Average Error: 18.2 → 1.3
Time: 49.3s
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 r1641295 = t1;
        double r1641296 = -r1641295;
        double r1641297 = v;
        double r1641298 = r1641296 * r1641297;
        double r1641299 = u;
        double r1641300 = r1641295 + r1641299;
        double r1641301 = r1641300 * r1641300;
        double r1641302 = r1641298 / r1641301;
        return r1641302;
}
↓
double f(double u, double v, double t1) {
        double r1641303 = t1;
        double r1641304 = u;
        double r1641305 = r1641303 + r1641304;
        double r1641306 = r1641303 / r1641305;
        double r1641307 = v;
        double r1641308 = r1641306 * r1641307;
        double r1641309 = r1641308 / r1641305;
        double r1641310 = -r1641309;
        return r1641310;
}

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-frac1.3

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

  5. Applied associate-*r/1.3

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

  6. Final simplification1.3

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

Reproduce

herbie shell --seed 2019146 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))