Average Error: 18.5 → 1.4
Time: 18.0s
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 r21621 = t1;
        double r21622 = -r21621;
        double r21623 = v;
        double r21624 = r21622 * r21623;
        double r21625 = u;
        double r21626 = r21621 + r21625;
        double r21627 = r21626 * r21626;
        double r21628 = r21624 / r21627;
        return r21628;
}
↓
double f(double u, double v, double t1) {
        double r21629 = t1;
        double r21630 = -r21629;
        double r21631 = u;
        double r21632 = r21629 + r21631;
        double r21633 = r21630 / r21632;
        double r21634 = v;
        double r21635 = r21633 * r21634;
        double r21636 = r21635 / r21632;
        return r21636;
}

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 18.5

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

  3. Applied times-frac1.4

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

  5. Applied associate-*r/1.4

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

  6. Final simplification1.4

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

Reproduce

herbie shell --seed 2019323 +o rules:numerics
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  :precision binary64
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))