Average Error: 0.3 → 0.1
Time: 15.7s
Precision: 64
\[\frac{\left(\frac{\left(d1 \cdot d2\right)}{\left(\left(\frac{d3}{\left(5\right)}\right) \cdot d1\right)}\right)}{\left(d1 \cdot \left(32\right)\right)}\]
↓
\[\left(\mathsf{qma}\left(\left(\mathsf{qma}\left(\left(\left(d1 \cdot d2\right)\right), \left(d3 + 5\right), d1\right)\right), d1, 32\right)\right)\]
\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(\mathsf{qma}\left(\left(\mathsf{qma}\left(\left(\left(d1 \cdot d2\right)\right), \left(d3 + 5\right), d1\right)\right), d1, 32\right)\right)
double f(double d1, double d2, double d3) {
        double r781752 = d1;
        double r781753 = d2;
        double r781754 = r781752 * r781753;
        double r781755 = d3;
        double r781756 = 5.0;
        double r781757 = /* ERROR: no posit support in C */;
        double r781758 = r781755 + r781757;
        double r781759 = r781758 * r781752;
        double r781760 = r781754 + r781759;
        double r781761 = 32.0;
        double r781762 = /* ERROR: no posit support in C */;
        double r781763 = r781752 * r781762;
        double r781764 = r781760 + r781763;
        return r781764;
}
↓
double f(double d1, double d2, double d3) {
        double r781765 = d1;
        double r781766 = d2;
        double r781767 = r781765 * r781766;
        double r781768 = /*Error: no posit support in C */;
        double r781769 = d3;
        double r781770 = 5.0;
        double r781771 = r781769 + r781770;
        double r781772 = /*Error: no posit support in C */;
        double r781773 = 32.0;
        double r781774 = /*Error: no posit support in C */;
        double r781775 = /*Error: no posit support in C */;
        return r781775;
}

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. Using strategy rm

  3. Applied introduce-quire0.3

    \[\leadsto \frac{\left(\frac{\color{blue}{\left(\left(\left(d1 \cdot d2\right)\right)\right)}}{\left(\left(\frac{d3}{\left(5\right)}\right) \cdot d1\right)}\right)}{\left(d1 \cdot \left(32\right)\right)}\]

  4. Applied insert-quire-fdp-add0.3

    \[\leadsto \frac{\color{blue}{\left(\left(\mathsf{qma}\left(\left(\left(d1 \cdot d2\right)\right), \left(\frac{d3}{\left(5\right)}\right), d1\right)\right)\right)}}{\left(d1 \cdot \left(32\right)\right)}\]

  5. Applied insert-quire-fdp-add0.1

    \[\leadsto \color{blue}{\left(\mathsf{qma}\left(\left(\mathsf{qma}\left(\left(\left(d1 \cdot d2\right)\right), \left(\frac{d3}{\left(5\right)}\right), d1\right)\right), d1, \left(32\right)\right)\right)}\]

  6. Final simplification0.1

    \[\leadsto \left(\mathsf{qma}\left(\left(\mathsf{qma}\left(\left(\left(d1 \cdot d2\right)\right), \left(d3 + 5\right), d1\right)\right), d1, 32\right)\right)\]

Reproduce

herbie shell --seed 2019156 +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))))