Average Error: 17.9 → 1.3
Time: 20.8s
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 r23739 = t1;
        double r23740 = -r23739;
        double r23741 = v;
        double r23742 = r23740 * r23741;
        double r23743 = u;
        double r23744 = r23739 + r23743;
        double r23745 = r23744 * r23744;
        double r23746 = r23742 / r23745;
        return r23746;
}
↓
double f(double u, double v, double t1) {
        double r23747 = t1;
        double r23748 = -r23747;
        double r23749 = u;
        double r23750 = r23747 + r23749;
        double r23751 = r23748 / r23750;
        double r23752 = v;
        double r23753 = r23752 / r23750;
        double r23754 = r23751 * r23753;
        return r23754;
}

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 17.9

    \[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
  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 2019304 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  :precision binary64
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))