Average Error: 18.1 → 1.2
Time: 3.7s
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 r27488 = t1;
        double r27489 = -r27488;
        double r27490 = v;
        double r27491 = r27489 * r27490;
        double r27492 = u;
        double r27493 = r27488 + r27492;
        double r27494 = r27493 * r27493;
        double r27495 = r27491 / r27494;
        return r27495;
}
↓
double f(double u, double v, double t1) {
        double r27496 = t1;
        double r27497 = -r27496;
        double r27498 = 1.0;
        double r27499 = u;
        double r27500 = r27496 + r27499;
        double r27501 = r27498 / r27500;
        double r27502 = r27497 * r27501;
        double r27503 = v;
        double r27504 = r27503 / r27500;
        double r27505 = r27502 * r27504;
        return r27505;
}

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-frac1.2

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

  5. Applied div-inv1.2

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

  6. Final simplification1.2

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

Reproduce

herbie shell --seed 2020018 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  :precision binary64
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))