Average Error: 17.7 → 1.2
Time: 45.4s
Precision: 64
\[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
↓
\[\frac{v}{t1 + u} \cdot \frac{-t1}{t1 + u}\]
double f(double u, double v, double t1) {
        double r3577301 = t1;
        double r3577302 = -r3577301;
        double r3577303 = v;
        double r3577304 = r3577302 * r3577303;
        double r3577305 = u;
        double r3577306 = r3577301 + r3577305;
        double r3577307 = r3577306 * r3577306;
        double r3577308 = r3577304 / r3577307;
        return r3577308;
}
↓
double f(double u, double v, double t1) {
        double r3577309 = v;
        double r3577310 = t1;
        double r3577311 = u;
        double r3577312 = r3577310 + r3577311;
        double r3577313 = r3577309 / r3577312;
        double r3577314 = -r3577310;
        double r3577315 = r3577314 / r3577312;
        double r3577316 = r3577313 * r3577315;
        return r3577316;
}


\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}
↓
\frac{v}{t1 + u} \cdot \frac{-t1}{t1 + u}

Error

Bits error versus u

Bits error versus v

Bits error versus t1

Derivation

  1. Initial program 17.7

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

  3. Applied times-frac1.2

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

  4. Final simplification1.2

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

Reproduce

herbie shell --seed 2019101 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))