Average Error: 17.6 → 1.1
Time: 26.3s
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 r987368 = t1;
        double r987369 = -r987368;
        double r987370 = v;
        double r987371 = r987369 * r987370;
        double r987372 = u;
        double r987373 = r987368 + r987372;
        double r987374 = r987373 * r987373;
        double r987375 = r987371 / r987374;
        return r987375;
}
↓
double f(double u, double v, double t1) {
        double r987376 = t1;
        double r987377 = u;
        double r987378 = r987376 + r987377;
        double r987379 = r987376 / r987378;
        double r987380 = v;
        double r987381 = r987379 * r987380;
        double r987382 = r987381 / r987378;
        double r987383 = -r987382;
        return r987383;
}

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 17.6

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

  3. Applied times-frac1.5

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

  5. Applied associate-*r/1.1

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

  6. Final simplification1.1

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

Reproduce

herbie shell --seed 2019132 +o rules:numerics
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))