if y.im < -1.0358282f+21 or 1.3808528f+21 < y.im

1. Started with
   \[\frac{x.im \cdot y.re - x.re \cdot y.im}{y.re \cdot y.re + y.im \cdot y.im}\]
   20.9
2. Using strategy rm
   20.9
3. Applied add-exp-log to get
   \[\frac{x.im \cdot y.re - x.re \cdot y.im}{\color{red}{y.re \cdot y.re + y.im \cdot y.im}} \leadsto \frac{x.im \cdot y.re - x.re \cdot y.im}{\color{blue}{e^{\log \left(y.re \cdot y.re + y.im \cdot y.im\right)}}}\]
   20.9
4. Applied add-exp-log to get
   \[\frac{\color{red}{x.im \cdot y.re - x.re \cdot y.im}}{e^{\log \left(y.re \cdot y.re + y.im \cdot y.im\right)}} \leadsto \frac{\color{blue}{e^{\log \left(x.im \cdot y.re - x.re \cdot y.im\right)}}}{e^{\log \left(y.re \cdot y.re + y.im \cdot y.im\right)}}\]
   25.9
5. Applied div-exp to get
   \[\color{red}{\frac{e^{\log \left(x.im \cdot y.re - x.re \cdot y.im\right)}}{e^{\log \left(y.re \cdot y.re + y.im \cdot y.im\right)}}} \leadsto \color{blue}{e^{\log \left(x.im \cdot y.re - x.re \cdot y.im\right) - \log \left(y.re \cdot y.re + y.im \cdot y.im\right)}}\]
   25.9
6. Applied taylor to get
   \[e^{\log \left(x.im \cdot y.re - x.re \cdot y.im\right) - \log \left(y.re \cdot y.re + y.im \cdot y.im\right)} \leadsto e^{\left(\log x.re + \log -1\right) - \log y.im}\]
   30.9
7. Taylor expanded around 0 to get
   \[\color{red}{e^{\left(\log x.re + \log -1\right) - \log y.im}} \leadsto \color{blue}{e^{\left(\log x.re + \log -1\right) - \log y.im}}\]
   30.9
8. Applied simplify to get
   \[e^{\left(\log x.re + \log -1\right) - \log y.im} \leadsto \frac{-1}{y.im} \cdot x.re\]
   0.2

---

9. Applied final simplification
10. Applied simplify to get
    \[\color{red}{\frac{-1}{y.im} \cdot x.re} \leadsto \color{blue}{-\frac{x.re}{y.im}}\]
    0

if -1.0358282f+21 < y.im < -3.9317606f-27

1. Started with
   \[\frac{x.im \cdot y.re - x.re \cdot y.im}{y.re \cdot y.re + y.im \cdot y.im}\]
   9.0
2. Using strategy rm
   9.0
3. Applied div-sub to get
   \[\color{red}{\frac{x.im \cdot y.re - x.re \cdot y.im}{y.re \cdot y.re + y.im \cdot y.im}} \leadsto \color{blue}{\frac{x.im \cdot y.re}{y.re \cdot y.re + y.im \cdot y.im} - \frac{x.re \cdot y.im}{y.re \cdot y.re + y.im \cdot y.im}}\]
   9.0
4. Using strategy rm
   9.0
5. Applied *-un-lft-identity to get
   \[\frac{x.im \cdot y.re}{\color{red}{y.re \cdot y.re + y.im \cdot y.im}} - \frac{x.re \cdot y.im}{y.re \cdot y.re + y.im \cdot y.im} \leadsto \frac{x.im \cdot y.re}{\color{blue}{1 \cdot \left(y.re \cdot y.re + y.im \cdot y.im\right)}} - \frac{x.re \cdot y.im}{y.re \cdot y.re + y.im \cdot y.im}\]
   9.0
6. Applied times-frac to get
   \[\color{red}{\frac{x.im \cdot y.re}{1 \cdot \left(y.re \cdot y.re + y.im \cdot y.im\right)}} - \frac{x.re \cdot y.im}{y.re \cdot y.re + y.im \cdot y.im} \leadsto \color{blue}{\frac{x.im}{1} \cdot \frac{y.re}{y.re \cdot y.re + y.im \cdot y.im}} - \frac{x.re \cdot y.im}{y.re \cdot y.re + y.im \cdot y.im}\]
   8.3
7. Applied simplify to get
   \[\frac{x.im}{1} \cdot \color{red}{\frac{y.re}{y.re \cdot y.re + y.im \cdot y.im}} - \frac{x.re \cdot y.im}{y.re \cdot y.re + y.im \cdot y.im} \leadsto \frac{x.im}{1} \cdot \color{blue}{\frac{y.re}{{y.re}^2 + y.im \cdot y.im}} - \frac{x.re \cdot y.im}{y.re \cdot y.re + y.im \cdot y.im}\]
   8.3

