Average Error: 18.3 → 1.2
Time: 5.6s
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 r38974 = t1;
        double r38975 = -r38974;
        double r38976 = v;
        double r38977 = r38975 * r38976;
        double r38978 = u;
        double r38979 = r38974 + r38978;
        double r38980 = r38979 * r38979;
        double r38981 = r38977 / r38980;
        return r38981;
}
↓
double f(double u, double v, double t1) {
        double r38982 = t1;
        double r38983 = -r38982;
        double r38984 = u;
        double r38985 = r38982 + r38984;
        double r38986 = r38983 / r38985;
        double r38987 = v;
        double r38988 = r38987 / r38985;
        double r38989 = r38986 * r38988;
        return r38989;
}

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 18.3

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

  3. Applied times-frac1.2

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

  4. Final simplification1.2

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

Reproduce

herbie shell --seed 2020024 +o rules:numerics
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  :precision binary64
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))