Average Error: 18.1 → 1.5
Time: 52.7s
Precision: 64
Internal Precision: 576
\[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
↓
\[\left(\sqrt[3]{\frac{-t1}{t1 + u}} \cdot \sqrt[3]{\frac{-t1}{t1 + u}}\right) \cdot \left(\sqrt[3]{\frac{-t1}{t1 + u}} \cdot \frac{v}{t1 + u}\right)\]

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 add-cube-cbrt1.5

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

  6. Applied associate-*l*1.5

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

Runtime

Time bar (total: 52.7s)Debug logProfile

herbie shell --seed '#(1071215679 2002590028 935158157 1944352234 2656991306 2955288481)' +o rules:numerics
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))