FastMath test2

Average Error: 0.3 → 0.3

Time: 9.2s

Precision: 64

Math

\[\frac{\left(\frac{\left(d1 \cdot \left(10\right)\right)}{\left(d1 \cdot d2\right)}\right)}{\left(d1 \cdot \left(20\right)\right)}\]

↓

\[\left(\left(20 + 10\right) + d2\right) \cdot d1\]

C

double f(double d1, double d2) {
        double r1629071 = d1;
        double r1629072 = 10.0;
        double r1629073 = /* ERROR: no posit support in C */;
        double r1629074 = r1629071 * r1629073;
        double r1629075 = d2;
        double r1629076 = r1629071 * r1629075;
        double r1629077 = r1629074 + r1629076;
        double r1629078 = 20.0;
        double r1629079 = /* ERROR: no posit support in C */;
        double r1629080 = r1629071 * r1629079;
        double r1629081 = r1629077 + r1629080;
        return r1629081;
}

↓

double f(double d1, double d2) {
        double r1629082 = 20.0;
        double r1629083 = 10.0;
        double r1629084 = r1629082 + r1629083;
        double r1629085 = d2;
        double r1629086 = r1629084 + r1629085;
        double r1629087 = d1;
        double r1629088 = r1629086 * r1629087;
        return r1629088;
}

Error

Bits error versus d1

Bits error versus d2

Derivation

1. Initial program 0.3

   \[\frac{\left(\frac{\left(d1 \cdot \left(10\right)\right)}{\left(d1 \cdot d2\right)}\right)}{\left(d1 \cdot \left(20\right)\right)}\]

2. Simplified 0.3

   \[\leadsto \color{blue}{\left(\frac{\left(20\right)}{\left(\frac{\left(10\right)}{d2}\right)}\right) \cdot d1}\]
3. Using strategy rm

4. Applied associate-+r+ 0.3

   \[\leadsto \color{blue}{\left(\frac{\left(\frac{\left(20\right)}{\left(10\right)}\right)}{d2}\right)} \cdot d1\]

5. Final simplification 0.3

   \[\leadsto \left(\left(20 + 10\right) + d2\right) \cdot d1\]

Reproduce

herbie shell --seed 2019107 +o rules:numerics
(FPCore (d1 d2)
  :name "FastMath test2"
  (+.p16 (+.p16 (*.p16 d1 (real->posit16 10)) (*.p16 d1 d2)) (*.p16 d1 (real->posit16 20))))