Average Error: 18.0 → 1.4
Time: 3.4s
Precision: 64
\[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
↓
\[\frac{1}{\frac{t1 + u}{-t1}} \cdot \frac{v}{t1 + u}\]
\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}
↓
\frac{1}{\frac{t1 + u}{-t1}} \cdot \frac{v}{t1 + u}
double f(double u, double v, double t1) {
        double r27603 = t1;
        double r27604 = -r27603;
        double r27605 = v;
        double r27606 = r27604 * r27605;
        double r27607 = u;
        double r27608 = r27603 + r27607;
        double r27609 = r27608 * r27608;
        double r27610 = r27606 / r27609;
        return r27610;
}
↓
double f(double u, double v, double t1) {
        double r27611 = 1.0;
        double r27612 = t1;
        double r27613 = u;
        double r27614 = r27612 + r27613;
        double r27615 = -r27612;
        double r27616 = r27614 / r27615;
        double r27617 = r27611 / r27616;
        double r27618 = v;
        double r27619 = r27618 / r27614;
        double r27620 = r27617 * r27619;
        return r27620;
}

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 18.0

    \[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
  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 clear-num1.4

    \[\leadsto \color{blue}{\frac{1}{\frac{t1 + u}{-t1}}} \cdot \frac{v}{t1 + u}\]

  6. Final simplification1.4

    \[\leadsto \frac{1}{\frac{t1 + u}{-t1}} \cdot \frac{v}{t1 + u}\]

Reproduce

herbie shell --seed 2020049 +o rules:numerics
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  :precision binary64
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))