Average Error: 18.4 → 1.6
Time: 46.4s
Precision: 64
\[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
↓
\[\frac{v}{t1 + u} \cdot \frac{-t1}{t1 + u}\]
\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}
↓
\frac{v}{t1 + u} \cdot \frac{-t1}{t1 + u}
double f(double u, double v, double t1) {
        double r1433275 = t1;
        double r1433276 = -r1433275;
        double r1433277 = v;
        double r1433278 = r1433276 * r1433277;
        double r1433279 = u;
        double r1433280 = r1433275 + r1433279;
        double r1433281 = r1433280 * r1433280;
        double r1433282 = r1433278 / r1433281;
        return r1433282;
}
↓
double f(double u, double v, double t1) {
        double r1433283 = v;
        double r1433284 = t1;
        double r1433285 = u;
        double r1433286 = r1433284 + r1433285;
        double r1433287 = r1433283 / r1433286;
        double r1433288 = -r1433284;
        double r1433289 = r1433288 / r1433286;
        double r1433290 = r1433287 * r1433289;
        return r1433290;
}

Error

Bits error versus u

Bits error versus v

Bits error versus t1

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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-frac1.6

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

  4. Final simplification1.6

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

Reproduce

herbie shell --seed 2019168 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))