Average Error: 18.2 → 1.3
Time: 35.5s
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 r2182615 = t1;
        double r2182616 = -r2182615;
        double r2182617 = v;
        double r2182618 = r2182616 * r2182617;
        double r2182619 = u;
        double r2182620 = r2182615 + r2182619;
        double r2182621 = r2182620 * r2182620;
        double r2182622 = r2182618 / r2182621;
        return r2182622;
}
↓
double f(double u, double v, double t1) {
        double r2182623 = t1;
        double r2182624 = u;
        double r2182625 = r2182623 + r2182624;
        double r2182626 = r2182623 / r2182625;
        double r2182627 = v;
        double r2182628 = r2182626 * r2182627;
        double r2182629 = r2182628 / r2182625;
        double r2182630 = -r2182629;
        return r2182630;
}

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 18.2

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

  3. Applied times-frac1.2

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

  5. Applied associate-*r/1.3

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

  6. Final simplification1.3

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

Reproduce

herbie shell --seed 2019120 +o rules:numerics
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))