Average Error: 0.2 → 0
Time: 2.9s
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 r1293927 = d;
        double r1293928 = 10.0;
        double r1293929 = /* ERROR: no posit support in C */;
        double r1293930 = r1293927 * r1293929;
        double r1293931 = 20.0;
        double r1293932 = /* ERROR: no posit support in C */;
        double r1293933 = r1293927 * r1293932;
        double r1293934 = r1293930 + r1293933;
        return r1293934;
}
↓
double f(double d) {
        double r1293935 = d;
        double r1293936 = 20.0;
        double r1293937 = 10.0;
        double r1293938 = r1293936 + r1293937;
        double r1293939 = r1293935 * r1293938;
        return r1293939;
}

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 2019104 
(FPCore (d)
  :name "FastMath test1"
  (+.p16 (*.p16 d (real->posit16 10)) (*.p16 d (real->posit16 20))))