Average Error: 0.3 → 0.1
Time: 28.8s
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 r4910945 = d1;
        double r4910946 = d2;
        double r4910947 = r4910945 * r4910946;
        double r4910948 = d3;
        double r4910949 = 5.0;
        double r4910950 = /* ERROR: no posit support in C */;
        double r4910951 = r4910948 + r4910950;
        double r4910952 = r4910951 * r4910945;
        double r4910953 = r4910947 + r4910952;
        double r4910954 = 32.0;
        double r4910955 = /* ERROR: no posit support in C */;
        double r4910956 = r4910945 * r4910955;
        double r4910957 = r4910953 + r4910956;
        return r4910957;
}
↓
double f(double d1, double d2, double d3) {
        double r4910958 = d1;
        double r4910959 = d2;
        double r4910960 = r4910958 * r4910959;
        double r4910961 = /*Error: no posit support in C */;
        double r4910962 = d3;
        double r4910963 = 5.0;
        double r4910964 = r4910962 + r4910963;
        double r4910965 = /*Error: no posit support in C */;
        double r4910966 = 32.0;
        double r4910967 = /*Error: no posit support in C */;
        double r4910968 = /*Error: no posit support in C */;
        return r4910968;
}

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 2019163 +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))))