if d < -3.8275299274957544e+122 or 9.200072780005278e+67 < d

1. Started with
   \[\frac{b \cdot c - a \cdot d}{{c}^2 + {d}^2}\]
   38.8
2. Using strategy rm
   38.8
3. Applied div-sub to get
   \[\color{red}{\frac{b \cdot c - a \cdot d}{{c}^2 + {d}^2}} \leadsto \color{blue}{\frac{b \cdot c}{{c}^2 + {d}^2} - \frac{a \cdot d}{{c}^2 + {d}^2}}\]
   38.8
4. Using strategy rm
   38.8
5. Applied associate-/l* to get
   \[\frac{b \cdot c}{{c}^2 + {d}^2} - \color{red}{\frac{a \cdot d}{{c}^2 + {d}^2}} \leadsto \frac{b \cdot c}{{c}^2 + {d}^2} - \color{blue}{\frac{a}{\frac{{c}^2 + {d}^2}{d}}}\]
   36.4
6. Applied taylor to get
   \[\frac{b \cdot c}{{c}^2 + {d}^2} - \frac{a}{\frac{{c}^2 + {d}^2}{d}} \leadsto \frac{b \cdot c}{{c}^2 + {d}^2} - \frac{a}{d + \frac{{c}^2}{d}}\]
   16.9
7. Taylor expanded around 0 to get
   \[\frac{b \cdot c}{{c}^2 + {d}^2} - \frac{a}{\color{red}{d + \frac{{c}^2}{d}}} \leadsto \frac{b \cdot c}{{c}^2 + {d}^2} - \frac{a}{\color{blue}{d + \frac{{c}^2}{d}}}\]
   16.9
8. Applied simplify to get
   \[\frac{b \cdot c}{{c}^2 + {d}^2} - \frac{a}{d + \frac{{c}^2}{d}} \leadsto \frac{c \cdot b}{(d * d + \left(c \cdot c\right))_*} - \frac{a}{d + \frac{c}{\frac{d}{c}}}\]
   13.2

---

9. Applied final simplification
10. Applied simplify to get
    \[\color{red}{\frac{c \cdot b}{(d * d + \left(c \cdot c\right))_*} - \frac{a}{d + \frac{c}{\frac{d}{c}}}} \leadsto \color{blue}{\frac{b \cdot c}{(d * d + \left({c}^2\right))_*} - \frac{a}{(\left(\frac{c}{d}\right) * c + d)_*}}\]
    13.2

if -3.8275299274957544e+122 < d < 9.200072780005278e+67

1. Started with
   \[\frac{b \cdot c - a \cdot d}{{c}^2 + {d}^2}\]
   18.8
2. Using strategy rm
   18.8
3. Applied div-sub to get
   \[\color{red}{\frac{b \cdot c - a \cdot d}{{c}^2 + {d}^2}} \leadsto \color{blue}{\frac{b \cdot c}{{c}^2 + {d}^2} - \frac{a \cdot d}{{c}^2 + {d}^2}}\]
   18.9
4. Using strategy rm
   18.9
5. Applied associate-/l* to get
   \[\color{red}{\frac{b \cdot c}{{c}^2 + {d}^2}} - \frac{a \cdot d}{{c}^2 + {d}^2} \leadsto \color{blue}{\frac{b}{\frac{{c}^2 + {d}^2}{c}}} - \frac{a \cdot d}{{c}^2 + {d}^2}\]
   16.6
6. Applied taylor to get
   \[\frac{b}{\frac{{c}^2 + {d}^2}{c}} - \frac{a \cdot d}{{c}^2 + {d}^2} \leadsto \frac{b}{c + \frac{{d}^2}{c}} - \frac{a \cdot d}{{c}^2 + {d}^2}\]
   6.2
7. Taylor expanded around 0 to get
   \[\frac{b}{\color{red}{c + \frac{{d}^2}{c}}} - \frac{a \cdot d}{{c}^2 + {d}^2} \leadsto \frac{b}{\color{blue}{c + \frac{{d}^2}{c}}} - \frac{a \cdot d}{{c}^2 + {d}^2}\]
   6.2
8. Applied simplify to get
   \[\frac{b}{c + \frac{{d}^2}{c}} - \frac{a \cdot d}{{c}^2 + {d}^2} \leadsto \frac{b}{\frac{d}{\frac{c}{d}} + c} - \frac{a \cdot d}{(c * c + \left(d \cdot d\right))_*}\]
   6.2

---

9. Applied final simplification
10. Applied simplify to get
    \[\color{red}{\frac{b}{\frac{d}{\frac{c}{d}} + c} - \frac{a \cdot d}{(c * c + \left(d \cdot d\right))_*}} \leadsto \color{blue}{\frac{b}{(\left(\frac{d}{c}\right) * d + c)_*} - \frac{d \cdot a}{(c * c + \left(d \cdot d\right))_*}}\]
    6.2