if c < -4.9221833f+10 or 4.1923042f+15 < c

1. Started with
   \[\frac{b \cdot c - a \cdot d}{{c}^2 + {d}^2}\]
   20.3
2. Using strategy rm
   20.3
3. Applied add-sqr-sqrt to get
   \[\frac{b \cdot c - a \cdot d}{\color{red}{{c}^2 + {d}^2}} \leadsto \frac{b \cdot c - a \cdot d}{\color{blue}{{\left(\sqrt{{c}^2 + {d}^2}\right)}^2}}\]
   20.3
4. Applied taylor to get
   \[\frac{b \cdot c - a \cdot d}{{\left(\sqrt{{c}^2 + {d}^2}\right)}^2} \leadsto \frac{b \cdot c - a \cdot d}{{\left(-1 \cdot c\right)}^2}\]
   19.0
5. Taylor expanded around -inf to get
   \[\frac{b \cdot c - a \cdot d}{{\color{red}{\left(-1 \cdot c\right)}}^2} \leadsto \frac{b \cdot c - a \cdot d}{{\color{blue}{\left(-1 \cdot c\right)}}^2}\]
   19.0
6. Applied simplify to get
   \[\color{red}{\frac{b \cdot c - a \cdot d}{{\left(-1 \cdot c\right)}^2}} \leadsto \color{blue}{\frac{b}{c} - \frac{d}{c} \cdot \frac{a}{c}}\]
   0.4

if -4.9221833f+10 < c < 4.1923042f+15

1. Started with
   \[\frac{b \cdot c - a \cdot d}{{c}^2 + {d}^2}\]
   8.7
2. Using strategy rm
   8.7
3. Applied div-sub to get
   \[\color{red}{\frac{b \cdot c - a \cdot d}{{c}^2 + {d}^2}} \leadsto \color{blue}{\frac{b \cdot c}{{c}^2 + {d}^2} - \frac{a \cdot d}{{c}^2 + {d}^2}}\]
   8.8
4. Using strategy rm
   8.8
5. Applied associate-/l* to get
   \[\frac{b \cdot c}{{c}^2 + {d}^2} - \color{red}{\frac{a \cdot d}{{c}^2 + {d}^2}} \leadsto \frac{b \cdot c}{{c}^2 + {d}^2} - \color{blue}{\frac{a}{\frac{{c}^2 + {d}^2}{d}}}\]
   7.7
6. Applied taylor to get
   \[\frac{b \cdot c}{{c}^2 + {d}^2} - \frac{a}{\frac{{c}^2 + {d}^2}{d}} \leadsto \frac{b \cdot c}{{c}^2 + {d}^2} - \frac{a}{d + \frac{{c}^2}{d}}\]
   2.8
7. Taylor expanded around 0 to get
   \[\frac{b \cdot c}{{c}^2 + {d}^2} - \frac{a}{\color{red}{d + \frac{{c}^2}{d}}} \leadsto \frac{b \cdot c}{{c}^2 + {d}^2} - \frac{a}{\color{blue}{d + \frac{{c}^2}{d}}}\]
   2.8
8. Applied simplify to get
   \[\frac{b \cdot c}{{c}^2 + {d}^2} - \frac{a}{d + \frac{{c}^2}{d}} \leadsto \frac{c \cdot b}{d \cdot d + c \cdot c} - \frac{a}{d + \frac{c}{d} \cdot c}\]
   2.8

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9. Applied final simplification
10. Applied simplify to get
    \[\color{red}{\frac{c \cdot b}{d \cdot d + c \cdot c} - \frac{a}{d + \frac{c}{d} \cdot c}} \leadsto \color{blue}{\frac{b \cdot c}{{c}^2 + d \cdot d} - \frac{a}{d + \frac{{c}^2}{d}}}\]
    2.8