Average Error: 17.7 → 1.4
Time: 8.4s
Precision: 64
\[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
↓
\[\left(\left(-t1\right) \cdot \frac{v}{t1 + u}\right) \cdot \frac{1}{t1 + u}\]
\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}
↓
\left(\left(-t1\right) \cdot \frac{v}{t1 + u}\right) \cdot \frac{1}{t1 + u}
double f(double u, double v, double t1) {
        double r19455 = t1;
        double r19456 = -r19455;
        double r19457 = v;
        double r19458 = r19456 * r19457;
        double r19459 = u;
        double r19460 = r19455 + r19459;
        double r19461 = r19460 * r19460;
        double r19462 = r19458 / r19461;
        return r19462;
}
↓
double f(double u, double v, double t1) {
        double r19463 = t1;
        double r19464 = -r19463;
        double r19465 = v;
        double r19466 = u;
        double r19467 = r19463 + r19466;
        double r19468 = r19465 / r19467;
        double r19469 = r19464 * r19468;
        double r19470 = 1.0;
        double r19471 = r19470 / r19467;
        double r19472 = r19469 * r19471;
        return r19472;
}

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 associate-/r*11.1

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

  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

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

  7. Final simplification1.4

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

Reproduce

herbie shell --seed 2020043 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  :precision binary64
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))