Initial program 0.6
\[\left(\frac{\left(real->posit(1)\right)}{\left(\frac{x}{\left(real->posit(1)\right)}\right)}\right) - \left(\frac{\left(real->posit(1)\right)}{x}\right)\]
- Using strategy
rm Applied p16-flip--1.3
\[\leadsto \color{blue}{\frac{\left(\left(\left(\frac{\left(real->posit(1)\right)}{\left(\frac{x}{\left(real->posit(1)\right)}\right)}\right) \cdot \left(\frac{\left(real->posit(1)\right)}{\left(\frac{x}{\left(real->posit(1)\right)}\right)}\right)\right) - \left(\left(\frac{\left(real->posit(1)\right)}{x}\right) \cdot \left(\frac{\left(real->posit(1)\right)}{x}\right)\right)\right)}{\left(\frac{\left(\frac{\left(real->posit(1)\right)}{\left(\frac{x}{\left(real->posit(1)\right)}\right)}\right)}{\left(\frac{\left(real->posit(1)\right)}{x}\right)}\right)}}\]
- Using strategy
rm Applied difference-of-squares1.0
\[\leadsto \frac{\color{blue}{\left(\left(\frac{\left(\frac{\left(real->posit(1)\right)}{\left(\frac{x}{\left(real->posit(1)\right)}\right)}\right)}{\left(\frac{\left(real->posit(1)\right)}{x}\right)}\right) \cdot \left(\left(\frac{\left(real->posit(1)\right)}{\left(\frac{x}{\left(real->posit(1)\right)}\right)}\right) - \left(\frac{\left(real->posit(1)\right)}{x}\right)\right)\right)}}{\left(\frac{\left(\frac{\left(real->posit(1)\right)}{\left(\frac{x}{\left(real->posit(1)\right)}\right)}\right)}{\left(\frac{\left(real->posit(1)\right)}{x}\right)}\right)}\]
Final simplification1.0
\[\leadsto \frac{\left(\frac{1}{x + 1} + \frac{1}{x}\right) \cdot \left(\frac{1}{x + 1} - \frac{1}{x}\right)}{\frac{1}{x + 1} + \frac{1}{x}}\]
