Error

Derivation

1. Initial program 14.4

   \[\frac{1}{x + 1} - \frac{1}{x}\]
2. Using strategy rm

3. Applied frac-sub13.8

   \[\leadsto \color{blue}{\frac{1 \cdot x - \left(x + 1\right) \cdot 1}{\left(x + 1\right) \cdot x}}\]

4. Simplified0.3

   \[\leadsto \frac{\color{blue}{-1}}{\left(x + 1\right) \cdot x}\]

5. Simplified0.3

   \[\leadsto \frac{-1}{\color{blue}{x \cdot x + x}}\]
6. Using strategy rm

7. Applied *-un-lft-identity0.3

   \[\leadsto \frac{-1}{x \cdot x + \color{blue}{1 \cdot x}}\]

8. Applied distribute-rgt-out0.3

   \[\leadsto \frac{-1}{\color{blue}{x \cdot \left(x + 1\right)}}\]

9. Applied associate-/r*0.1

   \[\leadsto \color{blue}{\frac{\frac{-1}{x}}{x + 1}}\]

10. Final simplification0.1

    \[\leadsto \frac{\frac{-1}{x}}{x + 1}\]

Reproduce

herbie shell --seed 2019091 
(FPCore (x)
  :name "2frac (problem 3.3.1)"
  (- (/ 1 (+ x 1)) (/ 1 x)))