Average Error: 17.7 → 1.2
Time: 45.5s
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 r3444649 = t1;
        double r3444650 = -r3444649;
        double r3444651 = v;
        double r3444652 = r3444650 * r3444651;
        double r3444653 = u;
        double r3444654 = r3444649 + r3444653;
        double r3444655 = r3444654 * r3444654;
        double r3444656 = r3444652 / r3444655;
        return r3444656;
}
↓
double f(double u, double v, double t1) {
        double r3444657 = v;
        double r3444658 = t1;
        double r3444659 = u;
        double r3444660 = r3444658 + r3444659;
        double r3444661 = r3444657 / r3444660;
        double r3444662 = -r3444658;
        double r3444663 = r3444662 / r3444660;
        double r3444664 = r3444661 * r3444663;
        return r3444664;
}


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