Average Error: 18.0 → 1.4
Time: 1.6m
Precision: 64
Internal Precision: 576
\[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
↓
\[\frac{-1}{t1 + u} \cdot \left(t1 \cdot \frac{v}{t1 + u}\right)\]

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 18.0

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

  2. Initial simplification1.4

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

  4. Applied div-inv1.5

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

  5. Applied *-un-lft-identity1.5

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

  6. Applied times-frac1.3

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

  7. Simplified1.4

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

  8. Final simplification1.4

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

Runtime

Time bar (total: 1.6m)Debug logProfile

herbie shell --seed 2018252 +o rules:numerics
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))