if c < -1.5817318f+16 or 2.7754534f+19 < c

1. Started with
   \[\frac{b \cdot c - a \cdot d}{{c}^2 + {d}^2}\]
   20.5
2. Using strategy rm
   20.5
3. Applied add-sqr-sqrt to get
   \[\frac{b \cdot c - a \cdot d}{{c}^2 + \color{red}{{d}^2}} \leadsto \frac{b \cdot c - a \cdot d}{{c}^2 + \color{blue}{{\left(\sqrt{{d}^2}\right)}^2}}\]
   20.5
4. Applied simplify to get
   \[\frac{b \cdot c - a \cdot d}{{c}^2 + {\color{red}{\left(\sqrt{{d}^2}\right)}}^2} \leadsto \frac{b \cdot c - a \cdot d}{{c}^2 + {\color{blue}{\left(\left|d\right|\right)}}^2}\]
   20.4
5. Using strategy rm
   20.4
6. Applied add-cube-cbrt to get
   \[\frac{b \cdot c - \color{red}{a \cdot d}}{{c}^2 + {\left(\left|d\right|\right)}^2} \leadsto \frac{b \cdot c - \color{blue}{{\left(\sqrt[3]{a \cdot d}\right)}^3}}{{c}^2 + {\left(\left|d\right|\right)}^2}\]
   20.4
7. Applied taylor to get
   \[\frac{b \cdot c - {\left(\sqrt[3]{a \cdot d}\right)}^3}{{c}^2 + {\left(\left|d\right|\right)}^2} \leadsto \frac{b}{c} - \frac{b \cdot {\left(\left|\frac{1}{d}\right|\right)}^2}{{c}^{3}}\]
   0.1
8. Taylor expanded around inf to get
   \[\color{red}{\frac{b}{c} - \frac{b \cdot {\left(\left|\frac{1}{d}\right|\right)}^2}{{c}^{3}}} \leadsto \color{blue}{\frac{b}{c} - \frac{b \cdot {\left(\left|\frac{1}{d}\right|\right)}^2}{{c}^{3}}}\]
   0.1
9. Applied taylor to get
   \[\frac{b}{c} - \frac{b \cdot {\left(\left|\frac{1}{d}\right|\right)}^2}{{c}^{3}} \leadsto \frac{b}{c}\]
   0
10. Taylor expanded around inf to get
    \[\color{red}{\frac{b}{c}} \leadsto \color{blue}{\frac{b}{c}}\]
    0
11. Applied simplify to get
    \[\frac{b}{c} \leadsto \frac{b}{c}\]
    0

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12. Applied final simplification

if -1.5817318f+16 < c < 2.7754534f+19

1. Started with
   \[\frac{b \cdot c - a \cdot d}{{c}^2 + {d}^2}\]
   8.9
2. Using strategy rm
   8.9
3. Applied add-sqr-sqrt to get
   \[\frac{b \cdot c - a \cdot d}{{c}^2 + \color{red}{{d}^2}} \leadsto \frac{b \cdot c - a \cdot d}{{c}^2 + \color{blue}{{\left(\sqrt{{d}^2}\right)}^2}}\]
   8.9
4. Applied simplify to get
   \[\frac{b \cdot c - a \cdot d}{{c}^2 + {\color{red}{\left(\sqrt{{d}^2}\right)}}^2} \leadsto \frac{b \cdot c - a \cdot d}{{c}^2 + {\color{blue}{\left(\left|d\right|\right)}}^2}\]
   6.0
5. Using strategy rm
   6.0
6. Applied add-cube-cbrt to get
   \[\frac{b \cdot c - \color{red}{a \cdot d}}{{c}^2 + {\left(\left|d\right|\right)}^2} \leadsto \frac{b \cdot c - \color{blue}{{\left(\sqrt[3]{a \cdot d}\right)}^3}}{{c}^2 + {\left(\left|d\right|\right)}^2}\]
   6.2
7. Using strategy rm
   6.2
8. Applied cbrt-prod to get
   \[\frac{b \cdot c - {\color{red}{\left(\sqrt[3]{a \cdot d}\right)}}^3}{{c}^2 + {\left(\left|d\right|\right)}^2} \leadsto \frac{b \cdot c - {\color{blue}{\left(\sqrt[3]{a} \cdot \sqrt[3]{d}\right)}}^3}{{c}^2 + {\left(\left|d\right|\right)}^2}\]
   2.5