Average Error: 18.2 → 1.3
Time: 10.2s
Precision: 64
\[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
↓
\[\left(\left(-t1\right) \cdot \frac{1}{t1 + u}\right) \cdot \frac{v}{t1 + u}\]
\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}
↓
\left(\left(-t1\right) \cdot \frac{1}{t1 + u}\right) \cdot \frac{v}{t1 + u}
double f(double u, double v, double t1) {
        double r28421 = t1;
        double r28422 = -r28421;
        double r28423 = v;
        double r28424 = r28422 * r28423;
        double r28425 = u;
        double r28426 = r28421 + r28425;
        double r28427 = r28426 * r28426;
        double r28428 = r28424 / r28427;
        return r28428;
}
↓
double f(double u, double v, double t1) {
        double r28429 = t1;
        double r28430 = -r28429;
        double r28431 = 1.0;
        double r28432 = u;
        double r28433 = r28429 + r28432;
        double r28434 = r28431 / r28433;
        double r28435 = r28430 * r28434;
        double r28436 = v;
        double r28437 = r28436 / r28433;
        double r28438 = r28435 * r28437;
        return r28438;
}

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-frac1.2

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

  5. Applied div-inv1.3

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

  6. Final simplification1.3

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

Reproduce

herbie shell --seed 2019350 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  :precision binary64
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))