Average Error: 18.2 → 1.4
Time: 3.0s
Precision: 64
\[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
↓
\[\frac{-t1}{t1 + u} \cdot \frac{v}{t1 + u}\]
\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}
↓
\frac{-t1}{t1 + u} \cdot \frac{v}{t1 + u}
double f(double u, double v, double t1) {
        double r22569 = t1;
        double r22570 = -r22569;
        double r22571 = v;
        double r22572 = r22570 * r22571;
        double r22573 = u;
        double r22574 = r22569 + r22573;
        double r22575 = r22574 * r22574;
        double r22576 = r22572 / r22575;
        return r22576;
}
↓
double f(double u, double v, double t1) {
        double r22577 = t1;
        double r22578 = -r22577;
        double r22579 = u;
        double r22580 = r22577 + r22579;
        double r22581 = r22578 / r22580;
        double r22582 = v;
        double r22583 = r22582 / r22580;
        double r22584 = r22581 * r22583;
        return r22584;
}

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-frac1.4

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

  4. Final simplification1.4

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

Reproduce

herbie shell --seed 2020062 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  :precision binary64
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))