FastMath test2

Average Error: 0.3 → 0.3

Time: 8.6s

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 r1498998 = d1;
        double r1498999 = 10.0;
        double r1499000 = /* ERROR: no posit support in C */;
        double r1499001 = r1498998 * r1499000;
        double r1499002 = d2;
        double r1499003 = r1498998 * r1499002;
        double r1499004 = r1499001 + r1499003;
        double r1499005 = 20.0;
        double r1499006 = /* ERROR: no posit support in C */;
        double r1499007 = r1498998 * r1499006;
        double r1499008 = r1499004 + r1499007;
        return r1499008;
}

↓

double f(double d1, double d2) {
        double r1499009 = 20.0;
        double r1499010 = 10.0;
        double r1499011 = r1499009 + r1499010;
        double r1499012 = d2;
        double r1499013 = r1499011 + r1499012;
        double r1499014 = d1;
        double r1499015 = r1499013 * r1499014;
        return r1499015;
}

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 2019124 
(FPCore (d1 d2)
  :name "FastMath test2"
  (+.p16 (+.p16 (*.p16 d1 (real->posit16 10)) (*.p16 d1 d2)) (*.p16 d1 (real->posit16 20))))