Average Error: 18.4 → 1.4
Time: 5.3s
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 r36493 = t1;
        double r36494 = -r36493;
        double r36495 = v;
        double r36496 = r36494 * r36495;
        double r36497 = u;
        double r36498 = r36493 + r36497;
        double r36499 = r36498 * r36498;
        double r36500 = r36496 / r36499;
        return r36500;
}
↓
double f(double u, double v, double t1) {
        double r36501 = t1;
        double r36502 = -r36501;
        double r36503 = u;
        double r36504 = r36501 + r36503;
        double r36505 = r36502 / r36504;
        double r36506 = v;
        double r36507 = r36506 / r36504;
        double r36508 = r36505 * r36507;
        return r36508;
}

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 18.4

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

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

Reproduce

herbie shell --seed 2020083 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  :precision binary64
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))