Average Error: 17.8 → 1.2
Time: 16.8s
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 r1374653 = t1;
        double r1374654 = -r1374653;
        double r1374655 = v;
        double r1374656 = r1374654 * r1374655;
        double r1374657 = u;
        double r1374658 = r1374653 + r1374657;
        double r1374659 = r1374658 * r1374658;
        double r1374660 = r1374656 / r1374659;
        return r1374660;
}
↓
double f(double u, double v, double t1) {
        double r1374661 = t1;
        double r1374662 = u;
        double r1374663 = r1374661 + r1374662;
        double r1374664 = r1374661 / r1374663;
        double r1374665 = v;
        double r1374666 = r1374664 * r1374665;
        double r1374667 = r1374666 / r1374663;
        double r1374668 = -r1374667;
        return r1374668;
}

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 17.8

    \[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
  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 2019158 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))