Average Error: 0.5 → 0.3
Time: 9.2s
Precision: 64
\[\frac{\left(\frac{\left(d1 \cdot \left(3\right)\right)}{\left(d1 \cdot d2\right)}\right)}{\left(d1 \cdot d3\right)}\]
↓
\[\left(3 + \left(d2 + d3\right)\right) \cdot d1\]
\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 r6002708 = d1;
        double r6002709 = 3.0;
        double r6002710 = /* ERROR: no posit support in C */;
        double r6002711 = r6002708 * r6002710;
        double r6002712 = d2;
        double r6002713 = r6002708 * r6002712;
        double r6002714 = r6002711 + r6002713;
        double r6002715 = d3;
        double r6002716 = r6002708 * r6002715;
        double r6002717 = r6002714 + r6002716;
        return r6002717;
}
↓
double f(double d1, double d2, double d3) {
        double r6002718 = 3.0;
        double r6002719 = d2;
        double r6002720 = d3;
        double r6002721 = r6002719 + r6002720;
        double r6002722 = r6002718 + r6002721;
        double r6002723 = d1;
        double r6002724 = r6002722 * r6002723;
        return r6002724;
}

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