Average Error: 17.7 → 0.7
Time: 28.6s
Precision: 64
Internal Precision: 384
\[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{-t1}{t1 + u} \cdot \frac{v}{t1 + u} \le -1.7033420111400328 \cdot 10^{-298}:\\ \;\;\;\;\frac{-t1}{t1 + u} \cdot \frac{v}{t1 + u}\\ \mathbf{if}\;\frac{-t1}{t1 + u} \cdot \frac{v}{t1 + u} \le -0.0:\\ \;\;\;\;\frac{\frac{\left(-t1\right) \cdot v}{t1 + u}}{t1 + u}\\ \mathbf{else}:\\ \;\;\;\;\frac{-t1}{t1 + u} \cdot \frac{v}{t1 + u}\\ \end{array}\]

Error

Bits error versus u

Bits error versus v

Bits error versus t1

Derivation

  1. Split input into 2 regimes

  2. if (* (/ (- t1) (+ t1 u)) (/ v (+ t1 u))) < -1.7033420111400328e-298 or -0.0 < (* (/ (- t1) (+ t1 u)) (/ v (+ t1 u)))

    1. Initial program 27.5

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

    3. Applied times-frac1.1

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

    if -1.7033420111400328e-298 < (* (/ (- t1) (+ t1 u)) (/ v (+ t1 u))) < -0.0

    1. Initial program 1.2

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

    3. Applied associate-/r*0.1

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

Runtime

Time bar (total: 28.6s)Debug logProfile

herbie shell --seed '#(1064300848 3212030778 2049303162 3567222883 2277747821 1384278011)' 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))