Error

Try it out

Derivation

1. Split input into 3 regimes

2. if u < -4.472424846204476e-93

   1. Initial program 14.9

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

   2. Initial simplification1.4

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

   4. Applied div-inv1.4

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

   5. Applied div-inv1.4

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

   6. Applied times-frac1.3

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

   7. Simplified1.2

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

   9. Applied associate-*l/0.7

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

   11. Applied clear-num1.3

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

   if -4.472424846204476e-93 < u < 2079839125663728.8

   1. Initial program 22.7

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

   2. Initial simplification1.6

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

   4. Applied div-inv1.7

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

   5. Applied associate-/r*0.4

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

   if 2079839125663728.8 < u

   1. Initial program 14.5

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

   2. Initial simplification1.5

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

   4. Applied div-inv1.5

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

   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-frac1.3

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

   7. Simplified1.3

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

   9. Applied associate-*l/0.1

      \[\leadsto \color{blue}{\frac{\left(-t1\right) \cdot \frac{v}{t1 + u}}{t1 + u}}\]
3. Recombined 3 regimes into one program.

4. Final simplification0.6

   \[\leadsto \begin{array}{l} \mathbf{if}\;u \le -4.472424846204476 \cdot 10^{-93}:\\ \;\;\;\;\frac{1}{\frac{u + t1}{\frac{-v}{u + t1} \cdot t1}}\\ \mathbf{elif}\;u \le 2079839125663728.8:\\ \;\;\;\;\frac{\frac{\frac{-t1}{u + t1}}{u + t1}}{\frac{1}{v}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{-v}{u + t1} \cdot t1}{u + t1}\\ \end{array}\]

Reproduce

herbie shell --seed 2018360 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))

Details

Time bar (total: 18.0s)Debug log