Error

Try it out

Derivation

1. Split input into 2 regimes

2. if t1 < -3.766463914764075e-226 or 9.865971802478837e-217 < t1

   1. Initial program 19.1

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

   2. Initial simplification0.9

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

   4. Applied div-inv1.0

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

   5. Applied div-inv1.0

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

   6. Applied times-frac0.7

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

   7. Simplified0.5

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

   9. Applied associate-*l/0.5

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

   if -3.766463914764075e-226 < t1 < 9.865971802478837e-217

   1. Initial program 16.2

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

   2. Initial simplification6.1

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

   4. Applied associate-/r/4.3

      \[\leadsto \color{blue}{\frac{\frac{t1}{t1 + u}}{t1 + u} \cdot \left(-v\right)}\]
3. Recombined 2 regimes into one program.

4. Final simplification1.0

   \[\leadsto \begin{array}{l} \mathbf{if}\;t1 \le -3.766463914764075 \cdot 10^{-226} \lor \neg \left(t1 \le 9.865971802478837 \cdot 10^{-217}\right):\\ \;\;\;\;\frac{\frac{-v}{u + t1} \cdot t1}{u + t1}\\ \mathbf{else}:\\ \;\;\;\;\left(-v\right) \cdot \frac{\frac{t1}{u + t1}}{u + t1}\\ \end{array}\]

Runtime

Time bar (total: 1.2m)Debug logProfile

herbie shell --seed 2018234 +o rules:numerics
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))