Rosa's DopplerBench

Average Error: 18.2 → 1.2

Time: 9.6s

Precision: 64

Math

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

↓

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

C

double f(double u, double v, double t1) {
        double r408232 = t1;
        double r408233 = -r408232;
        double r408234 = v;
        double r408235 = r408233 * r408234;
        double r408236 = u;
        double r408237 = r408232 + r408236;
        double r408238 = r408237 * r408237;
        double r408239 = r408235 / r408238;
        return r408239;
}

↓

double f(double u, double v, double t1) {
        double r408240 = t1;
        double r408241 = u;
        double r408242 = r408240 + r408241;
        double r408243 = r408240 / r408242;
        double r408244 = v;
        double r408245 = r408243 * r408244;
        double r408246 = -r408245;
        double r408247 = r408246 / r408242;
        return r408247;
}

Error

Bits error versus u

Bits error versus v

Bits error versus t1

Derivation

1. Initial program 18.2

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

3. Applied times-frac 1.4

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

5. Applied div-inv 1.5

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

7. Applied associate-*r/ 1.3

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

8. Simplified 1.2

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

9. Final simplification 1.2

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

Reproduce

herbie shell --seed 2019156 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))