Error

Derivation

1. Initial program 0.0

   \[\frac{-\left(f + n\right)}{f - n}\]
2. Using strategy rm

3. Applied *-un-lft-identity0.0

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

4. Applied *-un-lft-identity0.0

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

5. Applied distribute-lft-out0.0

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

6. Applied distribute-lft-neg-in0.0

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

7. Applied associate-/l*0.0

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

8. Simplified0.0

   \[\leadsto \frac{\color{blue}{-1}}{\frac{f - n}{f + n}}\]
9. Using strategy rm

10. Applied div-sub0.0

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

11. Final simplification0.0

    \[\leadsto \frac{-1}{\frac{f}{f + n} - \frac{n}{f + n}}\]

Reproduce

herbie shell --seed 2019091 +o rules:numerics
(FPCore (f n)
  :name "subtraction fraction"
  (/ (- (+ f n)) (- f n)))