if d < -3.3416373575121975e+67 or 1.2610866829211587e+151 < d

1. Started with
   \[\frac{b \cdot c - a \cdot d}{{c}^2 + {d}^2}\]
   40.3
2. Using strategy rm
   40.3
3. Applied add-exp-log to get
   \[\color{red}{\frac{b \cdot c - a \cdot d}{{c}^2 + {d}^2}} \leadsto \color{blue}{e^{\log \left(\frac{b \cdot c - a \cdot d}{{c}^2 + {d}^2}\right)}}\]
   43.1
4. Applied taylor to get
   \[e^{\log \left(\frac{b \cdot c - a \cdot d}{{c}^2 + {d}^2}\right)} \leadsto e^{\left(\log a + \log -1\right) - \log d}\]
   62.9
5. Taylor expanded around 0 to get
   \[e^{\color{red}{\left(\log a + \log -1\right) - \log d}} \leadsto e^{\color{blue}{\left(\log a + \log -1\right) - \log d}}\]
   62.9
6. Applied simplify to get
   \[e^{\left(\log a + \log -1\right) - \log d} \leadsto \frac{-1}{d} \cdot a\]
   0.2

---

7. Applied final simplification
8. Applied simplify to get
   \[\color{red}{\frac{-1}{d} \cdot a} \leadsto \color{blue}{-\frac{a}{d}}\]
   0

if -3.3416373575121975e+67 < d < -2.818412928592266e-174

1. Started with
   \[\frac{b \cdot c - a \cdot d}{{c}^2 + {d}^2}\]
   15.5
2. Using strategy rm
   15.5
3. Applied clear-num to get
   \[\color{red}{\frac{b \cdot c - a \cdot d}{{c}^2 + {d}^2}} \leadsto \color{blue}{\frac{1}{\frac{{c}^2 + {d}^2}{b \cdot c - a \cdot d}}}\]
   15.7

if -2.818412928592266e-174 < d < 6.657343370671305e-139

1. Started with
   \[\frac{b \cdot c - a \cdot d}{{c}^2 + {d}^2}\]
   22.9
2. Using strategy rm
   22.9
3. Applied div-inv to get
   \[\color{red}{\frac{b \cdot c - a \cdot d}{{c}^2 + {d}^2}} \leadsto \color{blue}{\left(b \cdot c - a \cdot d\right) \cdot \frac{1}{{c}^2 + {d}^2}}\]
   23.2
4. Using strategy rm
   23.2
5. Applied add-sqr-sqrt to get
   \[\left(b \cdot c - a \cdot d\right) \cdot \color{red}{\frac{1}{{c}^2 + {d}^2}} \leadsto \left(b \cdot c - a \cdot d\right) \cdot \color{blue}{{\left(\sqrt{\frac{1}{{c}^2 + {d}^2}}\right)}^2}\]
   23.3
6. Using strategy rm
   23.3
7. Applied add-cube-cbrt to get
   \[\left(b \cdot c - a \cdot d\right) \cdot {\color{red}{\left(\sqrt{\frac{1}{{c}^2 + {d}^2}}\right)}}^2 \leadsto \left(b \cdot c - a \cdot d\right) \cdot {\color{blue}{\left({\left(\sqrt[3]{\sqrt{\frac{1}{{c}^2 + {d}^2}}}\right)}^3\right)}}^2\]
   24.0
8. Applied taylor to get
   \[\left(b \cdot c - a \cdot d\right) \cdot {\left({\left(\sqrt[3]{\sqrt{\frac{1}{{c}^2 + {d}^2}}}\right)}^3\right)}^2 \leadsto \frac{b}{c} - \frac{d \cdot a}{{c}^2}\]
   8.2
9. Taylor expanded around inf to get
   \[\color{red}{\frac{b}{c} - \frac{d \cdot a}{{c}^2}} \leadsto \color{blue}{\frac{b}{c} - \frac{d \cdot a}{{c}^2}}\]
   8.2
10. Applied simplify to get
    \[\frac{b}{c} - \frac{d \cdot a}{{c}^2} \leadsto \frac{b}{c} - \frac{a \cdot d}{c \cdot c}\]
    8.2

---

11. Applied final simplification

if 6.657343370671305e-139 < d < 1.2610866829211587e+151

1. Started with
   \[\frac{b \cdot c - a \cdot d}{{c}^2 + {d}^2}\]
   16.6
2. Using strategy rm
   16.6
3. Applied clear-num to get
   \[\color{red}{\frac{b \cdot c - a \cdot d}{{c}^2 + {d}^2}} \leadsto \color{blue}{\frac{1}{\frac{{c}^2 + {d}^2}{b \cdot c - a \cdot d}}}\]
   16.8