Error

Derivation

1. Initial program 18.4

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

3. Applied *-commutative18.4

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

4. Applied times-frac1.3

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

6. Applied *-un-lft-identity1.3

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

7. Applied distribute-rgt-neg-in1.3

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

8. Applied associate-/l*1.5

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

9. Applied un-div-inv1.5

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

10. Taylor expanded around -inf 1.4

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

11. Final simplification1.4

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

Reproduce

herbie shell --seed 2019088 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))