Average Error: 0.3 → 0.1
Time: 16.7s
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 r1201716 = d1;
        double r1201717 = 10.0;
        double r1201718 = /* ERROR: no posit support in C */;
        double r1201719 = r1201716 * r1201718;
        double r1201720 = d2;
        double r1201721 = r1201716 * r1201720;
        double r1201722 = r1201719 + r1201721;
        double r1201723 = 20.0;
        double r1201724 = /* ERROR: no posit support in C */;
        double r1201725 = r1201716 * r1201724;
        double r1201726 = r1201722 + r1201725;
        return r1201726;
}
↓
double f(double d1, double d2) {
        double r1201727 = d1;
        double r1201728 = 10.0;
        double r1201729 = r1201727 * r1201728;
        double r1201730 = /*Error: no posit support in C */;
        double r1201731 = d2;
        double r1201732 = /*Error: no posit support in C */;
        double r1201733 = 20.0;
        double r1201734 = /*Error: no posit support in C */;
        double r1201735 = /*Error: no posit support in C */;
        return r1201735;
}

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 +o rules:numerics
(FPCore (d1 d2)
  :name "FastMath test2"
  (+.p16 (+.p16 (*.p16 d1 (real->posit16 10)) (*.p16 d1 d2)) (*.p16 d1 (real->posit16 20))))