- Started with
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
1.9
- Applied simplify to get
\[\color{red}{\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}} \leadsto \color{blue}{\frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{{a}^{\left(t - 1.0\right)}}}}\]
11.9
- Applied taylor to get
\[\frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{{a}^{\left(t - 1.0\right)}}} \leadsto \frac{e^{-1 \cdot \left(\log a \cdot \left(\frac{1}{t} - 1.0\right)\right)} \cdot \left(e^{-1 \cdot \frac{\log z}{y}} \cdot x\right)}{y \cdot e^{\frac{1}{b}}}\]
18.1
- Taylor expanded around inf to get
\[\color{red}{\frac{e^{-1 \cdot \left(\log a \cdot \left(\frac{1}{t} - 1.0\right)\right)} \cdot \left(e^{-1 \cdot \frac{\log z}{y}} \cdot x\right)}{y \cdot e^{\frac{1}{b}}}} \leadsto \color{blue}{\frac{e^{-1 \cdot \left(\log a \cdot \left(\frac{1}{t} - 1.0\right)\right)} \cdot \left(e^{-1 \cdot \frac{\log z}{y}} \cdot x\right)}{y \cdot e^{\frac{1}{b}}}}\]
18.1
- Applied simplify to get
\[\color{red}{\frac{e^{-1 \cdot \left(\log a \cdot \left(\frac{1}{t} - 1.0\right)\right)} \cdot \left(e^{-1 \cdot \frac{\log z}{y}} \cdot x\right)}{y \cdot e^{\frac{1}{b}}}} \leadsto \color{blue}{\frac{e^{(\left(-\log a\right) * \left(\frac{1}{t} - 1.0\right) + \left(\frac{-1}{y} \cdot \log z\right))_*}}{\frac{y}{x} \cdot e^{\frac{1}{b}}}}\]
17.4
- Applied taylor to get
\[\frac{e^{(\left(-\log a\right) * \left(\frac{1}{t} - 1.0\right) + \left(\frac{-1}{y} \cdot \log z\right))_*}}{\frac{y}{x} \cdot e^{\frac{1}{b}}} \leadsto \frac{e^{(\left(-\log \left(\frac{1}{a}\right)\right) * \left(t - 1.0\right) + \left(-1 \cdot \left(y \cdot \log \left(\frac{1}{z}\right)\right)\right))_*} \cdot x}{y} - \frac{e^{(\left(-\log \left(\frac{1}{a}\right)\right) * \left(t - 1.0\right) + \left(-1 \cdot \left(y \cdot \log \left(\frac{1}{z}\right)\right)\right))_*} \cdot x}{y \cdot b}\]
0
- Taylor expanded around inf to get
\[\color{red}{\frac{e^{(\left(-\log \left(\frac{1}{a}\right)\right) * \left(t - 1.0\right) + \left(-1 \cdot \left(y \cdot \log \left(\frac{1}{z}\right)\right)\right))_*} \cdot x}{y} - \frac{e^{(\left(-\log \left(\frac{1}{a}\right)\right) * \left(t - 1.0\right) + \left(-1 \cdot \left(y \cdot \log \left(\frac{1}{z}\right)\right)\right))_*} \cdot x}{y \cdot b}} \leadsto \color{blue}{\frac{e^{(\left(-\log \left(\frac{1}{a}\right)\right) * \left(t - 1.0\right) + \left(-1 \cdot \left(y \cdot \log \left(\frac{1}{z}\right)\right)\right))_*} \cdot x}{y} - \frac{e^{(\left(-\log \left(\frac{1}{a}\right)\right) * \left(t - 1.0\right) + \left(-1 \cdot \left(y \cdot \log \left(\frac{1}{z}\right)\right)\right))_*} \cdot x}{y \cdot b}}\]
0
- Applied simplify to get
\[\frac{e^{(\left(-\log \left(\frac{1}{a}\right)\right) * \left(t - 1.0\right) + \left(-1 \cdot \left(y \cdot \log \left(\frac{1}{z}\right)\right)\right))_*} \cdot x}{y} - \frac{e^{(\left(-\log \left(\frac{1}{a}\right)\right) * \left(t - 1.0\right) + \left(-1 \cdot \left(y \cdot \log \left(\frac{1}{z}\right)\right)\right))_*} \cdot x}{y \cdot b} \leadsto \frac{e^{(\left(\log a\right) * \left(t - 1.0\right) + \left(y \cdot \log z\right))_*}}{y} \cdot \left(x - \frac{x}{b}\right)\]
3.9
- Applied final simplification