if c < -7.7955364f+09 or 6.144087f+15 < c

1. Started with
   \[\frac{b \cdot c - a \cdot d}{{c}^2 + {d}^2}\]
   20.5
2. Using strategy rm
   20.5
3. Applied add-sqr-sqrt to get
   \[\frac{b \cdot c - a \cdot d}{\color{red}{{c}^2 + {d}^2}} \leadsto \frac{b \cdot c - a \cdot d}{\color{blue}{{\left(\sqrt{{c}^2 + {d}^2}\right)}^2}}\]
   20.5
4. Applied taylor to get
   \[\frac{b \cdot c - a \cdot d}{{\left(\sqrt{{c}^2 + {d}^2}\right)}^2} \leadsto \frac{b \cdot c - a \cdot d}{{\left(-1 \cdot c\right)}^2}\]
   19.2
5. Taylor expanded around -inf to get
   \[\frac{b \cdot c - a \cdot d}{{\color{red}{\left(-1 \cdot c\right)}}^2} \leadsto \frac{b \cdot c - a \cdot d}{{\color{blue}{\left(-1 \cdot c\right)}}^2}\]
   19.2
6. Applied simplify to get
   \[\color{red}{\frac{b \cdot c - a \cdot d}{{\left(-1 \cdot c\right)}^2}} \leadsto \color{blue}{\frac{b}{c} - \frac{d}{c} \cdot \frac{a}{c}}\]
   0.3

if -7.7955364f+09 < c < 6.144087f+15

1. Started with
   \[\frac{b \cdot c - a \cdot d}{{c}^2 + {d}^2}\]
   8.6
2. Using strategy rm
   8.6
3. Applied div-sub to get
   \[\color{red}{\frac{b \cdot c - a \cdot d}{{c}^2 + {d}^2}} \leadsto \color{blue}{\frac{b \cdot c}{{c}^2 + {d}^2} - \frac{a \cdot d}{{c}^2 + {d}^2}}\]
   8.7
4. Using strategy rm
   8.7
5. Applied *-un-lft-identity to get
   \[\frac{b \cdot c}{{c}^2 + {d}^2} - \frac{a \cdot d}{\color{red}{{c}^2 + {d}^2}} \leadsto \frac{b \cdot c}{{c}^2 + {d}^2} - \frac{a \cdot d}{\color{blue}{1 \cdot \left({c}^2 + {d}^2\right)}}\]
   8.7
6. Applied times-frac to get
   \[\frac{b \cdot c}{{c}^2 + {d}^2} - \color{red}{\frac{a \cdot d}{1 \cdot \left({c}^2 + {d}^2\right)}} \leadsto \frac{b \cdot c}{{c}^2 + {d}^2} - \color{blue}{\frac{a}{1} \cdot \frac{d}{{c}^2 + {d}^2}}\]
   7.7