Average Error: 17.7 → 0.9
Time: 1.8m
Precision: 64
Internal Precision: 320
\[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
↓
\[\begin{array}{l} \mathbf{if}\;u \le -1825993146.3651237 \lor \neg \left(u \le 4.966018932776704 \cdot 10^{+50}\right):\\ \;\;\;\;\frac{t1}{t1 + u} \cdot \frac{-v}{t1 + u}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{t1 \cdot \frac{-1}{t1 + u}}{t1 + u}}{\frac{1}{v}}\\ \end{array}\]

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 u < -1825993146.3651237 or 4.966018932776704e+50 < u

    1. Initial program 14.5

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

    2. Initial simplification1.6

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

    4. Applied div-inv1.6

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

    5. Applied div-inv1.6

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

    6. Applied times-frac1.4

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

    7. Simplified1.4

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

    if -1825993146.3651237 < u < 4.966018932776704e+50

    1. Initial program 20.5

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

    2. Initial simplification1.8

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

    4. Applied div-inv1.9

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

    5. Applied associate-/r*0.5

      \[\leadsto \color{blue}{\frac{\frac{\frac{-t1}{t1 + u}}{t1 + u}}{\frac{1}{v}}}\]
    6. Using strategy rm

    7. Applied div-inv0.5

      \[\leadsto \frac{\frac{\color{blue}{\left(-t1\right) \cdot \frac{1}{t1 + u}}}{t1 + u}}{\frac{1}{v}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;u \le -1825993146.3651237 \lor \neg \left(u \le 4.966018932776704 \cdot 10^{+50}\right):\\ \;\;\;\;\frac{t1}{t1 + u} \cdot \frac{-v}{t1 + u}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{t1 \cdot \frac{-1}{t1 + u}}{t1 + u}}{\frac{1}{v}}\\ \end{array}\]

Runtime

Time bar (total: 1.8m)Debug logProfile

BaselineHerbieOracleSpan%
Regimes1.40.90.01.435.7%
herbie shell --seed 2018295 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))