if d < -4.3477835f+20 or 1.0322674f+10 < d

1. Started with
   \[\frac{b \cdot c - a \cdot d}{{c}^2 + {d}^2}\]
   20.4
2. Using strategy rm
   20.4
3. Applied add-exp-log to get
   \[\frac{b \cdot c - a \cdot d}{\color{red}{{c}^2 + {d}^2}} \leadsto \frac{b \cdot c - a \cdot d}{\color{blue}{e^{\log \left({c}^2 + {d}^2\right)}}}\]
   20.6
4. Applied add-exp-log to get
   \[\frac{\color{red}{b \cdot c - a \cdot d}}{e^{\log \left({c}^2 + {d}^2\right)}} \leadsto \frac{\color{blue}{e^{\log \left(b \cdot c - a \cdot d\right)}}}{e^{\log \left({c}^2 + {d}^2\right)}}\]
   26.0
5. Applied div-exp to get
   \[\color{red}{\frac{e^{\log \left(b \cdot c - a \cdot d\right)}}{e^{\log \left({c}^2 + {d}^2\right)}}} \leadsto \color{blue}{e^{\log \left(b \cdot c - a \cdot d\right) - \log \left({c}^2 + {d}^2\right)}}\]
   26.0
6. Applied taylor to get
   \[e^{\log \left(b \cdot c - a \cdot d\right) - \log \left({c}^2 + {d}^2\right)} \leadsto e^{\left(\log a + \log -1\right) - \log d}\]
   30.9
7. Taylor expanded around 0 to get
   \[\color{red}{e^{\left(\log a + \log -1\right) - \log d}} \leadsto \color{blue}{e^{\left(\log a + \log -1\right) - \log d}}\]
   30.9
8. Applied simplify to get
   \[e^{\left(\log a + \log -1\right) - \log d} \leadsto \frac{-1}{d} \cdot a\]
   0.2

---

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

if -4.3477835f+20 < d < -8.791166f-22

1. Started with
   \[\frac{b \cdot c - a \cdot d}{{c}^2 + {d}^2}\]
   9.2
2. Using strategy rm
   9.2
3. Applied add-sqr-sqrt to get
   \[\frac{b \cdot c - a \cdot d}{\color{red}{{c}^2 + {d}^2}} \leadsto \frac{b \cdot c - a \cdot d}{\color{blue}{{\left(\sqrt{{c}^2 + {d}^2}\right)}^2}}\]
   9.2

if -8.791166f-22 < d < 1.0322674f+10

1. Started with
   \[\frac{b \cdot c - a \cdot d}{{c}^2 + {d}^2}\]
   13.3
2. Using strategy rm
   13.3
3. Applied add-sqr-sqrt to get
   \[\frac{b \cdot c - a \cdot d}{\color{red}{{c}^2 + {d}^2}} \leadsto \frac{b \cdot c - a \cdot d}{\color{blue}{{\left(\sqrt{{c}^2 + {d}^2}\right)}^2}}\]
   13.3
4. Applied taylor to get
   \[\frac{b \cdot c - a \cdot d}{{\left(\sqrt{{c}^2 + {d}^2}\right)}^2} \leadsto \frac{b \cdot c - a \cdot d}{{\left(-1 \cdot c\right)}^2}\]
   10.7
5. Taylor expanded around -inf to get
   \[\frac{b \cdot c - a \cdot d}{{\color{red}{\left(-1 \cdot c\right)}}^2} \leadsto \frac{b \cdot c - a \cdot d}{{\color{blue}{\left(-1 \cdot c\right)}}^2}\]
   10.7
6. Applied simplify to get
   \[\color{red}{\frac{b \cdot c - a \cdot d}{{\left(-1 \cdot c\right)}^2}} \leadsto \color{blue}{\frac{b}{c} - \frac{d}{c} \cdot \frac{a}{c}}\]
   0.9