Average Error: 0.3 → 0.1
Time: 18.3s
Precision: 64
\[\frac{\left(\frac{\left(d1 \cdot \left(10\right)\right)}{\left(d1 \cdot d2\right)}\right)}{\left(d1 \cdot \left(20\right)\right)}\]
↓
\[\left(\mathsf{qma}\left(\left(\mathsf{qma}\left(\left(\left(d1 \cdot \left(10\right)\right)\right), d1, d2\right)\right), d1, \left(20\right)\right)\right)\]
\frac{\left(\frac{\left(d1 \cdot \left(10\right)\right)}{\left(d1 \cdot d2\right)}\right)}{\left(d1 \cdot \left(20\right)\right)}
↓
\left(\mathsf{qma}\left(\left(\mathsf{qma}\left(\left(\left(d1 \cdot \left(10\right)\right)\right), d1, d2\right)\right), d1, \left(20\right)\right)\right)
double f(double d1, double d2) {
        double r2837268 = d1;
        double r2837269 = 10.0;
        double r2837270 = /* ERROR: no posit support in C */;
        double r2837271 = r2837268 * r2837270;
        double r2837272 = d2;
        double r2837273 = r2837268 * r2837272;
        double r2837274 = r2837271 + r2837273;
        double r2837275 = 20.0;
        double r2837276 = /* ERROR: no posit support in C */;
        double r2837277 = r2837268 * r2837276;
        double r2837278 = r2837274 + r2837277;
        return r2837278;
}
↓
double f(double d1, double d2) {
        double r2837279 = d1;
        double r2837280 = 10.0;
        double r2837281 = /* ERROR: no posit support in C */;
        double r2837282 = r2837279 * r2837281;
        double r2837283 = /*Error: no posit support in C */;
        double r2837284 = d2;
        double r2837285 = /*Error: no posit support in C */;
        double r2837286 = 20.0;
        double r2837287 = /* ERROR: no posit support in C */;
        double r2837288 = /*Error: no posit support in C */;
        double r2837289 = /*Error: no posit support in C */;
        return r2837289;
}

Error

Bits error versus d1

Bits error versus d2

Derivation

  1. Initial program 0.3

    \[\frac{\left(\frac{\left(d1 \cdot \left(10\right)\right)}{\left(d1 \cdot d2\right)}\right)}{\left(d1 \cdot \left(20\right)\right)}\]
  2. Using strategy rm

  3. Applied introduce-quire0.3

    \[\leadsto \frac{\left(\frac{\color{blue}{\left(\left(\left(d1 \cdot \left(10\right)\right)\right)\right)}}{\left(d1 \cdot d2\right)}\right)}{\left(d1 \cdot \left(20\right)\right)}\]

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

    \[\leadsto \frac{\color{blue}{\left(\left(\mathsf{qma}\left(\left(\left(d1 \cdot \left(10\right)\right)\right), d1, d2\right)\right)\right)}}{\left(d1 \cdot \left(20\right)\right)}\]

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

    \[\leadsto \color{blue}{\left(\mathsf{qma}\left(\left(\mathsf{qma}\left(\left(\left(d1 \cdot \left(10\right)\right)\right), d1, d2\right)\right), d1, \left(20\right)\right)\right)}\]

  6. Final simplification0.1

    \[\leadsto \left(\mathsf{qma}\left(\left(\mathsf{qma}\left(\left(\left(d1 \cdot \left(10\right)\right)\right), d1, d2\right)\right), d1, \left(20\right)\right)\right)\]

Reproduce

herbie shell --seed 2019163 +o rules:numerics
(FPCore (d1 d2)
  :name "FastMath test2"
  (+.p16 (+.p16 (*.p16 d1 (real->posit16 10)) (*.p16 d1 d2)) (*.p16 d1 (real->posit16 20))))