if c < -6.683374268310304e+118 or 1.2667703140962172e+134 < c

1. Started with
   \[\frac{b \cdot c - a \cdot d}{{c}^2 + {d}^2}\]
   40.2
2. Using strategy rm
   40.2
3. Applied clear-num to get
   \[\color{red}{\frac{b \cdot c - a \cdot d}{{c}^2 + {d}^2}} \leadsto \color{blue}{\frac{1}{\frac{{c}^2 + {d}^2}{b \cdot c - a \cdot d}}}\]
   40.2
4. Using strategy rm
   40.2
5. Applied add-cbrt-cube to get
   \[\frac{1}{\color{red}{\frac{{c}^2 + {d}^2}{b \cdot c - a \cdot d}}} \leadsto \frac{1}{\color{blue}{\sqrt[3]{{\left(\frac{{c}^2 + {d}^2}{b \cdot c - a \cdot d}\right)}^3}}}\]
   41.5
6. Applied taylor to get
   \[\frac{1}{\sqrt[3]{{\left(\frac{{c}^2 + {d}^2}{b \cdot c - a \cdot d}\right)}^3}} \leadsto \frac{b}{c}\]
   0
7. Taylor expanded around 0 to get
   \[\color{red}{\frac{b}{c}} \leadsto \color{blue}{\frac{b}{c}}\]
   0
8. Applied simplify to get
   \[\frac{b}{c} \leadsto \frac{b}{c}\]
   0

---

9. Applied final simplification

if -6.683374268310304e+118 < c < -1.0134394410721208e-159 or 7.847989728268068e-133 < c < 1.2667703140962172e+134

1. Started with
   \[\frac{b \cdot c - a \cdot d}{{c}^2 + {d}^2}\]
   16.9

if -1.0134394410721208e-159 < c < 7.847989728268068e-133

1. Started with
   \[\frac{b \cdot c - a \cdot d}{{c}^2 + {d}^2}\]
   32.3
2. Using strategy rm
   32.3
3. Applied clear-num to get
   \[\color{red}{\frac{b \cdot c - a \cdot d}{{c}^2 + {d}^2}} \leadsto \color{blue}{\frac{1}{\frac{{c}^2 + {d}^2}{b \cdot c - a \cdot d}}}\]
   32.3
4. Using strategy rm
   32.3
5. Applied add-exp-log to get
   \[\frac{1}{\frac{{c}^2 + {d}^2}{\color{red}{b \cdot c - a \cdot d}}} \leadsto \frac{1}{\frac{{c}^2 + {d}^2}{\color{blue}{e^{\log \left(b \cdot c - a \cdot d\right)}}}}\]
   48.9
6. Applied add-exp-log to get
   \[\frac{1}{\frac{\color{red}{{c}^2 + {d}^2}}{e^{\log \left(b \cdot c - a \cdot d\right)}}} \leadsto \frac{1}{\frac{\color{blue}{e^{\log \left({c}^2 + {d}^2\right)}}}{e^{\log \left(b \cdot c - a \cdot d\right)}}}\]
   49.0
7. Applied div-exp to get
   \[\frac{1}{\color{red}{\frac{e^{\log \left({c}^2 + {d}^2\right)}}{e^{\log \left(b \cdot c - a \cdot d\right)}}}} \leadsto \frac{1}{\color{blue}{e^{\log \left({c}^2 + {d}^2\right) - \log \left(b \cdot c - a \cdot d\right)}}}\]
   49.1
8. Applied taylor to get
   \[\frac{1}{e^{\log \left({c}^2 + {d}^2\right) - \log \left(b \cdot c - a \cdot d\right)}} \leadsto \frac{1}{e^{\log d - \left(\log a + \log -1\right)}}\]
   62.7
9. Taylor expanded around 0 to get
   \[\frac{1}{\color{red}{e^{\log d - \left(\log a + \log -1\right)}}} \leadsto \frac{1}{\color{blue}{e^{\log d - \left(\log a + \log -1\right)}}}\]
   62.7
10. Applied simplify to get
    \[\frac{1}{e^{\log d - \left(\log a + \log -1\right)}} \leadsto \frac{1}{d} \cdot \left(a \cdot -1\right)\]
    0.2

---

11. Applied final simplification
12. Applied simplify to get
    \[\color{red}{\frac{1}{d} \cdot \left(a \cdot -1\right)} \leadsto \color{blue}{-\frac{a}{d}}\]
    0