Error

Derivation

1. Initial program 0.0

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

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

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

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 log1p-expm1-u0.0

   \[\leadsto \color{blue}{\log_* (1 + (e^{\frac{-1}{\frac{f - n}{f + n}}} - 1)^*)}\]

9. Final simplification0.0

   \[\leadsto \log_* (1 + (e^{\frac{-1}{\frac{f - n}{f + n}}} - 1)^*)\]

Reproduce

herbie shell --seed 2019093 +o rules:numerics
(FPCore (f n)
  :name "subtraction fraction"
  (/ (- (+ f n)) (- f n)))