Average Error: 17.8 → 1.3
Time: 1.6m
Precision: 64
Internal Precision: 320
\[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
↓
\[\frac{t1 \cdot \frac{-v}{u + t1}}{u + t1}\]

Error

Bits error versus u

Bits error versus v

Bits error versus t1

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 17.8

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

  2. Initial simplification1.4

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

  4. Applied associate-*r/1.3

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

  5. Final simplification1.3

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

Runtime

Time bar (total: 1.6m)Debug logProfile

herbie shell --seed 2018214 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))