Rosa's DopplerBench

Average Error: 17.9 → 1.3

Time: 35.0s

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 r1071802 = t1;
        double r1071803 = -r1071802;
        double r1071804 = v;
        double r1071805 = r1071803 * r1071804;
        double r1071806 = u;
        double r1071807 = r1071802 + r1071806;
        double r1071808 = r1071807 * r1071807;
        double r1071809 = r1071805 / r1071808;
        return r1071809;
}

↓

double f(double u, double v, double t1) {
        double r1071810 = t1;
        double r1071811 = -r1071810;
        double r1071812 = u;
        double r1071813 = r1071810 + r1071812;
        double r1071814 = r1071811 / r1071813;
        double r1071815 = v;
        double r1071816 = r1071814 * r1071815;
        double r1071817 = 1.0;
        double r1071818 = r1071817 / r1071813;
        double r1071819 = r1071816 * r1071818;
        return r1071819;
}

Error

Bits error versus u

Bits error versus v

Bits error versus t1

Derivation

1. Initial program 17.9

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

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

6. Applied associate-*r* 1.3

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

7. Final simplification 1.3

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

Reproduce

herbie shell --seed 2019134 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))