Average Error: 0.5 → 0.3
Time: 9.5s
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 r5201365 = d1;
        double r5201366 = 3.0;
        double r5201367 = /* ERROR: no posit support in C */;
        double r5201368 = r5201365 * r5201367;
        double r5201369 = d2;
        double r5201370 = r5201365 * r5201369;
        double r5201371 = r5201368 + r5201370;
        double r5201372 = d3;
        double r5201373 = r5201365 * r5201372;
        double r5201374 = r5201371 + r5201373;
        return r5201374;
}
↓
double f(double d1, double d2, double d3) {
        double r5201375 = 3.0;
        double r5201376 = d2;
        double r5201377 = r5201375 + r5201376;
        double r5201378 = d3;
        double r5201379 = r5201377 + r5201378;
        double r5201380 = d1;
        double r5201381 = r5201379 * r5201380;
        return r5201381;
}

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 2019133 +o rules:numerics
(FPCore (d1 d2 d3)
  :name "FastMath test3"
  (+.p16 (+.p16 (*.p16 d1 (real->posit16 3)) (*.p16 d1 d2)) (*.p16 d1 d3)))