if -3.9317606f-27 < y.im < 0.0038476672f0

1. Started with
   \[\frac{x.im \cdot y.re - x.re \cdot y.im}{y.re \cdot y.re + y.im \cdot y.im}\]
   12.0
2. Using strategy rm
   12.0
3. Applied add-sqr-sqrt to get
   \[\frac{x.im \cdot y.re - x.re \cdot y.im}{\color{red}{y.re \cdot y.re + y.im \cdot y.im}} \leadsto \frac{x.im \cdot y.re - x.re \cdot y.im}{\color{blue}{{\left(\sqrt{y.re \cdot y.re + y.im \cdot y.im}\right)}^2}}\]
   11.9
4. Applied simplify to get
   \[\frac{x.im \cdot y.re - x.re \cdot y.im}{{\color{red}{\left(\sqrt{y.re \cdot y.re + y.im \cdot y.im}\right)}}^2} \leadsto \frac{x.im \cdot y.re - x.re \cdot y.im}{{\color{blue}{\left(\sqrt{{y.re}^2 + y.im \cdot y.im}\right)}}^2}\]
   11.9
5. Applied taylor to get
   \[\frac{x.im \cdot y.re - x.re \cdot y.im}{{\left(\sqrt{{y.re}^2 + y.im \cdot y.im}\right)}^2} \leadsto \frac{x.im \cdot y.re - x.re \cdot y.im}{{\left(-1 \cdot y.re\right)}^2}\]
   10.8
6. Taylor expanded around -inf to get
   \[\frac{x.im \cdot y.re - x.re \cdot y.im}{{\color{red}{\left(-1 \cdot y.re\right)}}^2} \leadsto \frac{x.im \cdot y.re - x.re \cdot y.im}{{\color{blue}{\left(-1 \cdot y.re\right)}}^2}\]
   10.8
7. Applied simplify to get
   \[\color{red}{\frac{x.im \cdot y.re - x.re \cdot y.im}{{\left(-1 \cdot y.re\right)}^2}} \leadsto \color{blue}{\frac{x.im}{y.re} - \frac{y.im}{y.re} \cdot \frac{x.re}{y.re}}\]
   1.0

if 0.0038476672f0 < y.im < 1.3808528f+21

1. Started with
   \[\frac{x.im \cdot y.re - x.re \cdot y.im}{y.re \cdot y.re + y.im \cdot y.im}\]
   10.6
2. Using strategy rm
   10.6
3. Applied div-sub to get
   \[\color{red}{\frac{x.im \cdot y.re - x.re \cdot y.im}{y.re \cdot y.re + y.im \cdot y.im}} \leadsto \color{blue}{\frac{x.im \cdot y.re}{y.re \cdot y.re + y.im \cdot y.im} - \frac{x.re \cdot y.im}{y.re \cdot y.re + y.im \cdot y.im}}\]
   10.6
4. Using strategy rm
   10.6
5. Applied *-un-lft-identity to get
   \[\frac{x.im \cdot y.re}{y.re \cdot y.re + y.im \cdot y.im} - \frac{x.re \cdot y.im}{\color{red}{y.re \cdot y.re + y.im \cdot y.im}} \leadsto \frac{x.im \cdot y.re}{y.re \cdot y.re + y.im \cdot y.im} - \frac{x.re \cdot y.im}{\color{blue}{1 \cdot \left(y.re \cdot y.re + y.im \cdot y.im\right)}}\]
   10.6
6. Applied times-frac to get
   \[\frac{x.im \cdot y.re}{y.re \cdot y.re + y.im \cdot y.im} - \color{red}{\frac{x.re \cdot y.im}{1 \cdot \left(y.re \cdot y.re + y.im \cdot y.im\right)}} \leadsto \frac{x.im \cdot y.re}{y.re \cdot y.re + y.im \cdot y.im} - \color{blue}{\frac{x.re}{1} \cdot \frac{y.im}{y.re \cdot y.re + y.im \cdot y.im}}\]
   8.5
7. Applied simplify to get
   \[\frac{x.im \cdot y.re}{y.re \cdot y.re + y.im \cdot y.im} - \frac{x.re}{1} \cdot \color{red}{\frac{y.im}{y.re \cdot y.re + y.im \cdot y.im}} \leadsto \frac{x.im \cdot y.re}{y.re \cdot y.re + y.im \cdot y.im} - \frac{x.re}{1} \cdot \color{blue}{\frac{y.im}{y.re \cdot y.re + {y.im}^2}}\]
   8.5