Average Error: 0.3 → 0.3
Time: 13.4s
Precision: 64
\[\frac{\left(\frac{\left(d1 \cdot d2\right)}{\left(\left(\frac{d3}{\left(5\right)}\right) \cdot d1\right)}\right)}{\left(d1 \cdot \left(32\right)\right)}\]
↓
\[\left(d1 \cdot d2 + \left(d3 + 5\right) \cdot d1\right) + d1 \cdot 32\]
\frac{\left(\frac{\left(d1 \cdot d2\right)}{\left(\left(\frac{d3}{\left(5\right)}\right) \cdot d1\right)}\right)}{\left(d1 \cdot \left(32\right)\right)}
↓
\left(d1 \cdot d2 + \left(d3 + 5\right) \cdot d1\right) + d1 \cdot 32
double f(double d1, double d2, double d3) {
        double r6180355 = d1;
        double r6180356 = d2;
        double r6180357 = r6180355 * r6180356;
        double r6180358 = d3;
        double r6180359 = 5.0;
        double r6180360 = /* ERROR: no posit support in C */;
        double r6180361 = r6180358 + r6180360;
        double r6180362 = r6180361 * r6180355;
        double r6180363 = r6180357 + r6180362;
        double r6180364 = 32.0;
        double r6180365 = /* ERROR: no posit support in C */;
        double r6180366 = r6180355 * r6180365;
        double r6180367 = r6180363 + r6180366;
        return r6180367;
}
↓
double f(double d1, double d2, double d3) {
        double r6180368 = d1;
        double r6180369 = d2;
        double r6180370 = r6180368 * r6180369;
        double r6180371 = d3;
        double r6180372 = 5.0;
        double r6180373 = r6180371 + r6180372;
        double r6180374 = r6180373 * r6180368;
        double r6180375 = r6180370 + r6180374;
        double r6180376 = 32.0;
        double r6180377 = r6180368 * r6180376;
        double r6180378 = r6180375 + r6180377;
        return r6180378;
}

Error

Bits error versus d1

Bits error versus d2

Bits error versus d3

Derivation

  1. Initial program 0.3

    \[\frac{\left(\frac{\left(d1 \cdot d2\right)}{\left(\left(\frac{d3}{\left(5\right)}\right) \cdot d1\right)}\right)}{\left(d1 \cdot \left(32\right)\right)}\]

  2. Final simplification0.3

    \[\leadsto \left(d1 \cdot d2 + \left(d3 + 5\right) \cdot d1\right) + d1 \cdot 32\]

Reproduce

herbie shell --seed 2019130 
(FPCore (d1 d2 d3)
  :name "FastMath dist3"
  (+.p16 (+.p16 (*.p16 d1 d2) (*.p16 (+.p16 d3 (real->posit16 5)) d1)) (*.p16 d1 (real->posit16 32))))