Average Error: 0.3 → 0.1
Time: 25.1s
Precision: 64
\[\frac{\left(\frac{\left(d1 \cdot d2\right)}{\left(\left(\frac{d3}{\left(5\right)}\right) \cdot d1\right)}\right)}{\left(d1 \cdot \left(32\right)\right)}\]
↓
\[\left(\mathsf{qma}\left(\left(\mathsf{qma}\left(\left(\left(d1 \cdot d2\right)\right), \left(\frac{d3}{\left(5\right)}\right), d1\right)\right), d1, \left(32\right)\right)\right)\]
\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(\frac{d3}{\left(5\right)}\right), d1\right)\right), d1, \left(32\right)\right)\right)
double f(double d1, double d2, double d3) {
        double r4049596 = d1;
        double r4049597 = d2;
        double r4049598 = r4049596 * r4049597;
        double r4049599 = d3;
        double r4049600 = 5.0;
        double r4049601 = /* ERROR: no posit support in C */;
        double r4049602 = r4049599 + r4049601;
        double r4049603 = r4049602 * r4049596;
        double r4049604 = r4049598 + r4049603;
        double r4049605 = 32.0;
        double r4049606 = /* ERROR: no posit support in C */;
        double r4049607 = r4049596 * r4049606;
        double r4049608 = r4049604 + r4049607;
        return r4049608;
}
↓
double f(double d1, double d2, double d3) {
        double r4049609 = d1;
        double r4049610 = d2;
        double r4049611 = r4049609 * r4049610;
        double r4049612 = /*Error: no posit support in C */;
        double r4049613 = d3;
        double r4049614 = 5.0;
        double r4049615 = /* ERROR: no posit support in C */;
        double r4049616 = r4049613 + r4049615;
        double r4049617 = /*Error: no posit support in C */;
        double r4049618 = 32.0;
        double r4049619 = /* ERROR: no posit support in C */;
        double r4049620 = /*Error: no posit support in C */;
        double r4049621 = /*Error: no posit support in C */;
        return r4049621;
}

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

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

Reproduce

herbie shell --seed 2019164 
(FPCore (d1 d2 d3)
  :name "FastMath dist3"
  (+.p16 (+.p16 (*.p16 d1 d2) (*.p16 (+.p16 d3 (real->posit16 5)) d1)) (*.p16 d1 (real->posit16 32))))