Average Error: 18.3 → 1.2
Time: 22.7s
Precision: 64
Internal precision: 128
\[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
⬇
\[\frac{-t1}{t1 + u} \cdot \frac{v}{t1 + u}\]

Error

Bits error versus u

Bits error versus v

Bits error versus t1

Derivation

  1. Initial program 18.3

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

  3. Applied times-frac 1.2

    \[\leadsto \color{blue}{\frac{-t1}{t1 + u} \cdot \frac{v}{t1 + u}}\]
  4. Removed slow pow expressions

Runtime

Time bar (total: 22.7s) Debug log

Please include this information when filing a bug report:

herbie --seed '#(184072865 576139169 4215531491 3330140573 505220215 4145156294)'
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))