Average Error: 0.3 → 0.3
Time: 12.1s
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 r4820340 = d1;
        double r4820341 = d2;
        double r4820342 = r4820340 * r4820341;
        double r4820343 = d3;
        double r4820344 = 5.0;
        double r4820345 = /* ERROR: no posit support in C */;
        double r4820346 = r4820343 + r4820345;
        double r4820347 = r4820346 * r4820340;
        double r4820348 = r4820342 + r4820347;
        double r4820349 = 32.0;
        double r4820350 = /* ERROR: no posit support in C */;
        double r4820351 = r4820340 * r4820350;
        double r4820352 = r4820348 + r4820351;
        return r4820352;
}
↓
double f(double d1, double d2, double d3) {
        double r4820353 = d1;
        double r4820354 = d2;
        double r4820355 = r4820353 * r4820354;
        double r4820356 = d3;
        double r4820357 = 5.0;
        double r4820358 = r4820356 + r4820357;
        double r4820359 = r4820358 * r4820353;
        double r4820360 = r4820355 + r4820359;
        double r4820361 = 32.0;
        double r4820362 = r4820353 * r4820361;
        double r4820363 = r4820360 + r4820362;
        return r4820363;
}

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 2019135 
(FPCore (d1 d2 d3)
  :name "FastMath dist3"
  (+.p16 (+.p16 (*.p16 d1 d2) (*.p16 (+.p16 d3 (real->posit16 5)) d1)) (*.p16 d1 (real->posit16 32))))