Average Error: 0.5 → 0.2
Time: 18.9s
Precision: 64
\[\frac{\left(\frac{\left(d1 \cdot \left(3\right)\right)}{\left(d1 \cdot d2\right)}\right)}{\left(d1 \cdot d3\right)}\]
↓
\[\left(\mathsf{qma}\left(\left(\mathsf{qma}\left(\left(3\right), d3, 1.0\right)\right), d2, 1.0\right)\right) \cdot d1\]
\frac{\left(\frac{\left(d1 \cdot \left(3\right)\right)}{\left(d1 \cdot d2\right)}\right)}{\left(d1 \cdot d3\right)}
↓
\left(\mathsf{qma}\left(\left(\mathsf{qma}\left(\left(3\right), d3, 1.0\right)\right), d2, 1.0\right)\right) \cdot d1
double f(double d1, double d2, double d3) {
        double r1223913 = d1;
        double r1223914 = 3.0;
        double r1223915 = /* ERROR: no posit support in C */;
        double r1223916 = r1223913 * r1223915;
        double r1223917 = d2;
        double r1223918 = r1223913 * r1223917;
        double r1223919 = r1223916 + r1223918;
        double r1223920 = d3;
        double r1223921 = r1223913 * r1223920;
        double r1223922 = r1223919 + r1223921;
        return r1223922;
}
↓
double f(double d1, double d2, double d3) {
        double r1223923 = 3.0;
        double r1223924 = /*Error: no posit support in C */;
        double r1223925 = d3;
        double r1223926 = 1.0;
        double r1223927 = /*Error: no posit support in C */;
        double r1223928 = d2;
        double r1223929 = /*Error: no posit support in C */;
        double r1223930 = /*Error: no posit support in C */;
        double r1223931 = d1;
        double r1223932 = r1223930 * r1223931;
        return r1223932;
}

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

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

  4. Applied introduce-quire0.3

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

  5. Applied insert-quire-add0.3

    \[\leadsto \left(\frac{\color{blue}{\left(\left(\mathsf{qma}\left(\left(\left(3\right)\right), d3, \left(1.0\right)\right)\right)\right)}}{d2}\right) \cdot d1\]

  6. Applied insert-quire-add0.2

    \[\leadsto \color{blue}{\left(\left(\mathsf{qma}\left(\left(\mathsf{qma}\left(\left(\left(3\right)\right), d3, \left(1.0\right)\right)\right), d2, \left(1.0\right)\right)\right)\right)} \cdot d1\]

  7. Final simplification0.2

    \[\leadsto \left(\mathsf{qma}\left(\left(\mathsf{qma}\left(\left(3\right), d3, 1.0\right)\right), d2, 1.0\right)\right) \cdot d1\]

Reproduce

herbie shell --seed 2019154 +o rules:numerics
(FPCore (d1 d2 d3)
  :name "FastMath test3"
  (+.p16 (+.p16 (*.p16 d1 (real->posit16 3)) (*.p16 d1 d2)) (*.p16 d1 d3)))