Rosa's DopplerBench

Average Error: 17.8 → 1.4

Time: 20.6s

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 r1364192 = t1;
        double r1364193 = -r1364192;
        double r1364194 = v;
        double r1364195 = r1364193 * r1364194;
        double r1364196 = u;
        double r1364197 = r1364192 + r1364196;
        double r1364198 = r1364197 * r1364197;
        double r1364199 = r1364195 / r1364198;
        return r1364199;
}

↓

double f(double u, double v, double t1) {
        double r1364200 = t1;
        double r1364201 = u;
        double r1364202 = r1364200 + r1364201;
        double r1364203 = r1364200 / r1364202;
        double r1364204 = v;
        double r1364205 = r1364203 * r1364204;
        double r1364206 = -1.0;
        double r1364207 = r1364206 / r1364202;
        double r1364208 = r1364205 * r1364207;
        return r1364208;
}

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 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 2019164 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))