Average Error: 17.9 → 0.9
Time: 1.3m
Precision: 64
Internal Precision: 320
\[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
↓
\[\begin{array}{l} \mathbf{if}\;\sqrt{\frac{-t1}{t1 + u}} \cdot \left(\sqrt{\frac{-t1}{t1 + u}} \cdot \frac{v}{t1 + u}\right) \le -9.94669522250427 \cdot 10^{-281}:\\ \;\;\;\;\frac{-t1}{t1 + u} \cdot \frac{v}{t1 + u}\\ \mathbf{if}\;\sqrt{\frac{-t1}{t1 + u}} \cdot \left(\sqrt{\frac{-t1}{t1 + u}} \cdot \frac{v}{t1 + u}\right) \le 2.85557859754982 \cdot 10^{-308}:\\ \;\;\;\;\frac{\frac{\left(-t1\right) \cdot v}{t1 + u}}{t1 + u}\\ \mathbf{else}:\\ \;\;\;\;\frac{-t1}{t1 + u} \cdot \frac{v}{t1 + u}\\ \end{array}\]

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. Split input into 2 regimes

  2. if (* (sqrt (/ (- t1) (+ t1 u))) (* (sqrt (/ (- t1) (+ t1 u))) (/ v (+ t1 u)))) < -9.94669522250427e-281 or 2.85557859754982e-308 < (* (sqrt (/ (- t1) (+ t1 u))) (* (sqrt (/ (- t1) (+ t1 u))) (/ v (+ t1 u))))

    1. Initial program 21.7

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

    3. Applied times-frac1.0

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

    if -9.94669522250427e-281 < (* (sqrt (/ (- t1) (+ t1 u))) (* (sqrt (/ (- t1) (+ t1 u))) (/ v (+ t1 u)))) < 2.85557859754982e-308

    1. Initial program 2.0

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

    3. Applied associate-/r*0.5

      \[\leadsto \color{blue}{\frac{\frac{\left(-t1\right) \cdot v}{t1 + u}}{t1 + u}}\]
  3. Recombined 2 regimes into one program.

Runtime

Time bar (total: 1.3m)Debug logProfile

herbie shell --seed 2020178 +o rules:numerics
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))