Average Error: 18.2 → 1.2
Time: 50.0s
Precision: 64
\[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
↓
\[\frac{v}{t1 + u} \cdot \frac{-t1}{t1 + u}\]
\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}
↓
\frac{v}{t1 + u} \cdot \frac{-t1}{t1 + u}
double f(double u, double v, double t1) {
        double r1955352 = t1;
        double r1955353 = -r1955352;
        double r1955354 = v;
        double r1955355 = r1955353 * r1955354;
        double r1955356 = u;
        double r1955357 = r1955352 + r1955356;
        double r1955358 = r1955357 * r1955357;
        double r1955359 = r1955355 / r1955358;
        return r1955359;
}
↓
double f(double u, double v, double t1) {
        double r1955360 = v;
        double r1955361 = t1;
        double r1955362 = u;
        double r1955363 = r1955361 + r1955362;
        double r1955364 = r1955360 / r1955363;
        double r1955365 = -r1955361;
        double r1955366 = r1955365 / r1955363;
        double r1955367 = r1955364 * r1955366;
        return r1955367;
}

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-frac1.2

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

  4. Final simplification1.2

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

Reproduce

herbie shell --seed 2019151 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))