Average Error: 18.4 → 1.1
Time: 26.6s
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 r3061856 = t1;
        double r3061857 = -r3061856;
        double r3061858 = v;
        double r3061859 = r3061857 * r3061858;
        double r3061860 = u;
        double r3061861 = r3061856 + r3061860;
        double r3061862 = r3061861 * r3061861;
        double r3061863 = r3061859 / r3061862;
        return r3061863;
}
↓
double f(double u, double v, double t1) {
        double r3061864 = t1;
        double r3061865 = -r3061864;
        double r3061866 = u;
        double r3061867 = r3061864 + r3061866;
        double r3061868 = r3061865 / r3061867;
        double r3061869 = v;
        double r3061870 = r3061868 * r3061869;
        double r3061871 = r3061870 / r3061867;
        return r3061871;
}

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 18.4

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

  3. Applied times-frac1.4

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

  5. Applied associate-*r/1.1

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

  6. Final simplification1.1

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

Reproduce

herbie shell --seed 2019174 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))