if c < -6.6080815f+13 or 3.5788512f+20 < c

1. Started with
   \[\frac{b \cdot c - a \cdot d}{{c}^2 + {d}^2}\]
   21.4
2. Using strategy rm
   21.4
3. Applied add-sqr-sqrt to get
   \[\frac{b \cdot c - a \cdot d}{{c}^2 + \color{red}{{d}^2}} \leadsto \frac{b \cdot c - a \cdot d}{{c}^2 + \color{blue}{{\left(\sqrt{{d}^2}\right)}^2}}\]
   21.4
4. Applied simplify to get
   \[\frac{b \cdot c - a \cdot d}{{c}^2 + {\color{red}{\left(\sqrt{{d}^2}\right)}}^2} \leadsto \frac{b \cdot c - a \cdot d}{{c}^2 + {\color{blue}{\left(\left|d\right|\right)}}^2}\]
   21.4
5. Applied taylor to get
   \[\frac{b \cdot c - a \cdot d}{{c}^2 + {\left(\left|d\right|\right)}^2} \leadsto \left(\frac{b}{c} + \frac{d \cdot \left(a \cdot {\left(\left|\frac{1}{d}\right|\right)}^2\right)}{{c}^{4}}\right) - \frac{d \cdot a}{{c}^2}\]
   6.5
6. Taylor expanded around inf to get
   \[\color{red}{\left(\frac{b}{c} + \frac{d \cdot \left(a \cdot {\left(\left|\frac{1}{d}\right|\right)}^2\right)}{{c}^{4}}\right) - \frac{d \cdot a}{{c}^2}} \leadsto \color{blue}{\left(\frac{b}{c} + \frac{d \cdot \left(a \cdot {\left(\left|\frac{1}{d}\right|\right)}^2\right)}{{c}^{4}}\right) - \frac{d \cdot a}{{c}^2}}\]
   6.5
7. Applied taylor to get
   \[\left(\frac{b}{c} + \frac{d \cdot \left(a \cdot {\left(\left|\frac{1}{d}\right|\right)}^2\right)}{{c}^{4}}\right) - \frac{d \cdot a}{{c}^2} \leadsto \left(\frac{b}{c} + 0\right) - \frac{d \cdot a}{{c}^2}\]
   6.5
8. Taylor expanded around inf to get
   \[\left(\frac{b}{c} + \color{red}{0}\right) - \frac{d \cdot a}{{c}^2} \leadsto \left(\frac{b}{c} + \color{blue}{0}\right) - \frac{d \cdot a}{{c}^2}\]
   6.5
9. Applied simplify to get
   \[\left(\frac{b}{c} + 0\right) - \frac{d \cdot a}{{c}^2} \leadsto \frac{b}{c} - \frac{d}{c} \cdot \frac{a}{c}\]
   0.2

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10. Applied final simplification

if -6.6080815f+13 < c < 3.5788512f+20

1. Started with
   \[\frac{b \cdot c - a \cdot d}{{c}^2 + {d}^2}\]
   9.1
2. Using strategy rm
   9.1
3. Applied add-sqr-sqrt to get
   \[\frac{b \cdot c - a \cdot d}{{c}^2 + \color{red}{{d}^2}} \leadsto \frac{b \cdot c - a \cdot d}{{c}^2 + \color{blue}{{\left(\sqrt{{d}^2}\right)}^2}}\]
   9.1
4. Applied simplify to get
   \[\frac{b \cdot c - a \cdot d}{{c}^2 + {\color{red}{\left(\sqrt{{d}^2}\right)}}^2} \leadsto \frac{b \cdot c - a \cdot d}{{c}^2 + {\color{blue}{\left(\left|d\right|\right)}}^2}\]
   6.3
5. Using strategy rm
   6.3
6. Applied add-cube-cbrt to get
   \[\frac{b \cdot c - \color{red}{a \cdot d}}{{c}^2 + {\left(\left|d\right|\right)}^2} \leadsto \frac{b \cdot c - \color{blue}{{\left(\sqrt[3]{a \cdot d}\right)}^3}}{{c}^2 + {\left(\left|d\right|\right)}^2}\]
   6.5
7. Using strategy rm
   6.5
8. Applied cbrt-prod to get
   \[\frac{b \cdot c - {\color{red}{\left(\sqrt[3]{a \cdot d}\right)}}^3}{{c}^2 + {\left(\left|d\right|\right)}^2} \leadsto \frac{b \cdot c - {\color{blue}{\left(\sqrt[3]{a} \cdot \sqrt[3]{d}\right)}}^3}{{c}^2 + {\left(\left|d\right|\right)}^2}\]
   2.6