if d < -3.1052615f+11 or 1.1137253f+10 < d

1. Started with
   \[\frac{a \cdot c + b \cdot d}{{c}^2 + {d}^2}\]
   19.6
2. Using strategy rm
   19.6
3. Applied add-exp-log to get
   \[\color{red}{\frac{a \cdot c + b \cdot d}{{c}^2 + {d}^2}} \leadsto \color{blue}{e^{\log \left(\frac{a \cdot c + b \cdot d}{{c}^2 + {d}^2}\right)}}\]
   21.6
4. Applied taylor to get
   \[e^{\log \left(\frac{a \cdot c + b \cdot d}{{c}^2 + {d}^2}\right)} \leadsto e^{\log b - \log d}\]
   23.8
5. Taylor expanded around 0 to get
   \[e^{\color{red}{\log b - \log d}} \leadsto e^{\color{blue}{\log b - \log d}}\]
   23.8
6. Applied simplify to get
   \[e^{\log b - \log d} \leadsto \frac{b}{d}\]
   0

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7. Applied final simplification

if -3.1052615f+11 < d < 9.972299f-21

1. Started with
   \[\frac{a \cdot c + b \cdot d}{{c}^2 + {d}^2}\]
   13.2
2. Using strategy rm
   13.2
3. Applied add-cube-cbrt to get
   \[\frac{a \cdot c + b \cdot d}{\color{red}{{c}^2 + {d}^2}} \leadsto \frac{a \cdot c + b \cdot d}{\color{blue}{{\left(\sqrt[3]{{c}^2 + {d}^2}\right)}^3}}\]
   13.4
4. Applied taylor to get
   \[\frac{a \cdot c + b \cdot d}{{\left(\sqrt[3]{{c}^2 + {d}^2}\right)}^3} \leadsto \frac{a}{c} + \frac{b \cdot d}{{c}^2}\]
   3.2
5. Taylor expanded around inf to get
   \[\color{red}{\frac{a}{c} + \frac{b \cdot d}{{c}^2}} \leadsto \color{blue}{\frac{a}{c} + \frac{b \cdot d}{{c}^2}}\]
   3.2
6. Applied simplify to get
   \[\frac{a}{c} + \frac{b \cdot d}{{c}^2} \leadsto \frac{a}{c} + \frac{b}{c} \cdot \frac{d}{c}\]
   0.9

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7. Applied final simplification

if 9.972299f-21 < d < 1.1137253f+10

1. Started with
   \[\frac{a \cdot c + b \cdot d}{{c}^2 + {d}^2}\]
   7.1