\(\frac{\frac{\left({\left(\frac{\beta}{(i * 2 + \beta)_* + \left(2.0 + \alpha\right)}\right)}^2 - {\left(\frac{\alpha}{(i * 2 + \beta)_* + \left(2.0 + \alpha\right)}\right)}^2\right) \cdot \left(\alpha + \beta\right)}{\left(\frac{\beta}{(i * 2 + \beta)_* + \left(2.0 + \alpha\right)} + \frac{\alpha}{(i * 2 + \beta)_* + \left(2.0 + \alpha\right)}\right) \cdot (2 * i + \left(\alpha + \beta\right))_*} + 1.0}{2.0}\)
- Started with
\[\frac{\frac{\frac{\left(\alpha + \beta\right) \cdot \left(\beta - \alpha\right)}{\left(\alpha + \beta\right) + 2 \cdot i}}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) + 2.0} + 1.0}{2.0}\]
11.1
- Applied simplify to get
\[\color{red}{\frac{\frac{\frac{\left(\alpha + \beta\right) \cdot \left(\beta - \alpha\right)}{\left(\alpha + \beta\right) + 2 \cdot i}}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) + 2.0} + 1.0}{2.0}} \leadsto \color{blue}{\frac{(\left(\frac{\beta - \alpha}{(i * 2 + \beta)_* + \left(2.0 + \alpha\right)}\right) * \left(\frac{\alpha + \beta}{(2 * i + \left(\alpha + \beta\right))_*}\right) + 1.0)_*}{2.0}}\]
4.9
- Using strategy
rm 4.9
- Applied fma-udef to get
\[\frac{\color{red}{(\left(\frac{\beta - \alpha}{(i * 2 + \beta)_* + \left(2.0 + \alpha\right)}\right) * \left(\frac{\alpha + \beta}{(2 * i + \left(\alpha + \beta\right))_*}\right) + 1.0)_*}}{2.0} \leadsto \frac{\color{blue}{\frac{\beta - \alpha}{(i * 2 + \beta)_* + \left(2.0 + \alpha\right)} \cdot \frac{\alpha + \beta}{(2 * i + \left(\alpha + \beta\right))_*} + 1.0}}{2.0}\]
4.5
- Using strategy
rm 4.5
- Applied div-sub to get
\[\frac{\color{red}{\frac{\beta - \alpha}{(i * 2 + \beta)_* + \left(2.0 + \alpha\right)}} \cdot \frac{\alpha + \beta}{(2 * i + \left(\alpha + \beta\right))_*} + 1.0}{2.0} \leadsto \frac{\color{blue}{\left(\frac{\beta}{(i * 2 + \beta)_* + \left(2.0 + \alpha\right)} - \frac{\alpha}{(i * 2 + \beta)_* + \left(2.0 + \alpha\right)}\right)} \cdot \frac{\alpha + \beta}{(2 * i + \left(\alpha + \beta\right))_*} + 1.0}{2.0}\]
4.2
- Using strategy
rm 4.2
- Applied flip-- to get
\[\frac{\color{red}{\left(\frac{\beta}{(i * 2 + \beta)_* + \left(2.0 + \alpha\right)} - \frac{\alpha}{(i * 2 + \beta)_* + \left(2.0 + \alpha\right)}\right)} \cdot \frac{\alpha + \beta}{(2 * i + \left(\alpha + \beta\right))_*} + 1.0}{2.0} \leadsto \frac{\color{blue}{\frac{{\left(\frac{\beta}{(i * 2 + \beta)_* + \left(2.0 + \alpha\right)}\right)}^2 - {\left(\frac{\alpha}{(i * 2 + \beta)_* + \left(2.0 + \alpha\right)}\right)}^2}{\frac{\beta}{(i * 2 + \beta)_* + \left(2.0 + \alpha\right)} + \frac{\alpha}{(i * 2 + \beta)_* + \left(2.0 + \alpha\right)}}} \cdot \frac{\alpha + \beta}{(2 * i + \left(\alpha + \beta\right))_*} + 1.0}{2.0}\]
4.3
- Applied frac-times to get
\[\frac{\color{red}{\frac{{\left(\frac{\beta}{(i * 2 + \beta)_* + \left(2.0 + \alpha\right)}\right)}^2 - {\left(\frac{\alpha}{(i * 2 + \beta)_* + \left(2.0 + \alpha\right)}\right)}^2}{\frac{\beta}{(i * 2 + \beta)_* + \left(2.0 + \alpha\right)} + \frac{\alpha}{(i * 2 + \beta)_* + \left(2.0 + \alpha\right)}} \cdot \frac{\alpha + \beta}{(2 * i + \left(\alpha + \beta\right))_*}} + 1.0}{2.0} \leadsto \frac{\color{blue}{\frac{\left({\left(\frac{\beta}{(i * 2 + \beta)_* + \left(2.0 + \alpha\right)}\right)}^2 - {\left(\frac{\alpha}{(i * 2 + \beta)_* + \left(2.0 + \alpha\right)}\right)}^2\right) \cdot \left(\alpha + \beta\right)}{\left(\frac{\beta}{(i * 2 + \beta)_* + \left(2.0 + \alpha\right)} + \frac{\alpha}{(i * 2 + \beta)_* + \left(2.0 + \alpha\right)}\right) \cdot (2 * i + \left(\alpha + \beta\right))_*}} + 1.0}{2.0}\]
4.3
- Removed slow pow expressions
