Average Error: 0.3 → 0.3
Time: 9.7s
Precision: 64
\[\left(d1 \cdot d2 + \left(d3 + 5\right) \cdot d1\right) + d1 \cdot 32\]
↓
\[\left(d1 \cdot d2 + \left(d3 + 5\right) \cdot d1\right) + d1 \cdot 32\]
double f(double d1, double d2, double d3) {
        double r567985 = d1;
        double r567986 = d2;
        double r567987 = r567985 * r567986;
        double r567988 = d3;
        double r567989 = 5.0;
        double r567990 = r567988 + r567989;
        double r567991 = r567990 * r567985;
        double r567992 = r567987 + r567991;
        double r567993 = 32.0;
        double r567994 = r567985 * r567993;
        double r567995 = r567992 + r567994;
        return r567995;
}
↓
double f(double d1, double d2, double d3) {
        double r567996 = d1;
        double r567997 = d2;
        double r567998 = r567996 * r567997;
        double r567999 = d3;
        double r568000 = 5.0;
        double r568001 = r567999 + r568000;
        double r568002 = r568001 * r567996;
        double r568003 = r567998 + r568002;
        double r568004 = 32.0;
        double r568005 = r567996 * r568004;
        double r568006 = r568003 + r568005;
        return r568006;
}


\left(d1 \cdot d2 + \left(d3 + 5\right) \cdot d1\right) + d1 \cdot 32
↓
\left(d1 \cdot d2 + \left(d3 + 5\right) \cdot d1\right) + d1 \cdot 32

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 2019102 +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))))