Average Error: 18.4 → 1.6
Time: 3.7s
Precision: 64
\[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
↓
\[\left(\left(-t1\right) \cdot \frac{v}{t1 + u}\right) \cdot \frac{1}{t1 + u}\]
\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}
↓
\left(\left(-t1\right) \cdot \frac{v}{t1 + u}\right) \cdot \frac{1}{t1 + u}
double f(double u, double v, double t1) {
        double r19538 = t1;
        double r19539 = -r19538;
        double r19540 = v;
        double r19541 = r19539 * r19540;
        double r19542 = u;
        double r19543 = r19538 + r19542;
        double r19544 = r19543 * r19543;
        double r19545 = r19541 / r19544;
        return r19545;
}
↓
double f(double u, double v, double t1) {
        double r19546 = t1;
        double r19547 = -r19546;
        double r19548 = v;
        double r19549 = u;
        double r19550 = r19546 + r19549;
        double r19551 = r19548 / r19550;
        double r19552 = r19547 * r19551;
        double r19553 = 1.0;
        double r19554 = r19553 / r19550;
        double r19555 = r19552 * r19554;
        return r19555;
}

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 18.4

    \[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
  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 div-inv1.6

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

  6. Applied associate-*r*1.3

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

  7. Simplified1.6

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

  8. Final simplification1.6

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

Reproduce

herbie shell --seed 2020003 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  :precision binary64
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))