Average Error: 17.7 → 1.3
Time: 3.7s
Precision: 64
\[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
↓
\[\frac{-t1}{t1 + u} \cdot \frac{v}{t1 + u}\]
\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}
↓
\frac{-t1}{t1 + u} \cdot \frac{v}{t1 + u}
double f(double u, double v, double t1) {
        double r27977 = t1;
        double r27978 = -r27977;
        double r27979 = v;
        double r27980 = r27978 * r27979;
        double r27981 = u;
        double r27982 = r27977 + r27981;
        double r27983 = r27982 * r27982;
        double r27984 = r27980 / r27983;
        return r27984;
}
↓
double f(double u, double v, double t1) {
        double r27985 = t1;
        double r27986 = -r27985;
        double r27987 = u;
        double r27988 = r27985 + r27987;
        double r27989 = r27986 / r27988;
        double r27990 = v;
        double r27991 = r27990 / r27988;
        double r27992 = r27989 * r27991;
        return r27992;
}

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 17.7

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

  3. Applied times-frac1.3

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

  4. Final simplification1.3

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

Reproduce

herbie shell --seed 2020100 +o rules:numerics
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  :precision binary64
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))