Average Error: 18.1 → 1.9
Time: 46.0s
Precision: 64
Internal Precision: 576
\[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
↓
\[\left(\frac{-t1}{t1 + u} \cdot v\right) \cdot \left(\left(\sqrt[3]{\frac{1}{t1 + u}} \cdot \sqrt[3]{\frac{1}{t1 + u}}\right) \cdot \sqrt[3]{\frac{1}{t1 + u}}\right)\]

Error

Bits error versus u

Bits error versus v

Bits error versus t1

Derivation

  1. Initial program 18.1

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

  3. Applied times-frac1.2

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

  5. Applied div-inv1.3

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

  6. Applied associate-*r*1.2

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

  8. Applied add-cube-cbrt1.9

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

Runtime

Time bar (total: 46.0s)Debug logProfile

herbie shell --seed '#(1072330854 3074818769 591214268 3603999196 3863745332 3332387116)' 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))