Average Error: 0.6 → 0.6
Time: 18.3s
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 r1781514 = 1.0;
        double r1781515 = /* ERROR: no posit support in C */;
        double r1781516 = x;
        double r1781517 = sqrt(r1781516);
        double r1781518 = r1781515 / r1781517;
        double r1781519 = r1781516 + r1781515;
        double r1781520 = sqrt(r1781519);
        double r1781521 = r1781515 / r1781520;
        double r1781522 = r1781518 - r1781521;
        return r1781522;
}
↓
double f(double x) {
        double r1781523 = 1.0;
        double r1781524 = x;
        double r1781525 = sqrt(r1781524);
        double r1781526 = r1781523 / r1781525;
        double r1781527 = r1781524 + r1781523;
        double r1781528 = sqrt(r1781527);
        double r1781529 = r1781523 / r1781528;
        double r1781530 = r1781526 - r1781529;
        return r1781530;
}

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 2019154 
(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))))))