\(\frac{\frac{\left({\left(\frac{\beta}{\left(\alpha + 2.0\right) + (i * 2 + \beta)_*}\right)}^3 - {\left(\frac{\alpha}{\left(\alpha + 2.0\right) + (i * 2 + \beta)_*}\right)}^3\right) \cdot \left(\beta + \alpha\right)}{\left({\left(\frac{\beta}{(i * 2 + \beta)_* + \left(2.0 + \alpha\right)}\right)}^2 + \left({\left(\frac{\alpha}{(i * 2 + \beta)_* + \left(2.0 + \alpha\right)}\right)}^2 + \frac{\beta}{(i * 2 + \beta)_* + \left(2.0 + \alpha\right)} \cdot \frac{\alpha}{(i * 2 + \beta)_* + \left(2.0 + \alpha\right)}\right)\right) \cdot (2 * i + \left(\alpha + \beta\right))_*} + 1.0}{2.0}\)
- Started with
\[\frac{\frac{\frac{\left(\alpha + \beta\right) \cdot \left(\beta - \alpha\right)}{\left(\alpha + \beta\right) + 2 \cdot i}}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) + 2.0} + 1.0}{2.0}\]
11.0
- 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 flip3-- to get
\[\frac{\color{red}{\left(\frac{\beta}{(i * 2 + \beta)_* + \left(2.0 + \alpha\right)} - \frac{\alpha}{(i * 2 + \beta)_* + \left(2.0 + \alpha\right)}\right)} \cdot \frac{\alpha + \beta}{(2 * i + \left(\alpha + \beta\right))_*} + 1.0}{2.0} \leadsto \frac{\color{blue}{\frac{{\left(\frac{\beta}{(i * 2 + \beta)_* + \left(2.0 + \alpha\right)}\right)}^{3} - {\left(\frac{\alpha}{(i * 2 + \beta)_* + \left(2.0 + \alpha\right)}\right)}^{3}}{{\left(\frac{\beta}{(i * 2 + \beta)_* + \left(2.0 + \alpha\right)}\right)}^2 + \left({\left(\frac{\alpha}{(i * 2 + \beta)_* + \left(2.0 + \alpha\right)}\right)}^2 + \frac{\beta}{(i * 2 + \beta)_* + \left(2.0 + \alpha\right)} \cdot \frac{\alpha}{(i * 2 + \beta)_* + \left(2.0 + \alpha\right)}\right)}} \cdot \frac{\alpha + \beta}{(2 * i + \left(\alpha + \beta\right))_*} + 1.0}{2.0}\]
5.1
- Applied frac-times to get
\[\frac{\color{red}{\frac{{\left(\frac{\beta}{(i * 2 + \beta)_* + \left(2.0 + \alpha\right)}\right)}^{3} - {\left(\frac{\alpha}{(i * 2 + \beta)_* + \left(2.0 + \alpha\right)}\right)}^{3}}{{\left(\frac{\beta}{(i * 2 + \beta)_* + \left(2.0 + \alpha\right)}\right)}^2 + \left({\left(\frac{\alpha}{(i * 2 + \beta)_* + \left(2.0 + \alpha\right)}\right)}^2 + \frac{\beta}{(i * 2 + \beta)_* + \left(2.0 + \alpha\right)} \cdot \frac{\alpha}{(i * 2 + \beta)_* + \left(2.0 + \alpha\right)}\right)} \cdot \frac{\alpha + \beta}{(2 * i + \left(\alpha + \beta\right))_*}} + 1.0}{2.0} \leadsto \frac{\color{blue}{\frac{\left({\left(\frac{\beta}{(i * 2 + \beta)_* + \left(2.0 + \alpha\right)}\right)}^{3} - {\left(\frac{\alpha}{(i * 2 + \beta)_* + \left(2.0 + \alpha\right)}\right)}^{3}\right) \cdot \left(\alpha + \beta\right)}{\left({\left(\frac{\beta}{(i * 2 + \beta)_* + \left(2.0 + \alpha\right)}\right)}^2 + \left({\left(\frac{\alpha}{(i * 2 + \beta)_* + \left(2.0 + \alpha\right)}\right)}^2 + \frac{\beta}{(i * 2 + \beta)_* + \left(2.0 + \alpha\right)} \cdot \frac{\alpha}{(i * 2 + \beta)_* + \left(2.0 + \alpha\right)}\right)\right) \cdot (2 * i + \left(\alpha + \beta\right))_*}} + 1.0}{2.0}\]
5.1
- Applied simplify to get
\[\frac{\frac{\color{red}{\left({\left(\frac{\beta}{(i * 2 + \beta)_* + \left(2.0 + \alpha\right)}\right)}^{3} - {\left(\frac{\alpha}{(i * 2 + \beta)_* + \left(2.0 + \alpha\right)}\right)}^{3}\right) \cdot \left(\alpha + \beta\right)}}{\left({\left(\frac{\beta}{(i * 2 + \beta)_* + \left(2.0 + \alpha\right)}\right)}^2 + \left({\left(\frac{\alpha}{(i * 2 + \beta)_* + \left(2.0 + \alpha\right)}\right)}^2 + \frac{\beta}{(i * 2 + \beta)_* + \left(2.0 + \alpha\right)} \cdot \frac{\alpha}{(i * 2 + \beta)_* + \left(2.0 + \alpha\right)}\right)\right) \cdot (2 * i + \left(\alpha + \beta\right))_*} + 1.0}{2.0} \leadsto \frac{\frac{\color{blue}{\left({\left(\frac{\beta}{\left(\alpha + 2.0\right) + (i * 2 + \beta)_*}\right)}^3 - {\left(\frac{\alpha}{\left(\alpha + 2.0\right) + (i * 2 + \beta)_*}\right)}^3\right) \cdot \left(\beta + \alpha\right)}}{\left({\left(\frac{\beta}{(i * 2 + \beta)_* + \left(2.0 + \alpha\right)}\right)}^2 + \left({\left(\frac{\alpha}{(i * 2 + \beta)_* + \left(2.0 + \alpha\right)}\right)}^2 + \frac{\beta}{(i * 2 + \beta)_* + \left(2.0 + \alpha\right)} \cdot \frac{\alpha}{(i * 2 + \beta)_* + \left(2.0 + \alpha\right)}\right)\right) \cdot (2 * i + \left(\alpha + \beta\right))_*} + 1.0}{2.0}\]
4.3
