if t < -4.863619482882732e+66 or 5.863831885407645e+171 < t

1. Started with
   \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
   36.5
2. Applied simplify to get
   \[\color{red}{\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}} \leadsto \color{blue}{\frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{{a}^{\left(t - 1.0\right)}}}}\]
   27.2
3. Using strategy rm
   27.2
4. Applied sub-neg to get
   \[\frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{{a}^{\color{red}{\left(t - 1.0\right)}}}} \leadsto \frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{{a}^{\color{blue}{\left(t + \left(-1.0\right)\right)}}}}\]
   27.2
5. Applied unpow-prod-up to get
   \[\frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{\color{red}{{a}^{\left(t + \left(-1.0\right)\right)}}}} \leadsto \frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{\color{blue}{{a}^{t} \cdot {a}^{\left(-1.0\right)}}}}\]
   27.2
6. Applied div-inv to get
   \[\frac{\frac{x}{e^{b}}}{\frac{\color{red}{\frac{y}{{z}^{y}}}}{{a}^{t} \cdot {a}^{\left(-1.0\right)}}} \leadsto \frac{\frac{x}{e^{b}}}{\frac{\color{blue}{y \cdot \frac{1}{{z}^{y}}}}{{a}^{t} \cdot {a}^{\left(-1.0\right)}}}\]
   27.2
7. Applied times-frac to get
   \[\frac{\frac{x}{e^{b}}}{\color{red}{\frac{y \cdot \frac{1}{{z}^{y}}}{{a}^{t} \cdot {a}^{\left(-1.0\right)}}}} \leadsto \frac{\frac{x}{e^{b}}}{\color{blue}{\frac{y}{{a}^{t}} \cdot \frac{\frac{1}{{z}^{y}}}{{a}^{\left(-1.0\right)}}}}\]
   27.2
8. Applied *-un-lft-identity to get
   \[\frac{\color{red}{\frac{x}{e^{b}}}}{\frac{y}{{a}^{t}} \cdot \frac{\frac{1}{{z}^{y}}}{{a}^{\left(-1.0\right)}}} \leadsto \frac{\color{blue}{1 \cdot \frac{x}{e^{b}}}}{\frac{y}{{a}^{t}} \cdot \frac{\frac{1}{{z}^{y}}}{{a}^{\left(-1.0\right)}}}\]
   27.2
9. Applied times-frac to get
   \[\color{red}{\frac{1 \cdot \frac{x}{e^{b}}}{\frac{y}{{a}^{t}} \cdot \frac{\frac{1}{{z}^{y}}}{{a}^{\left(-1.0\right)}}}} \leadsto \color{blue}{\frac{1}{\frac{y}{{a}^{t}}} \cdot \frac{\frac{x}{e^{b}}}{\frac{\frac{1}{{z}^{y}}}{{a}^{\left(-1.0\right)}}}}\]
   28.3
10. Applied simplify to get
    \[\color{red}{\frac{1}{\frac{y}{{a}^{t}}}} \cdot \frac{\frac{x}{e^{b}}}{\frac{\frac{1}{{z}^{y}}}{{a}^{\left(-1.0\right)}}} \leadsto \color{blue}{\frac{{a}^{t}}{y}} \cdot \frac{\frac{x}{e^{b}}}{\frac{\frac{1}{{z}^{y}}}{{a}^{\left(-1.0\right)}}}\]
    28.3
11. Applied simplify to get
    \[\frac{{a}^{t}}{y} \cdot \color{red}{\frac{\frac{x}{e^{b}}}{\frac{\frac{1}{{z}^{y}}}{{a}^{\left(-1.0\right)}}}} \leadsto \frac{{a}^{t}}{y} \cdot \color{blue}{\left({a}^{\left(-1.0\right)} \cdot \left(\frac{x}{e^{b}} \cdot {z}^{y}\right)\right)}\]
    28.3
12. Applied taylor to get
    \[\frac{{a}^{t}}{y} \cdot \left({a}^{\left(-1.0\right)} \cdot \left(\frac{x}{e^{b}} \cdot {z}^{y}\right)\right) \leadsto \frac{{a}^{t}}{y} \cdot \left({a}^{\left(-1.0\right)} \cdot \left(\left(y \cdot \left(\log z \cdot x\right) + x\right) - b \cdot x\right)\right)\]
    17.8
13. Taylor expanded around 0 to get
    \[\frac{{a}^{t}}{y} \cdot \left({a}^{\left(-1.0\right)} \cdot \color{red}{\left(\left(y \cdot \left(\log z \cdot x\right) + x\right) - b \cdot x\right)}\right) \leadsto \frac{{a}^{t}}{y} \cdot \left({a}^{\left(-1.0\right)} \cdot \color{blue}{\left(\left(y \cdot \left(\log z \cdot x\right) + x\right) - b \cdot x\right)}\right)\]
    17.8
14. Applied simplify to get
    \[\frac{{a}^{t}}{y} \cdot \left({a}^{\left(-1.0\right)} \cdot \left(\left(y \cdot \left(\log z \cdot x\right) + x\right) - b \cdot x\right)\right) \leadsto \left({a}^{\left(-1.0\right)} \cdot \frac{{a}^{t}}{y}\right) \cdot (\left(\log z \cdot y\right) * x + \left(x - x \cdot b\right))_*\]
    12.5

