Average Error: 17.9 → 1.4
Time: 16.4s
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 r747510 = t1;
        double r747511 = -r747510;
        double r747512 = v;
        double r747513 = r747511 * r747512;
        double r747514 = u;
        double r747515 = r747510 + r747514;
        double r747516 = r747515 * r747515;
        double r747517 = r747513 / r747516;
        return r747517;
}
↓
double f(double u, double v, double t1) {
        double r747518 = t1;
        double r747519 = u;
        double r747520 = r747518 + r747519;
        double r747521 = r747518 / r747520;
        double r747522 = v;
        double r747523 = r747521 * r747522;
        double r747524 = r747523 / r747520;
        double r747525 = -r747524;
        return r747525;
}

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 17.9

    \[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
  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 2019135 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))