Average Error: 0.3 → 0.1
Time: 18.8s
Precision: 64
\[\frac{\left(\frac{\left(d1 \cdot \left(10\right)\right)}{\left(d1 \cdot d2\right)}\right)}{\left(d1 \cdot \left(20\right)\right)}\]
↓
\[\left(\mathsf{qma}\left(\left(\mathsf{qma}\left(\left(\left(d1 \cdot 10\right)\right), d1, d2\right)\right), d1, 20\right)\right)\]
\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 10\right)\right), d1, d2\right)\right), d1, 20\right)\right)
double f(double d1, double d2) {
        double r4837313 = d1;
        double r4837314 = 10.0;
        double r4837315 = /* ERROR: no posit support in C */;
        double r4837316 = r4837313 * r4837315;
        double r4837317 = d2;
        double r4837318 = r4837313 * r4837317;
        double r4837319 = r4837316 + r4837318;
        double r4837320 = 20.0;
        double r4837321 = /* ERROR: no posit support in C */;
        double r4837322 = r4837313 * r4837321;
        double r4837323 = r4837319 + r4837322;
        return r4837323;
}
↓
double f(double d1, double d2) {
        double r4837324 = d1;
        double r4837325 = 10.0;
        double r4837326 = r4837324 * r4837325;
        double r4837327 = /*Error: no posit support in C */;
        double r4837328 = d2;
        double r4837329 = /*Error: no posit support in C */;
        double r4837330 = 20.0;
        double r4837331 = /*Error: no posit support in C */;
        double r4837332 = /*Error: no posit support in C */;
        return r4837332;
}

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

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

Reproduce

herbie shell --seed 2019158 +o rules:numerics
(FPCore (d1 d2)
  :name "FastMath test2"
  (+.p16 (+.p16 (*.p16 d1 (real->posit16 10)) (*.p16 d1 d2)) (*.p16 d1 (real->posit16 20))))