Average Error: 1.0 → 1.0
Time: 5.6m
Precision: 64
\[\frac{\left(\left(\frac{\left(1\right)}{\left(\frac{x}{\left(1\right)}\right)}\right) - \left(\frac{\left(2\right)}{x}\right)\right)}{\left(\frac{\left(1\right)}{\left(x - \left(1\right)\right)}\right)}\]
↓
\[\left(\mathsf{qma}\left(\left(\mathsf{qms}\left(\left(\left(\frac{\left(1\right)}{\left(\frac{x}{\left(1\right)}\right)}\right)\right), \left(\frac{\left(2\right)}{x}\right), \left(1.0\right)\right)\right), \left(\frac{\left(1\right)}{\left(x - \left(1\right)\right)}\right), \left(1.0\right)\right)\right)\]
\frac{\left(\left(\frac{\left(1\right)}{\left(\frac{x}{\left(1\right)}\right)}\right) - \left(\frac{\left(2\right)}{x}\right)\right)}{\left(\frac{\left(1\right)}{\left(x - \left(1\right)\right)}\right)}
↓
\left(\mathsf{qma}\left(\left(\mathsf{qms}\left(\left(\left(\frac{\left(1\right)}{\left(\frac{x}{\left(1\right)}\right)}\right)\right), \left(\frac{\left(2\right)}{x}\right), \left(1.0\right)\right)\right), \left(\frac{\left(1\right)}{\left(x - \left(1\right)\right)}\right), \left(1.0\right)\right)\right)
double f(double x) {
        double r5667584 = 1.0;
        double r5667585 = /* ERROR: no posit support in C */;
        double r5667586 = x;
        double r5667587 = r5667586 + r5667585;
        double r5667588 = r5667585 / r5667587;
        double r5667589 = 2.0;
        double r5667590 = /* ERROR: no posit support in C */;
        double r5667591 = r5667590 / r5667586;
        double r5667592 = r5667588 - r5667591;
        double r5667593 = r5667586 - r5667585;
        double r5667594 = r5667585 / r5667593;
        double r5667595 = r5667592 + r5667594;
        return r5667595;
}
↓
double f(double x) {
        double r5667596 = 1.0;
        double r5667597 = /* ERROR: no posit support in C */;
        double r5667598 = x;
        double r5667599 = r5667598 + r5667597;
        double r5667600 = r5667597 / r5667599;
        double r5667601 = /*Error: no posit support in C */;
        double r5667602 = 2.0;
        double r5667603 = /* ERROR: no posit support in C */;
        double r5667604 = r5667603 / r5667598;
        double r5667605 = 1.0;
        double r5667606 = /* ERROR: no posit support in C */;
        double r5667607 = /*Error: no posit support in C */;
        double r5667608 = r5667598 - r5667597;
        double r5667609 = r5667597 / r5667608;
        double r5667610 = /*Error: no posit support in C */;
        double r5667611 = /*Error: no posit support in C */;
        return r5667611;
}

Error

Bits error versus x

Derivation

  1. Initial program 1.0

    \[\frac{\left(\left(\frac{\left(1\right)}{\left(\frac{x}{\left(1\right)}\right)}\right) - \left(\frac{\left(2\right)}{x}\right)\right)}{\left(\frac{\left(1\right)}{\left(x - \left(1\right)\right)}\right)}\]
  2. Using strategy rm

  3. Applied introduce-quire1.0

    \[\leadsto \frac{\left(\color{blue}{\left(\left(\left(\frac{\left(1\right)}{\left(\frac{x}{\left(1\right)}\right)}\right)\right)\right)} - \left(\frac{\left(2\right)}{x}\right)\right)}{\left(\frac{\left(1\right)}{\left(x - \left(1\right)\right)}\right)}\]

  4. Applied insert-quire-sub1.0

    \[\leadsto \frac{\color{blue}{\left(\left(\mathsf{qms}\left(\left(\left(\frac{\left(1\right)}{\left(\frac{x}{\left(1\right)}\right)}\right)\right), \left(\frac{\left(2\right)}{x}\right), \left(1.0\right)\right)\right)\right)}}{\left(\frac{\left(1\right)}{\left(x - \left(1\right)\right)}\right)}\]

  5. Applied insert-quire-add1.0

    \[\leadsto \color{blue}{\left(\mathsf{qma}\left(\left(\mathsf{qms}\left(\left(\left(\frac{\left(1\right)}{\left(\frac{x}{\left(1\right)}\right)}\right)\right), \left(\frac{\left(2\right)}{x}\right), \left(1.0\right)\right)\right), \left(\frac{\left(1\right)}{\left(x - \left(1\right)\right)}\right), \left(1.0\right)\right)\right)}\]

  6. Final simplification1.0

    \[\leadsto \left(\mathsf{qma}\left(\left(\mathsf{qms}\left(\left(\left(\frac{\left(1\right)}{\left(\frac{x}{\left(1\right)}\right)}\right)\right), \left(\frac{\left(2\right)}{x}\right), \left(1.0\right)\right)\right), \left(\frac{\left(1\right)}{\left(x - \left(1\right)\right)}\right), \left(1.0\right)\right)\right)\]

Reproduce

herbie shell --seed 2019164 +o rules:numerics
(FPCore (x)
  :name "3frac (problem 3.3.3)"
  (+.p16 (-.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 2) x)) (/.p16 (real->posit16 1) (-.p16 x (real->posit16 1)))))