Rosa's DopplerBench

Average Error: 18.7 → 1.3

Time: 5.5s

Precision: binary64

• Falling back on racket egraph because egg-herbie package not installed

Math

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

↓

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

Error

Bits error versus u

Bits error versus v

Bits error versus t1

Derivation

1. Initial program 18.7

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

3. Applied associate-/r* 11.6

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

4. Simplified 1.3

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

5. Final simplification 1.3

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

Reproduce

herbie shell --seed 2020182 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  :precision binary64
  (/ (* (neg t1) v) (* (+ t1 u) (+ t1 u))))