Average Error: 0.3 → 0.1
Time: 31.9s
Precision: 64
\[\frac{\left(\frac{\left(d1 \cdot d2\right)}{\left(\left(\frac{d3}{\left(5\right)}\right) \cdot d1\right)}\right)}{\left(d1 \cdot \left(32\right)\right)}\]
↓
\[\left(\mathsf{qma}\left(\left(\mathsf{qma}\left(\left(\left(d1 \cdot d2\right)\right), \left(d3 + 5\right), d1\right)\right), d1, 32\right)\right)\]
\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(d3 + 5\right), d1\right)\right), d1, 32\right)\right)
double f(double d1, double d2, double d3) {
        double r519005 = d1;
        double r519006 = d2;
        double r519007 = r519005 * r519006;
        double r519008 = d3;
        double r519009 = 5.0;
        double r519010 = /* ERROR: no posit support in C */;
        double r519011 = r519008 + r519010;
        double r519012 = r519011 * r519005;
        double r519013 = r519007 + r519012;
        double r519014 = 32.0;
        double r519015 = /* ERROR: no posit support in C */;
        double r519016 = r519005 * r519015;
        double r519017 = r519013 + r519016;
        return r519017;
}
↓
double f(double d1, double d2, double d3) {
        double r519018 = d1;
        double r519019 = d2;
        double r519020 = r519018 * r519019;
        double r519021 = /*Error: no posit support in C */;
        double r519022 = d3;
        double r519023 = 5.0;
        double r519024 = r519022 + r519023;
        double r519025 = /*Error: no posit support in C */;
        double r519026 = 32.0;
        double r519027 = /*Error: no posit support in C */;
        double r519028 = /*Error: no posit support in C */;
        return r519028;
}

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

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

Reproduce

herbie shell --seed 2019152 
(FPCore (d1 d2 d3)
  :name "FastMath dist3"
  (+.p16 (+.p16 (*.p16 d1 d2) (*.p16 (+.p16 d3 (real->posit16 5)) d1)) (*.p16 d1 (real->posit16 32))))