Average Error: 0.5 → 0.3
Time: 8.6s
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 r1710212 = d1;
        double r1710213 = 3.0;
        double r1710214 = /* ERROR: no posit support in C */;
        double r1710215 = r1710212 * r1710214;
        double r1710216 = d2;
        double r1710217 = r1710212 * r1710216;
        double r1710218 = r1710215 + r1710217;
        double r1710219 = d3;
        double r1710220 = r1710212 * r1710219;
        double r1710221 = r1710218 + r1710220;
        return r1710221;
}
↓
double f(double d1, double d2, double d3) {
        double r1710222 = 3.0;
        double r1710223 = d2;
        double r1710224 = r1710222 + r1710223;
        double r1710225 = d3;
        double r1710226 = r1710224 + r1710225;
        double r1710227 = d1;
        double r1710228 = r1710226 * r1710227;
        return r1710228;
}

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 2019125 
(FPCore (d1 d2 d3)
  :name "FastMath test3"
  (+.p16 (+.p16 (*.p16 d1 (real->posit16 3)) (*.p16 d1 d2)) (*.p16 d1 d3)))