Average Error: 0.2 → 0
Time: 4.0s
Precision: 64
\[\frac{\left(d \cdot \left(10\right)\right)}{\left(d \cdot \left(20\right)\right)}\]
↓
\[d \cdot \left(20 + 10\right)\]
\frac{\left(d \cdot \left(10\right)\right)}{\left(d \cdot \left(20\right)\right)}
↓
d \cdot \left(20 + 10\right)
double f(double d) {
        double r2862790 = d;
        double r2862791 = 10.0;
        double r2862792 = /* ERROR: no posit support in C */;
        double r2862793 = r2862790 * r2862792;
        double r2862794 = 20.0;
        double r2862795 = /* ERROR: no posit support in C */;
        double r2862796 = r2862790 * r2862795;
        double r2862797 = r2862793 + r2862796;
        return r2862797;
}
↓
double f(double d) {
        double r2862798 = d;
        double r2862799 = 20.0;
        double r2862800 = 10.0;
        double r2862801 = r2862799 + r2862800;
        double r2862802 = r2862798 * r2862801;
        return r2862802;
}

Error

Bits error versus d

Derivation

  1. Initial program 0.2

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

  2. Simplified0

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

  3. Final simplification0

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

Reproduce

herbie shell --seed 2019133 +o rules:numerics
(FPCore (d)
  :name "FastMath test1"
  (+.p16 (*.p16 d (real->posit16 10)) (*.p16 d (real->posit16 20))))