Average Error: 0.5 → 0.2
Time: 32.2s
Precision: 64
\[\frac{\left(\frac{\left(d1 \cdot \left(3\right)\right)}{\left(d1 \cdot d2\right)}\right)}{\left(d1 \cdot d3\right)}\]
↓
\[\left(\mathsf{qma}\left(\left(\mathsf{qma}\left(\left(3\right), d3, 1.0\right)\right), d2, 1.0\right)\right) \cdot d1\]
\frac{\left(\frac{\left(d1 \cdot \left(3\right)\right)}{\left(d1 \cdot d2\right)}\right)}{\left(d1 \cdot d3\right)}
↓
\left(\mathsf{qma}\left(\left(\mathsf{qma}\left(\left(3\right), d3, 1.0\right)\right), d2, 1.0\right)\right) \cdot d1
double f(double d1, double d2, double d3) {
        double r4064281 = d1;
        double r4064282 = 3.0;
        double r4064283 = /* ERROR: no posit support in C */;
        double r4064284 = r4064281 * r4064283;
        double r4064285 = d2;
        double r4064286 = r4064281 * r4064285;
        double r4064287 = r4064284 + r4064286;
        double r4064288 = d3;
        double r4064289 = r4064281 * r4064288;
        double r4064290 = r4064287 + r4064289;
        return r4064290;
}
↓
double f(double d1, double d2, double d3) {
        double r4064291 = 3.0;
        double r4064292 = /*Error: no posit support in C */;
        double r4064293 = d3;
        double r4064294 = 1.0;
        double r4064295 = /*Error: no posit support in C */;
        double r4064296 = d2;
        double r4064297 = /*Error: no posit support in C */;
        double r4064298 = /*Error: no posit support in C */;
        double r4064299 = d1;
        double r4064300 = r4064298 * r4064299;
        return r4064300;
}

Error

Bits error versus d1

Bits error versus d2

Bits error versus d3

Derivation

  1. Initial program 0.5

    \[\frac{\left(\frac{\left(d1 \cdot \left(3\right)\right)}{\left(d1 \cdot d2\right)}\right)}{\left(d1 \cdot d3\right)}\]

  2. Simplified0.3

    \[\leadsto \color{blue}{\left(\frac{\left(\frac{\left(3\right)}{d3}\right)}{d2}\right) \cdot d1}\]
  3. Using strategy rm

  4. Applied introduce-quire0.3

    \[\leadsto \left(\frac{\left(\frac{\color{blue}{\left(\left(\left(3\right)\right)\right)}}{d3}\right)}{d2}\right) \cdot d1\]

  5. Applied insert-quire-add0.3

    \[\leadsto \left(\frac{\color{blue}{\left(\left(\mathsf{qma}\left(\left(\left(3\right)\right), d3, \left(1.0\right)\right)\right)\right)}}{d2}\right) \cdot d1\]

  6. Applied insert-quire-add0.2

    \[\leadsto \color{blue}{\left(\left(\mathsf{qma}\left(\left(\mathsf{qma}\left(\left(\left(3\right)\right), d3, \left(1.0\right)\right)\right), d2, \left(1.0\right)\right)\right)\right)} \cdot d1\]

  7. Final simplification0.2

    \[\leadsto \left(\mathsf{qma}\left(\left(\mathsf{qma}\left(\left(3\right), d3, 1.0\right)\right), d2, 1.0\right)\right) \cdot d1\]

Reproduce

herbie shell --seed 2019158 +o rules:numerics
(FPCore (d1 d2 d3)
  :name "FastMath test3"
  (+.p16 (+.p16 (*.p16 d1 (real->posit16 3)) (*.p16 d1 d2)) (*.p16 d1 d3)))