Average Error: 18.1 → 1.4
Time: 3.9s
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 r31549 = t1;
        double r31550 = -r31549;
        double r31551 = v;
        double r31552 = r31550 * r31551;
        double r31553 = u;
        double r31554 = r31549 + r31553;
        double r31555 = r31554 * r31554;
        double r31556 = r31552 / r31555;
        return r31556;
}
↓
double f(double u, double v, double t1) {
        double r31557 = t1;
        double r31558 = -r31557;
        double r31559 = v;
        double r31560 = u;
        double r31561 = r31557 + r31560;
        double r31562 = r31559 / r31561;
        double r31563 = r31558 * r31562;
        double r31564 = 1.0;
        double r31565 = r31564 / r31561;
        double r31566 = r31563 * r31565;
        return r31566;
}

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 18.1

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

  3. Applied times-frac1.4

    \[\leadsto \color{blue}{\frac{-t1}{t1 + u} \cdot \frac{v}{t1 + u}}\]
  4. Using strategy rm

  5. Applied div-inv1.5

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

  6. Applied associate-*r*1.3

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

  7. Simplified1.4

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

  8. Final simplification1.4

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

Reproduce

herbie shell --seed 2019356 +o rules:numerics
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  :precision binary64
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))