Average Error: 0.3 → 0.2
Time: 14.4s
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 r986195 = d1;
        double r986196 = 10.0;
        double r986197 = /* ERROR: no posit support in C */;
        double r986198 = r986195 * r986197;
        double r986199 = d2;
        double r986200 = r986195 * r986199;
        double r986201 = r986198 + r986200;
        double r986202 = 20.0;
        double r986203 = /* ERROR: no posit support in C */;
        double r986204 = r986195 * r986203;
        double r986205 = r986201 + r986204;
        return r986205;
}
↓
double f(double d1, double d2) {
        double r986206 = d1;
        double r986207 = 10.0;
        double r986208 = r986206 * r986207;
        double r986209 = /*Error: no posit support in C */;
        double r986210 = d2;
        double r986211 = /*Error: no posit support in C */;
        double r986212 = 20.0;
        double r986213 = r986206 * r986212;
        double r986214 = 1.0;
        double r986215 = /*Error: no posit support in C */;
        double r986216 = /*Error: no posit support in C */;
        return r986216;
}

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