---

15. Applied final simplification

if -4.863619482882732e+66 < t < -3.165378118206651e+38

1. Started with
   \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
   35.6
2. Applied simplify to get
   \[\color{red}{\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}} \leadsto \color{blue}{\frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{{a}^{\left(t - 1.0\right)}}}}\]
   44.6
3. Applied taylor to get
   \[\frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{{a}^{\left(t - 1.0\right)}}} \leadsto \frac{\frac{x}{e^{b}}}{y \cdot a - \left({y}^2 \cdot \left(\log z \cdot a\right) + y \cdot \left(\log a \cdot \left(a \cdot t\right)\right)\right)}\]
   13.7
4. Taylor expanded around 0 to get
   \[\frac{\frac{x}{e^{b}}}{\color{red}{y \cdot a - \left({y}^2 \cdot \left(\log z \cdot a\right) + y \cdot \left(\log a \cdot \left(a \cdot t\right)\right)\right)}} \leadsto \frac{\frac{x}{e^{b}}}{\color{blue}{y \cdot a - \left({y}^2 \cdot \left(\log z \cdot a\right) + y \cdot \left(\log a \cdot \left(a \cdot t\right)\right)\right)}}\]
   13.7
5. Applied simplify to get
   \[\color{red}{\frac{\frac{x}{e^{b}}}{y \cdot a - \left({y}^2 \cdot \left(\log z \cdot a\right) + y \cdot \left(\log a \cdot \left(a \cdot t\right)\right)\right)}} \leadsto \color{blue}{\frac{\frac{x}{e^{b}}}{y \cdot a - \left(y \cdot a\right) \cdot (\left(\log z\right) * y + \left(t \cdot \log a\right))_*}}\]
   11.4

if -3.165378118206651e+38 < t < 3.90113396965012e+24

1. Started with
   \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
   21.4
2. Applied simplify to get
   \[\color{red}{\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}} \leadsto \color{blue}{\frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{{a}^{\left(t - 1.0\right)}}}}\]
   4.9
3. Using strategy rm
   4.9
4. Applied sub-neg to get
   \[\frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{{a}^{\color{red}{\left(t - 1.0\right)}}}} \leadsto \frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{{a}^{\color{blue}{\left(t + \left(-1.0\right)\right)}}}}\]
   4.9
5. Applied unpow-prod-up to get
   \[\frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{\color{red}{{a}^{\left(t + \left(-1.0\right)\right)}}}} \leadsto \frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{\color{blue}{{a}^{t} \cdot {a}^{\left(-1.0\right)}}}}\]
   4.8
6. Applied div-inv to get
   \[\frac{\frac{x}{e^{b}}}{\frac{\color{red}{\frac{y}{{z}^{y}}}}{{a}^{t} \cdot {a}^{\left(-1.0\right)}}} \leadsto \frac{\frac{x}{e^{b}}}{\frac{\color{blue}{y \cdot \frac{1}{{z}^{y}}}}{{a}^{t} \cdot {a}^{\left(-1.0\right)}}}\]
   4.8
7. Applied times-frac to get
   \[\frac{\frac{x}{e^{b}}}{\color{red}{\frac{y \cdot \frac{1}{{z}^{y}}}{{a}^{t} \cdot {a}^{\left(-1.0\right)}}}} \leadsto \frac{\frac{x}{e^{b}}}{\color{blue}{\frac{y}{{a}^{t}} \cdot \frac{\frac{1}{{z}^{y}}}{{a}^{\left(-1.0\right)}}}}\]
   4.8
8. Applied associate-/r* to get
   \[\color{red}{\frac{\frac{x}{e^{b}}}{\frac{y}{{a}^{t}} \cdot \frac{\frac{1}{{z}^{y}}}{{a}^{\left(-1.0\right)}}}} \leadsto \color{blue}{\frac{\frac{\frac{x}{e^{b}}}{\frac{y}{{a}^{t}}}}{\frac{\frac{1}{{z}^{y}}}{{a}^{\left(-1.0\right)}}}}\]
   2.8

