Average Error: 18.2 → 1.3
Time: 12.1s
Precision: 64
\[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
↓
\[\frac{\left(-t1\right) \cdot \frac{v}{t1 + u}}{t1 + u}\]
\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}
↓
\frac{\left(-t1\right) \cdot \frac{v}{t1 + u}}{t1 + u}
double f(double u, double v, double t1) {
        double r23446 = t1;
        double r23447 = -r23446;
        double r23448 = v;
        double r23449 = r23447 * r23448;
        double r23450 = u;
        double r23451 = r23446 + r23450;
        double r23452 = r23451 * r23451;
        double r23453 = r23449 / r23452;
        return r23453;
}
↓
double f(double u, double v, double t1) {
        double r23454 = t1;
        double r23455 = -r23454;
        double r23456 = v;
        double r23457 = u;
        double r23458 = r23454 + r23457;
        double r23459 = r23456 / r23458;
        double r23460 = r23455 * r23459;
        double r23461 = r23460 / r23458;
        return r23461;
}

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/1.2

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

  6. Simplified1.3

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

  7. Final simplification1.3

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

Reproduce

herbie shell --seed 2019298 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  :precision binary64
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))