Average Error: 17.6 → 1.2
Time: 16.4s
Precision: 64
\[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
↓
\[-\frac{\frac{t1}{t1 + u} \cdot v}{t1 + u}\]
\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}
↓
-\frac{\frac{t1}{t1 + u} \cdot v}{t1 + u}
double f(double u, double v, double t1) {
        double r1292687 = t1;
        double r1292688 = -r1292687;
        double r1292689 = v;
        double r1292690 = r1292688 * r1292689;
        double r1292691 = u;
        double r1292692 = r1292687 + r1292691;
        double r1292693 = r1292692 * r1292692;
        double r1292694 = r1292690 / r1292693;
        return r1292694;
}
↓
double f(double u, double v, double t1) {
        double r1292695 = t1;
        double r1292696 = u;
        double r1292697 = r1292695 + r1292696;
        double r1292698 = r1292695 / r1292697;
        double r1292699 = v;
        double r1292700 = r1292698 * r1292699;
        double r1292701 = r1292700 / r1292697;
        double r1292702 = -r1292701;
        return r1292702;
}

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 17.6

    \[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
  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 associate-*r/1.2

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

  6. Final simplification1.2

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

Reproduce

herbie shell --seed 2019163 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))