Average Error: 18.1 → 1.2
Time: 22.0s
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 r21699 = t1;
        double r21700 = -r21699;
        double r21701 = v;
        double r21702 = r21700 * r21701;
        double r21703 = u;
        double r21704 = r21699 + r21703;
        double r21705 = r21704 * r21704;
        double r21706 = r21702 / r21705;
        return r21706;
}
↓
double f(double u, double v, double t1) {
        double r21707 = t1;
        double r21708 = -r21707;
        double r21709 = u;
        double r21710 = r21707 + r21709;
        double r21711 = r21708 / r21710;
        double r21712 = v;
        double r21713 = r21711 * r21712;
        double r21714 = r21713 / r21710;
        return r21714;
}

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 18.1

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

  3. Applied times-frac1.3

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

  5. Applied associate-*r/1.2

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

  6. Final simplification1.2

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

Reproduce

herbie shell --seed 2019235 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  :precision binary64
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))