Average Error: 0.5 → 0.3
Time: 7.9s
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 r1175187 = d1;
        double r1175188 = 3.0;
        double r1175189 = /* ERROR: no posit support in C */;
        double r1175190 = r1175187 * r1175189;
        double r1175191 = d2;
        double r1175192 = r1175187 * r1175191;
        double r1175193 = r1175190 + r1175192;
        double r1175194 = d3;
        double r1175195 = r1175187 * r1175194;
        double r1175196 = r1175193 + r1175195;
        return r1175196;
}
↓
double f(double d1, double d2, double d3) {
        double r1175197 = 3.0;
        double r1175198 = d2;
        double r1175199 = r1175197 + r1175198;
        double r1175200 = d3;
        double r1175201 = r1175199 + r1175200;
        double r1175202 = d1;
        double r1175203 = r1175201 * r1175202;
        return r1175203;
}

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 2019132 +o rules:numerics
(FPCore (d1 d2 d3)
  :name "FastMath test3"
  (+.p16 (+.p16 (*.p16 d1 (real->posit16 3)) (*.p16 d1 d2)) (*.p16 d1 d3)))