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Derivation

1. Initial program 18.3

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

2. Initial simplification1.4

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

4. Applied neg-mul-11.4

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

5. Applied associate-/l*1.5

   \[\leadsto \frac{\color{blue}{\frac{-1}{\frac{t1 + u}{t1}}}}{\frac{t1 + u}{v}}\]
6. Using strategy rm

7. Applied *-un-lft-identity1.5

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

8. Applied div-inv1.5

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

9. Applied times-frac1.5

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

10. Simplified1.5

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

11. Simplified1.1

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

12. Final simplification1.1

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

Runtime

Time bar (total: 38.6s)Debug logProfile

herbie shell --seed 2018273 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))