Average Error: 18.0 → 1.5
Time: 1.1m
Precision: 64
Internal Precision: 576
\[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
↓
\[\begin{array}{l} \mathbf{if}\;t1 \le -8.186180642881193 \cdot 10^{-286} \lor \neg \left(t1 \le 1.2576659648664622 \cdot 10^{-240}\right):\\ \;\;\;\;\frac{t1}{u + t1} \cdot \frac{-v}{u + t1}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\left(-t1\right) \cdot v}{u + t1}}{u + t1}\\ \end{array}\]

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. Split input into 2 regimes

  2. if t1 < -8.186180642881193e-286 or 1.2576659648664622e-240 < t1

    1. Initial program 18.3

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

    3. Applied times-frac0.9

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

    if -8.186180642881193e-286 < t1 < 1.2576659648664622e-240

    1. Initial program 13.5

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

    3. Applied associate-/r*9.9

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

  4. Applied simplify1.5

    \[\leadsto \color{blue}{\begin{array}{l} \mathbf{if}\;t1 \le -8.186180642881193 \cdot 10^{-286} \lor \neg \left(t1 \le 1.2576659648664622 \cdot 10^{-240}\right):\\ \;\;\;\;\frac{t1}{u + t1} \cdot \frac{-v}{u + t1}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\left(-t1\right) \cdot v}{u + t1}}{u + t1}\\ \end{array}}\]

Runtime

Time bar (total: 1.1m)Debug logProfile

herbie shell --seed '#(1072967564 1937075727 894099792 790700740 1036514779 1027793188)' +o rules:numerics
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))