Average Error: 0.6 → 0.6
Time: 15.5s
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 r4378845 = 1.0;
        double r4378846 = /* ERROR: no posit support in C */;
        double r4378847 = x;
        double r4378848 = sqrt(r4378847);
        double r4378849 = r4378846 / r4378848;
        double r4378850 = r4378847 + r4378846;
        double r4378851 = sqrt(r4378850);
        double r4378852 = r4378846 / r4378851;
        double r4378853 = r4378849 - r4378852;
        return r4378853;
}
↓
double f(double x) {
        double r4378854 = 1.0;
        double r4378855 = x;
        double r4378856 = sqrt(r4378855);
        double r4378857 = r4378854 / r4378856;
        double r4378858 = r4378855 + r4378854;
        double r4378859 = sqrt(r4378858);
        double r4378860 = r4378854 / r4378859;
        double r4378861 = r4378857 - r4378860;
        return r4378861;
}

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 +o rules:numerics
(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))))))