Average Error: 0.3 → 0.2
Time: 15.4s
Precision: 64
\[\frac{\left(\frac{\left(d1 \cdot \left(10\right)\right)}{\left(d1 \cdot d2\right)}\right)}{\left(d1 \cdot \left(20\right)\right)}\]
↓
\[\left(\mathsf{qma}\left(\left(\mathsf{qma}\left(\left(\left(d1 \cdot 10\right)\right), d1, d2\right)\right), \left(d1 \cdot 20\right), 1.0\right)\right)\]
\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), \left(d1 \cdot 20\right), 1.0\right)\right)
double f(double d1, double d2) {
        double r1201027 = d1;
        double r1201028 = 10.0;
        double r1201029 = /* ERROR: no posit support in C */;
        double r1201030 = r1201027 * r1201029;
        double r1201031 = d2;
        double r1201032 = r1201027 * r1201031;
        double r1201033 = r1201030 + r1201032;
        double r1201034 = 20.0;
        double r1201035 = /* ERROR: no posit support in C */;
        double r1201036 = r1201027 * r1201035;
        double r1201037 = r1201033 + r1201036;
        return r1201037;
}
↓
double f(double d1, double d2) {
        double r1201038 = d1;
        double r1201039 = 10.0;
        double r1201040 = r1201038 * r1201039;
        double r1201041 = /*Error: no posit support in C */;
        double r1201042 = d2;
        double r1201043 = /*Error: no posit support in C */;
        double r1201044 = 20.0;
        double r1201045 = r1201038 * r1201044;
        double r1201046 = 1.0;
        double r1201047 = /*Error: no posit support in C */;
        double r1201048 = /*Error: no posit support in C */;
        return r1201048;
}

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-add0.2

    \[\leadsto \color{blue}{\left(\mathsf{qma}\left(\left(\mathsf{qma}\left(\left(\left(d1 \cdot \left(10\right)\right)\right), d1, d2\right)\right), \left(d1 \cdot \left(20\right)\right), \left(1.0\right)\right)\right)}\]

  6. Final simplification0.2

    \[\leadsto \left(\mathsf{qma}\left(\left(\mathsf{qma}\left(\left(\left(d1 \cdot 10\right)\right), d1, d2\right)\right), \left(d1 \cdot 20\right), 1.0\right)\right)\]

Reproduce

herbie shell --seed 2019156 +o rules:numerics
(FPCore (d1 d2)
  :name "FastMath test2"
  (+.p16 (+.p16 (*.p16 d1 (real->posit16 10)) (*.p16 d1 d2)) (*.p16 d1 (real->posit16 20))))