Average Error: 18.4 → 1.3
Time: 4.1s
Precision: 64
\[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
↓
\[\frac{v \cdot \frac{-t1}{t1 + u}}{t1 + u}\]
\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}
↓
\frac{v \cdot \frac{-t1}{t1 + u}}{t1 + u}
double f(double u, double v, double t1) {
        double r27980 = t1;
        double r27981 = -r27980;
        double r27982 = v;
        double r27983 = r27981 * r27982;
        double r27984 = u;
        double r27985 = r27980 + r27984;
        double r27986 = r27985 * r27985;
        double r27987 = r27983 / r27986;
        return r27987;
}
↓
double f(double u, double v, double t1) {
        double r27988 = v;
        double r27989 = t1;
        double r27990 = -r27989;
        double r27991 = u;
        double r27992 = r27989 + r27991;
        double r27993 = r27990 / r27992;
        double r27994 = r27988 * r27993;
        double r27995 = r27994 / r27992;
        return r27995;
}

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-frac1.6

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

  5. Applied add-cube-cbrt1.9

    \[\leadsto \color{blue}{\left(\left(\sqrt[3]{\frac{-t1}{t1 + u}} \cdot \sqrt[3]{\frac{-t1}{t1 + u}}\right) \cdot \sqrt[3]{\frac{-t1}{t1 + u}}\right)} \cdot \frac{v}{t1 + u}\]
  6. Using strategy rm

  7. Applied associate-*r/1.6

    \[\leadsto \color{blue}{\frac{\left(\left(\sqrt[3]{\frac{-t1}{t1 + u}} \cdot \sqrt[3]{\frac{-t1}{t1 + u}}\right) \cdot \sqrt[3]{\frac{-t1}{t1 + u}}\right) \cdot v}{t1 + u}}\]

  8. Simplified1.3

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

  9. Final simplification1.3

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

Reproduce

herbie shell --seed 2020020 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  :precision binary64
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))