Average Error: 0.6 → 0.6
Time: 15.6s
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 r4139727 = 1.0;
        double r4139728 = /* ERROR: no posit support in C */;
        double r4139729 = x;
        double r4139730 = sqrt(r4139729);
        double r4139731 = r4139728 / r4139730;
        double r4139732 = r4139729 + r4139728;
        double r4139733 = sqrt(r4139732);
        double r4139734 = r4139728 / r4139733;
        double r4139735 = r4139731 - r4139734;
        return r4139735;
}
↓
double f(double x) {
        double r4139736 = 1.0;
        double r4139737 = x;
        double r4139738 = sqrt(r4139737);
        double r4139739 = r4139736 / r4139738;
        double r4139740 = r4139737 + r4139736;
        double r4139741 = sqrt(r4139740);
        double r4139742 = r4139736 / r4139741;
        double r4139743 = r4139739 - r4139742;
        return r4139743;
}

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 2019119 
(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))))))