Average Error: 0.3 → 0.3
Time: 11.8s
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 r3412748 = d1;
        double r3412749 = d2;
        double r3412750 = r3412748 * r3412749;
        double r3412751 = d3;
        double r3412752 = 5.0;
        double r3412753 = /* ERROR: no posit support in C */;
        double r3412754 = r3412751 + r3412753;
        double r3412755 = r3412754 * r3412748;
        double r3412756 = r3412750 + r3412755;
        double r3412757 = 32.0;
        double r3412758 = /* ERROR: no posit support in C */;
        double r3412759 = r3412748 * r3412758;
        double r3412760 = r3412756 + r3412759;
        return r3412760;
}
↓
double f(double d1, double d2, double d3) {
        double r3412761 = d1;
        double r3412762 = d2;
        double r3412763 = r3412761 * r3412762;
        double r3412764 = d3;
        double r3412765 = 5.0;
        double r3412766 = r3412764 + r3412765;
        double r3412767 = r3412766 * r3412761;
        double r3412768 = r3412763 + r3412767;
        double r3412769 = 32.0;
        double r3412770 = r3412761 * r3412769;
        double r3412771 = r3412768 + r3412770;
        return r3412771;
}

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 2019134 
(FPCore (d1 d2 d3)
  :name "FastMath dist3"
  (+.p16 (+.p16 (*.p16 d1 d2) (*.p16 (+.p16 d3 (real->posit16 5)) d1)) (*.p16 d1 (real->posit16 32))))