if c < -1.3842965018545015e+45 or 2.962024194070207e+128 < c

1. Started with
   \[\frac{b \cdot c - a \cdot d}{{c}^2 + {d}^2}\]
   39.5
2. Using strategy rm
   39.5
3. Applied add-cbrt-cube to get
   \[\frac{b \cdot c - a \cdot d}{\color{red}{{c}^2 + {d}^2}} \leadsto \frac{b \cdot c - a \cdot d}{\color{blue}{\sqrt[3]{{\left({c}^2 + {d}^2\right)}^3}}}\]
   47.8
4. Applied taylor to get
   \[\frac{b \cdot c - a \cdot d}{\sqrt[3]{{\left({c}^2 + {d}^2\right)}^3}} \leadsto \frac{b}{c} - \frac{d \cdot a}{{c}^2}\]
   11.8
5. Taylor expanded around inf to get
   \[\color{red}{\frac{b}{c} - \frac{d \cdot a}{{c}^2}} \leadsto \color{blue}{\frac{b}{c} - \frac{d \cdot a}{{c}^2}}\]
   11.8
6. Applied simplify to get
   \[\frac{b}{c} - \frac{d \cdot a}{{c}^2} \leadsto \frac{b}{c} - \frac{a \cdot d}{c \cdot c}\]
   11.8

---

7. Applied final simplification

if -1.3842965018545015e+45 < c < 2.962024194070207e+128

1. Started with
   \[\frac{b \cdot c - a \cdot d}{{c}^2 + {d}^2}\]
   18.4
2. Using strategy rm
   18.4
3. Applied div-sub to get
   \[\color{red}{\frac{b \cdot c - a \cdot d}{{c}^2 + {d}^2}} \leadsto \color{blue}{\frac{b \cdot c}{{c}^2 + {d}^2} - \frac{a \cdot d}{{c}^2 + {d}^2}}\]
   18.4
4. Using strategy rm
   18.4
5. Applied *-un-lft-identity to get
   \[\frac{b \cdot c}{{c}^2 + {d}^2} - \frac{a \cdot d}{\color{red}{{c}^2 + {d}^2}} \leadsto \frac{b \cdot c}{{c}^2 + {d}^2} - \frac{a \cdot d}{\color{blue}{1 \cdot \left({c}^2 + {d}^2\right)}}\]
   18.4
6. Applied times-frac to get
   \[\frac{b \cdot c}{{c}^2 + {d}^2} - \color{red}{\frac{a \cdot d}{1 \cdot \left({c}^2 + {d}^2\right)}} \leadsto \frac{b \cdot c}{{c}^2 + {d}^2} - \color{blue}{\frac{a}{1} \cdot \frac{d}{{c}^2 + {d}^2}}\]
   16.1