Average Error: 0.5 → 0.3
Time: 8.2s
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 r1072544 = d1;
        double r1072545 = 3.0;
        double r1072546 = /* ERROR: no posit support in C */;
        double r1072547 = r1072544 * r1072546;
        double r1072548 = d2;
        double r1072549 = r1072544 * r1072548;
        double r1072550 = r1072547 + r1072549;
        double r1072551 = d3;
        double r1072552 = r1072544 * r1072551;
        double r1072553 = r1072550 + r1072552;
        return r1072553;
}
↓
double f(double d1, double d2, double d3) {
        double r1072554 = 3.0;
        double r1072555 = d2;
        double r1072556 = r1072554 + r1072555;
        double r1072557 = d3;
        double r1072558 = r1072556 + r1072557;
        double r1072559 = d1;
        double r1072560 = r1072558 * r1072559;
        return r1072560;
}

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 2019104 
(FPCore (d1 d2 d3)
  :name "FastMath test3"
  (+.p16 (+.p16 (*.p16 d1 (real->posit16 3)) (*.p16 d1 d2)) (*.p16 d1 d3)))