Average Error: 0.6 → 0.6
Time: 18.4s
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 r4153073 = 1.0;
        double r4153074 = /* ERROR: no posit support in C */;
        double r4153075 = x;
        double r4153076 = sqrt(r4153075);
        double r4153077 = r4153074 / r4153076;
        double r4153078 = r4153075 + r4153074;
        double r4153079 = sqrt(r4153078);
        double r4153080 = r4153074 / r4153079;
        double r4153081 = r4153077 - r4153080;
        return r4153081;
}
↓
double f(double x) {
        double r4153082 = 1.0;
        double r4153083 = x;
        double r4153084 = sqrt(r4153083);
        double r4153085 = r4153082 / r4153084;
        double r4153086 = r4153083 + r4153082;
        double r4153087 = sqrt(r4153086);
        double r4153088 = r4153082 / r4153087;
        double r4153089 = r4153085 - r4153088;
        return r4153089;
}

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 2019121 
(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))))))