Average Error: 0.5 → 0.3
Time: 7.8s
Precision: 64
\[\frac{\left(\frac{\left(d1 \cdot \left(3\right)\right)}{\left(d1 \cdot d2\right)}\right)}{\left(d1 \cdot d3\right)}\]
↓
\[\left(\left(3 + d2\right) + d3\right) \cdot d1\]
\frac{\left(\frac{\left(d1 \cdot \left(3\right)\right)}{\left(d1 \cdot d2\right)}\right)}{\left(d1 \cdot d3\right)}
↓
\left(\left(3 + d2\right) + d3\right) \cdot d1
double f(double d1, double d2, double d3) {
        double r2442840 = d1;
        double r2442841 = 3.0;
        double r2442842 = /* ERROR: no posit support in C */;
        double r2442843 = r2442840 * r2442842;
        double r2442844 = d2;
        double r2442845 = r2442840 * r2442844;
        double r2442846 = r2442843 + r2442845;
        double r2442847 = d3;
        double r2442848 = r2442840 * r2442847;
        double r2442849 = r2442846 + r2442848;
        return r2442849;
}
↓
double f(double d1, double d2, double d3) {
        double r2442850 = 3.0;
        double r2442851 = d2;
        double r2442852 = r2442850 + r2442851;
        double r2442853 = d3;
        double r2442854 = r2442852 + r2442853;
        double r2442855 = d1;
        double r2442856 = r2442854 * r2442855;
        return r2442856;
}

Error

Bits error versus d1

Bits error versus d2

Bits error versus d3

Derivation

  1. Initial program 0.5

    \[\frac{\left(\frac{\left(d1 \cdot \left(3\right)\right)}{\left(d1 \cdot d2\right)}\right)}{\left(d1 \cdot d3\right)}\]

  2. Simplified0.3

    \[\leadsto \color{blue}{\left(\frac{\left(3\right)}{\left(\frac{d2}{d3}\right)}\right) \cdot d1}\]
  3. Using strategy rm

  4. Applied associate-+r+0.3

    \[\leadsto \color{blue}{\left(\frac{\left(\frac{\left(3\right)}{d2}\right)}{d3}\right)} \cdot d1\]

  5. Final simplification0.3

    \[\leadsto \left(\left(3 + d2\right) + d3\right) \cdot d1\]

Reproduce

herbie shell --seed 2019119 
(FPCore (d1 d2 d3)
  :name "FastMath test3"
  (+.p16 (+.p16 (*.p16 d1 (real->posit16 3)) (*.p16 d1 d2)) (*.p16 d1 d3)))