Average Error: 0.3 → 0.3
Time: 7.7s
Precision: 64
\[\frac{\left(\frac{\left(d1 \cdot \left(10\right)\right)}{\left(d1 \cdot d2\right)}\right)}{\left(d1 \cdot \left(20\right)\right)}\]
↓
\[\left(20 + \left(10 + d2\right)\right) \cdot d1\]
\frac{\left(\frac{\left(d1 \cdot \left(10\right)\right)}{\left(d1 \cdot d2\right)}\right)}{\left(d1 \cdot \left(20\right)\right)}
↓
\left(20 + \left(10 + d2\right)\right) \cdot d1
double f(double d1, double d2) {
        double r4178791 = d1;
        double r4178792 = 10.0;
        double r4178793 = /* ERROR: no posit support in C */;
        double r4178794 = r4178791 * r4178793;
        double r4178795 = d2;
        double r4178796 = r4178791 * r4178795;
        double r4178797 = r4178794 + r4178796;
        double r4178798 = 20.0;
        double r4178799 = /* ERROR: no posit support in C */;
        double r4178800 = r4178791 * r4178799;
        double r4178801 = r4178797 + r4178800;
        return r4178801;
}
↓
double f(double d1, double d2) {
        double r4178802 = 20.0;
        double r4178803 = 10.0;
        double r4178804 = d2;
        double r4178805 = r4178803 + r4178804;
        double r4178806 = r4178802 + r4178805;
        double r4178807 = d1;
        double r4178808 = r4178806 * r4178807;
        return r4178808;
}

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. Simplified0.3

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

  3. Final simplification0.3

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

Reproduce

herbie shell --seed 2019125 
(FPCore (d1 d2)
  :name "FastMath test2"
  (+.p16 (+.p16 (*.p16 d1 (real->posit16 10)) (*.p16 d1 d2)) (*.p16 d1 (real->posit16 20))))