Average Error: 0.5 → 0.3
Time: 9.9s
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 r2442829 = d1;
        double r2442830 = 3.0;
        double r2442831 = /* ERROR: no posit support in C */;
        double r2442832 = r2442829 * r2442831;
        double r2442833 = d2;
        double r2442834 = r2442829 * r2442833;
        double r2442835 = r2442832 + r2442834;
        double r2442836 = d3;
        double r2442837 = r2442829 * r2442836;
        double r2442838 = r2442835 + r2442837;
        return r2442838;
}
↓
double f(double d1, double d2, double d3) {
        double r2442839 = 3.0;
        double r2442840 = d2;
        double r2442841 = r2442839 + r2442840;
        double r2442842 = d3;
        double r2442843 = r2442841 + r2442842;
        double r2442844 = d1;
        double r2442845 = r2442843 * r2442844;
        return r2442845;
}

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 2019121 
(FPCore (d1 d2 d3)
  :name "FastMath test3"
  (+.p16 (+.p16 (*.p16 d1 (real->posit16 3)) (*.p16 d1 d2)) (*.p16 d1 d3)))