Average Error: 17.7 → 1.3
Time: 3.4s
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 r23449 = t1;
        double r23450 = -r23449;
        double r23451 = v;
        double r23452 = r23450 * r23451;
        double r23453 = u;
        double r23454 = r23449 + r23453;
        double r23455 = r23454 * r23454;
        double r23456 = r23452 / r23455;
        return r23456;
}
↓
double f(double u, double v, double t1) {
        double r23457 = t1;
        double r23458 = -r23457;
        double r23459 = u;
        double r23460 = r23457 + r23459;
        double r23461 = r23458 / r23460;
        double r23462 = v;
        double r23463 = r23462 / r23460;
        double r23464 = r23461 * r23463;
        return r23464;
}

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 17.7

    \[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
  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 2020100 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  :precision binary64
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))