Average Error: 0.3 → 0.2
Time: 28.6s
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 r3444681 = d1;
        double r3444682 = d2;
        double r3444683 = r3444681 * r3444682;
        double r3444684 = d3;
        double r3444685 = 5.0;
        double r3444686 = /* ERROR: no posit support in C */;
        double r3444687 = r3444684 + r3444686;
        double r3444688 = r3444687 * r3444681;
        double r3444689 = r3444683 + r3444688;
        double r3444690 = 32.0;
        double r3444691 = /* ERROR: no posit support in C */;
        double r3444692 = r3444681 * r3444691;
        double r3444693 = r3444689 + r3444692;
        return r3444693;
}
↓
double f(double d1, double d2, double d3) {
        double r3444694 = d1;
        double r3444695 = d2;
        double r3444696 = r3444694 * r3444695;
        double r3444697 = /*Error: no posit support in C */;
        double r3444698 = d3;
        double r3444699 = 5.0;
        double r3444700 = r3444698 + r3444699;
        double r3444701 = r3444700 * r3444694;
        double r3444702 = 1.0;
        double r3444703 = /*Error: no posit support in C */;
        double r3444704 = 32.0;
        double r3444705 = /*Error: no posit support in C */;
        double r3444706 = /*Error: no posit support in C */;
        return r3444706;
}

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))))