Average Error: 18.3 → 1.4
Time: 21.6s
Precision: 64
Internal Precision: 576
\[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
↓
\[\left(\frac{t1}{t1 + u} \cdot v\right) \cdot \frac{-1}{t1 + u}\]

Error

Bits error versus u

Bits error versus v

Bits error versus t1

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 18.3

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

  2. Initial simplification1.3

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

  4. Applied div-inv1.4

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

  5. Applied associate-*r*1.4

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

  6. Final simplification1.4

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

Runtime

Time bar (total: 21.6s)Debug logProfile

herbie shell --seed 2018215 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))