Average Error: 0.3 → 0.1
Time: 19.6s
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 r1497297 = d1;
        double r1497298 = d2;
        double r1497299 = r1497297 * r1497298;
        double r1497300 = d3;
        double r1497301 = 5.0;
        double r1497302 = /* ERROR: no posit support in C */;
        double r1497303 = r1497300 + r1497302;
        double r1497304 = r1497303 * r1497297;
        double r1497305 = r1497299 + r1497304;
        double r1497306 = 32.0;
        double r1497307 = /* ERROR: no posit support in C */;
        double r1497308 = r1497297 * r1497307;
        double r1497309 = r1497305 + r1497308;
        return r1497309;
}
↓
double f(double d1, double d2, double d3) {
        double r1497310 = d1;
        double r1497311 = d2;
        double r1497312 = r1497310 * r1497311;
        double r1497313 = /*Error: no posit support in C */;
        double r1497314 = d3;
        double r1497315 = 5.0;
        double r1497316 = r1497314 + r1497315;
        double r1497317 = /*Error: no posit support in C */;
        double r1497318 = 32.0;
        double r1497319 = /*Error: no posit support in C */;
        double r1497320 = /*Error: no posit support in C */;
        return r1497320;
}

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))))