Initial program 14.3
\[\sqrt{\left|\frac{a \cdot a - b \cdot b}{a \cdot a}\right|}\]
Applied simplify0.0
\[\leadsto \color{blue}{\sqrt{\left|1 - \frac{b}{a} \cdot \frac{b}{a}\right|}}\]
- Using strategy
rm Applied flip--0.0
\[\leadsto \sqrt{\left|\color{blue}{\frac{1 \cdot 1 - \left(\frac{b}{a} \cdot \frac{b}{a}\right) \cdot \left(\frac{b}{a} \cdot \frac{b}{a}\right)}{1 + \frac{b}{a} \cdot \frac{b}{a}}}\right|}\]
Applied simplify0.0
\[\leadsto \sqrt{\left|\frac{\color{blue}{1 - {\left(\frac{b}{a}\right)}^{\left(3 + 1\right)}}}{1 + \frac{b}{a} \cdot \frac{b}{a}}\right|}\]
- Using strategy
rm Applied add-cbrt-cube0.0
\[\leadsto \sqrt{\left|\frac{1 - {\left(\frac{b}{a}\right)}^{\left(3 + 1\right)}}{1 + \frac{b}{a} \cdot \color{blue}{\sqrt[3]{\left(\frac{b}{a} \cdot \frac{b}{a}\right) \cdot \frac{b}{a}}}}\right|}\]
Applied add-cbrt-cube0.0
\[\leadsto \sqrt{\left|\frac{1 - {\left(\frac{b}{a}\right)}^{\left(3 + 1\right)}}{1 + \color{blue}{\sqrt[3]{\left(\frac{b}{a} \cdot \frac{b}{a}\right) \cdot \frac{b}{a}}} \cdot \sqrt[3]{\left(\frac{b}{a} \cdot \frac{b}{a}\right) \cdot \frac{b}{a}}}\right|}\]
Applied cbrt-unprod0.0
\[\leadsto \sqrt{\left|\frac{1 - {\left(\frac{b}{a}\right)}^{\left(3 + 1\right)}}{1 + \color{blue}{\sqrt[3]{\left(\left(\frac{b}{a} \cdot \frac{b}{a}\right) \cdot \frac{b}{a}\right) \cdot \left(\left(\frac{b}{a} \cdot \frac{b}{a}\right) \cdot \frac{b}{a}\right)}}}\right|}\]
Applied simplify0.0
\[\leadsto \sqrt{\left|\frac{1 - {\left(\frac{b}{a}\right)}^{\left(3 + 1\right)}}{1 + \sqrt[3]{\color{blue}{{\left(\frac{b}{a}\right)}^{3} \cdot {\left(\frac{b}{a}\right)}^{3}}}}\right|}\]
