Error

Derivation

1. Initial program 17.7

   \[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
2. Using strategy rm

3. Applied times-frac1.2

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

5. Applied div-inv1.3

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

7. Applied associate-*r/1.2

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

8. Final simplification1.2

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

Reproduce

herbie shell --seed 2019068 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))