Average Error: 18.6 → 1.3
Time: 9.0s
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 r24763 = t1;
        double r24764 = -r24763;
        double r24765 = v;
        double r24766 = r24764 * r24765;
        double r24767 = u;
        double r24768 = r24763 + r24767;
        double r24769 = r24768 * r24768;
        double r24770 = r24766 / r24769;
        return r24770;
}
↓
double f(double u, double v, double t1) {
        double r24771 = t1;
        double r24772 = -r24771;
        double r24773 = u;
        double r24774 = r24771 + r24773;
        double r24775 = r24772 / r24774;
        double r24776 = v;
        double r24777 = r24775 * r24776;
        double r24778 = r24777 / r24774;
        return r24778;
}

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 18.6

    \[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
  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/1.3

    \[\leadsto \color{blue}{\frac{\frac{-t1}{t1 + u} \cdot v}{t1 + u}}\]

  6. Final simplification1.3

    \[\leadsto \frac{\frac{-t1}{t1 + u} \cdot v}{t1 + u}\]

Reproduce

herbie shell --seed 2020042 +o rules:numerics
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  :precision binary64
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))