Average Error: 18.4 → 1.6
Time: 48.2s
Precision: 64
\[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
↓
\[\frac{v}{t1 + u} \cdot \frac{-t1}{t1 + u}\]
\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}
↓
\frac{v}{t1 + u} \cdot \frac{-t1}{t1 + u}
double f(double u, double v, double t1) {
        double r1163365 = t1;
        double r1163366 = -r1163365;
        double r1163367 = v;
        double r1163368 = r1163366 * r1163367;
        double r1163369 = u;
        double r1163370 = r1163365 + r1163369;
        double r1163371 = r1163370 * r1163370;
        double r1163372 = r1163368 / r1163371;
        return r1163372;
}
↓
double f(double u, double v, double t1) {
        double r1163373 = v;
        double r1163374 = t1;
        double r1163375 = u;
        double r1163376 = r1163374 + r1163375;
        double r1163377 = r1163373 / r1163376;
        double r1163378 = -r1163374;
        double r1163379 = r1163378 / r1163376;
        double r1163380 = r1163377 * r1163379;
        return r1163380;
}

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 18.4

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

  3. Applied times-frac1.6

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

  4. Final simplification1.6

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

Reproduce

herbie shell --seed 2019168 +o rules:numerics
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))