Average Error: 0.3 → 0.1
Time: 17.9s
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 r5654283 = d1;
        double r5654284 = 10.0;
        double r5654285 = /* ERROR: no posit support in C */;
        double r5654286 = r5654283 * r5654285;
        double r5654287 = d2;
        double r5654288 = r5654283 * r5654287;
        double r5654289 = r5654286 + r5654288;
        double r5654290 = 20.0;
        double r5654291 = /* ERROR: no posit support in C */;
        double r5654292 = r5654283 * r5654291;
        double r5654293 = r5654289 + r5654292;
        return r5654293;
}
↓
double f(double d1, double d2) {
        double r5654294 = d1;
        double r5654295 = 10.0;
        double r5654296 = r5654294 * r5654295;
        double r5654297 = /*Error: no posit support in C */;
        double r5654298 = d2;
        double r5654299 = /*Error: no posit support in C */;
        double r5654300 = 20.0;
        double r5654301 = /*Error: no posit support in C */;
        double r5654302 = /*Error: no posit support in C */;
        return r5654302;
}

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 2019162 
(FPCore (d1 d2)
  :name "FastMath test2"
  (+.p16 (+.p16 (*.p16 d1 (real->posit16 10)) (*.p16 d1 d2)) (*.p16 d1 (real->posit16 20))))