Error

Try it out

Derivation

1. Initial program 17.5

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

2. Initial simplification1.6

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

4. Applied div-inv1.6

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

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-frac1.5

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

7. Simplified1.3

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

9. Applied add-cube-cbrt2.1

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

10. Applied add-cube-cbrt1.7

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

11. Applied times-frac1.7

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

12. Applied associate-*l*1.1

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

13. Final simplification1.1

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

Runtime

Time bar (total: 28.5s)Debug logProfile

herbie shell --seed 2018258 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))