Average Error: 0.2 → 0
Time: 4.6s
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 r1078842 = d;
        double r1078843 = 10.0;
        double r1078844 = /* ERROR: no posit support in C */;
        double r1078845 = r1078842 * r1078844;
        double r1078846 = 20.0;
        double r1078847 = /* ERROR: no posit support in C */;
        double r1078848 = r1078842 * r1078847;
        double r1078849 = r1078845 + r1078848;
        return r1078849;
}
↓
double f(double d) {
        double r1078850 = d;
        double r1078851 = 20.0;
        double r1078852 = 10.0;
        double r1078853 = r1078851 + r1078852;
        double r1078854 = r1078850 * r1078853;
        return r1078854;
}

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 2019153 +o rules:numerics
(FPCore (d)
  :name "FastMath test1"
  (+.p16 (*.p16 d (real->posit16 10)) (*.p16 d (real->posit16 20))))