Average Error: 0.3 → 0.1
Time: 25.7s
Precision: 64
\[\frac{\left(\frac{\left(d1 \cdot d2\right)}{\left(\left(\frac{d3}{\left(5\right)}\right) \cdot d1\right)}\right)}{\left(d1 \cdot \left(32\right)\right)}\]
↓
\[\left(\mathsf{qma}\left(\left(\mathsf{qma}\left(\left(\left(d1 \cdot d2\right)\right), \left(\frac{d3}{\left(5\right)}\right), d1\right)\right), d1, \left(32\right)\right)\right)\]
\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(\mathsf{qma}\left(\left(\left(d1 \cdot d2\right)\right), \left(\frac{d3}{\left(5\right)}\right), d1\right)\right), d1, \left(32\right)\right)\right)
double f(double d1, double d2, double d3) {
        double r4139224 = d1;
        double r4139225 = d2;
        double r4139226 = r4139224 * r4139225;
        double r4139227 = d3;
        double r4139228 = 5.0;
        double r4139229 = /* ERROR: no posit support in C */;
        double r4139230 = r4139227 + r4139229;
        double r4139231 = r4139230 * r4139224;
        double r4139232 = r4139226 + r4139231;
        double r4139233 = 32.0;
        double r4139234 = /* ERROR: no posit support in C */;
        double r4139235 = r4139224 * r4139234;
        double r4139236 = r4139232 + r4139235;
        return r4139236;
}
↓
double f(double d1, double d2, double d3) {
        double r4139237 = d1;
        double r4139238 = d2;
        double r4139239 = r4139237 * r4139238;
        double r4139240 = /*Error: no posit support in C */;
        double r4139241 = d3;
        double r4139242 = 5.0;
        double r4139243 = /* ERROR: no posit support in C */;
        double r4139244 = r4139241 + r4139243;
        double r4139245 = /*Error: no posit support in C */;
        double r4139246 = 32.0;
        double r4139247 = /* ERROR: no posit support in C */;
        double r4139248 = /*Error: no posit support in C */;
        double r4139249 = /*Error: no posit support in C */;
        return r4139249;
}

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

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

  4. Applied insert-quire-fdp-add0.3

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

  5. Applied insert-quire-fdp-add0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2019164 +o rules:numerics
(FPCore (d1 d2 d3)
  :name "FastMath dist3"
  (+.p16 (+.p16 (*.p16 d1 d2) (*.p16 (+.p16 d3 (real->posit16 5)) d1)) (*.p16 d1 (real->posit16 32))))