Average Error: 18.0 → 1.2
Time: 17.2s
Precision: 64
\[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
↓
\[\frac{\left(-t1\right) \cdot \frac{v}{t1 + u}}{t1 + u}\]
\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}
↓
\frac{\left(-t1\right) \cdot \frac{v}{t1 + u}}{t1 + u}
double f(double u, double v, double t1) {
        double r20323 = t1;
        double r20324 = -r20323;
        double r20325 = v;
        double r20326 = r20324 * r20325;
        double r20327 = u;
        double r20328 = r20323 + r20327;
        double r20329 = r20328 * r20328;
        double r20330 = r20326 / r20329;
        return r20330;
}
↓
double f(double u, double v, double t1) {
        double r20331 = t1;
        double r20332 = -r20331;
        double r20333 = v;
        double r20334 = u;
        double r20335 = r20331 + r20334;
        double r20336 = r20333 / r20335;
        double r20337 = r20332 * r20336;
        double r20338 = r20337 / r20335;
        return r20338;
}

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-frac1.4

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

  5. Applied associate-*l/1.2

    \[\leadsto \color{blue}{\frac{\left(-t1\right) \cdot \frac{v}{t1 + u}}{t1 + u}}\]

  6. Final simplification1.2

    \[\leadsto \frac{\left(-t1\right) \cdot \frac{v}{t1 + u}}{t1 + u}\]

Reproduce

herbie shell --seed 2019209 +o rules:numerics
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  :precision binary64
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))