if x < -0.0007312005f0

1. Started with
   \[\sqrt{\frac{e^{2 \cdot x} - 1}{e^{x} - 1}}\]
   0.2
2. Using strategy rm
   0.2
3. Applied add-sqr-sqrt to get
   \[\sqrt{\frac{\color{red}{e^{2 \cdot x}} - 1}{e^{x} - 1}} \leadsto \sqrt{\frac{\color{blue}{{\left(\sqrt{e^{2 \cdot x}}\right)}^2} - 1}{e^{x} - 1}}\]
   0.0
4. Applied difference-of-sqr-1 to get
   \[\sqrt{\frac{\color{red}{{\left(\sqrt{e^{2 \cdot x}}\right)}^2 - 1}}{e^{x} - 1}} \leadsto \sqrt{\frac{\color{blue}{\left(\sqrt{e^{2 \cdot x}} + 1\right) \cdot \left(\sqrt{e^{2 \cdot x}} - 1\right)}}{e^{x} - 1}}\]
   0.0
5. Using strategy rm
   0.0
6. Applied flip3-- to get
   \[\sqrt{\frac{\left(\sqrt{e^{2 \cdot x}} + 1\right) \cdot \left(\sqrt{e^{2 \cdot x}} - 1\right)}{\color{red}{e^{x} - 1}}} \leadsto \sqrt{\frac{\left(\sqrt{e^{2 \cdot x}} + 1\right) \cdot \left(\sqrt{e^{2 \cdot x}} - 1\right)}{\color{blue}{\frac{{\left(e^{x}\right)}^{3} - {1}^{3}}{{\left(e^{x}\right)}^2 + \left({1}^2 + e^{x} \cdot 1\right)}}}}\]
   0.1
7. Applied simplify to get
   \[\sqrt{\frac{\left(\sqrt{e^{2 \cdot x}} + 1\right) \cdot \left(\sqrt{e^{2 \cdot x}} - 1\right)}{\frac{\color{red}{{\left(e^{x}\right)}^{3} - {1}^{3}}}{{\left(e^{x}\right)}^2 + \left({1}^2 + e^{x} \cdot 1\right)}}} \leadsto \sqrt{\frac{\left(\sqrt{e^{2 \cdot x}} + 1\right) \cdot \left(\sqrt{e^{2 \cdot x}} - 1\right)}{\frac{\color{blue}{{\left(e^{x}\right)}^3 - 1}}{{\left(e^{x}\right)}^2 + \left({1}^2 + e^{x} \cdot 1\right)}}}\]
   0.0
8. Applied simplify to get
   \[\sqrt{\frac{\left(\sqrt{e^{2 \cdot x}} + 1\right) \cdot \left(\sqrt{e^{2 \cdot x}} - 1\right)}{\frac{{\left(e^{x}\right)}^3 - 1}{\color{red}{{\left(e^{x}\right)}^2 + \left({1}^2 + e^{x} \cdot 1\right)}}}} \leadsto \sqrt{\frac{\left(\sqrt{e^{2 \cdot x}} + 1\right) \cdot \left(\sqrt{e^{2 \cdot x}} - 1\right)}{\frac{{\left(e^{x}\right)}^3 - 1}{\color{blue}{\left(e^{x} + 1\right) + e^{x} \cdot e^{x}}}}}\]
   0.0
9. Applied simplify to get
   \[\sqrt{\frac{\left(\sqrt{e^{2 \cdot x}} + 1\right) \cdot \left(\sqrt{e^{2 \cdot x}} - 1\right)}{\frac{{\left(e^{x}\right)}^3 - 1}{\left(e^{x} + 1\right) + \color{red}{e^{x} \cdot e^{x}}}}} \leadsto \sqrt{\frac{\left(\sqrt{e^{2 \cdot x}} + 1\right) \cdot \left(\sqrt{e^{2 \cdot x}} - 1\right)}{\frac{{\left(e^{x}\right)}^3 - 1}{\left(e^{x} + 1\right) + \color{blue}{e^{x + x}}}}}\]
   0.0

if -0.0007312005f0 < x

1. Started with
   \[\sqrt{\frac{e^{2 \cdot x} - 1}{e^{x} - 1}}\]
   27.1
2. Applied taylor to get
   \[\sqrt{\frac{e^{2 \cdot x} - 1}{e^{x} - 1}} \leadsto \left(\frac{1}{2} \cdot \frac{x}{\sqrt{2}} + \left(\sqrt{2} + \frac{1}{4} \cdot \frac{{x}^2}{\sqrt{2}}\right)\right) - \frac{1}{8} \cdot \frac{{x}^2}{{\left(\sqrt{2}\right)}^{3}}\]
   0.2
3. Taylor expanded around 0 to get
   \[\color{red}{\left(\frac{1}{2} \cdot \frac{x}{\sqrt{2}} + \left(\sqrt{2} + \frac{1}{4} \cdot \frac{{x}^2}{\sqrt{2}}\right)\right) - \frac{1}{8} \cdot \frac{{x}^2}{{\left(\sqrt{2}\right)}^{3}}} \leadsto \color{blue}{\left(\frac{1}{2} \cdot \frac{x}{\sqrt{2}} + \left(\sqrt{2} + \frac{1}{4} \cdot \frac{{x}^2}{\sqrt{2}}\right)\right) - \frac{1}{8} \cdot \frac{{x}^2}{{\left(\sqrt{2}\right)}^{3}}}\]
   0.2
4. Applied simplify to get
   \[\color{red}{\left(\frac{1}{2} \cdot \frac{x}{\sqrt{2}} + \left(\sqrt{2} + \frac{1}{4} \cdot \frac{{x}^2}{\sqrt{2}}\right)\right) - \frac{1}{8} \cdot \frac{{x}^2}{{\left(\sqrt{2}\right)}^{3}}} \leadsto \color{blue}{\left(\frac{x \cdot \frac{1}{2}}{\sqrt{2}} + \sqrt{2}\right) + \frac{x \cdot x}{\sqrt{2}} \cdot \left(\frac{1}{4} - \frac{\frac{1}{8}}{2}\right)}\]
   0.2
5. Applied simplify to get
   \[\left(\frac{x \cdot \frac{1}{2}}{\sqrt{2}} + \sqrt{2}\right) + \color{red}{\frac{x \cdot x}{\sqrt{2}} \cdot \left(\frac{1}{4} - \frac{\frac{1}{8}}{2}\right)} \leadsto \left(\frac{x \cdot \frac{1}{2}}{\sqrt{2}} + \sqrt{2}\right) + \color{blue}{\left(\frac{1}{4} - \frac{\frac{1}{8}}{2}\right) \cdot \frac{{x}^2}{\sqrt{2}}}\]
   0.2