Initial program 1.6
\[\left(\sqrt{\left(\frac{x}{\left(real->posit(1)\right)}\right)}\right) - \left(\sqrt{x}\right)\]
- Using strategy
rm Applied p16-flip--1.2
\[\leadsto \color{blue}{\frac{\left(\left(\left(\sqrt{\left(\frac{x}{\left(real->posit(1)\right)}\right)}\right) \cdot \left(\sqrt{\left(\frac{x}{\left(real->posit(1)\right)}\right)}\right)\right) - \left(\left(\sqrt{x}\right) \cdot \left(\sqrt{x}\right)\right)\right)}{\left(\frac{\left(\sqrt{\left(\frac{x}{\left(real->posit(1)\right)}\right)}\right)}{\left(\sqrt{x}\right)}\right)}}\]
- Using strategy
rm Applied sqrt-sqrd.p160.9
\[\leadsto \frac{\left(\color{blue}{\left(\frac{x}{\left(real->posit(1)\right)}\right)} - \left(\left(\sqrt{x}\right) \cdot \left(\sqrt{x}\right)\right)\right)}{\left(\frac{\left(\sqrt{\left(\frac{x}{\left(real->posit(1)\right)}\right)}\right)}{\left(\sqrt{x}\right)}\right)}\]
- Using strategy
rm Applied +-commutative0.9
\[\leadsto \frac{\left(\color{blue}{\left(\frac{\left(real->posit(1)\right)}{x}\right)} - \left(\left(\sqrt{x}\right) \cdot \left(\sqrt{x}\right)\right)\right)}{\left(\frac{\left(\sqrt{\left(\frac{x}{\left(real->posit(1)\right)}\right)}\right)}{\left(\sqrt{x}\right)}\right)}\]
Applied associate--l+0.6
\[\leadsto \frac{\color{blue}{\left(\frac{\left(real->posit(1)\right)}{\left(x - \left(\left(\sqrt{x}\right) \cdot \left(\sqrt{x}\right)\right)\right)}\right)}}{\left(\frac{\left(\sqrt{\left(\frac{x}{\left(real->posit(1)\right)}\right)}\right)}{\left(\sqrt{x}\right)}\right)}\]
- Using strategy
rm Applied sqrt-sqrd.p160.4
\[\leadsto \frac{\left(\frac{\left(real->posit(1)\right)}{\left(x - \color{blue}{x}\right)}\right)}{\left(\frac{\left(\sqrt{\left(\frac{x}{\left(real->posit(1)\right)}\right)}\right)}{\left(\sqrt{x}\right)}\right)}\]
Final simplification0.4
\[\leadsto \frac{1 + \left(x - x\right)}{\sqrt{x + 1} + \sqrt{x}}\]
