Average Error: 0.3 → 0.2
Time: 12.2s
Precision: 64
\[\frac{\left(\frac{\left(d1 \cdot \left(10\right)\right)}{\left(d1 \cdot d2\right)}\right)}{\left(d1 \cdot \left(20\right)\right)}\]
↓
\[\left(\mathsf{qma}\left(\left(\left(\left(10 + d2\right) \cdot d1\right)\right), 20, d1\right)\right)\]
\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(\left(\left(10 + d2\right) \cdot d1\right)\right), 20, d1\right)\right)
double f(double d1, double d2) {
        double r4257672 = d1;
        double r4257673 = 10.0;
        double r4257674 = /* ERROR: no posit support in C */;
        double r4257675 = r4257672 * r4257674;
        double r4257676 = d2;
        double r4257677 = r4257672 * r4257676;
        double r4257678 = r4257675 + r4257677;
        double r4257679 = 20.0;
        double r4257680 = /* ERROR: no posit support in C */;
        double r4257681 = r4257672 * r4257680;
        double r4257682 = r4257678 + r4257681;
        return r4257682;
}
↓
double f(double d1, double d2) {
        double r4257683 = 10.0;
        double r4257684 = d2;
        double r4257685 = r4257683 + r4257684;
        double r4257686 = d1;
        double r4257687 = r4257685 * r4257686;
        double r4257688 = /*Error: no posit support in C */;
        double r4257689 = 20.0;
        double r4257690 = /*Error: no posit support in C */;
        double r4257691 = /*Error: no posit support in C */;
        return r4257691;
}

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. Simplified0.3

    \[\leadsto \color{blue}{d1 \cdot \left(\frac{\left(10\right)}{\left(\frac{d2}{\left(20\right)}\right)}\right)}\]
  3. Using strategy rm

  4. Applied associate-+r+0.3

    \[\leadsto d1 \cdot \color{blue}{\left(\frac{\left(\frac{\left(10\right)}{d2}\right)}{\left(20\right)}\right)}\]
  5. Using strategy rm

  6. Applied distribute-rgt-in0.3

    \[\leadsto \color{blue}{\frac{\left(\left(\frac{\left(10\right)}{d2}\right) \cdot d1\right)}{\left(\left(20\right) \cdot d1\right)}}\]
  7. Using strategy rm

  8. Applied introduce-quire0.3

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

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

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

  10. Final simplification0.2

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

Reproduce

herbie shell --seed 2019165 
(FPCore (d1 d2)
  :name "FastMath test2"
  (+.p16 (+.p16 (*.p16 d1 (real->posit16 10)) (*.p16 d1 d2)) (*.p16 d1 (real->posit16 20))))