Average Error: 0.5 → 0.3
Time: 8.4s
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 r4622257 = d1;
        double r4622258 = 3.0;
        double r4622259 = /* ERROR: no posit support in C */;
        double r4622260 = r4622257 * r4622259;
        double r4622261 = d2;
        double r4622262 = r4622257 * r4622261;
        double r4622263 = r4622260 + r4622262;
        double r4622264 = d3;
        double r4622265 = r4622257 * r4622264;
        double r4622266 = r4622263 + r4622265;
        return r4622266;
}
↓
double f(double d1, double d2, double d3) {
        double r4622267 = 3.0;
        double r4622268 = d2;
        double r4622269 = r4622267 + r4622268;
        double r4622270 = d3;
        double r4622271 = r4622269 + r4622270;
        double r4622272 = d1;
        double r4622273 = r4622271 * r4622272;
        return r4622273;
}

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 2019135 
(FPCore (d1 d2 d3)
  :name "FastMath test3"
  (+.p16 (+.p16 (*.p16 d1 (real->posit16 3)) (*.p16 d1 d2)) (*.p16 d1 d3)))