if 3.90113396965012e+24 < t < 5.863831885407645e+171

1. Started with
   \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
   0
2. Applied simplify to get
   \[\color{red}{\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}} \leadsto \color{blue}{\frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{{a}^{\left(t - 1.0\right)}}}}\]
   25.7
3. Using strategy rm
   25.7
4. Applied sub-neg to get
   \[\frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{{a}^{\color{red}{\left(t - 1.0\right)}}}} \leadsto \frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{{a}^{\color{blue}{\left(t + \left(-1.0\right)\right)}}}}\]
   25.7
5. Applied unpow-prod-up to get
   \[\frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{\color{red}{{a}^{\left(t + \left(-1.0\right)\right)}}}} \leadsto \frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{\color{blue}{{a}^{t} \cdot {a}^{\left(-1.0\right)}}}}\]
   25.7
6. Applied div-inv to get
   \[\frac{\frac{x}{e^{b}}}{\frac{\color{red}{\frac{y}{{z}^{y}}}}{{a}^{t} \cdot {a}^{\left(-1.0\right)}}} \leadsto \frac{\frac{x}{e^{b}}}{\frac{\color{blue}{y \cdot \frac{1}{{z}^{y}}}}{{a}^{t} \cdot {a}^{\left(-1.0\right)}}}\]
   25.7
7. Applied times-frac to get
   \[\frac{\frac{x}{e^{b}}}{\color{red}{\frac{y \cdot \frac{1}{{z}^{y}}}{{a}^{t} \cdot {a}^{\left(-1.0\right)}}}} \leadsto \frac{\frac{x}{e^{b}}}{\color{blue}{\frac{y}{{a}^{t}} \cdot \frac{\frac{1}{{z}^{y}}}{{a}^{\left(-1.0\right)}}}}\]
   25.7
8. Applied associate-/r* to get
   \[\color{red}{\frac{\frac{x}{e^{b}}}{\frac{y}{{a}^{t}} \cdot \frac{\frac{1}{{z}^{y}}}{{a}^{\left(-1.0\right)}}}} \leadsto \color{blue}{\frac{\frac{\frac{x}{e^{b}}}{\frac{y}{{a}^{t}}}}{\frac{\frac{1}{{z}^{y}}}{{a}^{\left(-1.0\right)}}}}\]
   25.7
9. Using strategy rm
   25.7
10. Applied add-exp-log to get
    \[\frac{\frac{\frac{x}{e^{b}}}{\frac{y}{{a}^{t}}}}{\color{red}{\frac{\frac{1}{{z}^{y}}}{{a}^{\left(-1.0\right)}}}} \leadsto \frac{\frac{\frac{x}{e^{b}}}{\frac{y}{{a}^{t}}}}{\color{blue}{e^{\log \left(\frac{\frac{1}{{z}^{y}}}{{a}^{\left(-1.0\right)}}\right)}}}\]
    25.7
11. Applied add-exp-log to get
    \[\frac{\color{red}{\frac{\frac{x}{e^{b}}}{\frac{y}{{a}^{t}}}}}{e^{\log \left(\frac{\frac{1}{{z}^{y}}}{{a}^{\left(-1.0\right)}}\right)}} \leadsto \frac{\color{blue}{e^{\log \left(\frac{\frac{x}{e^{b}}}{\frac{y}{{a}^{t}}}\right)}}}{e^{\log \left(\frac{\frac{1}{{z}^{y}}}{{a}^{\left(-1.0\right)}}\right)}}\]
    25.7
12. Applied div-exp to get
    \[\color{red}{\frac{e^{\log \left(\frac{\frac{x}{e^{b}}}{\frac{y}{{a}^{t}}}\right)}}{e^{\log \left(\frac{\frac{1}{{z}^{y}}}{{a}^{\left(-1.0\right)}}\right)}}} \leadsto \color{blue}{e^{\log \left(\frac{\frac{x}{e^{b}}}{\frac{y}{{a}^{t}}}\right) - \log \left(\frac{\frac{1}{{z}^{y}}}{{a}^{\left(-1.0\right)}}\right)}}\]
    25.7
13. Applied simplify to get
    \[e^{\color{red}{\log \left(\frac{\frac{x}{e^{b}}}{\frac{y}{{a}^{t}}}\right) - \log \left(\frac{\frac{1}{{z}^{y}}}{{a}^{\left(-1.0\right)}}\right)}} \leadsto e^{\color{blue}{(y * \left(\log z\right) + \left(\log a \cdot \left(t - 1.0\right)\right))_* + \left(\log \left(\frac{x}{y}\right) - b\right)}}\]
    7.6