Average Error: 0.3 → 0.2
Time: 6.9s
Precision: 64
\[\frac{\left(d1 \cdot d2\right)}{\left(d1 \cdot d3\right)}\]
↓
\[\left(\mathsf{qma}\left(\left(\left(d1 \cdot d2\right)\right), d1, d3\right)\right)\]
\frac{\left(d1 \cdot d2\right)}{\left(d1 \cdot d3\right)}
↓
\left(\mathsf{qma}\left(\left(\left(d1 \cdot d2\right)\right), d1, d3\right)\right)
double f(double d1, double d2, double d3) {
        double r1770761 = d1;
        double r1770762 = d2;
        double r1770763 = r1770761 * r1770762;
        double r1770764 = d3;
        double r1770765 = r1770761 * r1770764;
        double r1770766 = r1770763 + r1770765;
        return r1770766;
}
↓
double f(double d1, double d2, double d3) {
        double r1770767 = d1;
        double r1770768 = d2;
        double r1770769 = r1770767 * r1770768;
        double r1770770 = /*Error: no posit support in C */;
        double r1770771 = d3;
        double r1770772 = /*Error: no posit support in C */;
        double r1770773 = /*Error: no posit support in C */;
        return r1770773;
}

Error

Bits error versus d1

Bits error versus d2

Bits error versus d3

Derivation

  1. Initial program 0.3

    \[\frac{\left(d1 \cdot d2\right)}{\left(d1 \cdot d3\right)}\]
  2. Using strategy rm

  3. Applied introduce-quire0.3

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

  4. Applied insert-quire-fdp-add0.2

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

  5. Final simplification0.2

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

Reproduce

herbie shell --seed 2019151 
(FPCore (d1 d2 d3)
  :name "FastMath dist"
  (+.p16 (*.p16 d1 d2) (*.p16 d1 d3)))