Rosa's DopplerBench

Average Error: 17.8 → 1.5

Time: 3.2s

Precision: binary64

Math

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

↓

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

Error

Bits error versus u

Bits error versus v

Bits error versus t1

Derivation

1. Initial program 17.8

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

2. Simplified 3.4

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

4. Applied associate-/r* 1.5

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

5. Final simplification 1.5

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

Reproduce

herbie shell --seed 2020179 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  :precision binary64
  (/ (* (neg t1) v) (* (+ t1 u) (+ t1 u))))