Average Error: 0.3 → 0.2
Time: 22.1s
Precision: 64
\[\frac{\left(\frac{\left(d1 \cdot d2\right)}{\left(\left(\frac{d3}{\left(5\right)}\right) \cdot d1\right)}\right)}{\left(d1 \cdot \left(32\right)\right)}\]
↓
\[\left(\mathsf{qma}\left(\left(\left(d1 \cdot \left(d2 + 5\right) + d1 \cdot d3\right)\right), d1, 32\right)\right)\]
\frac{\left(\frac{\left(d1 \cdot d2\right)}{\left(\left(\frac{d3}{\left(5\right)}\right) \cdot d1\right)}\right)}{\left(d1 \cdot \left(32\right)\right)}
↓
\left(\mathsf{qma}\left(\left(\left(d1 \cdot \left(d2 + 5\right) + d1 \cdot d3\right)\right), d1, 32\right)\right)
double f(double d1, double d2, double d3) {
        double r1382041 = d1;
        double r1382042 = d2;
        double r1382043 = r1382041 * r1382042;
        double r1382044 = d3;
        double r1382045 = 5.0;
        double r1382046 = /* ERROR: no posit support in C */;
        double r1382047 = r1382044 + r1382046;
        double r1382048 = r1382047 * r1382041;
        double r1382049 = r1382043 + r1382048;
        double r1382050 = 32.0;
        double r1382051 = /* ERROR: no posit support in C */;
        double r1382052 = r1382041 * r1382051;
        double r1382053 = r1382049 + r1382052;
        return r1382053;
}
↓
double f(double d1, double d2, double d3) {
        double r1382054 = d1;
        double r1382055 = d2;
        double r1382056 = 5.0;
        double r1382057 = r1382055 + r1382056;
        double r1382058 = r1382054 * r1382057;
        double r1382059 = d3;
        double r1382060 = r1382054 * r1382059;
        double r1382061 = r1382058 + r1382060;
        double r1382062 = /*Error: no posit support in C */;
        double r1382063 = 32.0;
        double r1382064 = /*Error: no posit support in C */;
        double r1382065 = /*Error: no posit support in C */;
        return r1382065;
}

Error

Bits error versus d1

Bits error versus d2

Bits error versus d3

Derivation

  1. Initial program 0.3

    \[\frac{\left(\frac{\left(d1 \cdot d2\right)}{\left(\left(\frac{d3}{\left(5\right)}\right) \cdot d1\right)}\right)}{\left(d1 \cdot \left(32\right)\right)}\]
  2. Using strategy rm

  3. Applied introduce-quire0.3

    \[\leadsto \frac{\color{blue}{\left(\left(\left(\frac{\left(d1 \cdot d2\right)}{\left(\left(\frac{d3}{\left(5\right)}\right) \cdot d1\right)}\right)\right)\right)}}{\left(d1 \cdot \left(32\right)\right)}\]

  4. Applied insert-quire-fdp-add0.2

    \[\leadsto \color{blue}{\left(\mathsf{qma}\left(\left(\left(\frac{\left(d1 \cdot d2\right)}{\left(\left(\frac{d3}{\left(5\right)}\right) \cdot d1\right)}\right)\right), d1, \left(32\right)\right)\right)}\]

  5. Simplified0.2

    \[\leadsto \color{blue}{\left(\mathsf{qma}\left(\left(\left(d1 \cdot \left(\frac{\left(\frac{d2}{\left(5\right)}\right)}{d3}\right)\right)\right), d1, \left(32\right)\right)\right)}\]
  6. Using strategy rm

  7. Applied distribute-lft-in0.2

    \[\leadsto \left(\mathsf{qma}\left(\left(\color{blue}{\left(\frac{\left(d1 \cdot \left(\frac{d2}{\left(5\right)}\right)\right)}{\left(d1 \cdot d3\right)}\right)}\right), d1, \left(32\right)\right)\right)\]

  8. Final simplification0.2

    \[\leadsto \left(\mathsf{qma}\left(\left(\left(d1 \cdot \left(d2 + 5\right) + d1 \cdot d3\right)\right), d1, 32\right)\right)\]

Reproduce

herbie shell --seed 2019155 
(FPCore (d1 d2 d3)
  :name "FastMath dist3"
  (+.p16 (+.p16 (*.p16 d1 d2) (*.p16 (+.p16 d3 (real->posit16 5)) d1)) (*.p16 d1 (real->posit16 32))))