Average Error: 18.4 → 1.4
Time: 3.4s
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 r24390 = t1;
        double r24391 = -r24390;
        double r24392 = v;
        double r24393 = r24391 * r24392;
        double r24394 = u;
        double r24395 = r24390 + r24394;
        double r24396 = r24395 * r24395;
        double r24397 = r24393 / r24396;
        return r24397;
}
↓
double f(double u, double v, double t1) {
        double r24398 = t1;
        double r24399 = -r24398;
        double r24400 = u;
        double r24401 = r24398 + r24400;
        double r24402 = r24399 / r24401;
        double r24403 = v;
        double r24404 = r24403 / r24401;
        double r24405 = r24402 * r24404;
        return r24405;
}

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 2020001 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  :precision binary64
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))