Average Error: 0.3 → 0.3
Time: 10.1s
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 r4219793 = d1;
        double r4219794 = d2;
        double r4219795 = r4219793 * r4219794;
        double r4219796 = d3;
        double r4219797 = 5.0;
        double r4219798 = /* ERROR: no posit support in C */;
        double r4219799 = r4219796 + r4219798;
        double r4219800 = r4219799 * r4219793;
        double r4219801 = r4219795 + r4219800;
        double r4219802 = 32.0;
        double r4219803 = /* ERROR: no posit support in C */;
        double r4219804 = r4219793 * r4219803;
        double r4219805 = r4219801 + r4219804;
        return r4219805;
}
↓
double f(double d1, double d2, double d3) {
        double r4219806 = d1;
        double r4219807 = d2;
        double r4219808 = r4219806 * r4219807;
        double r4219809 = d3;
        double r4219810 = 5.0;
        double r4219811 = r4219809 + r4219810;
        double r4219812 = r4219811 * r4219806;
        double r4219813 = r4219808 + r4219812;
        double r4219814 = 32.0;
        double r4219815 = r4219806 * r4219814;
        double r4219816 = r4219813 + r4219815;
        return r4219816;
}

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 2019104 
(FPCore (d1 d2 d3)
  :name "FastMath dist3"
  (+.p16 (+.p16 (*.p16 d1 d2) (*.p16 (+.p16 d3 (real->posit16 5)) d1)) (*.p16 d1 (real->posit16 32))))