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Derivation

1. Initial program 0.0

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

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

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

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

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

5. Applied associate-/l*0.0

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

6. Simplified0.0

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

8. Applied div-sub0.0

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

10. Applied add-log-exp0.0

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

11. Final simplification0.0

    \[\leadsto \frac{-1}{\log \left(e^{\frac{f}{f + n}}\right) - \frac{n}{f + n}}\]

Runtime

Time bar (total: 33.2s)Debug logProfile

herbie shell --seed 2018297 +o rules:numerics
(FPCore (f n)
  :name "subtraction fraction"
  (/ (- (+ f n)) (- f n)))