Average Error: 18.2 → 1.3
Time: 41.5s
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 r948808 = t1;
        double r948809 = -r948808;
        double r948810 = v;
        double r948811 = r948809 * r948810;
        double r948812 = u;
        double r948813 = r948808 + r948812;
        double r948814 = r948813 * r948813;
        double r948815 = r948811 / r948814;
        return r948815;
}
↓
double f(double u, double v, double t1) {
        double r948816 = t1;
        double r948817 = u;
        double r948818 = r948816 + r948817;
        double r948819 = r948816 / r948818;
        double r948820 = v;
        double r948821 = r948819 * r948820;
        double r948822 = r948821 / r948818;
        double r948823 = -r948822;
        return r948823;
}

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 18.2

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

  3. Applied times-frac1.3

    \[\leadsto \color{blue}{\frac{-t1}{t1 + u} \cdot \frac{v}{t1 + u}}\]
  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 2019146 +o rules:numerics
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))