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 r715782 = d1;
        double r715783 = 3.0;
        double r715784 = /* ERROR: no posit support in C */;
        double r715785 = r715782 * r715784;
        double r715786 = d2;
        double r715787 = r715782 * r715786;
        double r715788 = r715785 + r715787;
        double r715789 = d3;
        double r715790 = r715782 * r715789;
        double r715791 = r715788 + r715790;
        return r715791;
}
↓
double f(double d1, double d2, double d3) {
        double r715792 = 3.0;
        double r715793 = d2;
        double r715794 = r715792 + r715793;
        double r715795 = d3;
        double r715796 = r715794 + r715795;
        double r715797 = d1;
        double r715798 = r715796 * r715797;
        return r715798;
}

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 2019112 +o rules:numerics
(FPCore (d1 d2 d3)
  :name "FastMath test3"
  (+.p16 (+.p16 (*.p16 d1 (real->posit16 3)) (*.p16 d1 d2)) (*.p16 d1 d3)))