Average Error: 0.5 → 0.2
Time: 17.1s
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 r1359842 = d1;
        double r1359843 = 3.0;
        double r1359844 = /* ERROR: no posit support in C */;
        double r1359845 = r1359842 * r1359844;
        double r1359846 = d2;
        double r1359847 = r1359842 * r1359846;
        double r1359848 = r1359845 + r1359847;
        double r1359849 = d3;
        double r1359850 = r1359842 * r1359849;
        double r1359851 = r1359848 + r1359850;
        return r1359851;
}
↓
double f(double d1, double d2, double d3) {
        double r1359852 = 3.0;
        double r1359853 = /*Error: no posit support in C */;
        double r1359854 = d3;
        double r1359855 = 1.0;
        double r1359856 = /*Error: no posit support in C */;
        double r1359857 = d2;
        double r1359858 = /*Error: no posit support in C */;
        double r1359859 = /*Error: no posit support in C */;
        double r1359860 = d1;
        double r1359861 = r1359859 * r1359860;
        return r1359861;
}

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 2019153 +o rules:numerics
(FPCore (d1 d2 d3)
  :name "FastMath test3"
  (+.p16 (+.p16 (*.p16 d1 (real->posit16 3)) (*.p16 d1 d2)) (*.p16 d1 d3)))