Average Error: 0.3 → 0.1
Time: 28.3s
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 r4781456 = d1;
        double r4781457 = d2;
        double r4781458 = r4781456 * r4781457;
        double r4781459 = d3;
        double r4781460 = 5.0;
        double r4781461 = /* ERROR: no posit support in C */;
        double r4781462 = r4781459 + r4781461;
        double r4781463 = r4781462 * r4781456;
        double r4781464 = r4781458 + r4781463;
        double r4781465 = 32.0;
        double r4781466 = /* ERROR: no posit support in C */;
        double r4781467 = r4781456 * r4781466;
        double r4781468 = r4781464 + r4781467;
        return r4781468;
}
↓
double f(double d1, double d2, double d3) {
        double r4781469 = d1;
        double r4781470 = d2;
        double r4781471 = r4781469 * r4781470;
        double r4781472 = /*Error: no posit support in C */;
        double r4781473 = d3;
        double r4781474 = 5.0;
        double r4781475 = /* ERROR: no posit support in C */;
        double r4781476 = r4781473 + r4781475;
        double r4781477 = /*Error: no posit support in C */;
        double r4781478 = 32.0;
        double r4781479 = /* ERROR: no posit support in C */;
        double r4781480 = /*Error: no posit support in C */;
        double r4781481 = /*Error: no posit support in C */;
        return r4781481;
}

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 2019168 
(FPCore (d1 d2 d3)
  :name "FastMath dist3"
  (+.p16 (+.p16 (*.p16 d1 d2) (*.p16 (+.p16 d3 (real->posit16 5)) d1)) (*.p16 d1 (real->posit16 32))))