Average Error: 0.3 → 0.3
Time: 10.2s
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 r1934285 = d1;
        double r1934286 = d2;
        double r1934287 = r1934285 * r1934286;
        double r1934288 = d3;
        double r1934289 = 5.0;
        double r1934290 = /* ERROR: no posit support in C */;
        double r1934291 = r1934288 + r1934290;
        double r1934292 = r1934291 * r1934285;
        double r1934293 = r1934287 + r1934292;
        double r1934294 = 32.0;
        double r1934295 = /* ERROR: no posit support in C */;
        double r1934296 = r1934285 * r1934295;
        double r1934297 = r1934293 + r1934296;
        return r1934297;
}
↓
double f(double d1, double d2, double d3) {
        double r1934298 = d1;
        double r1934299 = d2;
        double r1934300 = r1934298 * r1934299;
        double r1934301 = d3;
        double r1934302 = 5.0;
        double r1934303 = r1934301 + r1934302;
        double r1934304 = r1934303 * r1934298;
        double r1934305 = r1934300 + r1934304;
        double r1934306 = 32.0;
        double r1934307 = r1934298 * r1934306;
        double r1934308 = r1934305 + r1934307;
        return r1934308;
}

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 2019124 +o rules:numerics
(FPCore (d1 d2 d3)
  :name "FastMath dist3"
  (+.p16 (+.p16 (*.p16 d1 d2) (*.p16 (+.p16 d3 (real->posit16 5)) d1)) (*.p16 d1 (real->posit16 32))))