Average Error: 18.0 → 1.6
Time: 3.2s
Precision: 64
\[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
↓
\[\frac{-t1}{t1 + u} \cdot \left(v \cdot \frac{1}{t1 + u}\right)\]
\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}
↓
\frac{-t1}{t1 + u} \cdot \left(v \cdot \frac{1}{t1 + u}\right)
double f(double u, double v, double t1) {
        double r23701 = t1;
        double r23702 = -r23701;
        double r23703 = v;
        double r23704 = r23702 * r23703;
        double r23705 = u;
        double r23706 = r23701 + r23705;
        double r23707 = r23706 * r23706;
        double r23708 = r23704 / r23707;
        return r23708;
}
↓
double f(double u, double v, double t1) {
        double r23709 = t1;
        double r23710 = -r23709;
        double r23711 = u;
        double r23712 = r23709 + r23711;
        double r23713 = r23710 / r23712;
        double r23714 = v;
        double r23715 = 1.0;
        double r23716 = r23715 / r23712;
        double r23717 = r23714 * r23716;
        double r23718 = r23713 * r23717;
        return r23718;
}

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-frac1.5

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

  5. Applied div-inv1.6

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

  6. Final simplification1.6

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

Reproduce

herbie shell --seed 2020059 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  :precision binary64
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))