Average Error: 17.9 → 1.3
Time: 6.2s
Precision: 64
\[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
↓
\[\frac{-t1}{t1 + u} \cdot \frac{v}{t1 + u}\]
\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}
↓
\frac{-t1}{t1 + u} \cdot \frac{v}{t1 + u}
double f(double u, double v, double t1) {
        double r22383 = t1;
        double r22384 = -r22383;
        double r22385 = v;
        double r22386 = r22384 * r22385;
        double r22387 = u;
        double r22388 = r22383 + r22387;
        double r22389 = r22388 * r22388;
        double r22390 = r22386 / r22389;
        return r22390;
}
↓
double f(double u, double v, double t1) {
        double r22391 = t1;
        double r22392 = -r22391;
        double r22393 = u;
        double r22394 = r22391 + r22393;
        double r22395 = r22392 / r22394;
        double r22396 = v;
        double r22397 = r22396 / r22394;
        double r22398 = r22395 * r22397;
        return r22398;
}

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 17.9

    \[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
  2. Using strategy rm

  3. Applied times-frac1.3

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

  4. Final simplification1.3

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

Reproduce

herbie shell --seed 2019304 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  :precision binary64
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))