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Derivation

1. Initial program 0.0

   \[\frac{-\left(f + n\right)}{f - n}\]

2. Initial simplification0.0

   \[\leadsto -\frac{n + f}{f - n}\]
3. Using strategy rm

4. Applied add-cbrt-cube0.0

   \[\leadsto -\color{blue}{\sqrt[3]{\left(\frac{n + f}{f - n} \cdot \frac{n + f}{f - n}\right) \cdot \frac{n + f}{f - n}}}\]
5. Using strategy rm

6. Applied add-log-exp0.0

   \[\leadsto -\sqrt[3]{\left(\frac{n + f}{f - n} \cdot \color{blue}{\log \left(e^{\frac{n + f}{f - n}}\right)}\right) \cdot \frac{n + f}{f - n}}\]
7. Using strategy rm

8. Applied add-cube-cbrt0.3

   \[\leadsto -\sqrt[3]{\left(\frac{n + f}{f - n} \cdot \log \left(e^{\frac{n + f}{\color{blue}{\left(\sqrt[3]{f - n} \cdot \sqrt[3]{f - n}\right) \cdot \sqrt[3]{f - n}}}}\right)\right) \cdot \frac{n + f}{f - n}}\]

9. Applied add-cube-cbrt0.0

   \[\leadsto -\sqrt[3]{\left(\frac{n + f}{f - n} \cdot \log \left(e^{\frac{\color{blue}{\left(\sqrt[3]{n + f} \cdot \sqrt[3]{n + f}\right) \cdot \sqrt[3]{n + f}}}{\left(\sqrt[3]{f - n} \cdot \sqrt[3]{f - n}\right) \cdot \sqrt[3]{f - n}}}\right)\right) \cdot \frac{n + f}{f - n}}\]

10. Applied times-frac0.0

    \[\leadsto -\sqrt[3]{\left(\frac{n + f}{f - n} \cdot \log \left(e^{\color{blue}{\frac{\sqrt[3]{n + f} \cdot \sqrt[3]{n + f}}{\sqrt[3]{f - n} \cdot \sqrt[3]{f - n}} \cdot \frac{\sqrt[3]{n + f}}{\sqrt[3]{f - n}}}}\right)\right) \cdot \frac{n + f}{f - n}}\]

11. Final simplification0.0

    \[\leadsto -\sqrt[3]{\left(\frac{f + n}{f - n} \cdot \log \left(e^{\frac{\sqrt[3]{f + n} \cdot \sqrt[3]{f + n}}{\sqrt[3]{f - n} \cdot \sqrt[3]{f - n}} \cdot \frac{\sqrt[3]{f + n}}{\sqrt[3]{f - n}}}\right)\right) \cdot \frac{f + n}{f - n}}\]

Runtime

Time bar (total: 26.4s)Debug logProfile

herbie shell --seed 2018278 
(FPCore (f n)
  :name "subtraction fraction"
  (/ (- (+ f n)) (- f n)))