Average Error: 0.6 → 0.6
Time: 17.2s
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 r2751063 = 1.0;
        double r2751064 = /* ERROR: no posit support in C */;
        double r2751065 = x;
        double r2751066 = sqrt(r2751065);
        double r2751067 = r2751064 / r2751066;
        double r2751068 = r2751065 + r2751064;
        double r2751069 = sqrt(r2751068);
        double r2751070 = r2751064 / r2751069;
        double r2751071 = r2751067 - r2751070;
        return r2751071;
}
↓
double f(double x) {
        double r2751072 = 1.0;
        double r2751073 = x;
        double r2751074 = sqrt(r2751073);
        double r2751075 = r2751072 / r2751074;
        double r2751076 = r2751073 + r2751072;
        double r2751077 = sqrt(r2751076);
        double r2751078 = r2751072 / r2751077;
        double r2751079 = r2751075 - r2751078;
        return r2751079;
}

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 2019124 
(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))))))