0\right)}}}\]
12.7
- Applied times-frac to get
\[\frac{\frac{x}{e^{b}}}{\color{red}{\frac{1 \cdot \frac{y}{{z}^{y}}}{1 \cdot {a}^{\left(t - 1.0\right)}}}} \leadsto \frac{\frac{x}{e^{b}}}{\color{blue}{\frac{1}{1} \cdot \frac{\frac{y}{{z}^{y}}}{{a}^{\left(t - 1.0\right)}}}}\]
12.7
- Applied div-inv to get
\[\frac{\color{red}{\frac{x}{e^{b}}}}{\frac{1}{1} \cdot \frac{\frac{y}{{z}^{y}}}{{a}^{\left(t - 1.0\right)}}} \leadsto \frac{\color{blue}{x \cdot \frac{1}{e^{b}}}}{\frac{1}{1} \cdot \frac{\frac{y}{{z}^{y}}}{{a}^{\left(t - 1.0\right)}}}\]
12.7
- Applied times-frac to get
\[\color{red}{\frac{x \cdot \frac{1}{e^{b}}}{\frac{1}{1} \cdot \frac{\frac{y}{{z}^{y}}}{{a}^{\left(t - 1.0\right)}}}} \leadsto \color{blue}{\frac{x}{\frac{1}{1}} \cdot \frac{\frac{1}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{{a}^{\left(t - 1.0\right)}}}}\]
12.8
- Applied simplify to get
\[\color{red}{\frac{x}{\frac{1}{1}}} \cdot \frac{\frac{1}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{{a}^{\left(t - 1.0\right)}}} \leadsto \color{blue}{\frac{x}{1}} \cdot \frac{\frac{1}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{{a}^{\left(t - 1.0\right)}}}\]
12.8
- Applied simplify to get
\[\frac{x}{1} \cdot \color{red}{\frac{\frac{1}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{{a}^{\left(t - 1.0\right)}}}} \leadsto \frac{x}{1} \cdot \color{blue}{\left(\frac{{a}^{\left(t - 1.0\right)}}{e^{b}} \cdot \frac{{z}^{y}}{y}\right)}\]
9.8
- Using strategy
rm 9.8
- Applied pow-to-exp to get
\[\frac{x}{1} \cdot \left(\frac{\color{red}{{a}^{\left(t - 1.0\right)}}}{e^{b}} \cdot \frac{{z}^{y}}{y}\right) \leadsto \frac{x}{1} \cdot \left(\frac{\color{blue}{e^{\log a \cdot \left(t - 1.0\right)}}}{e^{b}} \cdot \frac{{z}^{y}}{y}\right)\]
11.1
- Applied div-exp to get
\[\frac{x}{1} \cdot \left(\color{red}{\frac{e^{\log a \cdot \left(t - 1.0\right)}}{e^{b}}} \cdot \frac{{z}^{y}}{y}\right) \leadsto \frac{x}{1} \cdot \left(\color{blue}{e^{\log a \cdot \left(t - 1.0\right) - b}} \cdot \frac{{z}^{y}}{y}\right)\]
4.0