Average Error: 18.2 → 1.4
Time: 39.2s
Precision: 64
\[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
↓
\[\frac{\frac{v}{u + t1} \cdot \left(-t1\right)}{u + t1}\]
\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}
↓
\frac{\frac{v}{u + t1} \cdot \left(-t1\right)}{u + t1}
double f(double u, double v, double t1) {
        double r1507346 = t1;
        double r1507347 = -r1507346;
        double r1507348 = v;
        double r1507349 = r1507347 * r1507348;
        double r1507350 = u;
        double r1507351 = r1507346 + r1507350;
        double r1507352 = r1507351 * r1507351;
        double r1507353 = r1507349 / r1507352;
        return r1507353;
}
↓
double f(double u, double v, double t1) {
        double r1507354 = v;
        double r1507355 = u;
        double r1507356 = t1;
        double r1507357 = r1507355 + r1507356;
        double r1507358 = r1507354 / r1507357;
        double r1507359 = -r1507356;
        double r1507360 = r1507358 * r1507359;
        double r1507361 = r1507360 / r1507357;
        return r1507361;
}

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-frac1.5

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

  5. Applied associate-*l/1.4

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

  6. Final simplification1.4

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

Reproduce

herbie shell --seed 2019142 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))