Average Error: 0.3 → 0.2
Time: 5.1s
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 r2463842 = d1;
        double r2463843 = d2;
        double r2463844 = r2463842 * r2463843;
        double r2463845 = d3;
        double r2463846 = r2463842 * r2463845;
        double r2463847 = r2463844 + r2463846;
        return r2463847;
}
↓
double f(double d1, double d2, double d3) {
        double r2463848 = d1;
        double r2463849 = d2;
        double r2463850 = r2463848 * r2463849;
        double r2463851 = /*Error: no posit support in C */;
        double r2463852 = d3;
        double r2463853 = /*Error: no posit support in C */;
        double r2463854 = /*Error: no posit support in C */;
        return r2463854;
}

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 2019163 +o rules:numerics
(FPCore (d1 d2 d3)
  :name "FastMath dist"
  (+.p16 (*.p16 d1 d2) (*.p16 d1 d3)))