if re < -6.457467f0

1. Started with
   \[0.5 \cdot \sqrt{2.0 \cdot \left(\sqrt{re \cdot re + im \cdot im} + re\right)}\]
   28.3
2. Using strategy rm
   28.3
3. Applied flip-+ to get
   \[0.5 \cdot \sqrt{2.0 \cdot \color{red}{\left(\sqrt{re \cdot re + im \cdot im} + re\right)}} \leadsto 0.5 \cdot \sqrt{2.0 \cdot \color{blue}{\frac{{\left(\sqrt{re \cdot re + im \cdot im}\right)}^2 - {re}^2}{\sqrt{re \cdot re + im \cdot im} - re}}}\]
   29.3
4. Applied associate-*r/ to get
   \[0.5 \cdot \sqrt{\color{red}{2.0 \cdot \frac{{\left(\sqrt{re \cdot re + im \cdot im}\right)}^2 - {re}^2}{\sqrt{re \cdot re + im \cdot im} - re}}} \leadsto 0.5 \cdot \sqrt{\color{blue}{\frac{2.0 \cdot \left({\left(\sqrt{re \cdot re + im \cdot im}\right)}^2 - {re}^2\right)}{\sqrt{re \cdot re + im \cdot im} - re}}}\]
   29.3
5. Applied sqrt-div to get
   \[0.5 \cdot \color{red}{\sqrt{\frac{2.0 \cdot \left({\left(\sqrt{re \cdot re + im \cdot im}\right)}^2 - {re}^2\right)}{\sqrt{re \cdot re + im \cdot im} - re}}} \leadsto 0.5 \cdot \color{blue}{\frac{\sqrt{2.0 \cdot \left({\left(\sqrt{re \cdot re + im \cdot im}\right)}^2 - {re}^2\right)}}{\sqrt{\sqrt{re \cdot re + im \cdot im} - re}}}\]
   29.3
6. Applied simplify to get
   \[0.5 \cdot \frac{\color{red}{\sqrt{2.0 \cdot \left({\left(\sqrt{re \cdot re + im \cdot im}\right)}^2 - {re}^2\right)}}}{\sqrt{\sqrt{re \cdot re + im \cdot im} - re}} \leadsto 0.5 \cdot \frac{\color{blue}{\sqrt{\left(2.0 \cdot im\right) \cdot im}}}{\sqrt{\sqrt{re \cdot re + im \cdot im} - re}}\]
   19.9
7. Applied simplify to get
   \[0.5 \cdot \frac{\sqrt{\left(2.0 \cdot im\right) \cdot im}}{\color{red}{\sqrt{\sqrt{re \cdot re + im \cdot im} - re}}} \leadsto 0.5 \cdot \frac{\sqrt{\left(2.0 \cdot im\right) \cdot im}}{\color{blue}{\sqrt{\sqrt{{re}^2 + im \cdot im} - re}}}\]
   19.9
8. Applied taylor to get
   \[0.5 \cdot \frac{\sqrt{\left(2.0 \cdot im\right) \cdot im}}{\sqrt{\sqrt{{re}^2 + im \cdot im} - re}} \leadsto 0.5 \cdot \frac{\sqrt{\left(2.0 \cdot im\right) \cdot im}}{\sqrt{-2 \cdot re}}\]
   10.9
9. Taylor expanded around -inf to get
   \[0.5 \cdot \frac{\sqrt{\left(2.0 \cdot im\right) \cdot im}}{\sqrt{\color{red}{-2 \cdot re}}} \leadsto 0.5 \cdot \frac{\sqrt{\left(2.0 \cdot im\right) \cdot im}}{\sqrt{\color{blue}{-2 \cdot re}}}\]
   10.9
10. Applied simplify to get
    \[0.5 \cdot \frac{\sqrt{\left(2.0 \cdot im\right) \cdot im}}{\sqrt{-2 \cdot re}} \leadsto \frac{\sqrt{\left(im \cdot im\right) \cdot 2.0}}{\frac{\sqrt{-2 \cdot re}}{0.5}}\]
    10.9

---

11. Applied final simplification
12. Applied simplify to get
    \[\color{red}{\frac{\sqrt{\left(im \cdot im\right) \cdot 2.0}}{\frac{\sqrt{-2 \cdot re}}{0.5}}} \leadsto \color{blue}{\sqrt{{im}^2 \cdot 2.0} \cdot \frac{0.5}{\sqrt{re \cdot -2}}}\]
    10.9

if -6.457467f0 < re < 2.8363323f+14

1. Started with
   \[0.5 \cdot \sqrt{2.0 \cdot \left(\sqrt{re \cdot re + im \cdot im} + re\right)}\]
   12.3

if 2.8363323f+14 < re

1. Started with
   \[0.5 \cdot \sqrt{2.0 \cdot \left(\sqrt{re \cdot re + im \cdot im} + re\right)}\]
   25.1
2. Applied taylor to get
   \[0.5 \cdot \sqrt{2.0 \cdot \left(\sqrt{re \cdot re + im \cdot im} + re\right)} \leadsto 0.5 \cdot \sqrt{2.0 \cdot \left(re + re\right)}\]
   0.5
3. Taylor expanded around inf to get
   \[0.5 \cdot \sqrt{2.0 \cdot \left(\color{red}{re} + re\right)} \leadsto 0.5 \cdot \sqrt{2.0 \cdot \left(\color{blue}{re} + re\right)}\]
   0.5