Average Error: 0.5 → 0.2
Time: 26.6s
Precision: 64
\[\frac{\left(\frac{\left(d1 \cdot \left(3\right)\right)}{\left(d1 \cdot d2\right)}\right)}{\left(d1 \cdot d3\right)}\]
↓
\[\left(\mathsf{qma}\left(\left(\mathsf{qma}\left(\left(3\right), d3, 1.0\right)\right), d2, 1.0\right)\right) \cdot d1\]
\frac{\left(\frac{\left(d1 \cdot \left(3\right)\right)}{\left(d1 \cdot d2\right)}\right)}{\left(d1 \cdot d3\right)}
↓
\left(\mathsf{qma}\left(\left(\mathsf{qma}\left(\left(3\right), d3, 1.0\right)\right), d2, 1.0\right)\right) \cdot d1
double f(double d1, double d2, double d3) {
        double r2070736 = d1;
        double r2070737 = 3.0;
        double r2070738 = /* ERROR: no posit support in C */;
        double r2070739 = r2070736 * r2070738;
        double r2070740 = d2;
        double r2070741 = r2070736 * r2070740;
        double r2070742 = r2070739 + r2070741;
        double r2070743 = d3;
        double r2070744 = r2070736 * r2070743;
        double r2070745 = r2070742 + r2070744;
        return r2070745;
}
↓
double f(double d1, double d2, double d3) {
        double r2070746 = 3.0;
        double r2070747 = /*Error: no posit support in C */;
        double r2070748 = d3;
        double r2070749 = 1.0;
        double r2070750 = /*Error: no posit support in C */;
        double r2070751 = d2;
        double r2070752 = /*Error: no posit support in C */;
        double r2070753 = /*Error: no posit support in C */;
        double r2070754 = d1;
        double r2070755 = r2070753 * r2070754;
        return r2070755;
}

Error

Bits error versus d1

Bits error versus d2

Bits error versus d3

Derivation

  1. Initial program 0.5

    \[\frac{\left(\frac{\left(d1 \cdot \left(3\right)\right)}{\left(d1 \cdot d2\right)}\right)}{\left(d1 \cdot d3\right)}\]

  2. Simplified0.3

    \[\leadsto \color{blue}{\left(\frac{\left(\frac{\left(3\right)}{d3}\right)}{d2}\right) \cdot d1}\]
  3. Using strategy rm

  4. Applied introduce-quire0.3

    \[\leadsto \left(\frac{\left(\frac{\color{blue}{\left(\left(\left(3\right)\right)\right)}}{d3}\right)}{d2}\right) \cdot d1\]

  5. Applied insert-quire-add0.3

    \[\leadsto \left(\frac{\color{blue}{\left(\left(\mathsf{qma}\left(\left(\left(3\right)\right), d3, \left(1.0\right)\right)\right)\right)}}{d2}\right) \cdot d1\]

  6. Applied insert-quire-add0.2

    \[\leadsto \color{blue}{\left(\left(\mathsf{qma}\left(\left(\mathsf{qma}\left(\left(\left(3\right)\right), d3, \left(1.0\right)\right)\right), d2, \left(1.0\right)\right)\right)\right)} \cdot d1\]

  7. Final simplification0.2

    \[\leadsto \left(\mathsf{qma}\left(\left(\mathsf{qma}\left(\left(3\right), d3, 1.0\right)\right), d2, 1.0\right)\right) \cdot d1\]

Reproduce

herbie shell --seed 2019158 
(FPCore (d1 d2 d3)
  :name "FastMath test3"
  (+.p16 (+.p16 (*.p16 d1 (real->posit16 3)) (*.p16 d1 d2)) (*.p16 d1 d3)))