if d < -1.0358282f+21 or 1.3808528f+21 < d

1. Started with
   \[\frac{b \cdot c - a \cdot d}{{c}^2 + {d}^2}\]
   20.9
2. Using strategy rm
   20.9
3. Applied add-exp-log to get
   \[\color{red}{\frac{b \cdot c - a \cdot d}{{c}^2 + {d}^2}} \leadsto \color{blue}{e^{\log \left(\frac{b \cdot c - a \cdot d}{{c}^2 + {d}^2}\right)}}\]
   20.9
4. Applied taylor to get
   \[e^{\log \left(\frac{b \cdot c - a \cdot d}{{c}^2 + {d}^2}\right)} \leadsto e^{\left(\log a + \log -1\right) - \log d}\]
   30.9
5. Taylor expanded around 0 to get
   \[e^{\color{red}{\left(\log a + \log -1\right) - \log d}} \leadsto e^{\color{blue}{\left(\log a + \log -1\right) - \log d}}\]
   30.9
6. Applied simplify to get
   \[e^{\left(\log a + \log -1\right) - \log d} \leadsto \frac{-1}{d} \cdot a\]
   0.2

---

7. Applied final simplification
8. Applied simplify to get
   \[\color{red}{\frac{-1}{d} \cdot a} \leadsto \color{blue}{-\frac{a}{d}}\]
   0

if -1.0358282f+21 < d < -3.9317606f-27

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

if -3.9317606f-27 < d < 0.0038476672f0

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

if 0.0038476672f0 < d < 1.3808528f+21

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