Rosa's DopplerBench

Average Error: 17.8 → 1.3

Time: 59.9s

Precision: 64

Math

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

↓

\[\left(v \cdot \frac{t1}{t1 + u}\right) \cdot \frac{-1}{t1 + u}\]

C

double f(double u, double v, double t1) {
        double r1043558 = t1;
        double r1043559 = -r1043558;
        double r1043560 = v;
        double r1043561 = r1043559 * r1043560;
        double r1043562 = u;
        double r1043563 = r1043558 + r1043562;
        double r1043564 = r1043563 * r1043563;
        double r1043565 = r1043561 / r1043564;
        return r1043565;
}

↓

double f(double u, double v, double t1) {
        double r1043566 = v;
        double r1043567 = t1;
        double r1043568 = u;
        double r1043569 = r1043567 + r1043568;
        double r1043570 = r1043567 / r1043569;
        double r1043571 = r1043566 * r1043570;
        double r1043572 = -1.0;
        double r1043573 = r1043572 / r1043569;
        double r1043574 = r1043571 * r1043573;
        return r1043574;
}

Error

Bits error versus u

Bits error versus v

Bits error versus t1

Derivation

1. Initial program 17.8

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

3. Applied times-frac 1.3

   \[\leadsto \color{blue}{\frac{-t1}{t1 + u} \cdot \frac{v}{t1 + u}}\]
4. Using strategy rm

5. Applied associate-*r/ 1.2

   \[\leadsto \color{blue}{\frac{\frac{-t1}{t1 + u} \cdot v}{t1 + u}}\]
6. Using strategy rm

7. Applied div-inv 1.3

   \[\leadsto \color{blue}{\left(\frac{-t1}{t1 + u} \cdot v\right) \cdot \frac{1}{t1 + u}}\]

8. Final simplification 1.3

   \[\leadsto \left(v \cdot \frac{t1}{t1 + u}\right) \cdot \frac{-1}{t1 + u}\]

Reproduce

herbie shell --seed 2019144 +o rules:numerics
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))