Average Error: 0.5 → 0.3
Time: 7.4s
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 r1496493 = d1;
        double r1496494 = 3.0;
        double r1496495 = /* ERROR: no posit support in C */;
        double r1496496 = r1496493 * r1496495;
        double r1496497 = d2;
        double r1496498 = r1496493 * r1496497;
        double r1496499 = r1496496 + r1496498;
        double r1496500 = d3;
        double r1496501 = r1496493 * r1496500;
        double r1496502 = r1496499 + r1496501;
        return r1496502;
}
↓
double f(double d1, double d2, double d3) {
        double r1496503 = 3.0;
        double r1496504 = d2;
        double r1496505 = r1496503 + r1496504;
        double r1496506 = d3;
        double r1496507 = r1496505 + r1496506;
        double r1496508 = d1;
        double r1496509 = r1496507 * r1496508;
        return r1496509;
}

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 2019120 
(FPCore (d1 d2 d3)
  :name "FastMath test3"
  (+.p16 (+.p16 (*.p16 d1 (real->posit16 3)) (*.p16 d1 d2)) (*.p16 d1 d3)))