Average Error: 18.4 → 1.4
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 r30248 = t1;
        double r30249 = -r30248;
        double r30250 = v;
        double r30251 = r30249 * r30250;
        double r30252 = u;
        double r30253 = r30248 + r30252;
        double r30254 = r30253 * r30253;
        double r30255 = r30251 / r30254;
        return r30255;
}
↓
double f(double u, double v, double t1) {
        double r30256 = t1;
        double r30257 = -r30256;
        double r30258 = u;
        double r30259 = r30256 + r30258;
        double r30260 = r30257 / r30259;
        double r30261 = v;
        double r30262 = r30261 / r30259;
        double r30263 = r30260 * r30262;
        return r30263;
}

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 2020002 +o rules:numerics
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  :precision binary64
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))