Average Error: 0.5 → 0.3
Time: 8.3s
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 r2662145 = d1;
        double r2662146 = 3.0;
        double r2662147 = /* ERROR: no posit support in C */;
        double r2662148 = r2662145 * r2662147;
        double r2662149 = d2;
        double r2662150 = r2662145 * r2662149;
        double r2662151 = r2662148 + r2662150;
        double r2662152 = d3;
        double r2662153 = r2662145 * r2662152;
        double r2662154 = r2662151 + r2662153;
        return r2662154;
}
↓
double f(double d1, double d2, double d3) {
        double r2662155 = 3.0;
        double r2662156 = d2;
        double r2662157 = r2662155 + r2662156;
        double r2662158 = d3;
        double r2662159 = r2662157 + r2662158;
        double r2662160 = d1;
        double r2662161 = r2662159 * r2662160;
        return r2662161;
}

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 2019121 +o rules:numerics
(FPCore (d1 d2 d3)
  :name "FastMath test3"
  (+.p16 (+.p16 (*.p16 d1 (real->posit16 3)) (*.p16 d1 d2)) (*.p16 d1 d3)))