Average Error: 18.5 → 1.3
Time: 3.6s
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 r29466 = t1;
        double r29467 = -r29466;
        double r29468 = v;
        double r29469 = r29467 * r29468;
        double r29470 = u;
        double r29471 = r29466 + r29470;
        double r29472 = r29471 * r29471;
        double r29473 = r29469 / r29472;
        return r29473;
}
↓
double f(double u, double v, double t1) {
        double r29474 = t1;
        double r29475 = -r29474;
        double r29476 = u;
        double r29477 = r29474 + r29476;
        double r29478 = r29475 / r29477;
        double r29479 = v;
        double r29480 = r29479 / r29477;
        double r29481 = r29478 * r29480;
        return r29481;
}

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 18.5

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

  3. Applied times-frac1.3

    \[\leadsto \color{blue}{\frac{-t1}{t1 + u} \cdot \frac{v}{t1 + u}}\]

  4. Final simplification1.3

    \[\leadsto \frac{-t1}{t1 + u} \cdot \frac{v}{t1 + u}\]

Reproduce

herbie shell --seed 2020039 +o rules:numerics
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  :precision binary64
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))