Average Error: 0.3 → 0.1
Time: 20.1s
Precision: 64
\[\frac{\left(\frac{\left(d1 \cdot \left(10\right)\right)}{\left(d1 \cdot d2\right)}\right)}{\left(d1 \cdot \left(20\right)\right)}\]
↓
\[\left(\mathsf{qma}\left(\left(\mathsf{qma}\left(\left(\left(d1 \cdot 10\right)\right), d1, d2\right)\right), d1, 20\right)\right)\]
\frac{\left(\frac{\left(d1 \cdot \left(10\right)\right)}{\left(d1 \cdot d2\right)}\right)}{\left(d1 \cdot \left(20\right)\right)}
↓
\left(\mathsf{qma}\left(\left(\mathsf{qma}\left(\left(\left(d1 \cdot 10\right)\right), d1, d2\right)\right), d1, 20\right)\right)
double f(double d1, double d2) {
        double r1746903 = d1;
        double r1746904 = 10.0;
        double r1746905 = /* ERROR: no posit support in C */;
        double r1746906 = r1746903 * r1746905;
        double r1746907 = d2;
        double r1746908 = r1746903 * r1746907;
        double r1746909 = r1746906 + r1746908;
        double r1746910 = 20.0;
        double r1746911 = /* ERROR: no posit support in C */;
        double r1746912 = r1746903 * r1746911;
        double r1746913 = r1746909 + r1746912;
        return r1746913;
}
↓
double f(double d1, double d2) {
        double r1746914 = d1;
        double r1746915 = 10.0;
        double r1746916 = r1746914 * r1746915;
        double r1746917 = /*Error: no posit support in C */;
        double r1746918 = d2;
        double r1746919 = /*Error: no posit support in C */;
        double r1746920 = 20.0;
        double r1746921 = /*Error: no posit support in C */;
        double r1746922 = /*Error: no posit support in C */;
        return r1746922;
}

Error

Bits error versus d1

Bits error versus d2

Derivation

  1. Initial program 0.3

    \[\frac{\left(\frac{\left(d1 \cdot \left(10\right)\right)}{\left(d1 \cdot d2\right)}\right)}{\left(d1 \cdot \left(20\right)\right)}\]
  2. Using strategy rm

  3. Applied introduce-quire0.3

    \[\leadsto \frac{\left(\frac{\color{blue}{\left(\left(\left(d1 \cdot \left(10\right)\right)\right)\right)}}{\left(d1 \cdot d2\right)}\right)}{\left(d1 \cdot \left(20\right)\right)}\]

  4. Applied insert-quire-fdp-add0.3

    \[\leadsto \frac{\color{blue}{\left(\left(\mathsf{qma}\left(\left(\left(d1 \cdot \left(10\right)\right)\right), d1, d2\right)\right)\right)}}{\left(d1 \cdot \left(20\right)\right)}\]

  5. Applied insert-quire-fdp-add0.1

    \[\leadsto \color{blue}{\left(\mathsf{qma}\left(\left(\mathsf{qma}\left(\left(\left(d1 \cdot \left(10\right)\right)\right), d1, d2\right)\right), d1, \left(20\right)\right)\right)}\]

  6. Final simplification0.1

    \[\leadsto \left(\mathsf{qma}\left(\left(\mathsf{qma}\left(\left(\left(d1 \cdot 10\right)\right), d1, d2\right)\right), d1, 20\right)\right)\]

Reproduce

herbie shell --seed 2019153 
(FPCore (d1 d2)
  :name "FastMath test2"
  (+.p16 (+.p16 (*.p16 d1 (real->posit16 10)) (*.p16 d1 d2)) (*.p16 d1 (real->posit16 20))))