Average Error: 18.6 → 1.3
Time: 17.9s
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 r19711 = t1;
        double r19712 = -r19711;
        double r19713 = v;
        double r19714 = r19712 * r19713;
        double r19715 = u;
        double r19716 = r19711 + r19715;
        double r19717 = r19716 * r19716;
        double r19718 = r19714 / r19717;
        return r19718;
}
↓
double f(double u, double v, double t1) {
        double r19719 = t1;
        double r19720 = u;
        double r19721 = r19719 + r19720;
        double r19722 = r19719 / r19721;
        double r19723 = v;
        double r19724 = r19722 * r19723;
        double r19725 = -1.0;
        double r19726 = r19725 / r19721;
        double r19727 = r19724 * r19726;
        return r19727;
}

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 div-inv1.5

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

  6. Applied associate-*r*1.3

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

  7. Final simplification1.3

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

Reproduce

herbie shell --seed 2019305 +o rules:numerics
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  :precision binary64
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))