Average Error: 0.5 → 0.3
Time: 9.7s
Precision: 64
\[\frac{\left(\frac{\left(d1 \cdot \left(3\right)\right)}{\left(d1 \cdot d2\right)}\right)}{\left(d1 \cdot d3\right)}\]
↓
\[\left(3 + \left(d2 + d3\right)\right) \cdot d1\]
\frac{\left(\frac{\left(d1 \cdot \left(3\right)\right)}{\left(d1 \cdot d2\right)}\right)}{\left(d1 \cdot d3\right)}
↓
\left(3 + \left(d2 + d3\right)\right) \cdot d1
double f(double d1, double d2, double d3) {
        double r5743298 = d1;
        double r5743299 = 3.0;
        double r5743300 = /* ERROR: no posit support in C */;
        double r5743301 = r5743298 * r5743300;
        double r5743302 = d2;
        double r5743303 = r5743298 * r5743302;
        double r5743304 = r5743301 + r5743303;
        double r5743305 = d3;
        double r5743306 = r5743298 * r5743305;
        double r5743307 = r5743304 + r5743306;
        return r5743307;
}
↓
double f(double d1, double d2, double d3) {
        double r5743308 = 3.0;
        double r5743309 = d2;
        double r5743310 = d3;
        double r5743311 = r5743309 + r5743310;
        double r5743312 = r5743308 + r5743311;
        double r5743313 = d1;
        double r5743314 = r5743312 * r5743313;
        return r5743314;
}

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. Final simplification0.3

    \[\leadsto \left(3 + \left(d2 + d3\right)\right) \cdot d1\]

Reproduce

herbie shell --seed 2019134 
(FPCore (d1 d2 d3)
  :name "FastMath test3"
  (+.p16 (+.p16 (*.p16 d1 (real->posit16 3)) (*.p16 d1 d2)) (*.p16 d1 d3)))