Average Error: 0.6 → 0.6
Time: 17.6s
Precision: 64
\[\left(\frac{\left(1\right)}{\left(\sqrt{x}\right)}\right) - \left(\frac{\left(1\right)}{\left(\sqrt{\left(\frac{x}{\left(1\right)}\right)}\right)}\right)\]
↓
\[\frac{1}{\sqrt{x}} - \frac{1}{\sqrt{x + 1}}\]
\left(\frac{\left(1\right)}{\left(\sqrt{x}\right)}\right) - \left(\frac{\left(1\right)}{\left(\sqrt{\left(\frac{x}{\left(1\right)}\right)}\right)}\right)
↓
\frac{1}{\sqrt{x}} - \frac{1}{\sqrt{x + 1}}
double f(double x) {
        double r6069566 = 1.0;
        double r6069567 = /* ERROR: no posit support in C */;
        double r6069568 = x;
        double r6069569 = sqrt(r6069568);
        double r6069570 = r6069567 / r6069569;
        double r6069571 = r6069568 + r6069567;
        double r6069572 = sqrt(r6069571);
        double r6069573 = r6069567 / r6069572;
        double r6069574 = r6069570 - r6069573;
        return r6069574;
}
↓
double f(double x) {
        double r6069575 = 1.0;
        double r6069576 = x;
        double r6069577 = sqrt(r6069576);
        double r6069578 = r6069575 / r6069577;
        double r6069579 = r6069576 + r6069575;
        double r6069580 = sqrt(r6069579);
        double r6069581 = r6069575 / r6069580;
        double r6069582 = r6069578 - r6069581;
        return r6069582;
}

Error

Bits error versus x

Derivation

  1. Initial program 0.6

    \[\left(\frac{\left(1\right)}{\left(\sqrt{x}\right)}\right) - \left(\frac{\left(1\right)}{\left(\sqrt{\left(\frac{x}{\left(1\right)}\right)}\right)}\right)\]

  2. Final simplification0.6

    \[\leadsto \frac{1}{\sqrt{x}} - \frac{1}{\sqrt{x + 1}}\]

Reproduce

herbie shell --seed 2019104 
(FPCore (x)
  :name "2isqrt (example 3.6)"
  (-.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))))