Average Error: 18.1 → 1.4
Time: 14.5s
Precision: 64
\[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
↓
\[\left(\frac{t1}{t1 + u} \cdot v\right) \cdot \frac{-1}{t1 + u}\]
\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}
↓
\left(\frac{t1}{t1 + u} \cdot v\right) \cdot \frac{-1}{t1 + u}
double f(double u, double v, double t1) {
        double r412694 = t1;
        double r412695 = -r412694;
        double r412696 = v;
        double r412697 = r412695 * r412696;
        double r412698 = u;
        double r412699 = r412694 + r412698;
        double r412700 = r412699 * r412699;
        double r412701 = r412697 / r412700;
        return r412701;
}
↓
double f(double u, double v, double t1) {
        double r412702 = t1;
        double r412703 = u;
        double r412704 = r412702 + r412703;
        double r412705 = r412702 / r412704;
        double r412706 = v;
        double r412707 = r412705 * r412706;
        double r412708 = -1.0;
        double r412709 = r412708 / r412704;
        double r412710 = r412707 * r412709;
        return r412710;
}

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 18.1

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

  3. Applied times-frac1.3

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

  5. Applied div-inv1.4

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

  6. Applied associate-*r*1.4

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

  7. Final simplification1.4

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

Reproduce

herbie shell --seed 2019153 +o rules:numerics
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))