Average Error: 0.3 → 0.3
Time: 8.6s
Precision: 64
\[\frac{\left(\frac{\left(d1 \cdot d2\right)}{\left(\left(\frac{d3}{\left(5\right)}\right) \cdot d1\right)}\right)}{\left(d1 \cdot \left(32\right)\right)}\]
↓
\[\left(d1 \cdot d2 + \left(d3 + 5\right) \cdot d1\right) + d1 \cdot 32\]
\frac{\left(\frac{\left(d1 \cdot d2\right)}{\left(\left(\frac{d3}{\left(5\right)}\right) \cdot d1\right)}\right)}{\left(d1 \cdot \left(32\right)\right)}
↓
\left(d1 \cdot d2 + \left(d3 + 5\right) \cdot d1\right) + d1 \cdot 32
double f(double d1, double d2, double d3) {
        double r551858 = d1;
        double r551859 = d2;
        double r551860 = r551858 * r551859;
        double r551861 = d3;
        double r551862 = 5.0;
        double r551863 = /* ERROR: no posit support in C */;
        double r551864 = r551861 + r551863;
        double r551865 = r551864 * r551858;
        double r551866 = r551860 + r551865;
        double r551867 = 32.0;
        double r551868 = /* ERROR: no posit support in C */;
        double r551869 = r551858 * r551868;
        double r551870 = r551866 + r551869;
        return r551870;
}
↓
double f(double d1, double d2, double d3) {
        double r551871 = d1;
        double r551872 = d2;
        double r551873 = r551871 * r551872;
        double r551874 = d3;
        double r551875 = 5.0;
        double r551876 = r551874 + r551875;
        double r551877 = r551876 * r551871;
        double r551878 = r551873 + r551877;
        double r551879 = 32.0;
        double r551880 = r551871 * r551879;
        double r551881 = r551878 + r551880;
        return r551881;
}

Error

Bits error versus d1

Bits error versus d2

Bits error versus d3

Derivation

  1. Initial program 0.3

    \[\frac{\left(\frac{\left(d1 \cdot d2\right)}{\left(\left(\frac{d3}{\left(5\right)}\right) \cdot d1\right)}\right)}{\left(d1 \cdot \left(32\right)\right)}\]

  2. Final simplification0.3

    \[\leadsto \left(d1 \cdot d2 + \left(d3 + 5\right) \cdot d1\right) + d1 \cdot 32\]

Reproduce

herbie shell --seed 2019120 +o rules:numerics
(FPCore (d1 d2 d3)
  :name "FastMath dist3"
  (+.p16 (+.p16 (*.p16 d1 d2) (*.p16 (+.p16 d3 (real->posit16 5)) d1)) (*.p16 d1 (real->posit16 32))))