Average Error: 0.3 → 0.1
Time: 17.9s
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 r3873772 = d1;
        double r3873773 = 10.0;
        double r3873774 = /* ERROR: no posit support in C */;
        double r3873775 = r3873772 * r3873774;
        double r3873776 = d2;
        double r3873777 = r3873772 * r3873776;
        double r3873778 = r3873775 + r3873777;
        double r3873779 = 20.0;
        double r3873780 = /* ERROR: no posit support in C */;
        double r3873781 = r3873772 * r3873780;
        double r3873782 = r3873778 + r3873781;
        return r3873782;
}
↓
double f(double d1, double d2) {
        double r3873783 = d1;
        double r3873784 = 10.0;
        double r3873785 = /* ERROR: no posit support in C */;
        double r3873786 = r3873783 * r3873785;
        double r3873787 = /*Error: no posit support in C */;
        double r3873788 = d2;
        double r3873789 = /*Error: no posit support in C */;
        double r3873790 = 20.0;
        double r3873791 = /* ERROR: no posit support in C */;
        double r3873792 = /*Error: no posit support in C */;
        double r3873793 = /*Error: no posit support in C */;
        return r3873793;
}

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 2019164 
(FPCore (d1 d2)
  :name "FastMath test2"
  (+.p16 (+.p16 (*.p16 d1 (real->posit16 10)) (*.p16 d1 d2)) (*.p16 d1 (real->posit16 20))))