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 r4531878 = 1.0;
        double r4531879 = /* ERROR: no posit support in C */;
        double r4531880 = x;
        double r4531881 = sqrt(r4531880);
        double r4531882 = r4531879 / r4531881;
        double r4531883 = r4531880 + r4531879;
        double r4531884 = sqrt(r4531883);
        double r4531885 = r4531879 / r4531884;
        double r4531886 = r4531882 - r4531885;
        return r4531886;
}
↓
double f(double x) {
        double r4531887 = 1.0;
        double r4531888 = x;
        double r4531889 = sqrt(r4531888);
        double r4531890 = r4531887 / r4531889;
        double r4531891 = r4531888 + r4531887;
        double r4531892 = sqrt(r4531891);
        double r4531893 = r4531887 / r4531892;
        double r4531894 = r4531890 - r4531893;
        return r4531894;
}

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 2019125 
(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))))))