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Derivation

1. Initial program 18.1

   \[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]

2. Initial simplification1.5

   \[\leadsto \frac{\frac{-t1}{t1 + u}}{\frac{t1 + u}{v}}\]
3. Using strategy rm

4. Applied div-inv1.5

   \[\leadsto \frac{\frac{-t1}{t1 + u}}{\color{blue}{\left(t1 + u\right) \cdot \frac{1}{v}}}\]

5. Applied div-inv1.6

   \[\leadsto \frac{\color{blue}{\left(-t1\right) \cdot \frac{1}{t1 + u}}}{\left(t1 + u\right) \cdot \frac{1}{v}}\]

6. Applied times-frac1.4

   \[\leadsto \color{blue}{\frac{-t1}{t1 + u} \cdot \frac{\frac{1}{t1 + u}}{\frac{1}{v}}}\]

7. Simplified1.3

   \[\leadsto \frac{-t1}{t1 + u} \cdot \color{blue}{\frac{v}{t1 + u}}\]
8. Using strategy rm

9. Applied associate-*r/1.2

   \[\leadsto \color{blue}{\frac{\frac{-t1}{t1 + u} \cdot v}{t1 + u}}\]
10. Using strategy rm

11. Applied div-inv1.3

    \[\leadsto \color{blue}{\left(\frac{-t1}{t1 + u} \cdot v\right) \cdot \frac{1}{t1 + u}}\]

12. Final simplification1.3

    \[\leadsto \left(\frac{t1}{t1 + u} \cdot v\right) \cdot \frac{-1}{t1 + u}\]

Runtime

Time bar (total: 23.3s)Debug logProfile

herbie shell --seed 2018354 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))