Average Error: 18.2 → 1.3
Time: 33.2s
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 r2171791 = t1;
        double r2171792 = -r2171791;
        double r2171793 = v;
        double r2171794 = r2171792 * r2171793;
        double r2171795 = u;
        double r2171796 = r2171791 + r2171795;
        double r2171797 = r2171796 * r2171796;
        double r2171798 = r2171794 / r2171797;
        return r2171798;
}
↓
double f(double u, double v, double t1) {
        double r2171799 = t1;
        double r2171800 = u;
        double r2171801 = r2171799 + r2171800;
        double r2171802 = r2171799 / r2171801;
        double r2171803 = v;
        double r2171804 = r2171802 * r2171803;
        double r2171805 = r2171804 / r2171801;
        double r2171806 = -r2171805;
        return r2171806;
}

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 18.2

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

  3. Applied times-frac1.2

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

  5. Applied associate-*r/1.3

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

  6. Final simplification1.3

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

Reproduce

herbie shell --seed 2019120 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))