Average Error: 18.5 → 1.4
Time: 16.5s
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 r21370 = t1;
        double r21371 = -r21370;
        double r21372 = v;
        double r21373 = r21371 * r21372;
        double r21374 = u;
        double r21375 = r21370 + r21374;
        double r21376 = r21375 * r21375;
        double r21377 = r21373 / r21376;
        return r21377;
}
↓
double f(double u, double v, double t1) {
        double r21378 = t1;
        double r21379 = -r21378;
        double r21380 = u;
        double r21381 = r21378 + r21380;
        double r21382 = r21379 / r21381;
        double r21383 = v;
        double r21384 = r21382 * r21383;
        double r21385 = r21384 / r21381;
        return r21385;
}

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