Average Error: 17.9 → 1.4
Time: 8.1s
Precision: 64
\[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
↓
\[\frac{\left(-t1\right) \cdot \left(v \cdot \frac{1}{t1 + u}\right)}{t1 + u}\]
\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}
↓
\frac{\left(-t1\right) \cdot \left(v \cdot \frac{1}{t1 + u}\right)}{t1 + u}
double f(double u, double v, double t1) {
        double r23458 = t1;
        double r23459 = -r23458;
        double r23460 = v;
        double r23461 = r23459 * r23460;
        double r23462 = u;
        double r23463 = r23458 + r23462;
        double r23464 = r23463 * r23463;
        double r23465 = r23461 / r23464;
        return r23465;
}
↓
double f(double u, double v, double t1) {
        double r23466 = t1;
        double r23467 = -r23466;
        double r23468 = v;
        double r23469 = 1.0;
        double r23470 = u;
        double r23471 = r23466 + r23470;
        double r23472 = r23469 / r23471;
        double r23473 = r23468 * r23472;
        double r23474 = r23467 * r23473;
        double r23475 = r23474 / r23471;
        return r23475;
}

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 associate-/r*11.2

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

  4. Simplified1.3

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

  6. Applied div-inv1.4

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

  7. Final simplification1.4

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

Reproduce

herbie shell --seed 2020045 +o rules:numerics
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  :precision binary64
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))