Average Error: 17.9 → 1.5
Time: 32.6s
Precision: 64
\[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
↓
\[\left(\frac{t1}{t1 + u} \cdot v\right) \cdot \frac{-1}{t1 + u}\]
\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}
↓
\left(\frac{t1}{t1 + u} \cdot v\right) \cdot \frac{-1}{t1 + u}
double f(double u, double v, double t1) {
        double r569652 = t1;
        double r569653 = -r569652;
        double r569654 = v;
        double r569655 = r569653 * r569654;
        double r569656 = u;
        double r569657 = r569652 + r569656;
        double r569658 = r569657 * r569657;
        double r569659 = r569655 / r569658;
        return r569659;
}
↓
double f(double u, double v, double t1) {
        double r569660 = t1;
        double r569661 = u;
        double r569662 = r569660 + r569661;
        double r569663 = r569660 / r569662;
        double r569664 = v;
        double r569665 = r569663 * r569664;
        double r569666 = -1.0;
        double r569667 = r569666 / r569662;
        double r569668 = r569665 * r569667;
        return r569668;
}

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 div-inv1.5

    \[\leadsto \frac{-t1}{t1 + u} \cdot \color{blue}{\left(v \cdot \frac{1}{t1 + u}\right)}\]

  6. Applied associate-*r*1.5

    \[\leadsto \color{blue}{\left(\frac{-t1}{t1 + u} \cdot v\right) \cdot \frac{1}{t1 + u}}\]

  7. Final simplification1.5

    \[\leadsto \left(\frac{t1}{t1 + u} \cdot v\right) \cdot \frac{-1}{t1 + u}\]

Reproduce

herbie shell --seed 2019135 +o rules:numerics
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))