Average Error: 17.9 → 1.6
Time: 24.7s
Precision: 64
Internal Precision: 384
\[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
↓
\[\frac{-t1}{t1 + u} \cdot \frac{1}{\frac{t1 + u}{v}}\]

Error

Bits error versus u

Bits error versus v

Bits error versus t1

Derivation

  1. Initial program 17.9

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

  3. Applied times-frac1.3

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

  5. Applied clear-num1.6

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

Runtime

Time bar (total: 24.7s)Debug logProfile

herbie shell --seed '#(1064269945 2896236262 301053905 1701069080 1701464310 1614783279)' 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))