Average Error: 0.3 → 0.2
Time: 33.1s
Precision: 64
\[\frac{\left(\frac{\left(d1 \cdot d2\right)}{\left(\left(\frac{d3}{\left(5\right)}\right) \cdot d1\right)}\right)}{\left(d1 \cdot \left(32\right)\right)}\]
↓
\[\left(\mathsf{qma}\left(\left(\mathsf{qma}\left(\left(\left(d1 \cdot d2\right)\right), \left(\left(d3 + 5\right) \cdot d1\right), 1.0\right)\right), d1, 32\right)\right)\]
\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 r7167707 = d1;
        double r7167708 = d2;
        double r7167709 = r7167707 * r7167708;
        double r7167710 = d3;
        double r7167711 = 5.0;
        double r7167712 = /* ERROR: no posit support in C */;
        double r7167713 = r7167710 + r7167712;
        double r7167714 = r7167713 * r7167707;
        double r7167715 = r7167709 + r7167714;
        double r7167716 = 32.0;
        double r7167717 = /* ERROR: no posit support in C */;
        double r7167718 = r7167707 * r7167717;
        double r7167719 = r7167715 + r7167718;
        return r7167719;
}
↓
double f(double d1, double d2, double d3) {
        double r7167720 = d1;
        double r7167721 = d2;
        double r7167722 = r7167720 * r7167721;
        double r7167723 = /*Error: no posit support in C */;
        double r7167724 = d3;
        double r7167725 = 5.0;
        double r7167726 = r7167724 + r7167725;
        double r7167727 = r7167726 * r7167720;
        double r7167728 = 1.0;
        double r7167729 = /*Error: no posit support in C */;
        double r7167730 = 32.0;
        double r7167731 = /*Error: no posit support in C */;
        double r7167732 = /*Error: no posit support in C */;
        return r7167732;
}

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