Rosa's DopplerBench

Average Error: 18.1 → 1.4

Time: 22.2s

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 r1262266 = t1;
        double r1262267 = -r1262266;
        double r1262268 = v;
        double r1262269 = r1262267 * r1262268;
        double r1262270 = u;
        double r1262271 = r1262266 + r1262270;
        double r1262272 = r1262271 * r1262271;
        double r1262273 = r1262269 / r1262272;
        return r1262273;
}

↓

double f(double u, double v, double t1) {
        double r1262274 = t1;
        double r1262275 = u;
        double r1262276 = r1262274 + r1262275;
        double r1262277 = r1262274 / r1262276;
        double r1262278 = v;
        double r1262279 = r1262277 * r1262278;
        double r1262280 = -1.0;
        double r1262281 = r1262280 / r1262276;
        double r1262282 = r1262279 * r1262281;
        return r1262282;
}

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))))