Error

Derivation

1. Initial program 17.5

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

3. Applied times-frac1.3

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

5. Applied add-cube-cbrt2.0

   \[\leadsto \frac{-t1}{\color{blue}{\left(\sqrt[3]{t1 + u} \cdot \sqrt[3]{t1 + u}\right) \cdot \sqrt[3]{t1 + u}}} \cdot \frac{v}{t1 + u}\]

6. Applied add-cube-cbrt1.6

   \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{-t1} \cdot \sqrt[3]{-t1}\right) \cdot \sqrt[3]{-t1}}}{\left(\sqrt[3]{t1 + u} \cdot \sqrt[3]{t1 + u}\right) \cdot \sqrt[3]{t1 + u}} \cdot \frac{v}{t1 + u}\]

7. Applied times-frac1.6

   \[\leadsto \color{blue}{\left(\frac{\sqrt[3]{-t1} \cdot \sqrt[3]{-t1}}{\sqrt[3]{t1 + u} \cdot \sqrt[3]{t1 + u}} \cdot \frac{\sqrt[3]{-t1}}{\sqrt[3]{t1 + u}}\right)} \cdot \frac{v}{t1 + u}\]

8. Applied associate-*l*1.0

   \[\leadsto \color{blue}{\frac{\sqrt[3]{-t1} \cdot \sqrt[3]{-t1}}{\sqrt[3]{t1 + u} \cdot \sqrt[3]{t1 + u}} \cdot \left(\frac{\sqrt[3]{-t1}}{\sqrt[3]{t1 + u}} \cdot \frac{v}{t1 + u}\right)}\]

9. Simplified1.0

   \[\leadsto \color{blue}{\left(\frac{\sqrt[3]{-t1}}{\sqrt[3]{t1 + u}} \cdot \frac{\sqrt[3]{-t1}}{\sqrt[3]{t1 + u}}\right)} \cdot \left(\frac{\sqrt[3]{-t1}}{\sqrt[3]{t1 + u}} \cdot \frac{v}{t1 + u}\right)\]

10. Final simplification1.0

    \[\leadsto \left(\frac{\sqrt[3]{-t1}}{\sqrt[3]{u + t1}} \cdot \frac{\sqrt[3]{-t1}}{\sqrt[3]{u + t1}}\right) \cdot \left(\frac{v}{u + t1} \cdot \frac{\sqrt[3]{-t1}}{\sqrt[3]{u + t1}}\right)\]

Reproduce

herbie shell --seed 2019053 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))