Average Error: 0.3 → 0.1
Time: 24.9s
Precision: 64
\[\frac{\left(\frac{\left(d1 \cdot d2\right)}{\left(\left(\frac{d3}{\left(5\right)}\right) \cdot d1\right)}\right)}{\left(d1 \cdot \left(32\right)\right)}\]
↓
\[\left(\mathsf{qma}\left(\left(\mathsf{qma}\left(\left(\left(d1 \cdot d2\right)\right), \left(d3 + 5\right), d1\right)\right), d1, 32\right)\right)\]
\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(\mathsf{qma}\left(\left(\left(d1 \cdot d2\right)\right), \left(d3 + 5\right), d1\right)\right), d1, 32\right)\right)
double f(double d1, double d2, double d3) {
        double r1957274 = d1;
        double r1957275 = d2;
        double r1957276 = r1957274 * r1957275;
        double r1957277 = d3;
        double r1957278 = 5.0;
        double r1957279 = /* ERROR: no posit support in C */;
        double r1957280 = r1957277 + r1957279;
        double r1957281 = r1957280 * r1957274;
        double r1957282 = r1957276 + r1957281;
        double r1957283 = 32.0;
        double r1957284 = /* ERROR: no posit support in C */;
        double r1957285 = r1957274 * r1957284;
        double r1957286 = r1957282 + r1957285;
        return r1957286;
}
↓
double f(double d1, double d2, double d3) {
        double r1957287 = d1;
        double r1957288 = d2;
        double r1957289 = r1957287 * r1957288;
        double r1957290 = /*Error: no posit support in C */;
        double r1957291 = d3;
        double r1957292 = 5.0;
        double r1957293 = r1957291 + r1957292;
        double r1957294 = /*Error: no posit support in C */;
        double r1957295 = 32.0;
        double r1957296 = /*Error: no posit support in C */;
        double r1957297 = /*Error: no posit support in C */;
        return r1957297;
}

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

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

Reproduce

herbie shell --seed 2019153 +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))))