Rosa's DopplerBench

Average Error: 18.1 → 1.4

Time: 16.4s

Precision: 64

Math

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

↓

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

C

double f(double u, double v, double t1) {
        double r1124796 = t1;
        double r1124797 = -r1124796;
        double r1124798 = v;
        double r1124799 = r1124797 * r1124798;
        double r1124800 = u;
        double r1124801 = r1124796 + r1124800;
        double r1124802 = r1124801 * r1124801;
        double r1124803 = r1124799 / r1124802;
        return r1124803;
}

↓

double f(double u, double v, double t1) {
        double r1124804 = t1;
        double r1124805 = u;
        double r1124806 = r1124804 + r1124805;
        double r1124807 = r1124804 / r1124806;
        double r1124808 = v;
        double r1124809 = r1124807 * r1124808;
        double r1124810 = -1.0;
        double r1124811 = r1124810 / r1124806;
        double r1124812 = r1124809 * r1124811;
        return r1124812;
}

Error

Bits error versus u

Bits error versus v

Bits error versus t1

Derivation

1. Initial program 18.1

   \[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
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 div-inv 1.4

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

6. Applied associate-*r* 1.4

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

7. Final simplification 1.4

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

Reproduce

herbie shell --seed 2019171 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))