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 r2835998 = 1.0;
        double r2835999 = /* ERROR: no posit support in C */;
        double r2836000 = x;
        double r2836001 = sqrt(r2836000);
        double r2836002 = r2835999 / r2836001;
        double r2836003 = r2836000 + r2835999;
        double r2836004 = sqrt(r2836003);
        double r2836005 = r2835999 / r2836004;
        double r2836006 = r2836002 - r2836005;
        return r2836006;
}
↓
double f(double x) {
        double r2836007 = 1.0;
        double r2836008 = x;
        double r2836009 = sqrt(r2836008);
        double r2836010 = r2836007 / r2836009;
        double r2836011 = r2836008 + r2836007;
        double r2836012 = sqrt(r2836011);
        double r2836013 = r2836007 / r2836012;
        double r2836014 = r2836010 - r2836013;
        return r2836014;
}

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 2019120 
(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))))))