Average Error: 0.5 → 0.3
Time: 8.2s
Precision: 64
\[\frac{\left(\frac{\left(d1 \cdot \left(3\right)\right)}{\left(d1 \cdot d2\right)}\right)}{\left(d1 \cdot d3\right)}\]
↓
\[\left(\left(3 + d2\right) + d3\right) \cdot d1\]
\frac{\left(\frac{\left(d1 \cdot \left(3\right)\right)}{\left(d1 \cdot d2\right)}\right)}{\left(d1 \cdot d3\right)}
↓
\left(\left(3 + d2\right) + d3\right) \cdot d1
double f(double d1, double d2, double d3) {
        double r6162035 = d1;
        double r6162036 = 3.0;
        double r6162037 = /* ERROR: no posit support in C */;
        double r6162038 = r6162035 * r6162037;
        double r6162039 = d2;
        double r6162040 = r6162035 * r6162039;
        double r6162041 = r6162038 + r6162040;
        double r6162042 = d3;
        double r6162043 = r6162035 * r6162042;
        double r6162044 = r6162041 + r6162043;
        return r6162044;
}
↓
double f(double d1, double d2, double d3) {
        double r6162045 = 3.0;
        double r6162046 = d2;
        double r6162047 = r6162045 + r6162046;
        double r6162048 = d3;
        double r6162049 = r6162047 + r6162048;
        double r6162050 = d1;
        double r6162051 = r6162049 * r6162050;
        return r6162051;
}

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. Using strategy rm

  4. Applied associate-+r+0.3

    \[\leadsto \color{blue}{\left(\frac{\left(\frac{\left(3\right)}{d2}\right)}{d3}\right)} \cdot d1\]

  5. Final simplification0.3

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

Reproduce

herbie shell --seed 2019130 
(FPCore (d1 d2 d3)
  :name "FastMath test3"
  (+.p16 (+.p16 (*.p16 d1 (real->posit16 3)) (*.p16 d1 d2)) (*.p16 d1 d3)))