if c < -2.2155360606085996e+134 or 6.209412377058245e+96 < c

1. Started with
   \[\frac{b \cdot c - a \cdot d}{{c}^2 + {d}^2}\]
   42.4
2. Using strategy rm
   42.4
3. Applied div-inv to get
   \[\color{red}{\frac{b \cdot c - a \cdot d}{{c}^2 + {d}^2}} \leadsto \color{blue}{\left(b \cdot c - a \cdot d\right) \cdot \frac{1}{{c}^2 + {d}^2}}\]
   42.4
4. Using strategy rm
   42.4
5. Applied add-cbrt-cube to get
   \[\left(b \cdot c - a \cdot d\right) \cdot \color{red}{\frac{1}{{c}^2 + {d}^2}} \leadsto \left(b \cdot c - a \cdot d\right) \cdot \color{blue}{\sqrt[3]{{\left(\frac{1}{{c}^2 + {d}^2}\right)}^3}}\]
   47.3
6. Applied taylor to get
   \[\left(b \cdot c - a \cdot d\right) \cdot \sqrt[3]{{\left(\frac{1}{{c}^2 + {d}^2}\right)}^3} \leadsto \frac{b}{c} - \frac{d \cdot a}{{c}^2}\]
   11.9
7. Taylor expanded around inf to get
   \[\color{red}{\frac{b}{c} - \frac{d \cdot a}{{c}^2}} \leadsto \color{blue}{\frac{b}{c} - \frac{d \cdot a}{{c}^2}}\]
   11.9
8. Applied simplify to get
   \[\frac{b}{c} - \frac{d \cdot a}{{c}^2} \leadsto \frac{b}{c} - \frac{a \cdot d}{c \cdot c}\]
   11.9

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9. Applied final simplification

if -2.2155360606085996e+134 < c < 6.209412377058245e+96

1. Started with
   \[\frac{b \cdot c - a \cdot d}{{c}^2 + {d}^2}\]
   18.2
2. Using strategy rm
   18.2
3. Applied clear-num to get
   \[\color{red}{\frac{b \cdot c - a \cdot d}{{c}^2 + {d}^2}} \leadsto \color{blue}{\frac{1}{\frac{{c}^2 + {d}^2}{b \cdot c - a \cdot d}}}\]
   18.4