if c < -2.668639f+09 or 3.5788512f+20 < c

1. Started with
   \[\frac{b \cdot c - a \cdot d}{{c}^2 + {d}^2}\]
   20.8
2. Using strategy rm
   20.8
3. Applied add-sqr-sqrt to get
   \[\frac{b \cdot c - a \cdot d}{{c}^2 + \color{red}{{d}^2}} \leadsto \frac{b \cdot c - a \cdot d}{{c}^2 + \color{blue}{{\left(\sqrt{{d}^2}\right)}^2}}\]
   20.8
4. Applied simplify to get
   \[\frac{b \cdot c - a \cdot d}{{c}^2 + {\color{red}{\left(\sqrt{{d}^2}\right)}}^2} \leadsto \frac{b \cdot c - a \cdot d}{{c}^2 + {\color{blue}{\left(\left|d\right|\right)}}^2}\]
   20.8
5. Applied taylor to get
   \[\frac{b \cdot c - a \cdot d}{{c}^2 + {\left(\left|d\right|\right)}^2} \leadsto \left(\frac{b}{c} + \frac{d \cdot \left(a \cdot {\left(\left|\frac{1}{d}\right|\right)}^2\right)}{{c}^{4}}\right) - \frac{d \cdot a}{{c}^2}\]
   6.3
6. Taylor expanded around inf to get
   \[\color{red}{\left(\frac{b}{c} + \frac{d \cdot \left(a \cdot {\left(\left|\frac{1}{d}\right|\right)}^2\right)}{{c}^{4}}\right) - \frac{d \cdot a}{{c}^2}} \leadsto \color{blue}{\left(\frac{b}{c} + \frac{d \cdot \left(a \cdot {\left(\left|\frac{1}{d}\right|\right)}^2\right)}{{c}^{4}}\right) - \frac{d \cdot a}{{c}^2}}\]
   6.3
7. Applied taylor to get
   \[\left(\frac{b}{c} + \frac{d \cdot \left(a \cdot {\left(\left|\frac{1}{d}\right|\right)}^2\right)}{{c}^{4}}\right) - \frac{d \cdot a}{{c}^2} \leadsto \left(\frac{b}{c} + 0\right) - \frac{d \cdot a}{{c}^2}\]
   6.3
8. Taylor expanded around inf to get
   \[\left(\frac{b}{c} + \color{red}{0}\right) - \frac{d \cdot a}{{c}^2} \leadsto \left(\frac{b}{c} + \color{blue}{0}\right) - \frac{d \cdot a}{{c}^2}\]
   6.3
9. Applied simplify to get
   \[\left(\frac{b}{c} + 0\right) - \frac{d \cdot a}{{c}^2} \leadsto \frac{b}{c} - \frac{d}{c} \cdot \frac{a}{c}\]
   0.3

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10. Applied final simplification

if -2.668639f+09 < c < -4.7155537f-14 or 4.2462024f-16 < c < 3.5788512f+20

1. Started with
   \[\frac{b \cdot c - a \cdot d}{{c}^2 + {d}^2}\]
   8.3
2. Using strategy rm
   8.3
3. Applied add-sqr-sqrt to get
   \[\frac{b \cdot c - a \cdot d}{{c}^2 + \color{red}{{d}^2}} \leadsto \frac{b \cdot c - a \cdot d}{{c}^2 + \color{blue}{{\left(\sqrt{{d}^2}\right)}^2}}\]
   8.3
4. Applied simplify to get
   \[\frac{b \cdot c - a \cdot d}{{c}^2 + {\color{red}{\left(\sqrt{{d}^2}\right)}}^2} \leadsto \frac{b \cdot c - a \cdot d}{{c}^2 + {\color{blue}{\left(\left|d\right|\right)}}^2}\]
   5.7
5. Using strategy rm
   5.7
6. Applied add-cube-cbrt to get
   \[\color{red}{\frac{b \cdot c - a \cdot d}{{c}^2 + {\left(\left|d\right|\right)}^2}} \leadsto \color{blue}{{\left(\sqrt[3]{\frac{b \cdot c - a \cdot d}{{c}^2 + {\left(\left|d\right|\right)}^2}}\right)}^3}\]
   6.1

if -4.7155537f-14 < c < 4.2462024f-16

1. Started with
   \[\frac{b \cdot c - a \cdot d}{{c}^2 + {d}^2}\]
   11.0
2. Using strategy rm
   11.0
3. Applied add-sqr-sqrt to get
   \[\frac{b \cdot c - a \cdot d}{{c}^2 + \color{red}{{d}^2}} \leadsto \frac{b \cdot c - a \cdot d}{{c}^2 + \color{blue}{{\left(\sqrt{{d}^2}\right)}^2}}\]
   10.9
4. Applied simplify to get
   \[\frac{b \cdot c - a \cdot d}{{c}^2 + {\color{red}{\left(\sqrt{{d}^2}\right)}}^2} \leadsto \frac{b \cdot c - a \cdot d}{{c}^2 + {\color{blue}{\left(\left|d\right|\right)}}^2}\]
   7.0
5. Applied taylor to get
   \[\frac{b \cdot c - a \cdot d}{{c}^2 + {\left(\left|d\right|\right)}^2} \leadsto \frac{b \cdot c}{{\left(\left|d\right|\right)}^2} - \frac{d \cdot a}{{\left(\left|d\right|\right)}^2}\]
   6.1
6. Taylor expanded around 0 to get
   \[\color{red}{\frac{b \cdot c}{{\left(\left|d\right|\right)}^2} - \frac{d \cdot a}{{\left(\left|d\right|\right)}^2}} \leadsto \color{blue}{\frac{b \cdot c}{{\left(\left|d\right|\right)}^2} - \frac{d \cdot a}{{\left(\left|d\right|\right)}^2}}\]
   6.1
7. Applied taylor to get
   \[\frac{b \cdot c}{{\left(\left|d\right|\right)}^2} - \frac{d \cdot a}{{\left(\left|d\right|\right)}^2} \leadsto \frac{b \cdot c}{{\left(\left|d\right|\right)}^2} - \frac{d \cdot a}{{\left(\left|d\right|\right)}^2}\]
   6.1
8. Taylor expanded around 0 to get
   \[\frac{b \cdot c}{{\left(\left|d\right|\right)}^2} - \color{red}{\frac{d \cdot a}{{\left(\left|d\right|\right)}^2}} \leadsto \frac{b \cdot c}{{\left(\left|d\right|\right)}^2} - \color{blue}{\frac{d \cdot a}{{\left(\left|d\right|\right)}^2}}\]
   6.1
9. Applied simplify to get
   \[\frac{b \cdot c}{{\left(\left|d\right|\right)}^2} - \frac{d \cdot a}{{\left(\left|d\right|\right)}^2} \leadsto \frac{b}{\left|d\right|} \cdot \frac{c}{\left|d\right|} - \frac{a}{\left|d\right|} \cdot \frac{d}{\left|d\right|}\]
   0

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10. Applied final simplification