if d < -3.2392491068805905e+80

1. Started with
   \[\frac{b \cdot c - a \cdot d}{{c}^2 + {d}^2}\]
   36.5
2. Using strategy rm
   36.5
3. Applied div-sub to get
   \[\color{red}{\frac{b \cdot c - a \cdot d}{{c}^2 + {d}^2}} \leadsto \color{blue}{\frac{b \cdot c}{{c}^2 + {d}^2} - \frac{a \cdot d}{{c}^2 + {d}^2}}\]
   36.5
4. Using strategy rm
   36.5
5. Applied associate-/l* to get
   \[\frac{b \cdot c}{{c}^2 + {d}^2} - \color{red}{\frac{a \cdot d}{{c}^2 + {d}^2}} \leadsto \frac{b \cdot c}{{c}^2 + {d}^2} - \color{blue}{\frac{a}{\frac{{c}^2 + {d}^2}{d}}}\]
   34.0
6. Applied taylor to get
   \[\frac{b \cdot c}{{c}^2 + {d}^2} - \frac{a}{\frac{{c}^2 + {d}^2}{d}} \leadsto \frac{b \cdot c}{{c}^2 + {d}^2} - \frac{a}{d + \frac{{c}^2}{d}}\]
   15.9
7. Taylor expanded around 0 to get
   \[\frac{b \cdot c}{{c}^2 + {d}^2} - \frac{a}{\color{red}{d + \frac{{c}^2}{d}}} \leadsto \frac{b \cdot c}{{c}^2 + {d}^2} - \frac{a}{\color{blue}{d + \frac{{c}^2}{d}}}\]
   15.9
8. Applied simplify to get
   \[\frac{b \cdot c}{{c}^2 + {d}^2} - \frac{a}{d + \frac{{c}^2}{d}} \leadsto \frac{c \cdot b}{d \cdot d + c \cdot c} - \frac{a}{d + \frac{c}{d} \cdot c}\]
   12.9

---

9. Applied final simplification
10. Applied simplify to get
    \[\color{red}{\frac{c \cdot b}{d \cdot d + c \cdot c} - \frac{a}{d + \frac{c}{d} \cdot c}} \leadsto \color{blue}{\frac{b \cdot c}{{c}^2 + d \cdot d} - \frac{a}{d + \frac{{c}^2}{d}}}\]
    15.9

if -3.2392491068805905e+80 < d < 1.0745561433792671e+141

1. Started with
   \[\frac{b \cdot c - a \cdot d}{{c}^2 + {d}^2}\]
   18.4
2. Using strategy rm
   18.4
3. Applied div-sub to get
   \[\color{red}{\frac{b \cdot c - a \cdot d}{{c}^2 + {d}^2}} \leadsto \color{blue}{\frac{b \cdot c}{{c}^2 + {d}^2} - \frac{a \cdot d}{{c}^2 + {d}^2}}\]
   18.5
4. Using strategy rm
   18.5
5. Applied associate-/l* to get
   \[\color{red}{\frac{b \cdot c}{{c}^2 + {d}^2}} - \frac{a \cdot d}{{c}^2 + {d}^2} \leadsto \color{blue}{\frac{b}{\frac{{c}^2 + {d}^2}{c}}} - \frac{a \cdot d}{{c}^2 + {d}^2}\]
   16.3
6. Applied taylor to get
   \[\frac{b}{\frac{{c}^2 + {d}^2}{c}} - \frac{a \cdot d}{{c}^2 + {d}^2} \leadsto \frac{b}{c + \frac{{d}^2}{c}} - \frac{a \cdot d}{{c}^2 + {d}^2}\]
   6.4
7. Taylor expanded around 0 to get
   \[\frac{b}{\color{red}{c + \frac{{d}^2}{c}}} - \frac{a \cdot d}{{c}^2 + {d}^2} \leadsto \frac{b}{\color{blue}{c + \frac{{d}^2}{c}}} - \frac{a \cdot d}{{c}^2 + {d}^2}\]
   6.4
8. Applied simplify to get
   \[\frac{b}{c + \frac{{d}^2}{c}} - \frac{a \cdot d}{{c}^2 + {d}^2} \leadsto \frac{b}{\frac{d \cdot d}{c} + c} - \frac{a \cdot d}{d \cdot d + c \cdot c}\]
   6.4

---

9. Applied final simplification

if 1.0745561433792671e+141 < d

1. Started with
   \[\frac{b \cdot c - a \cdot d}{{c}^2 + {d}^2}\]
   41.7
2. Using strategy rm
   41.7
3. Applied add-exp-log to get
   \[\frac{b \cdot c - a \cdot d}{\color{red}{{c}^2 + {d}^2}} \leadsto \frac{b \cdot c - a \cdot d}{\color{blue}{e^{\log \left({c}^2 + {d}^2\right)}}}\]
   41.8
4. Applied add-exp-log to get
   \[\frac{\color{red}{b \cdot c - a \cdot d}}{e^{\log \left({c}^2 + {d}^2\right)}} \leadsto \frac{\color{blue}{e^{\log \left(b \cdot c - a \cdot d\right)}}}{e^{\log \left({c}^2 + {d}^2\right)}}\]
   52.7
5. Applied div-exp to get
   \[\color{red}{\frac{e^{\log \left(b \cdot c - a \cdot d\right)}}{e^{\log \left({c}^2 + {d}^2\right)}}} \leadsto \color{blue}{e^{\log \left(b \cdot c - a \cdot d\right) - \log \left({c}^2 + {d}^2\right)}}\]
   52.7
6. Applied taylor to get
   \[e^{\log \left(b \cdot c - a \cdot d\right) - \log \left({c}^2 + {d}^2\right)} \leadsto e^{\left(\log a + \log -1\right) - \log d}\]
   62.9
7. Taylor expanded around 0 to get
   \[\color{red}{e^{\left(\log a + \log -1\right) - \log d}} \leadsto \color{blue}{e^{\left(\log a + \log -1\right) - \log d}}\]
   62.9
8. Applied simplify to get
   \[e^{\left(\log a + \log -1\right) - \log d} \leadsto \frac{-1}{d} \cdot a\]
   0.2

---

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