Average Error: 18.1 → 1.4
Time: 18.4s
Precision: 64
\[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
↓
\[\frac{\frac{v}{u + t1} \cdot \left(-t1\right)}{u + t1}\]
\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}
↓
\frac{\frac{v}{u + t1} \cdot \left(-t1\right)}{u + t1}
double f(double u, double v, double t1) {
        double r996768 = t1;
        double r996769 = -r996768;
        double r996770 = v;
        double r996771 = r996769 * r996770;
        double r996772 = u;
        double r996773 = r996768 + r996772;
        double r996774 = r996773 * r996773;
        double r996775 = r996771 / r996774;
        return r996775;
}
↓
double f(double u, double v, double t1) {
        double r996776 = v;
        double r996777 = u;
        double r996778 = t1;
        double r996779 = r996777 + r996778;
        double r996780 = r996776 / r996779;
        double r996781 = -r996778;
        double r996782 = r996780 * r996781;
        double r996783 = r996782 / r996779;
        return r996783;
}

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 18.1

    \[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
  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 associate-*l/1.4

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

  6. Final simplification1.4

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

Reproduce

herbie shell --seed 2019130 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))