Average Error: 0.3 → 0.3
Time: 9.3s
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 r1659259 = d1;
        double r1659260 = d2;
        double r1659261 = r1659259 * r1659260;
        double r1659262 = d3;
        double r1659263 = 5.0;
        double r1659264 = /* ERROR: no posit support in C */;
        double r1659265 = r1659262 + r1659264;
        double r1659266 = r1659265 * r1659259;
        double r1659267 = r1659261 + r1659266;
        double r1659268 = 32.0;
        double r1659269 = /* ERROR: no posit support in C */;
        double r1659270 = r1659259 * r1659269;
        double r1659271 = r1659267 + r1659270;
        return r1659271;
}
↓
double f(double d1, double d2, double d3) {
        double r1659272 = d1;
        double r1659273 = d2;
        double r1659274 = r1659272 * r1659273;
        double r1659275 = d3;
        double r1659276 = 5.0;
        double r1659277 = r1659275 + r1659276;
        double r1659278 = r1659277 * r1659272;
        double r1659279 = r1659274 + r1659278;
        double r1659280 = 32.0;
        double r1659281 = r1659272 * r1659280;
        double r1659282 = r1659279 + r1659281;
        return r1659282;
}

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 2019107 
(FPCore (d1 d2 d3)
  :name "FastMath dist3"
  (+.p16 (+.p16 (*.p16 d1 d2) (*.p16 (+.p16 d3 (real->posit16 5)) d1)) (*.p16 d1 (real->posit16 32))))