Average Error: 18.5 → 1.4
Time: 18.0s
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 r21583 = t1;
        double r21584 = -r21583;
        double r21585 = v;
        double r21586 = r21584 * r21585;
        double r21587 = u;
        double r21588 = r21583 + r21587;
        double r21589 = r21588 * r21588;
        double r21590 = r21586 / r21589;
        return r21590;
}
↓
double f(double u, double v, double t1) {
        double r21591 = t1;
        double r21592 = -r21591;
        double r21593 = u;
        double r21594 = r21591 + r21593;
        double r21595 = r21592 / r21594;
        double r21596 = v;
        double r21597 = r21595 * r21596;
        double r21598 = r21597 / r21594;
        return r21598;
}

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 18.5

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

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

  6. Final simplification1.4

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

Reproduce

herbie shell --seed 2019323 +o rules:numerics
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  :precision binary64
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))