if d < -1.0358282f+21 or 3.216231f+25 < d

1. Started with
   \[\frac{b \cdot c - a \cdot d}{{c}^2 + {d}^2}\]
   22.0
2. Using strategy rm
   22.0
3. Applied add-sqr-sqrt to get
   \[\frac{b \cdot c - a \cdot d}{\color{red}{{c}^2} + {d}^2} \leadsto \frac{b \cdot c - a \cdot d}{\color{blue}{{\left(\sqrt{{c}^2}\right)}^2} + {d}^2}\]
   22.0
4. Applied simplify to get
   \[\frac{b \cdot c - a \cdot d}{{\color{red}{\left(\sqrt{{c}^2}\right)}}^2 + {d}^2} \leadsto \frac{b \cdot c - a \cdot d}{{\color{blue}{\left(\left|c\right|\right)}}^2 + {d}^2}\]
   22.0
5. Applied taylor to get
   \[\frac{b \cdot c - a \cdot d}{{\left(\left|c\right|\right)}^2 + {d}^2} \leadsto \frac{b \cdot c}{{d}^2} - \frac{a}{d}\]
   6.0
6. Taylor expanded around inf to get
   \[\color{red}{\frac{b \cdot c}{{d}^2} - \frac{a}{d}} \leadsto \color{blue}{\frac{b \cdot c}{{d}^2} - \frac{a}{d}}\]
   6.0

if -1.0358282f+21 < d < 3.216231f+25

1. Started with
   \[\frac{b \cdot c - a \cdot d}{{c}^2 + {d}^2}\]
   10.2
2. Using strategy rm
   10.2
3. Applied add-sqr-sqrt to get
   \[\frac{b \cdot c - a \cdot d}{\color{red}{{c}^2} + {d}^2} \leadsto \frac{b \cdot c - a \cdot d}{\color{blue}{{\left(\sqrt{{c}^2}\right)}^2} + {d}^2}\]
   10.1
4. Applied simplify to get
   \[\frac{b \cdot c - a \cdot d}{{\color{red}{\left(\sqrt{{c}^2}\right)}}^2 + {d}^2} \leadsto \frac{b \cdot c - a \cdot d}{{\color{blue}{\left(\left|c\right|\right)}}^2 + {d}^2}\]
   7.4
5. Using strategy rm
   7.4
6. Applied add-sqr-sqrt to get
   \[\frac{b \cdot c - a \cdot d}{{\left(\left|c\right|\right)}^2 + \color{red}{{d}^2}} \leadsto \frac{b \cdot c - a \cdot d}{{\left(\left|c\right|\right)}^2 + \color{blue}{{\left(\sqrt{{d}^2}\right)}^2}}\]
   7.4
7. Applied simplify to get
   \[\frac{b \cdot c - a \cdot d}{{\left(\left|c\right|\right)}^2 + {\color{red}{\left(\sqrt{{d}^2}\right)}}^2} \leadsto \frac{b \cdot c - a \cdot d}{{\left(\left|c\right|\right)}^2 + {\color{blue}{\left(\left|d\right|\right)}}^2}\]
   6.3
8. Applied taylor to get
   \[\frac{b \cdot c - a \cdot d}{{\left(\left|c\right|\right)}^2 + {\left(\left|d\right|\right)}^2} \leadsto \frac{b \cdot c}{{\left(\left|d\right|\right)}^2 + {\left(\left|c\right|\right)}^2} - \frac{d \cdot a}{{\left(\left|d\right|\right)}^2 + {\left(\left|c\right|\right)}^2}\]
   6.3
9. Taylor expanded around 0 to get
   \[\color{red}{\frac{b \cdot c}{{\left(\left|d\right|\right)}^2 + {\left(\left|c\right|\right)}^2} - \frac{d \cdot a}{{\left(\left|d\right|\right)}^2 + {\left(\left|c\right|\right)}^2}} \leadsto \color{blue}{\frac{b \cdot c}{{\left(\left|d\right|\right)}^2 + {\left(\left|c\right|\right)}^2} - \frac{d \cdot a}{{\left(\left|d\right|\right)}^2 + {\left(\left|c\right|\right)}^2}}\]
   6.3