Average Error: 0.3 → 0.3
Time: 10.5s
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 r1380887 = d1;
        double r1380888 = d2;
        double r1380889 = r1380887 * r1380888;
        double r1380890 = d3;
        double r1380891 = 5.0;
        double r1380892 = /* ERROR: no posit support in C */;
        double r1380893 = r1380890 + r1380892;
        double r1380894 = r1380893 * r1380887;
        double r1380895 = r1380889 + r1380894;
        double r1380896 = 32.0;
        double r1380897 = /* ERROR: no posit support in C */;
        double r1380898 = r1380887 * r1380897;
        double r1380899 = r1380895 + r1380898;
        return r1380899;
}
↓
double f(double d1, double d2, double d3) {
        double r1380900 = d1;
        double r1380901 = d2;
        double r1380902 = r1380900 * r1380901;
        double r1380903 = d3;
        double r1380904 = 5.0;
        double r1380905 = r1380903 + r1380904;
        double r1380906 = r1380905 * r1380900;
        double r1380907 = r1380902 + r1380906;
        double r1380908 = 32.0;
        double r1380909 = r1380900 * r1380908;
        double r1380910 = r1380907 + r1380909;
        return r1380910;
}

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 2019124 
(FPCore (d1 d2 d3)
  :name "FastMath dist3"
  (+.p16 (+.p16 (*.p16 d1 d2) (*.p16 (+.p16 d3 (real->posit16 5)) d1)) (*.p16 d1 (real->posit16 32))))