Average Error: 0.3 → 0.1
Time: 23.1s
Precision: 64
\[\frac{\left(\frac{\left(d1 \cdot \left(10\right)\right)}{\left(d1 \cdot d2\right)}\right)}{\left(d1 \cdot \left(20\right)\right)}\]
↓
\[\left(\mathsf{qma}\left(\left(\mathsf{qma}\left(\left(\left(d1 \cdot \left(10\right)\right)\right), d1, d2\right)\right), d1, \left(20\right)\right)\right)\]
\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 \left(10\right)\right)\right), d1, d2\right)\right), d1, \left(20\right)\right)\right)
double f(double d1, double d2) {
        double r3432148 = d1;
        double r3432149 = 10.0;
        double r3432150 = /* ERROR: no posit support in C */;
        double r3432151 = r3432148 * r3432150;
        double r3432152 = d2;
        double r3432153 = r3432148 * r3432152;
        double r3432154 = r3432151 + r3432153;
        double r3432155 = 20.0;
        double r3432156 = /* ERROR: no posit support in C */;
        double r3432157 = r3432148 * r3432156;
        double r3432158 = r3432154 + r3432157;
        return r3432158;
}
↓
double f(double d1, double d2) {
        double r3432159 = d1;
        double r3432160 = 10.0;
        double r3432161 = /* ERROR: no posit support in C */;
        double r3432162 = r3432159 * r3432161;
        double r3432163 = /*Error: no posit support in C */;
        double r3432164 = d2;
        double r3432165 = /*Error: no posit support in C */;
        double r3432166 = 20.0;
        double r3432167 = /* ERROR: no posit support in C */;
        double r3432168 = /*Error: no posit support in C */;
        double r3432169 = /*Error: no posit support in C */;
        return r3432169;
}

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-fdp-add0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2019168 +o rules:numerics
(FPCore (d1 d2)
  :name "FastMath test2"
  (+.p16 (+.p16 (*.p16 d1 (real->posit16 10)) (*.p16 d1 d2)) (*.p16 d1 (real->posit16 20))))