Average Error: 17.8 → 1.2
Time: 20.9s
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 r995545 = t1;
        double r995546 = -r995545;
        double r995547 = v;
        double r995548 = r995546 * r995547;
        double r995549 = u;
        double r995550 = r995545 + r995549;
        double r995551 = r995550 * r995550;
        double r995552 = r995548 / r995551;
        return r995552;
}
↓
double f(double u, double v, double t1) {
        double r995553 = t1;
        double r995554 = -r995553;
        double r995555 = u;
        double r995556 = r995553 + r995555;
        double r995557 = r995554 / r995556;
        double r995558 = v;
        double r995559 = r995557 * r995558;
        double r995560 = r995559 / r995556;
        return r995560;
}

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 17.8

    \[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
  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 2019172 +o rules:numerics
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))