Average Error: 17.9 → 1.4
Time: 7.5s
Precision: 64
\[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
↓
\[\frac{\left(-t1\right) \cdot \left(v \cdot \frac{1}{t1 + u}\right)}{t1 + u}\]
\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}
↓
\frac{\left(-t1\right) \cdot \left(v \cdot \frac{1}{t1 + u}\right)}{t1 + u}
double f(double u, double v, double t1) {
        double r26705 = t1;
        double r26706 = -r26705;
        double r26707 = v;
        double r26708 = r26706 * r26707;
        double r26709 = u;
        double r26710 = r26705 + r26709;
        double r26711 = r26710 * r26710;
        double r26712 = r26708 / r26711;
        return r26712;
}
↓
double f(double u, double v, double t1) {
        double r26713 = t1;
        double r26714 = -r26713;
        double r26715 = v;
        double r26716 = 1.0;
        double r26717 = u;
        double r26718 = r26713 + r26717;
        double r26719 = r26716 / r26718;
        double r26720 = r26715 * r26719;
        double r26721 = r26714 * r26720;
        double r26722 = r26721 / r26718;
        return r26722;
}

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 associate-/r*11.2

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

  4. Simplified1.3

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

  6. Applied div-inv1.4

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

  7. Final simplification1.4

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

Reproduce

herbie shell --seed 2020045 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  :precision binary64
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))