Average Error: 17.4 → 1.5
Time: 1.6m
Precision: 64
Internal Precision: 576
\[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
↓
\[\frac{\frac{v}{t1 + u}}{\frac{t1 + u}{-t1}}\]

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 17.4

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

  2. Initial simplification1.5

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

  3. Final simplification1.5

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

Runtime

Time bar (total: 1.6m)Debug logProfile

herbie shell --seed 2018220 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))