Average Error: 0.3 → 0.2
Time: 32.9s
Precision: 64
\[\frac{\left(\frac{\left(d1 \cdot d2\right)}{\left(\left(\frac{d3}{\left(5\right)}\right) \cdot d1\right)}\right)}{\left(d1 \cdot \left(32\right)\right)}\]
↓
\[\left(\mathsf{qma}\left(\left(\mathsf{qma}\left(\left(\left(d1 \cdot d2\right)\right), \left(\left(d3 + 5\right) \cdot d1\right), 1.0\right)\right), d1, 32\right)\right)\]
\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(\left(d3 + 5\right) \cdot d1\right), 1.0\right)\right), d1, 32\right)\right)
double f(double d1, double d2, double d3) {
        double r6309439 = d1;
        double r6309440 = d2;
        double r6309441 = r6309439 * r6309440;
        double r6309442 = d3;
        double r6309443 = 5.0;
        double r6309444 = /* ERROR: no posit support in C */;
        double r6309445 = r6309442 + r6309444;
        double r6309446 = r6309445 * r6309439;
        double r6309447 = r6309441 + r6309446;
        double r6309448 = 32.0;
        double r6309449 = /* ERROR: no posit support in C */;
        double r6309450 = r6309439 * r6309449;
        double r6309451 = r6309447 + r6309450;
        return r6309451;
}
↓
double f(double d1, double d2, double d3) {
        double r6309452 = d1;
        double r6309453 = d2;
        double r6309454 = r6309452 * r6309453;
        double r6309455 = /*Error: no posit support in C */;
        double r6309456 = d3;
        double r6309457 = 5.0;
        double r6309458 = r6309456 + r6309457;
        double r6309459 = r6309458 * r6309452;
        double r6309460 = 1.0;
        double r6309461 = /*Error: no posit support in C */;
        double r6309462 = 32.0;
        double r6309463 = /*Error: no posit support in C */;
        double r6309464 = /*Error: no posit support in C */;
        return r6309464;
}

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-add0.3

    \[\leadsto \frac{\color{blue}{\left(\left(\mathsf{qma}\left(\left(\left(d1 \cdot d2\right)\right), \left(\left(\frac{d3}{\left(5\right)}\right) \cdot d1\right), \left(1.0\right)\right)\right)\right)}}{\left(d1 \cdot \left(32\right)\right)}\]

  5. Applied insert-quire-fdp-add0.2

    \[\leadsto \color{blue}{\left(\mathsf{qma}\left(\left(\mathsf{qma}\left(\left(\left(d1 \cdot d2\right)\right), \left(\left(\frac{d3}{\left(5\right)}\right) \cdot d1\right), \left(1.0\right)\right)\right), d1, \left(32\right)\right)\right)}\]

  6. Final simplification0.2

    \[\leadsto \left(\mathsf{qma}\left(\left(\mathsf{qma}\left(\left(\left(d1 \cdot d2\right)\right), \left(\left(d3 + 5\right) \cdot d1\right), 1.0\right)\right), d1, 32\right)\right)\]

Reproduce

herbie shell --seed 2019162 +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))))