Average Error: 0.3 → 0.1
Time: 28.0s
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 r4228461 = d1;
        double r4228462 = d2;
        double r4228463 = r4228461 * r4228462;
        double r4228464 = d3;
        double r4228465 = 5.0;
        double r4228466 = /* ERROR: no posit support in C */;
        double r4228467 = r4228464 + r4228466;
        double r4228468 = r4228467 * r4228461;
        double r4228469 = r4228463 + r4228468;
        double r4228470 = 32.0;
        double r4228471 = /* ERROR: no posit support in C */;
        double r4228472 = r4228461 * r4228471;
        double r4228473 = r4228469 + r4228472;
        return r4228473;
}
↓
double f(double d1, double d2, double d3) {
        double r4228474 = d1;
        double r4228475 = d2;
        double r4228476 = r4228474 * r4228475;
        double r4228477 = /*Error: no posit support in C */;
        double r4228478 = d3;
        double r4228479 = 5.0;
        double r4228480 = /* ERROR: no posit support in C */;
        double r4228481 = r4228478 + r4228480;
        double r4228482 = /*Error: no posit support in C */;
        double r4228483 = 32.0;
        double r4228484 = /* ERROR: no posit support in C */;
        double r4228485 = /*Error: no posit support in C */;
        double r4228486 = /*Error: no posit support in C */;
        return r4228486;
}

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