Average Error: 17.8 → 1.4
Time: 13.9s
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 r438454 = t1;
        double r438455 = -r438454;
        double r438456 = v;
        double r438457 = r438455 * r438456;
        double r438458 = u;
        double r438459 = r438454 + r438458;
        double r438460 = r438459 * r438459;
        double r438461 = r438457 / r438460;
        return r438461;
}
↓
double f(double u, double v, double t1) {
        double r438462 = v;
        double r438463 = t1;
        double r438464 = u;
        double r438465 = r438463 + r438464;
        double r438466 = r438462 / r438465;
        double r438467 = -r438463;
        double r438468 = r438467 / r438465;
        double r438469 = r438466 * r438468;
        return r438469;
}

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 17.8

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

  3. Applied times-frac1.4

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

  4. Final simplification1.4

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

Reproduce

herbie shell --seed 2019154 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))