Average Error: 0.3 → 0.3
Time: 9.3s
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 r969690 = d1;
        double r969691 = d2;
        double r969692 = r969690 * r969691;
        double r969693 = d3;
        double r969694 = 5.0;
        double r969695 = /* ERROR: no posit support in C */;
        double r969696 = r969693 + r969695;
        double r969697 = r969696 * r969690;
        double r969698 = r969692 + r969697;
        double r969699 = 32.0;
        double r969700 = /* ERROR: no posit support in C */;
        double r969701 = r969690 * r969700;
        double r969702 = r969698 + r969701;
        return r969702;
}
↓
double f(double d1, double d2, double d3) {
        double r969703 = d1;
        double r969704 = d2;
        double r969705 = r969703 * r969704;
        double r969706 = d3;
        double r969707 = 5.0;
        double r969708 = r969706 + r969707;
        double r969709 = r969708 * r969703;
        double r969710 = r969705 + r969709;
        double r969711 = 32.0;
        double r969712 = r969703 * r969711;
        double r969713 = r969710 + r969712;
        return r969713;
}

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 2019107 +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))))