Average Error: 18.2 → 1.4
Time: 3.4s
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 r19433 = t1;
        double r19434 = -r19433;
        double r19435 = v;
        double r19436 = r19434 * r19435;
        double r19437 = u;
        double r19438 = r19433 + r19437;
        double r19439 = r19438 * r19438;
        double r19440 = r19436 / r19439;
        return r19440;
}
↓
double f(double u, double v, double t1) {
        double r19441 = t1;
        double r19442 = -r19441;
        double r19443 = v;
        double r19444 = u;
        double r19445 = r19441 + r19444;
        double r19446 = r19443 / r19445;
        double r19447 = r19442 * r19446;
        double r19448 = 1.0;
        double r19449 = r19448 / r19445;
        double r19450 = r19447 * r19449;
        return r19450;
}

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-frac1.4

    \[\leadsto \color{blue}{\frac{-t1}{t1 + u} \cdot \frac{v}{t1 + u}}\]
  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. Simplified1.4

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

  8. Final simplification1.4

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

Reproduce

herbie shell --seed 2020025 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  :precision binary64
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))